NASA Technical Memorandum 4795

STARS--An Integrated,

Multidisciplinary, Finite-Element,

Structural, Fluids, Aeroelastic,

and Aeroservoelastic Analysis

Computer Program

K. K. Gupta

Dryden Flight Research Center

Edwards, California

National Aeronautics and

Space Administration

Office of Management

Scientific and Technical

Information Program

1997
NOTICE

Use of trade names or names of manufacturers in this document does not constitute an official

endorsement of such products or manufacturers, either expressed or implied, by the National

Aeronautics and Space Administration.
CONTENTS

1 ABSTRACT ..............................................................................................................................................

NOMENCLATURE ................................................................................................................................. 1

1. INTRODUCTION .............................................................................................................................. 2

2. STARS-SOLIDS MODULE DESCRIPTION ................................................................................ 5

2.1 Nodal and Element Data Generation .................................................................................... 6

2.2 Matrix Bandwidth Minimization .......................................................................................... 7

2.3 Deflection Boundary Conditions .......................................................................................... 7

2.4 Prescribed Loads ................................................................................................................... 8

2.5 Static Analysis ....................................................................................................................... 8

2.6 Elastic Buckling Analysis ..................................................................................................... 8

2.7 Free-Vibration Analysis ........................................................................................................ 8

2.8 Dynamic-Response Analysis .............................................................................................. 10

2.9 Nonlinear Structural Analysis ............................................................................................. 11

2.10 Shift Synthesis ..................................................................................................................... 15

2.11 Formulation for Nodal Centrifugal Forces in Finite Elements ........................................... 17

2.12 Material Properties .............................................................................................................. 17

2.13 Heat-Transfer Analysis ....................................................................................................... 17

2.14 Output of Analysis Results ................................................................................................. 19

2.15 Discussion ........................................................................................................................... 20

3. DATA INPUT PROCEDURE (STARS-SOLIDS and SOLIDS HEAT TRANSFER) .............. 20

3.1 Basic Data ........................................................................................................................... 20

3.2 Nodal Data .......................................................................................................................... 27

3.3 Element Data ....................................................................................................................... 29

3.4 Data in the Global or Local-Global Coordinate System ..................................................... 41

3.5 Additional Basic Data ......................................................................................................... 46

4. SAMPLE PROBLEMS .................................................................................................................... 48

4.1 STARS-SOLIDS (Linear Analysis) ................................................................................... 48

4.2 STARS-SOLIDS (Nonlinear Analysis) .............................................................................. 81

4.3 STARS-SOLIDS Heat Transfer (Linear Analysis) ............................................................ 97

4.4 STARS-SOLIDS Heat-Transfer (Nonlinear Analysis) .................................................... 108

5. STARS-AEROS AND STARS-ASE MODULE DESCRIPTIONS: LINEAR

AEROELASTIC AND AEROSERVOELASTIC ANALYSIS ............................................... 120

1

5.1

DATA

6.1

6.2

6.3

6.4

6.5

Numerical Formulation for Linear Aeroelastic and Aeroservoelastic Analysis ............... 121

INPUT PROCEDURE (STARS-AEROS and ASE) ...................................................... 129

GENMASS Data (STARS-AEROS-GENMASS) ........................................................... 129

AEROL Data (STARS-AEROS-AEROL) ...................................................................... 130

CONVERT Data (STARS-ASE-CONVERT) ................................................................. 151

ASE PADI_ Data (STARS-ASE-PAD]_) ......................................................................... 152

ASE CONTROL Data (STARS-ASE-CONTROL) ........................................................ 155

iii
7. SAMPLE PROBLEMS (STARS INTEGRATED AERO-STRUCTURAL-CONTROL

SYSTEMS ANALYSIS) ............................................................................................................. 163

7.1 Aircraft Test Model: Free Vibration Analysis (STARS-SOLIDS) .................................. 163

7.2 Aircraft Test Model: Generalized Mass Analysis (STARS-AEROS-GENMASS) ........ 178

7.3 Aircraft Test Model: Aeroelastic Analysis (STARS-AEROS-AEROL) ......................... 179

7.4 Aircraft Test Model: Aeroelastic Analysis (STARS-ASE-CONVERT) ......................... 186

7.5 Aircraft Test Model: Aeroservoelastic Analysis (STARS-ASE-PAD]_) ......................... 187

7.6 Aircraft Test Model: Aeroservoelastic Analysis (STARS-ASE-CONTROL) ................ 190

7.7 Aircraft Test Model: Run Stream Details ......................................................................... 195

8. STARS-CFDASE MODULE DESCRIPTION: COMPUTATIONAL FLUID DYNAMICS,

NONLINEAR AEROELASTICITY, AND AEROSERVOELASTICITY .......................... 203

8.1 Finite-Element Computational Fluid Dynamics ............................................................... 203

8.2 Nonlinear, Computational Fluid Dynamics-Based Aeroelastic and

Aeroservoelastic Analysis (CFDASE) ........................................................................... 205

9. DATA INPUT PROCEDURE (STARS-CFDASE) .................................................................... 208

9.1 Input Data for Background Grid (job.bac) ........................................................................ 208

9.2 Input Data for Surface Grid (job.sur) ................................................................................ 212

9.3 Input Data for Boundary Conditions (job.bco) ................................................................. 216

9.4 Input Data of Control File for Steady-State Computational Fluid Dynamics

(Euler) Solution (job.cons) ............................................................................................. 217

9.5 STARS-SOLIDS Vibration Analysis Data (solids.dat) ................................................... 218

9.6 STARS-AEROS-GENMASS Data (genmass.dat) .......................................................... 218

9.7 Input Data for Damping (damp.dat) .................................................................................. 219

9.8 Input Data for Unsteady Flow (job.scalars) ...................................................................... 220

9.9 Input Data of Control File for Unsteady Computational Fluid Dynamics (Euler)

Solution (job.conu) ......................................................................................................... 223

9.10 Input Data of Control File for STEADYDP (job.consdp) ................................................ 224

10. NUMERICAL EXAMPLE (STARS-CFDASE) ........................................................................ 233

10.1 Cantilever Wing Nonlinear Aeroelastic Analysis ............................................................. 233

11. COUPLED HEAT TRANSFER AND STRUCTURAL ANALYSIS ....................................... 253

i 1.1 Clamped-Clamped Beam: Thermal Loading .................................................................... 253

11.2 Cantilever Plate: Thermal Loading ................................................................................... 256

12. COUPLED COMPUTATIONAL FLUID DYNAMICS AND STRUCTURAL LOAD

TRANSFER PROBLEMS ....................................................................................................... 260

12.1 Cantilever Wing: Coupled Computational Fluid Dynamics and Structural Analysis ...... 260

APPENDIX A - PREPROCESSOR MANUAL ................................................................................ 265

APPENDIX B - POSTPROCESSOR MANUAL ............................................................................ 269

APPENDIX C - SYSTEMS DESCRIPTION .................................................................................... 271

REFERENCES ..................................................................................................................................... 273

iv
FIGURES

°

2.

3.

4.

5.

6.

7.

.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

2

Structural synthesis ........................................................................................................................

3

Major modules of STARS ..............................................................................................................

STARS-SOLIDS overview ........................................................................................................... 3

STARS-ASE flowchart ................................................................................................................. 4

7

Bandwidth minimization scheme ...................................................................................................

Three-dimensional general heat conduction ................................................................................ 18

STARS-SOLIDS typical element types

32

(a) Line element ...........................................................................................................................

32

(b) Quadrilateral shell element .....................................................................................................

32

(c) Triangular shell element .........................................................................................................

32

(d) Hexahedral solid element .......................................................................................................

32

(e) Tetrahedral solid element .......................................................................................................

(f) Composite shell/prism element .............................................................................................. 32

48

Space truss .................................................................................................................................... 51

Space frame structure ...................................................................................................................

Thick-wall cylinder under internal pressure

(a) Triangular mesh ...................................................................................................................... 52

(b) Quadrilateral mesh ................................................................................................................. 53

54

Square cantilever plate .................................................................................................................

Finite-element model of cylindrical shell

(a) Rectangular coordinate system ............................................................................................... 56

56

(b) Random coordinate system ....................................................................................................

59 Cube discretized by hexahedral elements ....................................................................................

61

Spinning cantilever beam .............................................................................................................

Coupled helicopter rotor/fuselage system

65 (a) Discrete element model ..........................................................................................................

65 (b) Structural mass distribution ....................................................................................................

(c) Structural stiffness distribution ............................................................................................... 65

Rocket subjected to dynamic loading

67

(a) Rocket structure ......................................................................................................................

(b) Pulse loading .......................................................................................................................... 67

Rocket nodal displacement as a function of time, node 1 ............................................................ 68

Rocket element force as a function of time, element 4 ................................................................ 68

71

Truss structure ..............................................................................................................................

Square composite plate ................................................................................................................ 72

74

Rectangular plate ..........................................................................................................................

Free-free composite square plate .................................................................................................. 78

Clamped plate with uniform load ................................................................................................. 81

Clamped plate center displacement as a function of load curve .................................................. 83

Cantilever beam with moment at tip ............................................................................................ 83

Deflection curves for cantilever beam with end moment ............................................................ 84

Cantilever tip deflection as a function of moment curve ............................................................. 85

Clamped cylindrical shell with uniform load ............................................................................... 85

Center deflection of a clamped cylindrical shell under uniform load .......................................... 89
30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

Clampedbeamwith concentratedload ........................................................................................ 89

Centerdisplacement:loadcurveof aclampedbeam................................................................... 91

Centerdisplacement:timecurveof aclampedbeam .................................................................. 91

Clampedsphericalcapwith apexload ......................................................................................... 91

One-quartercapmodel

(a)Triangularmesh...................................................................................................................... 93

(b) Quadrilateralmesh ................................................................................................................. 93

Capcenterdisplacementasafunctionof load ............................................................................. 94

Capcenterdisplacementasafunctionof time ............................................................................ 95

Clampedbeamunderuniformly distributedload

(a)Uniform distributedloadon thebeam.................................................................................... 95

(b) Finiteelementmodelof thebeam........................................................................................... 95

(c) Crosssection ........................................................................................................................... 96

Load-deflectioncurvefor a clampedbeam.................................................................................. 97

Coolingfin with convection......................................................................................................... 98

Three-dimensionalboxwith conduction...................................................................................... 99

Squareplatewith transientheating

(a) Platemodel ........................................................................................................................... 101

(b) Pulseheating......................................................................................................................... 101

Compositesquareplatewith transientheating

(a) Platemodel ........................................................................................................................... 105

(b) Pulseheating......................................................................................................................... 105

Coolingfin with radiation .......................................................................................................... 109

Three-dimensionalboxwith radiation ....................................................................................... 110

Compositesquareplatewith radiation ....................................................................................... 112

Three-dimensionalboxpulseheatflow ..................................................................................... 115

Two-dimensionalstripwith transientheatflow andradiationboundarycondition

(a) Stripmodel ........................................................................................................................... 116

(b) Pulseheatflow ..................................................................................................................... 117

Feedbackcontrolsystem............................................................................................................ 121

ASEanalysisdatainput scheme................................................................................................ 129

Aircraft testmodelsymmetricone-halffinite-elementmodelwith nodes................................163

Aircraft testmodelantisymmetriccase,direct-surfaceinterpolationscheme...........................164

Aircraft testmodelantisymmetriccase,elastic(_E) modeshapes............................................ 176

Aircraft testmodelantisymmetriccase,perfectrigid body(CI_pR) and

control (_C) modes ................................................................................................................. 177

Aircraft test model antisymmetric case, one-half aircraft aerodynamic boxes .......................... 179

Aircraft test model antisymmetric case, aerodynamic panels .................................................... 180

Aircraft test model antisymmetric case, aerodynamic boxes

(a) Aerodynamic boxes .............................................................................................................. 180

(b) Slender-body definitions ...................................................................................................... 181

Aircraft test model k flutter analysis m damping (g'), frequency (b), velocity (v)

plot, antisymmetric case, using direct interpolation where g' = g × 200 ................................ 184

Aircraft test model p-k flutter analysis m damping (g'), frequency (b), velocity (v)

plot, antisymmetric case, using direct interpolation where g' = g × 200 ................................. 185

vi
59.

60.

61.

62.

63.

64.

65.

66.

67.

68.

69.

70.

71.

72.

73.

74.

Aircraft testmodelASEflutter analysis-- damping(a),frequency(b),

velocity (v) plot, antisymmetriccase,usingdirectinterpolation............................................ 186

Aircraft testmodellateralmodeanalogcontrolsystem ............................................................ 190

Aircraft testmodellateralloopgains,roll mode 193

(a)Gain ...................................................................................................................................... 193

(b) Phase.....................................................................................................................................

Aircraft testmodellateralloop gains,yawmode 194

(a)Gain ...................................................................................................................................... 194

(b) Phase..................................................................................................................................... 195

Aircraft testmodelclosed-loopdamping,v-g, andfrequencies,v-f .......................................... 207

Nonlinearflutter analysismethodology..................................................................................... 209

Flowchartfor CFD-basedaeroelasticanalysis...........................................................................

Cantileverwing with aeroelasticsolutiondomain..................................................................... 233

Backgrounddomainfor aeroelasticanalysis ............................................................................ 234

Aerodynamicsurfacegrid of wing andsolutiondomain ._......................................................... _:'_

Cantileverwing steady-stateMachandpressuredistribuuons

(a)Machdistribution .................................................................................................................. 295s0

(b)Pressuredistribution ............................................................................................................ 251

Structuralmodesof cantileverwing ..........................................................................................

Typical wing generalizeddisplacementplotsfor flutter parameter(fp) = 0.95 ........................25522

Aeroelasticstabilityplot for cantileverwing .............................................................................

Finite-elementmodelof abeam 253

(a)Heat-transfermesh................................................................................................................ 253

(b) Structuralmesh.....................................................................................................................

Finite-elementmodelof aplate

(a)Heat-transfermesh................................................................................................................ 256 256

(b) Structuralmesh .................................................................................................................... 260

Cantileverwing with structuralmesh ........................................................................................

STARSsystemsdescription....................................................................................................... 272

k

vii
TABLES

°

2.

3.

4.

5.

,

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

Arrangement of nodal data input ................................................................................................. 27

Element data layout ...................................................................................................................... 31

Element temperature data input ................................................................................................... 40

Data layout for displacement boundary conditions ...................................................................... 43

Radial deformations of a circular cylinder subjected to uniformly distributed

internal pressures ....................................................................................................................... 54

Natural frequencies of a square cantilever plate .......................................................................... 55

Natural frequencies of a cylindrical cantilever shell .................................................................... 58

Natural frequencies of a solid cube .............................................................................................. 60

Natural frequencies of a spinning cantilever beam ...................................................................... 62

Natural frequencies of a non-spinning cantilever beam ............................................................... 63

Natural frequency parameters of a spinning square cantilever plate ........................................... 64

Natural frequencies of a helicopter structure ............................................................................... 66

Critical load of a simply-supported square plate ......................................................................... 70

Critical load of a cantilever beam ................................................................................................ 70

Critical load of a simple truss ...................................................................................................... 71

Natural frequencies of a square composite plate ......................................................................... 74

Natural frequencies of a rectangular free-free plate ..................................................................... 77

Natural frequencies of a free-free square composite plate ........................................................... 77

Center deflection for a clamped square plate with uniform load ................................................. 82

Tip displacement, v, for a cantilever beam with end moment ..................................................... 84

Center displacement for a clamped cylindrical shell under uniform load ................................... 88

Center displacement for a clamped beam with concentration load ............................................. 90

Center deflection for clamped spherical cap under apex load ..................................................... 94

Maximum uniformly distributed load for a clamped beam ......................................................... 97

Heat-transfer analysis results of a square plate with transient heating ...................................... 104

Heat-transfer analysis results of a composite square plate with transient heating ..................... 108

Heat-transfer analysis results for a composite plate with a radiation boundary condition ........ 114

Nonlinear transient heat-transfer analysis results for a composite box with a

radiation boundary condition .................................................................................................. 116

Nonlinear transient heat-transfer analysis results for a two-dimensional strip with

a radiation boundary condition ............................................................................................... 119

Aircraft test model: Antisymmetric free-vibration analysis results ........................................... 175

Aircraft test model rigid-body and control-mode generation parameters .................................. 178

Aircraft test model: An aeroelastic antisymmetric analysis using a direct

interpolation for AEROS paneling .......................................................................................... 189

Aircraft test model gain and phase margins ............................................................................... 192

Input files for linear aeroelastic and aeroservoelastic analysis .................................................. 196

(a) Thermally prestressed vibration analysis results .................................................................. 255

(b) Nodal deflection for static analysis ...................................................................................... 255

(c) Buckling load factor for buckling analysis ........................................................................... 255

J

viii
36.

37.

(a)Thermallyprestressedvibrationanalysisresultsfor cantileverplate 259

with varyingtemperaturedistribution ................................................................................ 259

(b) Nodaldeflectionfor staticanalysis ......................................................................................

(c) Buckling loadparameterforthermalloadbuckling analysis............................................... 259

(a)Maximumdeflectionin thez directionfor staticanalysis(free-edgedeformation) ............264 264

(b)Naturalfrequenciesfrom vibrationanalysis ........................................................................

ix

ABSTRACT

A multidisciplinary, finite element-based, highly graphics-oriented, linear and nonlinear analysis

capability that includes such disciplines as structures, heat transfer, linear aerodynamics, computational

fluid dynamics, and controls engineering has been achieved by integrating several new modules in the

original STARS (STructural Analysis RoutineS) computer program. Each individual analysis module

is general-purpose in nature and is effectively integrated to yield aeroelastic and aeroservoelastic

solution of complex engineering problems. Examples of advanced NASA Dryden Flight Research

Center projects analyzed by the code in recent years include the X-29A, F-18 High Alpha Research

Vehicle/Thrust Vectoring Control System, B-52/Pegasus ®, Generic Hypersonics, National AeroSpace

Plane (NASP), SR-71/Hypersonic Launch Vehicle, and High Speed Civil Transport (HSCT) projects.

Extensive graphics capabilities exist for convenient model development and postprocessing of

analysis results. The program is written in modular form in standard FORTRAN language to run on a

variety of computers, such as the IBM RISC/6000, SGI, DEC, Cray, and personal computer; associated

graphics codes use OpenGL and IBM/graPHIGS language for color depiction. This program is available

from COSMIC, the NASA agency for distribution of computer programs.

NOMENCLATURE

ASE

CFD

CPU

DEM

EAS

EPS

FDBC

GCS

GUI

GVS

IDBC

KEAS

LCS

LGCS

RL

STARS

TAS

VBO

ZDBC

aeroservoelastic

computational fluid dynamics

central processing unit

dynamic-element method

equivalent airspeed

solution accuracy parameter

finite displacement boundary conditions

global coordinate system

graphical user interface

ground vibration survey

interdependent displacement boundary conditions

knots equivalent airspeed

local coordinate system

local-global coordinate system

double-precision

STructural Analysis RoutineS

true airspeed

reduced velocity

zero displacement boundary conditions
1. INTRODUCTION

The highly integrated, digital computer program, STARS (STructural Analysis RoutineS), 1 has been

designed as an efficient tool for analyzing practical engineering problems and for supporting relevant

research and development activities. The program has also been an effective teaching aid, because all

such activities are mutually enhancing and interrelated (fig. 1). Each individual module (fig. 2) of the

program is general-purpose in nature, capable of solving a wide array of problems. The finite-element

analysis modules are also appropriately combined to yield unique, multidisciplinary modeling and

simulation capabilities of complex engineering problems.

The STRUCTURES (SOLIDS) module is capable of analyzing static, stability, vibration, and

dynamic-response problems for all types of structures, including spinning ones subjected to mechanical

and thermal loading. Both linear and nonlinear analyses are conveniently performed by the program. The

element library consists of an extensive number of one-, two-, and three-dimensional elements with

general material properties, including composite and sandwich elements. Structural as well as viscous

damping can be included in the analysis. Figure 3 shows an overview of the SOLIDS link.

The heat-conduction analysis capability in the program is effected through the SOLIDS HEAT

TRANSFER module. Both steady-state and transient analyses can be performed, including nonlinear

effects. The element library consists of line, shell, and solid elements, including composites.

R....rohI

deve°pmentl _"7 I --r-r--- I

T

_Dissemlnation-_. teaching /

970273

Figure 1. Structural synthesis.

Finite-element structural analysis

Spinning structures

Mechanical and thermal loading

General and composite materials

Static, buckling

Vibration, dynamic responses

Aeroelasticity:

Flutter and divergence

Flow-field analysis

Lift, drag, and moment

Aeroservoelasticity:

Frequency response, damping

and frequencies, digital

and analog controllers

Finite-element heat transfer

Finite-element computational fluid dynamics

Preprocessor - automatic finite-element

method model data generation

Postprocessor - color graphical

depiction of analysis results

2
Figure2. Major modulesof STARS.

Input

Correct model

I View

model

geometry

\ I Print * I

___ View

mode shapes

displacement

I rint I

Figure 3. STARS-SOLIDS overview.

View

dynamicresponse

stresses

_ 970275

Figure 4 shows a schematic of the associated linear aeroelastic and aeroservoelastic (ASE) analyses.

When the frequencies and mode shapes of the structure are derived from finite-element analysis

employing the STARS-SOLIDS module, the STARS-AEROS module is used to compute the unsteady

aerodynamic forces on the structure. An alternative option enables input of measured modal data in lieu

of calculated data. A flutter solution is then achieved using the k or p-k methods. The user has to input

details of the aerodynamic paneling to achieve the aeroelastic analysis.

Subsequent linear ASE analysis is achieved by employing the STARS-ASE module. The user

provides essential data to perform a polynomial curve fitting of unsteady aerodynamic forces resulting in

the state-space matrices. For an alternative open-loop flutter analysis, these data consist of information

3
on polynomial tension coefficients, previously calculatedgeneralizedmasses,damping and modal

characteristics,and a set of velocity values.Additional data, in lieu of velocity values,relating to

coordinatetransformationsfrom Earth-to body-centeredcoordinatesystemsand sensorlocationsare

neededfor the subsequentASE analysis for frequency-responsecalculations and for determining

dampingand frequencyvalues.Theseadditionaldataareachievedby the STARS-ASE-CONTROL

submodulein which the primary datainput relatesto analogor digital controller blocksconnectivity,

associatedtransferfunctionpolynomialdescriptionsandgaininput, specificationsfor systemoutputand

input,andconnectiondetailsbetweentheplantandtheblocks.This ASEanalysisprocedurecanalsobe

effectivelyusedasthethird flutter solutionoption.

FEM

Preprocessor

modeling -_

FEM

Aeropanellng

Interpolation

grid

I SOLIDS

Measured "\ I (vibration analysis)

I mode Input _---------_

option /

] Generalized mess, I_ ]

_ W, (_, and I_

Modal data

interpolation

¢ values at downwesh points

AERO

(DLM, CPM)

Generalized

equations of motion

Select vectors

ASE

polynomial (Pad6)

approximations

Flutter

solutions

(k and p-k)

Q: Postprocessor

;._ State-space (_, and B)

formulati/n (plant) J l coRn°t:ur

J, v I solution

y I(open'loop)

Transform I _L

(earth-to-body-fixed I

coordinat;: A and B), (_

I Sensor output (C and D) I _

Augment analog

elements; modify

A, B, C, and D

Augment analog

controller; modify

A, B, C, and D

I

Root contour solution:

equivalent open-loop

or closed-loop

(damping and

frequencies)

Hybrid technique:

augment digital

controller; modify

A, B, C, and D

Frequency responses:

equivalent open-loop

or closed-loop

(gain and phase)

LL 970276

Figure 4. STARS-ASE flowchart.

/

Nonlinear aeroelastic and ASE analysis capability has been implemented in the STARS-CFDASE

module. The STEADY submodule, which employs unstructured grids for domain discretization, can be

4
effectively employedfor the solutionof fluid flow problems.The STARS-CFDASE moduleenables

effectivecomputationof unsteadyaerodynamicforcesemployingthefinite element-basedstructuraland

computationalfluid dynamics(CFD) computations.Subsequentaeroelasticanalysispredictsflutter and

divergencecharacteristicsof the structure,whereasthe ASE analysiscomputesthe required stability

derivatives.The associatedPROPULSIONmoduleessentiallyemploysCFD techniquesfor simulation

of flow-mixing phenomenon.Data pertaining to advancedmaterial properties are stored in the

MATERIALS module.

TheNUMERICAL ANALYSIS modulecontainsa numberof efficient solutionproceduresfor large,

sparse,matrix linear equationsandeigenvalueproblems.A block Lanczosprocedureis availablefor

solution of free-vibration problemsfor nonspinningand spinning structuresas well asthe quadratic

matrix eigenvalueproblem associatedwith a finite-dynamic elementformulation. An alternative

procedure,basedon a combinedSturmsequenceandinverseiterationtechnique,is also availablethat

enablesextractionofrootsandassociatedvectorslying within any specifiedbound.

A separatepreprocessorsubmodule,PREPROCS,hasbeendevelopedfor automatedgenerationof

nodal, element, and other associatedinput datafor any continuum. The PREPROCSsubmoduleis

capable of generating complex structural forms through duplication, mirror-imaging, and crosssectioningof modularrepresentativestructures.AppendixA containsthe Preprocessormanual.A fully

automated,three-dimensionalmeshgenerationcapability is animportant featureof this module.The

STARS postprocessorsubmodules,POSTPLOTSand POSTPLOTF, are used for extensive color

plotting of various structural-, heat-transfer-and CFD-related solution results. Appendix B is the

Postprocessormanual.

Section 2 describesthe STARS-SOLIDS module of the program and highlights of someof its

important features,andsection3 providesthe datainput procedure.Section4 provides summariesof

input dataand analysisresults for sampletest casesrelevantto this module.Section 5 describesthe

various featuresof the aeroelasticandASE analysescapabilities,and section 6 providesdata input

details of various related submodules.A representative,integratedaero-structural-control sample

problemis workedin detailin section7.Section8 providesdetailsof CFD analysis,aswell asnonlinear

aeroelasticityandASE.AppendixC providestheSTARSsystemdescriptions.

2. STARS-SOLIDS MODULE DESCRIPTION

The structure to be analyzed by the STARS program, either linear or nonlinear, can be composed of

any suitable combination of one-, two-, and three-dimensional elements. The general features of the

STARS-SOLIDS module include the following:

1. A general-purpose, compact, finite-element code.

2. Elements:

3. Geometry:

4. Material:

bars, rods, beams, three-dimensional line elements, rigid bars, membranes,

triangular and quadrilateral planes, plates, shells, sandwich panels, composite

elements, and tetrahedral and hexahedral solids.

any relevant structure formed by a suitable combination of the elements.

general, isotropic, orthotropic, and anisotropic material.
5. Analysis: naturalfrequenciesandmodeshapesof nonrotatingandrotatingstructureswith

or without structuraldamping,viscousdamping,or both,including initial load

(prestress)effect; stability (buckling) analysis;dynamic-responseanalysisof

nonrotating and rotating structures;and static analysis for multiple sets of

mechanicalandthermalloading.Also, steady-stateandtransientheat-transfer

analysis,includingnonlinearradiationboundaryconditions.

Specialfeaturesof theSTARS-SOLIDSmoduleincludethefollowing:

1. Randomdatainput within a subset,using rectangular(Cartesian),cylindrical, and spherical

coordinatesystems.

2. Automaticnodeandelementgeneration.

3. Matrix bandwidthminimization.

4. Generalnodaldeflectionboundaryconditions.

5. Multiple setsof staticloadinput.

6. Preprocessorandpostprocessor.

7. Plot of initial geometry.

8. Plotsof modeshapes,nodaldeformations,andelementstressesasa functionof time, asrequired.

Structuralgeometryis describedin termsof the globalcoordinatesystem(GCS)or thelocal-global

coordinatesystem(LGCS) havinga right-handedCartesiansetof X-, Y-, andZ-coordinateaxes.Each

structuralnodeis assumedto havesixdegreesof freedom,consistingof threetranslations(UX, UY, UZ)

andthreerotations (UXR, UYR, UZR), that aretheundeterminedquantitiesin the associatedsolution

process.Detailsof someimportantfeaturesof themodulearesummarizedin thefollowing subsection.

2.1 Nodal and Element Data Generation

The STARS program provides simple linear interpolation schemes that enable automatic generation

of nodal and element data. Generation of nodal data depends on the occurrence of such features as nodes

lying on straight lines and common nodal displacement boundary conditions. Generation of element data

is possible if the finite-element mesh is repetitive in nature and elements possess common basic

properties. The module enables input of data employing the GCS or a number of rectangular LGCSes,

relevant to various substructures, in which the data can be read in rectangular, cylindrical, and spherical

coordinate systems.

A separate preprocessor submodule, PREPROCS, has been developed for automated generation of

nodal, element, and other associated input data for any continuum. The preprocessor is an interactive,

graphics, structures-modeling submodule. This preprocessor is capable of generating complex structures

through duplication, mirror-imaging, and cross-sectioning of modular representative structures.

6
2.2 Matrix Bandwidth Minimization

This feature enables effective bandwidth minimization of the stiffness, inertia, and all other relevant

system matrices by reordering input nodal numbers, taking into consideration first- and second-order

nodal connectivity conditions. The existing nodal numbering can be modified 2 to minimize bandwidth

of associated matrices (fig. 5). Therefore, any node with minimum first-order connectivity can be chosen

as the starting node. Accordingly, any one of nodes 1, 4, 7, 10, 13, and 16, all of which have a minimum

first-order nodal connectivity of two, can be selected as the first node to start the nodal numbering

scheme. Nodes 1, 4, 10, and 13, however, possess a higher second-order connectivity condition than

do nodes 7 and 16. For example, nodes connected to node 1 (namely, nodes 2 and 18) are, in

turn, connected to a total of seven nodes, whereas the connectivity number for nodes 7 and 16 is six. As

such, either node 7 or 16 can be chosen as the starting node for the renumbering scheme. Figure 5 shows

in parentheses a revised nodal numbering that minimizes matrix bandwidth. The present minimization

scheme also takes into consideration the presence of nodal interdependent displacement

boundary conditions.

i v,

13 12 11 10

16_ 116)

(7) (10' i_

1 2 3 4

I_ L

8

r(

970277

Figure 5. Bandwidth minimization scheme.

2.3 Deflection Boundary Conditions

The nodal displacement relationships can be classified as zero, finite, and interdependent

displacement boundary conditions (ZDBC, FDBC, and IDBC). Details of such a formulation are

provided in section 3.4. Thus, in addition to prescribed zero and finite displacements, the motion of any

node in a particular degree of freedom can be related in any desired manner to the motion of the same or

any other combination of nodes in any set of specified directions.
2.4 Prescribed Loads

A structure may be subjected to any combination of mechanical and thermal loadings. The loads in

the mechanical category can be either concentrated at nodes or distributed. Thus, uniform pressure can

be applied along the length of line elements acting in the direction of the local y and z axes. Such

uniform surface loads are assumed to act in the direction of the local z axis of the shell and solid

elements, acting respectively on the shell and solid-base surfaces. The effect of thermal loading can be

incorporated by the appropriate input of data pertaining to uniform element temperature increases and

thermal gradients.

2.5 Static Analysis

Static analysis, performed by setting the parameter IPROB = 8 in the input data, is effected by

solving the set of linear simultaneous equations

Ku = p (1)

where

K

U

P

IPROB

= system elastic stiffness matrix

= nodal displacement vector

= external nodal load vector

= integer designating problem type (defined in section 3.1)

A multiple set of load vectors is represented by the matrix p, incorporating effects of both mechanical

and thermal loading. The equations are solved once, initially by Gaussian elimination, and solutions

pertaining to multiple nodal load cases are obtained by simple back-substitution.

2.6 Elastic Buckling Analysis

A buckling analysis is performed by solving the eigenvalue problem

(K E + TKG)U = 0 (2)

in which K E and K G are elastic stiffness and geometric stiffness matrices, respectively; u represents the

buckled mode shapes; and T is the buckling load. This analysis is achieved by setting IPROB = 9.

2.7 Free-Vibration Analysis

The matrix equation of free vibration for the general case of a spinning structure with viscous and

structural damping is expressed 3 as

[KE(l+i*g) + K G +K']u + (C c + CD)ti + Mii = 0 (3)
in which a dot indicatesdifferentiation with respectto time. The previously

describedasfollows:

K' = centrifugalforcematrix

CC = Coriolis matrix

C D = viscous damping matrix

M = inertia matrix

g = structural damping parameter

1 = imaginary number, afL-]-

undefined terms are

Such a structure can have individual nonrotating and rotating components spinning with different spin

rates along arbitrary axes.

Various reduced sets of equations pertaining to specific cases of free vibration are given as follows:

1. Free, undamped vibration of nonspinning structures (IPROB = 1):

KEU + Mii = 0 (4)

2. Free, undamped vibration of spinning structures (IPROB = 2):

Ku + Ccu + Mii = 0

where K=K E+K G+K'.

3. Free, damped vibration of spinning structures (IPROB = 4, 5), defined by equation (3).

4. Free, damped vibration of nonspinning structures (IPROB = 6, 7):

KE(l+i*g)u + CDII + Mii = 0

(5)

(6)

The eigenvalue problems pertaining to the IPROB = 1 and IPROB = 9 cases are real in nature, but the

rest of the above problems involve complex-conjugate roots and vectors. In the special case of a

prestressed structure, the matrix K G is automatically included in equation (6).

In addition, the STARS program solves the quadratic matrix eigenvalue problem (IPROB = 3)

associated with a dynamic-element formulation, 4

(7) [K E - _,2M - X4(M 2 - K4)]q = 0

which is quadratic in terms of the eigenvalues X = _2. Both M 2 and K 4 are the higher-order dynamic

correction matrices; _, is the natural frequencies; and q is the eigenvectors. This option is currently being

updated to include a number of elements.

9
Structuresprestressedby initial loadscanalsobeanalyzed,in which cases the relevant eigenvalue

problem for undamped structures has the form

(Rz +I%- 2M)q =0 (8)

where the geometrical stiffness matrix K G is a function of initial stresses. Similar formulations are

obtained for structures with various forms of damping.

2.8 Dynamic-Response Analysis

The modal superposition method is employed for the dynamic-response analysis following the computation of structural frequencies and modes. For example, the associated eigenvalue problem of

equation (4) for a nonrotating, undamped structure is first solved to obtain the first few eigenvectors, q,

and also the eigenvalues. The vectors consist of a set of rigid-body modes, qr, and a number of elastic

modes, qe, that are next mass-orthonormalized so that the matrix product

qTMq = I (9)

is a unit matrix. A transformation relationship,

u = qrl (10)

is substituted in the dynamic equation

Mii + Ku = p(t) (11)

and, when premultiplied by qT, yields a set of uncoupled equations,

_r = qTp(t) (12)

and

i]e + _2Tle = q Tp(t) (13)

that incorporate rigid-body and elastic mode effects, respectively. The symbol p(t) is the externally

applied, time-dependent forcing function; _'22 is a diagonal matrix; and ¢-oiis the natural frequencies.

Solutions of equations (12) and (13) can be expressed in terms of Duhamel's integrals, which, in turn,

can be evaluated by standard procedures. 5 In the present analysis, the externally applied, time-dependent

forcing function must be applied to the structure in appropriate, small, incremental steps of rectangular

pulses. The forcing function can be either load or acceleration vectors; the program also allows

application of initial displacement and velocity vectors to the structure. For spinning and damped

structures, identified as IPROB = 2, 4, 5, 6, and 7, qT is replaced by its transjugate _T in the relevant

dynamic-response formulation.

10
2.9 Nonlinear Structural Analysis

For geometrical nonlinearity, a Newton-Raphson iterative procedure is used in which the stiffness

matrix is supplemented with the geometrical stiffness matrix, K G, so that large displacement and

rotation and the effect of in-plane stretching are taken into consideration.

Thus, for static analysis, the solution algorithm is as follows:

Let

n = number of load increments

i = number of iterations within a loop

Then, for each load increment ("n" loop), form

nKG, geometric stiffness matrix, based on accumulated element stresses cr' (= 0, for n = 1);

' denotes local coordinate system

nKE, elastic stiffness matrix, (= IK ° for n = 1; nK_ for n > 1)

nrs, residual forces (= 0, for n = 1; nr(_ ) for n > 1)

Then, for each iteration ("i" loop), solve

Update the geometry:

InK(El) + nKG]Au(i)= ___Ap- nr(i_ 1), for Au(i)

n

(14)

u(i) = u(i-1) + Au(i)

Obtain incremental deformation in the local coordinate system (LCS):

Au'(i) = [DIR](i)Au(i)

Calculate element stresses in the LCS and accumulate, based on Au '(i).

Obtain residual forces in the GCS: s

As(i) = InK(E1)+ nKG]Au(i) (15)

nr(_) = nr(is 1) + As(i) (16)

Check for convergence. If IAul > EPS, then compute K'(_) and K(iE), the element and global stiffness

matrices, respectively. Repeat the iteration ("i" loop), if it is not converged. Continue on the incremental

load loop ("n" loop) if convergence was achieved in the "i" loop. Stop computation upon completion of

the load cycle.

11
For dynamic-responseanalysisof geometricallynonlinear structures,a time-integration scheme

using a Newton-Raphsoniterative techniqueis adoptedfor the solution.The associatedalgorithm is

givenasfollows:

For a jth time increment, Atj ("j"loop),

accumulatedelementstresses,o' -- 0 (for j = 1).

Perform the iteration ("i" loop).

Form

Calculate

K(i-1), M, C, r(is 1)

Calculate

Solve

Update

form the jKG geometric

K i-1) = K(iE 1) + jKG] (r 0 = 0, for j = I)

4 2

_:=_t 2M+-C At + K(i-l)

Feff = Ft+At + M{ _t4 2ut+ 4 4 ,,(i-1)l C{ 2 2 ,(i-1)_-r(i-l) ilt+ lit - _t2 -t+Atf + At ut + lit- At "t+Atj s

Obtain deformation in the LCS:

_7,Au(i) = Feff

u (i) n0-1)+ Au(i)

t+At = -t+At

Au'(i) = [DIR](i)Au(i)

Calculate element stresses and accumulate, based on Au' (i).

Obtain residual forces in the GCS:

A._(i) = [K(iE -1) + jKG] Au(i)

r (i) = r (i-l) + As(i)

S S

Check for convergence, IAu(i)l - 0. If the loop is not converged, continue the iteration ("i" loop).

If converged, update

stiffness matrix based on

(17)

(18)

(19)

(20)

(21)

12

j_
2

dt+At = .-7- (ut+At - ut) - l_It

At

4

-- 4-- (llt+At -- Ut) --Art _It -- Ut t+At - At 2

If t _ tfinal, update the time ("j" loop). Stop at the end of the time cycle.

In problems that exhibit material nonlinearity, the Prandtl-Reuss equation of the stress-strain

relationship is combined with von Mises yield criteria for material characterization. An iterative solution

procedure is then employed for solution of the associated problems, as below:

Initialialize:

Set external loads (R E) and internal loads (R I) to zero

Set all stresses and deformations (uo) to zero

Set the yield function F = ---_yp *

Set the slope of the strain hardening curve to its inital value, Hin

Set the plastic strain Ep to zero

Set the incremental load, AP.

For each load ("j" loop):

Calculate the total load at the jth step

RE_ j ajE_1 +av

Calculate the norm

Find the residual force ("i" loop)

R res = R E - R I

i j i-1

Calculate II R res II; if IIR res II < eps x IIR E II, go to the end of the "j" loop.

l 1 J

Calculate Kep (initially Ke).

Solve the increment of displacement, Aui = K -1 1/res and the total elastoplastic displacement, ui =

ep'" i '

ui-1 + Aui.

For each element Cn" loop):

AEi = bAui, total increment in element strain (using e = bu for small strain)

13
Check last value of yield function Fi-1.

If Fi-I = 0, the element is already on yield surface; go to the elastoplastic loop.

If Fi-I < 0, the element is elastic at the start of the loop.

Calculate Aoi = DAei

Calculate Fi = oi + _YPi-i

O'i= O'i-1 + Aoi

If F i < 0, then it is elastic and store oi, Fi; go to the end of the "n" loop.

If Fi > 0, set SA = si-1, SB = si

Loop to bring oC onto the yield surface:

ac = (CA + aa)/2

Calculate FC = T_c - °YPi-1

If FC < 0, then ffA = OC

If FC > 0, then CB = aC

If I FC I > TOL, return to the top of the loop.

End of loop.

AEe i = D_pl(Oc - Oi-1)

AEpi = AEi - AEe i

Oi-I = OC, Fi becomes 0

Start of elastoplastic loop.

Set oi = oc, stress on yield surface

Loop 20 times, k = 1, 20 ("k" loop)

Calculate Dep, based on oC

AEpi

dAeep- 20

AC_k = Dep dA_ep

14
GC+k = GC+ AGk

Use GC+k to calculate normal

Calculate d(At3) = - x Fk

d_ d_

GC+k = C_C+k+ d(AG)

Set aC = (_C+k

End "k" loop.

Calculate Fi, which should be 0; set to 0 if not (may be very small).

Store GC+k and Fi.

Calculate elastic strain increment:

Store Epi = Epi_l + AEp

AEe = DeI{ _C+k - _i-l}

AEp = AEi - A_e

Calculate H' i = f(Epi ) from input data (may be assumed to have a constant slope/value)

End element "n" loop.

End residual force 'T' loop.

End load "j" loop.

2.10 Shift Synthesis

The module provides special eigenvalue switching provisions in the analysis to ensure numerical

stability. Such a problem may be encountered in the analysis of aerospace structures, which are designed

to be strong and lightweight. For example, the elements of the mass matrix of equation (4) may have

numerical values much smaller than those of the stiffness matrix. In such cases, the effect of the mass

matrix in the (K-k2M)y = 0 formulation may be insignificant. Such a problem also occurs in the

presence of rigid-body modes characterized by "zero" frequencies. An eigenvalue shift strategy has been

developed to accommodate such situations.

15
Thus, the eigenvalue problem pertaining to equation (4) representingthe problem defined as

IPROB= 1canbewritten as

(K - _.2M)y = 0 (22)

in which _, is the natural frequency of free vibration and y is the eigenvector. The stiffness and mass

matrices must be suitably perturbed to handle rigid-body modes and to maintain numerical stability by

negating effects of rounding error. Thus, equation (22) is rearranged as

[K + IM- (_ + I)lVI] y = 0 (23)

or

in which

(I_ - _.l_'l)y = 0 (24)

= K + IM (25)

lVl = FM (26)

_2

_. = _ (27)

F

_2

_, = if- + I (28)

F_- l i,iJ (29)

107

where IKi,il and IMi,il typically denote the norms of the diagonal elements, the number 107 relates to the

computational accuracy of the computer, and I is a suitable integer factor, such as 4. When the

eigenvalue problem defined by equation (24) is solved, the natural frequencies are obtained as

A similar procedure is adopted for the analysis of free-vibration problems defined by IPROB = 6 and

7 and for the buckling analysis (IPROB = 9). In the case of spinning structures, a somewhat similar

strategy is used in perturbing appropriate matrices to ensure effective computation of rigid-body modes

as well as numerical stability.

_j-"

16
2.11 Formulation for Nodal Centrifugal Forces in Finite Elements

The STARS-SOLIDS module can perform dynamic analyses of structures with nonrotating and

rotating parts having different spin rates. A general derivation for the in-plane centrifugal forces

generated in various elements because of the arbitrary spin rate, along with related formulation of the

associated normal components, has been given in detail. 6 Details of a block Lanczos algorithm developed for efficient, free-vibration analysis of spinning structures have also been given. 7

When the nodal centrifugal forces have been derived, as previously mentioned, and stored in array P,

the element stresses in the structure caused by these forces are simply obtained by solving equation (1),

repeated here for convenience:

Ku= p

The stresses are next used to derive the structural geometrical stiffness matrix, K G, required for solving

the free-vibration problems defined in section 2.7.

2.12 Material Properties

The structural material can be general in nature. Thus, the finite-element material properties can be

isotropic, orthotropic, or anisotropic. In the most general case of solid elements having anisotropic

material properties, defined as material type 3, the stress-strain matrix is expressed as

8 = E8 (31)

with Ei,j being elements of the general material matrix of the order 6, defining the relationship between

the stress vector, 8, and the strain vector, 8. The elements of the upper symmetric one-half of the E

matrix, as well as coefficients of thermal expansion and material density consisting of 28 coefficients,

are the required data input for the pertinent material type. In this connection, the material data input is

designed to be quite general; the user can easily incorporate effects of various related features, such as

varying material axes orientation, by appropriately calculating the elements of the material matrix. If the

material is orthotropic, the input scheme remains the same as for the anisotropic case.

Material type 2 pertains to thin-shell elements displaying anisotropic or orthotropic material properties and requires an input of 13 coefficients. For isotropic material classified as material type 1, only six

coefficients constitute the required input data. The isotropic case for sandwich-shell elements is

designated as material type 4, and type 5 pertains to the corresponding orthotropic-anisotropic case. For

the heat-transfer case, material types 6, 7, and 8 refer to isotropic-line, isotropic-shell, and orthotropicanisotropic-shell elements, respectively.

2.13 Heat-Transfer Analysis

A heat-conduction analysis capability for solids has been incorporated in the STARS-SOLIDS

module. Figure 6 shows a typical heat-transfer problem in a three-dimensional anisotropic solid solution

domain, D, bounded by a surface, S. The corresponding thermal energy equation is derived from the law

17
of conservationof energyand Fourier's law, and the resultingparabolicheat-conductionequationis

solvedsubjectto an initial condition and boundaryconditionson all portionsof the surface.A finiteelementdiscretizationof thecontinuumis achievedby themethodof weightedresiduals.8,9

Emlff,ed

edletive energy ./Abso.r.l_d

JF realetlve

__ energy

\ S I ./Specified

0

J Specified

_surface

Convective I temperature

heat transfer

_'_ X

970278

Figure 6. Three-dimensional general heat conduction.

The following analysis types are relevant to the current heat-transfer solution effort:

• Linear steady-state analysis,

[[K c] + [K hll{T} = {RQ}+ {Rq }+ {R h} (32)

in which the element conductance matrix has contributions from conduction and convection, and the

heat-load vector has contributions from internal heat generation, surface heating and surface convection.

The element matrices and heat-load vectors are constant, and a linear solution of a set of simultaneous

equations is required.

• Linear transient analysis,

[C]{'r(t)} +[[K c ]+ [Kh (t)]]{T(t)} = {RQ(t)} + {Rq (t)} + {Rh (t) } (33)

in which the element capacitance matrices are also required, element convection matrices and heat-load

vectors are time dependent, and a solution of the equations is achieved by the modal superposition

method employing a time-integration procedure.

• Nonlinear steady-state analysis,

[[Kc (T)] + [Kh (T)] + [Kr (T)]]{T} = {RQ(T)} + {Rq (T)} + {Rh (T)} + {Rr (T)} (34)

-j

18
in which theelementmatricesandheat-loadvectorshavecontributionsfrom radiation,andthe matrices

and vectorsare temperaturedependent;thus, the equationsare nonlinearand requiresolution by an

iterativeschemesuchastheNewton-Raphsonmethod.

Nonlineartransientanalysis,

[C(T)]{I"} + [[Kc(T)] + [Kh (T,t)] + [Kr (T)]]{T(t)} =

{RQ(T,t)} + {Rq(T,t)} + {Rh(T,t)} + {Rr (T,t)}

(35)

in which the elementmatricesandheat-loadvectorsareboth temperatureand time dependent,and

solution by an iterative, time-marchingschemeis required.In general,nonlinearities arecausedby

temperature-dependent anisotropicmaterialproperties,convectioncoefficients,andnonlinearradiation

boundaryconditions,andtherelevantNewton-Raphsoniterationis performedat eachtime step.

Thefollowing definitionspertainto theabove"numericalformulationsandfigure 6:

C

Kc, Kh,Kr

RT,RQ,Rq

Rh, Rr

qs' qr

= element capacitance matrix.

= element conductance matrices related to conduction, convection, and

radiation, respectively.

= Heat-load vectors arising from specified nodal temperatures, internal heat

generation, specified surface heating, surface convection, and incident

surface radiant heating, respectively.

= specified surface and incident radiant heat flow rates/unit area,

respectively.

2.14 Output of Analysis Results

A dynamic-response analysis, in general, yields an output of nodal deformations and element

stresses as appropriate functions of time. Additional printouts provide summaries of maximum deformations and stresses or loads, as appropriate, as well as principal stresses and relevant angles. For line

elements, member end loads and moments constitute the usual output of results. In the case of thin-shell

elements, the stresses Gxx, Gyy, and 6xy are calculated at the centroid of the element and at both its top

and bottom surfaces. For solid elements, all six components of stresses (Gxx, 6yy, Gzz, Gxy, Gyz, Gzx) are

computed at the center of the volume of the element. Because free-vibration analysis provides the

necessary data for the dynamic-response analysis, the natural frequencies and associated modes and

relevant element strain energies are computed by the module and can be printed out. Similar results are

obtained for elastic buckling analysis. For static problems, the nodal displacements and element stresses

are computed for multiple-load cases. A heat-transfer analysis yields unknown nodal temperatures as

the solution.

Special printout options make possible a selective output of analysis results. Thus, computed data

such as stiffness and inertia matrices can be printed out. Initially, the module automatically prints out

19
the generatednodal coordinates,element data, and other relevant input data. The POSTPLOTS

submodulecanbeeffectivelyusedfor color graphicsdepictionof solutionresults.

2.15 Discussion

Additional analysis features such as finite, dynamic-element discretizations, improved dynamic analysis capabilities, and various efficient numerical techniques are continuously being implemented in the

module. A nonlinear analysis capability has also been developed in parallel. Improved preprocessing

and postprocessing of data, using a number of graphics terminals, are being used to permit efficient

modeling, analysis, and display of the results pertaining to practical structural problems. An automatic

data conversion program, NSTARS, has also been developed to convert NASTRAN l0 program data into

the STARS format.

3. DATA INPUT PROCEDURE

(STARS-SOLIDS and SOLIDS HEAT TRANSFER)

3.1.1 Primary Job Title

Format (FREE)

3.1.1.1 Additional Job Details

Format (A1, FREE)

1. Description:

2. Notes:

3.1.2

°

2.

3.1 Basic Data

Various job-related descriptions; any number of input lines.

First line input is required, and subsequent lines of input must have a C in the first column;

a maximum of 80 characters for each line is accepted.

NN, NEL, NMAT, NMECN, NEP, NET, NLGCS, NMANGL, NSTACK, MAXLEL

Format (FREE)

Description:

Notes:

NN

NEL

NMAT

Basic data parameters (structural).

= total number of nodes

= total number of elements

= total number of element material types

20
3.1.3

°

2.

NMECN = number of material elastic or heat-transfer constants; a maximum of numbers,

as follows:

= 4, for isotropic material, elastic analysis

= 6, for isotropic material, elastoplastic analysis

= 13, for orthotropic-anisotropic material for two-dimensional shell elements

(types 2, 3, 6, and 7)

= 10, for isotropic sandwich-panel material for shell elements (types 2 and 3)

= 25, for orthotropic-anisotropic sandwich panel material for shell elements

(types 2 and 3)

= 28, for orthotropic-anisotropic material for three-dimensional solid elements

(types 4 and 5)

= 11, for isotropic heat-transfer problem pertaining to line elements (type l)

= 41, for isotropic heat-transfer problem pertaining to shell elements (types 2, 3,

6, and 7)

= 44, for orthotropic-anisotropic heat-transfer problem pertaining to shell

elements (types 2, 3, 6, and 7)

NEP = total number of line-element property types (type 1)

NET = total number of shell-element thickness types (types 2 and 3)

NLGCS = total number of local-global coordinate systems

NMANGL = total number of material angle types

NSTACK = total number of composite shell-element stack types

MAXLEL = maximum number of layers in a composite-shell element

NTMP, NPR, NSPIN, NC, NBUN, NLSEC, NCNTRL, NOUT, NEXP, NNA

Format (FREE)

Description: Basic data parameters (loads and displacements).

Notes:

NTMP total number of element temperature types

-1, for analysis involving temperature loading evolved from heat-transfer

solution (IPROB = 1, 8, or 9)

NPR total number of element uniform-pressure types

-1, for analysis involving aerodynamic loading evolved from steady-state

CFD solution (IPROB = 1, 8, or 9)

NSPIN = total number of different element spin types

k

21
3.1.4

NBUN

1. Description:

2. Notes:

IPROB

NC = numberof setsof nodalloadsfor IPROB= 8or 10

= 0, for IPROB = 1-7

= 1, for IPROB = 9 or 10

= NTTS, for NTTS _: 0

= NTTS+I, for NTTS ¢ 0 and IPROB = 10

= total number of interdependent and finite nodal displacement connectivity

conditions (includes IDBC and FDBC in section 2.3)

= total number of nodal temperature inputs for IPROB = 10, equivalent to the

FDBC case

NLSEC = total number of line-element special end conditions, excluding commonly

occurring cases of purely rigid or hinged ends

NCNTRL = total number of control-surface rigid-body modes used for ASE analyses;

may also be utilized for generating perfect rigid-body modes

NOUT = total number of output nodes where direct modal interpolation is effected

NEXP = total number of uniform external in-plane pressures for membranes

NNA = number of CFD nodes, if used for structural interpolation of pressure

IPROB, IEIG, IDRS, IBAN, IPLUMP, IMLUMP, INMM, IINTP

Format (FREE)

Data defining the nature of the required solution.

= index for problem type, to be set as follows:

= 1, undamped, free-vibration analysis of nonspinning structures

- 2, undamped, free-vibration analysis of spinning structures

= 3, quadratic matrix eigenproblem option for dynamic-element method (DEM)

analysis

= 4, free-vibration analysis of spinning structures with diagonal viscous

damping matrix

= 5, as for IPROB = 4 with structural damping

= 6, free-vibration analysis of nonspinning structures with general viscous

damping

= 7, as for IPROB = 6 with structural damping

= 8, static analysis of structures with thermal and multiple mechanical load

cases

= 9, elastic buckling analysis

= 10, heat-transfer analysis

= 11, solids nonlinear analysis, static and dynamic

22
IEIG = integer defining eigenproblem solution type

= 0, for solution based on a modified, combined Sturm sequence and inverse

iteration method

= 1, for an alternative solution technique based on a block Lanczos procedure

(recommended for computation of the first few roots and vectors when the

lower bound PL = 0 for cases where IPROB = 1, 2, 3, or 9)

IDRS = index for dynamic-response analysis

= 0, no response analysis required

= 1, performs response analysis

IBAN = bandwidth minimization option

= 0, performs minimization

= 1, minimization not required

= -1, option to perform minimization only and exit

IPLUMP = index for nodal external loads

= 0, no load input

= 1, concentrated nodal load input for IPROB = 8 and 9,

IPROB = 1-7 for prestressed structures

= -1, for analysis involving loading evolved from CFD solution

as well as for

IMLUMP = index for nodal lumped scalar mass

= 0, no lumped mass

= 1, lumped nodal mass input (IPROB = 1-7)

INMM = index for a nodal mass matrix of order 6

= 0, no mass matrix

= 1, nodal mass matrix input (IPROB = 1-7)

IINTP = integer defining modal data for direct interpolation

= 0, no interpolation required

= 1, performs interpolation on STARS-SOLIDS calculated modal data

= 2, performs interpolation on externally supplied modal data; for example,

ground vibration survey (GVS) results

3. Additional notes:

A dynamic-response analysis is achieved by specifying appropriate values for IPROB and

IDRS; at the end of problem solution, extensive options are available for plotting nodal

deformations, mode shapes, and element stresses by utilizing the postprocessor submodule,

POSTPLOT.

Initial static load (prestress) effect: in the case of dynamic problems, the presence of nonzero

values of integers IPLUMP, NPR, or NTMP activates computation of prestressing effect.

23
3.1.5

.

2.

Mass matrix: nodal lumped mass matrix is added to consistent mass matrix to evolve the final

mass matrix.

IPREC, IPLOT, IPRINT, INDATA, IERCHK, INCFOR, IEZDBC, IIDBC, IMATE,

NLOOP

Format (FREE)

Description: Additional basic data.

Notes:

IPREC = specification for solution precision

= 1, single precision

= 2, double precision

IPLOT = index for graphics display

= 0, no plotting needed

= 1, performs the display of input geometry; if satisfactory, a restart option

enables continuation of the current analysis

IPRINT = output print option

= 0, prints final results output only

- 1, prints global stiffness (K), mass (M), and damping or Coriolis (C) matrices,

as well as detailed output on deformations, stresses, and root convergence

characteristics

= 2, prints output as in IPRINT = 1 but omits K, M, and C matrices

= 3, prints output as in IPRINT = 0 but omits eigenvector printouts

= 4, prints output as in IPRINT = 2 but includes strain energy information

INDATA = input data option

= 0, basic matrices are automatically computed

= 1, to read the upper symmetric banded half of basic matrices K, M, and C

from user input files by row

IERCHK = integer defining the level of error checks in input data specified by user

= 0, usual level of error checkouts

= 1, additional extensive data checkouts

INCFOR = integer defining input data format

= 0, basic format

= 1, alternative format

= 2, free format

_ZDBC = integer to enforce ZDBC for problems with zero on the diagonal of the K

matrix

= 0, no enforcement of ZDBC

= 1, enforce ZDBC

24
3.1.6

l°

2.

HDBC = integer to enforce the IDBC solution strategy and to transfer CFD pressure

loads to structural mesh

= 0, out-of-core solution, for a very large number of IDBC or NNA

= 1, in-core solution (preferred option)

IMATE = index for the deletion of K and M matrices in EIGLAN

= 0, do not delete; enables running of EIGSOL and dynamic responses

= 1, delete

NLOOP = number of increments in external load application (used for IPROB = 11);

default is 1

INDEX, NR, INORM, PU, PL, TOL

Format (FREE) (Required if IPROB = 1-7 and 9 and IPROB = 10 with IDRS = 1 )

Description: Data specifications for eigenproblem solution.

Notes:

INDEX = indicator for the number of eigenvalues and vectors to be computed

= 1, computes NR smallest roots (and vectors) lying within bounds PU, PL

= 2, computes all roots (and vectors) lying within bounds PU, PL

NR = number of roots to be computed (any arbitrary root number input for

INDEX = 2)

INORM = index for vector normalization; any desired vector row number

= 0, normalizes with respect to a scalar of displacement vector Y having

largest modulus

= -1, normalizes with respect to a scalar of Y or YD (velocity) vector having

largest modulus

PU = upper bound of roots, rad/s

PL = lower bound of roots, rad/s

TOL = tolerance factor (eq. (29))

= 0, defaults to 25.0E + 08

= X, defaults to X (X = 1.0E + 07 can be useful for computation)

3.1.7 IUV, IDDI, NTTS, NDELT

Format (FREE)

(Required if IDRS = 1)

1. Description: Data related to dynamic-response analysis.

25
2. Notes:

3.1.8

.

2.

3.1.9

IUV

IDDI

= index for the initial displacement (U) and velocity (V) input

= 0, no initial data

= 1, either initial displacement or velocity or both are nonzero vectors

= index for dynamic data input

= 1, nodal load input

= 2, nodal acceleration input

NTTS = total number of sets of load or acceleration data input

NDELT = number of sets of uniform time increments for response calculation

G

Format (FREE)

Description:

Notes:

Structural damping in formulation [K = K(1 + i'G)].

G ._

1 =

K =

Mll

Format (FREE)

(Required if IPROB = 5 or 7)

structural damping parameter

imaginary number,

system stiffness matrix

1. Description: Half bandwidth of K, M, CD, or C.

3.1.10 (0B(I, J), I = 1, N), J = 1, NC)

Format (6E10.4)

1. Description: Load matrix of the order N = NN x 6.

3.1.11 ((K(I, J), J = 1, Mll), I = 1, N)

Format (6E10.4)

1. Description: Stiffness matrix.

3.1.12 ((M(I, J), J = 1, Mll), I = 1, N)

Format (6E10.4)

1. Description: Mass matrix.

(Required if INDATA = 1)

(Required if INDATA = 1 and IPROB = 8)

(Required if INDATA = 1 and IPROB = 1-8)

(Required if INDATA = 1 and IPROB = 1-7)

26

v
3.1.13 ((C(I, J), J = 1, Mll), I = 1, N)

Format (6E10.4)

(Required if INDATA = 1 and IPROB = 2--5)

1. Description: Coriolis (IPROB = 2, 4, or 5) or dynamic correction (IPROB = 3) matrix.

3.1.14 ((CD(I, J), J = 1, Mll), I = 1, N)

Format (6E10.4)

(Required if INDATA = 1 and IPROB = 4-7)

l° Description: Viscous damping matrix.

General note: If INDATA =1, no further input is required. Each set of data input in succeeding

sections is preceded with a comment statement having a dollar sign ($) at the first column.

3.2 Nodal Data

$ Nodal Data

IN, X, Y, Z, UX, UY, UZ, UXR, UYR, UZR, ILGCS, IZDRCS, IINC

Format (I5, 3E10.4, 915)

or (I5, 3E15.8, 612, 315)

or (FREE)

(INCFOR -- 0)

(INCFOR = 1)

(INCFOR - 2)

1. Description: NN sets of nodal data input in the GCS/LGCS, at random; table 1 provides a

description of the input data.

Node

number

Table 1. Arrangement of nodal data input.

Local-global ZDBC reference

Nodal Nodal zero displacement coordinate coordinate

coordinates boundary conditions (ZDBC) system type system Increment

(IN) (X/r) (Y/0) (ZI_) (UX) (UY) (UZ) (UXR) (UYR) (UZR) (ILGCS) (IZDRCS) (IINC)

1 2 3 4 5 6

2. Notes:

a. A right-handed Cartesian coordinate system (X, Y, Z) is to be chosen to define the GCS.

b° The asterisk (*) indicates a required data input in the GCS/LGCS using a rectangular (x,

y, z), cylindrical (r, 0, z), or spherical (r, 0, 0) coordinate system; r is the radius, 0 is the

angle the vector makes with respect to its projection on the X-Y plane and the X axis, and

is the angle between the vector and the Z axis.

C.

Each structural node is assumed to have six degrees of freedom consisting of three

translations, UX, UY, UZ, and three rotations, UXR, UYR, UZR, usually labeled as

displacement degrees of freedom 1, 2, 3, and 4, 5, 6, respectively.

27
d.

e,

For nodal ZDBC defined in the coordinate system referred to as IZDRCS, set the value to

= 0, for free motion

= 1, for constrained motion

For node generation by increment, set IINC to

= 0, for no increment

= I, to increment the node number of the previous input by I until the current node

number is attained; coordinates of intermediate nodes are linearly interpolated

f. In automatic node generation (note (e)), all relevant data of generated intermediate nodes

pertain to that of the last data set of the sequence.

g° Third-point nodes for line elements are assumed to lie on the element local x-y plane and

can be chosen as any existing active node or dummy nodes with UX through UZR set

to 1.

h. Final data are automatically formed in increasing sequence of node numbers.

3. Additional notes:

3.2.5

.

2.

ILGCS = integer specifying LGCS number

IZDRCS = integer defining zero displacement boundary condition reference coordinate

system (set to 0 for data in the GCS or an ILGCS number)

$ Local-Global Coordinate System Data (Required if NLGCS _ 0)

ILGCS, IDMOD, ICTYP

Format (315)

XOR, YOR, ZOR, X2, Y2, Z2, X3, Y3, Z3 or

XOR, YOR, ZOR, Dll, D12, D13, D21, D22, D23, D31, D32, D33

Format (2(6E10.4,/))

(IDMOD = 1)

(IDMOD = 2)

Description: NLGCS sets of LGCS definition data, at random.

Notes:

IDMOD = integer specifying nature of input data

= 1, input involves global coordinates of the origin of the LGCS (XOR, YOR,

ZOR) and two data points (X2 through Z3, pertaining to two points located on

LGCS X axis and X-Y plane, respectively) in the GCS

= 2, involves input of the origin of the LGCS (XOR, YOR, ZOR) and elements

of the direction cosine matrix of the LGCS

28
ICTYP = integer defining coordinate system type

= 0, rectangular

= 1, cylindrical

= 2, spherical

3. Special note:

If I/NTP = 2, no further data input is required until 3.5.7.

3.3. Element Data

3.3.1 $ Element Connectivity

3.3.2 lET, IEN, ND1, ND2, ND3, ND4, ND5, ND6, ND7, ND8, IMPP, IEPP/ITHTH, ITMPP,

IPRR, IST, INC

Format (1615)

1. Description: NEL sets of element data input at random; table 2 shows the definition.

2. Notes:

IECI

IMPP

IEPP(x)

ITHTH(t)

ITMPP

IPRR

IST

= data as defined; under element type 8, individual rigid elements are

characterized by the appropriate data entry

= third-point node for element types 1 and 8

= integer defining line-element end condition pertaining to end I

= 0, rigid-ended

= 1, pin-ended in three rotational degrees of freedom

= J, denoting special end condition number, to be set greater than 1; for scalar

springs, set IEC 1 to a negative value less than-1

= integer defining material property type number

= integer defining line-element property type

= integer defining shell-element thickness type

= integer defining element temperature type

= integer defining element pressure type

= integer defining element spin type

29
INC = integerfor elementgenerationby increment

= 0, noincrement

= J, incrementsnodenumbersof previouselementsby J until currentelement

nodalnumbersarereached

= ILGCS, integerdefiningtheLGCSassociatedwith a zero-lengthscalarspring

element;defaultsto theGCS

= IMANG, integerdefining materialangletype number, suitablefor layered

elements

= ISTACK, stacktypenumber,usedfor integratedcompositeelements(types6

and7)

= dependentdegreeof freedomatND1 to berigidly connectedto all six degrees

of freedomat ND2; rulesconcerninginterdependenceof nodesanddegreesof

freedomaredefinedin section3.4.4

= -1, if all six degreesof freedomatND1 areinvolved

= 0, for pin-endedrigid barelements

= integerdefiningprestresstype

Rigid elementscanbespecifiedto spananylength,including0. Rigid pin-endedbarelements

canbesimulatedby settingIEC1= IEC2 = 1.

In automatic element generation(seeINC, above),the generatedintermediateelements

acquirethe samepropertiesas the last elementin current sequence.A specialoption also

enablesrepetitiveuseof anelementwith aninput format(I3, 12, 1515);the integerIET is

thenreplacedby NELNO andIET, whereNELNO is the total numberof similar elements

connectingthespecifiednodes.

Sandwich-shellelementscanbe generatedby individual inputs of membrane,bending,and

transversesheareffects. Furthermore,the composite-shellelementsconsistingof layered

compositescanbeformedfor varyingstacksof materials.

For elementtype 8, definedby two nodes,if thefirst nodehassomeZDBC constraints,the

constraintsshouldalsobeappliedto thesecondnode.

30
Element Element

type number

(IET) (IEN)

Table 2. Element data layout.

Node number for vertices

1 2 3 4 5 6 7 8

(NDI) (ND2)(ND3) (ND4) (ND5)(ND6) (ND7) (ND8)

IEPP/

IMPP ITHTH ITMPP IPRR IST INC

Line (bars, rods, * *

beams, threedimensional lines)

1

Shell quadrilateral *

(plane, plate, shear,

usual, and sandwich

shell, solid of

revolution (22))

2,22

Shell triangular _

(plane, plate, shear,

usual, and sandwich

shell, solid of

revolution (33))

3,33

Solid hexahedron

4

Solid tetrahedron

5

Shell quadrilateral

composite element

(plane, plate, shear,

and shell)

6

Shell triangular *

composite element

(plane, plate, shear,

and shell)

7

Rigid element (pinended bar, rigid

body)

8

Prestressed

rectangular

membrane

I1

* ** IEC1 IEC2 •

, • • •

, , ** IEC1 IEC2 #

X

, t * * * *

, t * *

31
. Element description:

Figure 7 shows the various elements and associated degrees of freedom.

represented by X, Y, and Z; and x, y, and z relate to the LCS.

The GCS is

Y

l

]ul', _ = oi

_j1 _ U:_R

z _'X J

Z r 970307 Z v

(a) Line element.

UIR IY/ -_'N_- '

0;,-.¢%x

970308

(b) Quadrilateral shell element.

Y

JI\olR ul _.,-y

U_zR .._

/ _ ;x

Z X 970309

(c) Triangular shell element.

/ o_/\o;

y

\

.x ,J

970310 Z

(d) Hexahedral solid element.

\/

,(z

X

970_79

(e) Tetrahedral solid element.

Z 9 Z I

z

_Y I = I t n_

;X

!

970311

(f. 1) Basic composite triangular shell/prism element

(6 degrees of freedom for each node for shell element,

2 degrees of freedom for each node at top and bottom

for heat transfer case).

I(

J

(f.2) Substack description for heat transfer

case only (maximum of 5 substacks and

6 degrees of freedom for each node).

(f) Composite shell/prism element.

Figure 7. STARS-SOLIDS typical element types.

32
4. Notes:

a. A right-handedCartesiancoordinatesystem(x, y, z) is to bechosento defineanyelement

LCS.

b. Any nodecanbechosenasthefirst vertexof an element; the local x axis is along the line

connecting vertices 1 and 2.

c. For line elements, the local x-y plane is defined as the plane contained by vertices 1, 2,

and the specified third-point node.

d, The vertices of thin-and thick-shell elements are usually numbered in a counterclockwise

sequence when observed from any point along the local positive z axis; the vertices are

also used as plane and plate-bending elements, as appropriate. For highly ill-conditioned

problems, alternative elements 22 and 33 may yield better results than the preferred

element types 2 and 3, respectively.

e. For solid elements, the y axis lies in the plane formed by vertices 1, 2, and 3 and 1, 2, 3,

and 4 for the tetrahedral and hexahedral elements, respectively; the z axis is perpendicular

to the x-y plane, heading toward the fourth node for the tetrahedron element and toward

the plane containing the other four nodes for the hexahedral element.

f° The vertices of the solid elements are also numbered in a counterclockwise sequence

when viewed from any point on the positive z axis lying above the considered plane; the

fifth vertex of the hexahedron is the node directly above vertex 1.

g. For layered composite-shell element types 6 and 7, the layering sequence starts with the

layer that has the maximum -z coordinate expressed in the element LCS.

h. For element type 7, for heat-transfer analysis, the element also caters to radiation and

surface heat flow on all five surfaces. The averaged internal heat generation rate can be

applied to the element.

i. Element type 3 can be used for plane elastoplastic analysis. Element type 7 with eight

layers needs to be used for such an analysis for shell structures.

5. Structural modeling:

Because each node is assumed to possess six displacement degrees of freedom, any

individual structural form can be simply represented by suppressing appropriate displacement

terms. The following rules may be adopted:

Truss structures: to allow only two nodal translational deformations in the plane of

the structure; to use line elements.

Plane frame: all three in-plane displacements, namely, two translations and one

rotation, are retained in the formulation; to use line elements.

33
3.3.3

3.3.4

3.3.5

Plane stress/strain: displacement boundary conditions are similar to truss structures;

to use shell elements. Also valid for axisymmetric solid elements.

Plate bending: only the three out-of-plane displacements consisting of one translation

and two rotations are considered for the analysis; to use shell elements.

Solid structures: the three translational degrees of freedom are retained in the

analysis; to use solid elements.

Shell, space frame: all six degrees of freedom are to be retained in the solution

process; to use shell and line elements, respectively.

Heat-transfer analysis: only the first two nodal degrees of freedom are used for twodimensional or linear gradient in three-dimensional heat-transfer analysis. If different

temperature gradients in the Z direction are desired, the number of degrees of freedom

can be increased accordingly. A maximum of six degrees of freedom and five

different temperature gradients through the thickness can exist.

Suppression of derived nodal motion is achieved by using ZBDC and IDBC, defined in

sections 3.2 and 3.4, respectively.

$ Composite Shell Element Stack Description Data

(Required for composite-shell elements (types 6 and 7), and only if NSTACK _ 0)

ISTACK, NLAYER, NSUBST, SBT1NL, SBT2NL, SBT3NL, SBT4NL, SBT5NL

Format (815)

(IMATC(I), THCL(1), IMANGC(1), I = 1, NLAYER)

Format (15, El0.4, 15)

1. Description:

2. Notes:

NSTACK sets of composite-shell element data; layers are read from the bottom of

the element.

ISTACK = stack number

NLAYER = total number of layers in the stack

NSUBST = number of substacks in the stack (heat-transfer case only, a maximum of

five)

SBT1NLSBT5NL = number of layers in the Ith substack; any number of layers allowed within a

substack (required for heat-transfer case only)

IMATC(I) = material type number for the composite layer

34
3.3.8

.

2.

l°

2.

THCL(I) = thickness of the composite layer

IMANGC(I) = integer specifying material angle type number (IMANG)

Because the module allows a maximum of five substacks, six temperatures at a node are the

usual requirement (a substack is allowed to have any number of layers) using all six degrees

of freedom, starting from the bottom.

$ Specification For Material Axes Orientation

IMANG, IMAMD, ILGCS

Format (315)

Dll, D12, D13, D21, D22, D23, D31, D32, D33

Format (2(6E10.4,/)) or

THETA

Format (El0.4)

Description: NMANGL sets of material angle definition data.

Notes:

IMAMD =

(Required if NMANGL ;e 0)

(IMAMD = 1)

(IMAMD = 2)

integer defining the material angle data input mode

1, involves input of elements of the direction cosine matrix of material axes

with respect to the LGCS/GCS (set ILGCS - 0 for data in GCS)

2, requires input of material axis angle (THETA) with the shell-element local

x axis, in radians

ILGCS =

THETA =

$ Line Element Basic Properties

IEPP, A, JX, IY, IZ, SFY, SFZ

Format (I5, 6E10.4)

Description:

Notes:

IEPP

A

JX

integer specifying the LGCS number (set to 0 if data is in the GCS)

material axis angle with respect to the shell-element local x axis

(Required for line elements only)

NEP sets of line-element basic property data in the element LCS.

= integer denoting the line-element property type

= area of cross section

= torsional moment of inertia about the element x axis

= (P, perimeter of cross-sectional area for IPROB = 10)

35
IY = momentof inertiaabouttheelementy axis

IZ = moment of inertia about the element z axis

SFY = A/ASY, shear area (ASY) factor along the y axis

SFZ = A/ASZ, shear area (ASZ) factor along the z axis

For no shear area effect, SFY and SFZ are to be set at 0.0. Also, for heat-transfer problems

(IPROB = 10), only A and P are the required input.

3.3.11 $ Line-Element Special End Conditions (Required for line elements only if NLSEC ;e 0)

3.3.12 ILSEC, (k(I), I -- 1, 6)

Format (15, 6E10.4)

1. Description: NLSEC sets of line-element special end conditions data in the LCS.

2. Notes:

ILSEC = element end condition type (to be set greater than 1), referring to members

attached at the nodes by flexible connections, or members with free-end

degrees of freedom in the LCS (corresponds to IEC 1 and IEC2)

= set to a negative value, less than -1, for scalar springs connecting two nodes

(corresponds to IEC 1)

k(I) = additional spring stiffness along the Ith translational (x, y, and z direction)

degree of freedom and actual rotational Ith spring stiffness (x, y, and z

rotational constraint)

= -2, for rigid rotational Ith constraint

= -1, for release of corresponding member end degree of freedom, relevant also

to ILSEC value set greater than 1

= stiffness values for scalar springs associated with a negative ILSEC value less

than -2

Such elements can have zero or any finite length.

To simulate only a specified end condition, set Young's modulus to E = 0 for the

corresponding material type, IMPP.

3.3.13 $ Shell-Element Thickness (Required for shell elements (types 2, 22 and 3, 33) only)

3.3.14 ITHTH, TM, TB, TS

Format (15, 3E10.4)

1. Description: NET sets of element-thickness data.

36
2. Notes:

3.3.17

ITHTH = element-thickness type

TM = membrane element thickness

TB = bending element thickness

TS = transverse shear element thickness

The above shell thicknesses pertain to sandwich elements; in the absence of data for TB and

TS, the shell-element thickness T is taken as TM.

For consistent mass matrix formulation, the shell thickness T is taken as TM.

$ Element Material Properties

IMPP, MT, ISSSR

Format (315)

E, MU, ALP, RHO, SIGYP, HP

Ell, El2, El4, E22, E24, FA4, E55,

E56, E66, ALPX, ALPY, ALPXY, RHO

Ell, El2, E13, El4, El5, El6, E22,

E23, E24, E25, E26, E33, E34, E35,

E36, E44, E45, EA6, E55, E56, E66,

ALPX, ALPY, ALPZ, ALPXY, ALPYZ, ALPZX, RHO

EM, EB, ES, MUM, MUB, MUS,

ALPM, ALPB, ALPS, RHO

EllM, E12M, E14M, E22M, E24M, E44M,

EllB, E12B, E14B, E22B, E24B, FA4B,

E55S, E56S, E66S, ALPXM, ALPYM, ALPXYM,

ALPXB, ALPYB, ALPXYB, ALPXS, ALPYS, ALPXYS,

RHO

KL, H, Q, QS, TE, QR, STB,

EMS, SABS, CP, RHO

KS, H1, H2, H3, H4, HT, HB,

Q, QS1, QS2, QS3, QS4, QST, QSB,

T1, T2, T3, T4, TT, TB, QR1,

QR2, QR3, QR4, QRT, QRB, STB1, STB2,

STB3, STB4, STBT, STBB, EMS1, EMS2, EMS3,

EMS4, EMST, EMSB, SABS, CP, RHO

(material type 1); or

(material type 2); or

(material type 3); or

(material type 4); or

(material type 5); or

(material type 6); or

(material type 7); or

37
KSll, KS12,KS22,KS66,HI, H2, H3,

H4, HT, HB, Q, QS1, QS2, QS3,

QS4, QST, QSB, T1, T2, T3, T4,

TT, TB, QR1, QR2, QR3, QR4, QRT,

QRB, STB1, STB2, STB3, STB4, STBT, STBB,

EMS1, EMS2, EMS3, EMS4, EMST, EMSB, SABS,

CP, RHO

Format (7E10.4,/)

Format (6E10.4,/)

1. Description:

(material type 8)

(material types 1-3 and 6-8)

(material types 4 and 5)

2. Notes:

NMAT sets of element material property data; the individual material matrices are

derived from the symmetric matrix of order 6 for general solid material.

IMPP = material number

MT = material type

= 1, isotropic (= 11, for a plane-strain case, = 12, for a solid of revolution)

= 2, orthotropic-anisotropic, shell elements (= 22, for plane-strain case, = 23, for

a solid of revolution)

= 3, orthotropic-anisotropic, solid elements

= 4, isotropic, sandwich-shell elements incorporating individual membrane,

bending, and transverse shear effects

= 5, orthotropic-anisotropic sandwich-shell elements with individual effects,

as above

= 6, isotropic heat transfer, line elements

= 7, isotropic heat transfer, shell elements

= 8, orthotropic-anisotropic heat transfer, shell elements

ISSSR = integer defining special stress-strain relationship

= 0, no plane strain

= 1, plane strain

E = Young's modulus

EIJ = elements of material stress-strain matrix (I = 1, 6 ; J = 1, 6)

MU = Poisson's ratio

ALP = coefficient of thermal expansion for isotropic material

ALPX, ALPY,

ALPXY = elements of thermal expansion vector, shell elements

ALPXALPZX = elements of thermal expansion vector, solid elements

38
°

3.3.18

RHO =

SIGYP =

HP =

For sandwich

use a postscript

respectively.

of M, B, or

mass/unit volume

material yield stress subjected to unit axial loading; can be ignored or set to

0.0 for elastic analysis

slope of strain hardening curve as a function of plastic strain (effect stress as a

function of plastic strain), assumed constant; can be ignored or set to 0.0 for

elastic analysis

elements (material types 4 and 5), relevant notations defining such properties

S for membrane, bending, or transverse shear stiffness,

For heat-transfer problems:

KL, KS,

KSIJ

H, HI

TE, TI

QS, QSI

QR, QRI

STB, STBI

EMS, EMSI

Q

SABS

CP

Additional notes:

= relevant elements of symmetric conductivity tensor (I = 1, 2, 6; J = 1, 2, 6)

= convective heat-transfer coefficient for a line element and a quadrilateral/

triangular shell element, as pertaining to the edges and the top and bottom

surfaces, respectively (I = 1--4 and T and B)

= convective exchange temperature, for line and other elements, as defined for

H, HI

= specified surface heat flow, for line and other elements, defined as above

= specified incident surface radiant heat flow, for line and other elements,

defined as above

= Stefan-Boltzmann constant, for line and other elements, defined as above

= surface emissivity, for line and other elements, defined as above

= appropriate internal heat generation rate for each unit volume

= surface absorptivity

= specific heat

For radiation problems, in the absence of specified temperature, an initial temperature input

is needed on the radiating surface.

$ Element Temperature Data/Initial Nodal Temperature Data (Required if NTMP _ 0)

39
3.3.19 ITMPP, T, DTDY, DTDZ

Format (2(I5, 3E10.4)) or

IN, NDOF, TEMP

Format (215, El0.4)

(If IPROB _: 10)

(If IPROB = 10)

1. Description: NTMP number of element temperature types; table 3 shows compatible input data.

Table 3. Element temperature data input.

Element

type T DTDY DTDZ

I , , ,

2,3,6,7 _

4,5

,

.

Notes:

ITMPP

T

DTDY

DTDZ

_g

IN

NDOF

TEMP

Additional notes:

= element temperature-increase type

= uniform temperature increase; relates to all elements

= temperature gradient along the element local y axis; relates to line elements

only

= temperature gradient along the element local z axis; relates to line and shell

elements

= compatible input data

= node number

= nodal degree of freedom

= temperature

Each data set for IPROB = 10 is to be terminated by a negative value of IN.

$ Element Pressure Data (Required if NPR > O)

IPRR, PR

Format (5(15, El0.4)) or

Format (15, 6E10.4) or (15, 4E10.4,/, 5x, 4E10.4) for an axisymmetric, a triangular, or a

quadrilateral solid element, respectively

1. Description: NPR sets of element pressure data.

40
2. Notes:

IPRR = elementpressuretype

PR = uniform pressure

Pressuredirectionsfor line elements:uniform pressureis allowedin local y andz directions

only, and the modulecalculatesboth end loadsand momentsas input. Although pressure

correspondingto a first nodal input pertainsto the y direction, a subsequentinput for the

samenodesignifiespressureactingin thez direction.

Pressuredirectionsfor shellelements:uniform pressureis allowed in the local z direction

only; themodulecomputesnodalloadinput.

Pressuredirectionsfor solidelements:uniform pressureis allowedonbasesurfacesdefined

by nodes1,2, 3, and4 and1,2, and3 for hexahedralandtetrahedralelements,respectively,

actingin thelocalz direction;themodulecomputesnodalloadinput data.

Pressuredirection_for axisymmetricsolidelements:linearly varyingtwo endpressuresonall

threeedgesfor triangularelementsandon all four edgesfor quadrilateralelements,with the

pressuredirectionbeinginwardpositive-actingperpendicularto theedges.Edgeis definedin

relation to internalnodalnumbering.For example,the startinginput nodeis consideredas

internal node 1 and the edge oppositeto node 1 is termed as edge 1, and so on. For

quadrilateralelements,internalnodes2 and3, 3 and4, 4 and 1,and 1and2 defineedges1,2,

3, and4,respectively.

3.3.22 $ Prestressed Rectangular Membrane Element Data (Required if NEXP ;e 0)

3.3.23 IIEXP, SX, SY

Format (15, 2E10.4)

1. Description: NEXP sets of prestressed membrane stress data.

2. Notes:

IIEXP = integer defining stress combination type

SX, SY = membrane stresses in the element x and y directions, respectively

3.4 Data in the Global or Local-Global Coordinate System

General note: Data input can be at random within each data group.

3.4.1 $ Element Spin Rate Data (Required if NSPIN ;e 0)

41
3.4.2 IST, SPX, SPY, SPZ, ILGCS

Format (I5, 3E10.4, I5)

1. Description:

2. Notes:

NSPIN sets of spin data.

IST = spin type

SPX, SPY, SPZ

ILGCS

= components of the element spin rate in the GCS/LGCS X, Y, and Z

directions, respectively

= LGCS number, as defined in section 3.2.2

$ Displacement/Temperature Boundary-Condition Data

INI, IDOFJ, INIP, IDOFJP, CONFCT, IDRCS, NDBCON

INI, IDOFJ, INIP, IDOFJP, TEMP, IDRCS, NDBCON

Format (415, El0.4, 215)

1. Description: NBUN sets of nodal IDBC data.

2. Notes:

(Required if NBUN ;e 0)

(If IPROB _e 10)

(If IPROB ---10)

INI

IDOFJ

INIP

IDOFJP

CONFCT

TEMP

IDRCS

NDBCON

J and J' vary between 1 and 6.

are the required input.

= node number I

= Jth degree of freedom associated with node I

= node number I'

= J'th degree of freedom associated with node I'

= connectivity factor

= temperature at the boundary condition

= displacement/temperature boundary-condition reference coordinate system

= integer defining displacement/temperature boundary-condition increment

= 0, no increment

- an integer, to increment the IDOFJ and IDOFJP by 1 until the IDOFJ reaches

the NDBCON value

For IPROB = 10, only INI and CONFCT (nodal temperature)

42
. Additional notes:

The nodal displacement boundary-conditions relationship is expressed as

Ui, j = am,nUm, n

= ai, jUi, j + ai',j'Ui',j' +-..

Table 4 shows the input scheme.

Table 4. Data layout for displacement boundary conditions.

Reference Incremental

Node Degree of Node Degree of Connectivity coordinate degree-of1 freedom 2 freedom coefficient system freedom value Terminology

i j i' j' ai',j' IDRCS NDBCON IDBC

i j i j ai, j IDRCS NDBCON FDBC

i j i j 0 IDRCS NDBCON ZDBC

.

2.

in which

i, i' = node numbers,

j, j' = degrees of freedom,

ai, j, a i', j' = connectivity coefficients.

IDBC, FDBC, and ZDBC are, respectively, the interdependent, finite, and zero displacement

boundary conditions. The ZDBC can also be conveniently implemented by following the

rules given in table 1, which is generally recommended for such cases. It should be noted that

the dependent degrees of freedom appearing in columns 1 and 2 cannot appear subsequently

in columns 3 and 4 as independent degrees of freedom. However, the independent degrees of

freedom can subsequently be related; although in such an event, an automatic sorting

procedure is triggered to rectify the situation.

$ Nodal Load Data (Required if IPLUMP. 0)

IN, IDOF, P, IDOFE, ILGCS

Format (215, El0.4, 215)

Description: NC sets of nodal force data.

Notes:

IN = node number

43
1. Description:

2. Notes:

3.4.11

1. Description:

2. Notes:

IDOF andIDOFE are,respectively,the start and end degrees of freedom assigned with the

same P value; the default value for IDOFE is IDOF.

P = nodal load

Each data set is to be terminated by setting a negative value for IN.

$ Nodal Mass Data (Required if IMLUMP ;e 0)

IN, IDOF, M, IDOFE, ILGCS

Format (215, El0.4, 215)

Nodal lumped mass data.

M = nodal mass

Other definitions are as given in section 3.4.6.

$ Nodal Mass Matrix In LGCS/GCS

IN, ILGCS

Format (215)

(VNMDAT(1), I = 1, 36)

Format (6(6E10.4,/))

User input of a nodal mass matrix of order 6.

(Required if INMM _ 0)

The user can input data for only the upper symmetric elements; numbers in the lower onehalf can be set to zero as the module automatically symmetrizes the matrix.

For data in the GCS, set ILGCS = 0.

Each data set is to be terminated by setting a negative value for IN.

$ Nodal Initial Displacement and Velocity Data (Required if IUV = 1 and IDRS = 1)

IN, IDOF, UI, VI

Format (215, 2E15.5)

1. Description: Initial displacements and velocities data.

44
2. Notes:

3.4.14

3.4.15

3.4.16

IN = node number

IDOF = degree of freedom

UI = initial displacement value

VI = initial velocity value

The data set is terminated if IN is read as -1.

$ Nodal Force Acceleration Data/Element Heat-Transfer Data

(Required if NTTS ;_ 0 and IDRS = 1)

TZ

Format (E15.5)

IN, IDOF, PZ

Format (215, E15.5) or

IEN, ISURF, Q, QS, TI

Format(215, 3E15.5)

(If IPROB ¢ 10)

(If IPROB = 10)

1. Description:

2. Notes:

3.4.17

3.4.18

NTTS sets of dynamic nodal load (IDDI = 1) or acceleration (IDDI = 2) input data.

TZ = time duration of load application

PZ = nodal force or acceleration data

IEN = element number

ISURF = element surface indicator (fig. 7 (f. 1))

Each data set is terminated by setting the IN value to -1; other definitions are as given in

sections 3.3.17 and 3.4.6.

$ Incremental Time Data For Response Calculation

(Required if NDELT _ 0 and IDRS = 1)

DELT, IDELT

Format (E15.5, I5)

NDELT sets of uniform incremental time input data for dynamic-response

calculations.

1. Description:

45
. Notes:

DELT

IDELT

= uniform incremental time step

= total number of uniform time steps in the data set

1. Description:

2. Notes:

°

2.

3.5.5

3.5.6

3.5 Additional Basic Data

$ Viscous-Damping Data

(C(I, I), I = 1, N)

Format (6E10.4)

User input of the diagonal viscous-damping matrix.

(Required if IPROB = 4 or 5)

C = diagonal viscous-damping matrix

N = order of matrix

$ Coefficients For Proportional Viscous Damping (Required if IPROB = 6 or 7)

ALPHA, BETA

Format (2E10.4)

Description: Proportional viscous-damping formulation C = ALPHA x K + BETA x M

Notes:

ALPHA and BETA are damping parameters.

K and M are system stiffness and mass matrices.

$ User Input Option For Viscous-Damping Matrix

(Required if IPROB = 6 or 7 and ALPHA and BETA are set to 0)

((C(I, J), J = 1, Mll), I = 1, 6)

Format (6E10.4)

1. Description:

2. Notes:

NN sets of user input of the banded viscous-damping matrix C(N,M 11) in blocks of

six rows of bandwidth M 11, one row at a time (N = 6 x NN).

The data file must conform to IDBC, FDBC, and ZDBC, inherent in the problem.

46
°

2.

3.5.9

3.5.10

$ Measured Modal Data Input

(INODM(I), (DISPLM(I, J), J = 1, 6), I " 1, NN)

Format (15, 6E10.4)

Description: Measured modal displacement data input, NR sets of data.

Notes:

1. Description:

2. Notes:

(Required if IINTP = 2)

Each data set is to be terminated by setting INODM(I) value to -1.

$ Output Points Specification For Direct Interpolation Of Modal Data

(Required if NOUT _ 0)

(IOUTP(I), (ICONP(I, J), J = 1, 6), I = 1, NOUT)

Format (715)

To read the output point and a maximum of six connecting points

IOUTP(I) =

ICONP(I, J) =

$ Rigid Control Modes Data Input

INS, IDOF, DISP, INE, ININC

Format (215, El0.4, 215)

1. Description:

2. Notes:

output points on aerodynamic paneling interpolation lines

STARS-SOLIDS finite-element nodes whose deflections will be averaged to

calculate the deflection value at the interpolation point

(Required if NCNTRL ;e 0)

Modal displacement data for NCNTRL number of modes.

INS, INE

IDOF

DISP

ININC

= start and end node numbers; the default value for INE is INS

= degree of freedom, a value between 1 and 6

= associated displacement

= integer defining nodal incremental value; increment INS by ININC until INE

is attained

Each data set is to be terminated by setting INS value to -1.

47
4. SAMPLE PROBLEMS

4.1. STARS-SOLIDS (Linear Analysis)

This section provides the input data and relevant outputs of typical test cases involving static,

stability, free-vibration, and dynamic-response analyses of representative structures. Other analyses

involving solids of revolution problems under mechanical and thermal loading as well as stress analysis

for such rotating bodies are not included in this section. Analyses are performed by typing the command

"srun." The input data are prepared in accordance with the procedures described in section 3. Details of

such analyses are in the descriptions that follow in which each structural geometry is described in

a right-handed, rectangular coordinate system, and the associated input data are defined in consistent

unit form.

4.1.1 Space Truss: Static Analysis

The static analysis of the space truss shown in figure 811 was performed to yield nodal deformations

and element forces. A load of 300 lbf acts at node 7 along the axial direction of the member connecting

nodes 7 and 9; another load of 500 lbf is applied at node 10 in the direction of the structural base

centerline. Also, the three members in the upper tier of the structure are subjected to a uniform

temperature increase of 100 °F. Two rigid elements are, however, introduced between nodes 5 and 8 and

nodes 7 and 9.

Important data parameters:

Young's modulus, E

Poisson's ratio, _t

Coefficient of

thermal expansion,

z

2 970280

Figure 8. Space truss.

= 1.0 x 107

= 0.3

= 12.5 × 10-6

48
STARS-SOLIDSinput data:

SPACE TRUSS - MECHRNICRL AND THERMAL LORDING

11,21,1,4,1,0,0,0,0,0

I ,O,O,l,O,O,O,O,O

5,0,0,1,1,0,0,0

2,0,1,0,I,0,0,1,0,0

$ MODAL DRTfl

1 0.0

2 0.O

3 124.60

4 13.86

5 13.06

6 96. 972

7 27.708

8 27.708

9 69.276

I0 41 ,568

11 144.0

$ ELEMENT CONflECTIUITY

1 1 4

2 2 4

3 2 5

4 3 5

5 3 6

6 3 4

7 4 5

8 5 6

9 6 4

10 4 ?

11 5 ?

12 5 8

13 6 8

14 6 9

15 6 7

16 7 8

17 8 9

18 9 7

19 7 I0

20 8 IO

21 9 1O

72.0

-72.0

0.0

48.0

-48.0

0.0

24.0

-24.0

0.0

O.O

36.0

11

11

11

11

11

11

II

I1

11

II

11

11

11

11

11

11

I1

11

11

11

11

$ LINE ELEMENT BASIC PROPERTIES

I 0,01389

$ ELEMENT MATERIAL PROPERTIES

I I

10,0E6 0.3 12.5E-06

$ ELEMENT TEMPERATURE DATA

I 100,0

$ NODAL LOflO DATA

10 I -500.0

7 I -259.8

7 2 150.0

-I

0,0

0,0

0.0

72,0

72.0

72,0

144.0

144.0

144.0

216.0

0.0

-I

- RBRRS FROM NODES 5-8, 7-9

I I I 0 0 0

I I I 0 O 0

I I I 0 0 0

1 I I I I I

O O 0

I I

I I

I I

STARS-SOLIDS analysis results: nodal deformations and element stresses are presented below.

LORD CASE NO. I

NODE

EXT IHT X-DISPL. Y-DISPL. Z-DISPL. X-ROTN. Y-ROTN. Z-ROTN.

I I .OOOOOOE+O0 .O00OOOE+O0 .O000OOE+O0 ,000000E+O0 .OOO000E+OO .O00000E+OO

2 2 .O00000E÷OO .O00000E÷OO .OOOOOOE+OO .O00OOOE+O0 .OO0000E÷O0 .O0000OE+OO

3 3 .OO0000E+OO ,000000E+O0 .OOO000E+OO .O000OOE+OO .O00000E+O0 .OOOO00E+OO

4 4 -.302075E+00 .233760E+00 -.331469E+00 .OOOOOOE+OO .OOOO00E+O0 ,OOOO00E+OO

5 5 -.294400E*00 .233736E+00 -.297468E+00 -.149503E-01 -.310231E-D1 -.530793E-01

6 6 -,358099E-00 .344030E+00 .558126E+00 .O00OOOE+O0 .O00000E*O0 .O00OOOE+O0

7 7 -,161162E+01 .575100E+00 -.385535E+00 .O000OOE+OO .O00000E+OO ,OOOO00E÷O0

8 8 -,125416E+01 ,575114E+00 -,226667E+00 -,149503E-01 -,310231E-01 -,530793E-01

9 9 -.143290E+01 .884643E+00 ,696849E+OD ,O00000E+O0 .O00000E+OO ,O00000E+O0

IO 10 -.460499E*D1 ,916627E+00 ,131711E*00 .O00000E+OD ,O00OOOE+O0 ,O00000E*OO

II 11 .O00000E+O0 .O00000E*O0 ,O00OOOE+OO ,O000OOE ÷00 ,O00000E+OO .O0000OE*O0

12 12 .O0000OE+OO ,OOOO00E+OO ,O00000E*OO ,OOO000E*O0 ,OOO000E*OO .OO0000E+OO

49
ELEMENT STRESSES

ELEMEHT EHDI EHD2 EHD3 END4

NO,

END5 END6 END7 END8

1 I 4

2 2 4

3 2 5

4 3 5

5 3 6

6 3 4

7 4 5

8 5 6

9 6 4

I0 4 7

1t 5 7

12 5 8

13 6 8

Z4 6 9

15 6 ?

17 8 9

18 9 7

19 7 10

20 8 I0

21 9 I0

PXI/PX2

SXT

SXX

.785576E+03

-.785576E+03

-.704942E-02

,704942E-02

.464122E÷03

-,464122E+03

.814173E-01

-.814173E-01

-,I16939E+04

,116939E+04

-.14636SE+03

,14636SE+03

-.633498E-01

.633498E-01

-,653699E-12

,653699E-12

.150008E+03

-,150008E*03

.?05240E+03

-,705240E+03

,463655E-01

-,463655E-01

,O00000E+O0

.O00000E+O0

-,178447E*00

.178447E+00

-,g27915E+03

.927915E+03

-,321364E+03

,321364E+03

.416932E-01

-.416932E-01

.833364E-01

-.833364E-01

.O00000E+O0

.OO0000E+O0

,463998E+03

-.463998E+03

.463998E+03

-_463998E+03

-.927967E*03

,927967E+03

PYI/PY2

SYT

SYY

,O00000E*O0

,O00000E+O0

.O00000E*O0

.O00000E+O0

.O00000E*O0

.O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E÷O0

,O00000E+O0

,O00000E*O0

.O00000E÷O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

.O00OOOE+O0

.O00000E+O0

O00000E+O0

O00000E+O0

O00000E+O0

O00000E+O0

,O00000E÷O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E*O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

.OOO000E+O0

,O00000E+O0

,O00000E*O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E*O0

PZI/PZ2

SXYT

SZZ

.O00000E+O0

.O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E÷O0

.O00000E+O0

.O00000E+O0

,O00000E*O0

.O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E÷O0

.O00000E+OO

,O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E*O0

.O00000E+O0

,O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E*O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

MXI/MX2

SXB

SXY

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

,O00000E+O0

,O00000E+O0

.O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E*O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

.O00000E+O0

,O00000E*O0

.O00000E+O0

.O00000E÷O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

,O00000E+O0

,O00000E+O0

,O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

MYIIMV2

SYB

SYZ

,O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

,O00000E÷O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E*O0

.O00000E+O0

O00000E+O0

O00000E+O0

O00000E+O0

O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

,O00000E÷O0

.O00000E+O0

,O00000E*O0

.O00000E+O0

,O00000E+O0

.O00000E+O0

,O00000E+O0

.O00000E÷O0

,O00000E+O0

.O00000E÷O0

.O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E÷O0

.O00000E+O0

,O00000E+O0

.O00000E*O0

.O00000E+O0

,O00000E÷O0

,O00000E+O0

.O00000E÷O0

.O00000E÷O0

.O00000E+O0

MZI/MZ2

SXYB

SZX

.O00000E+O0

.O00000E÷O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E÷O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

.OOO000E÷O0

,O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E÷O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

,O00000E+O0

,O00000E*O0

.O00000E+O0

,O00000E+O0

,O00000E+O0

.O00000E+O0

,O00000E+O0

,O00000E*O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00000E+O0

.O00OOOE+O0

.O00000E+O0

.OO0000E*O0

,O00000E+O0

,O00000E+O0

.O00000E+O0

.O00000E+O0

5O
4.1.2 Space Frame: Static Analysis

A space frame with rigid connections (fig. 9)12 is subjected to nodal forces and moments. Results of

such an analysis are presented below.

Important data parameters:

3r//

4,0001bf

100,000 Ibf.in.

\\-

1

970281

Figure 9. Space frame structure.

Young's modulus, E = 30.24 × 106

Poisson's ratio, Ix = 0.2273

Cross-sectional area, A = 25.13

Memberlength, _ = 120

STARS-SOLIDS input data:

SPACE FRAME CASE

6,4,1,4,1,0,0,0,0,0

0,0,0,1,0,0,0,0,0

8,0,0,1,1,0,0,0

2,0,1,0,1,0,0,1,0,0

$ NODAL OflTA

I 120.0 0.0 0.0

2 120.D 0.0 120.0

3 0.0 0,0 120.0

4 0.0 -120,0 120.0

5 0,0 120,0 120.0

6 10,0 10.0 0,0

$ ELEMENT CONNECTIVITY

I I I 2 6 0 0

I 2 2 3 6 0 0

I 3 3 4 6 0 0

I 4 3 5 6 0 0

$ LIHE ELEMENT BASIC PROPERTIES

1 25,13 125.7 62.83

$ ELEMENT MATERIAL PADPERTIES

1 I

30,24E06 0.2273

$ NODAL LOAD DATA

2 4 100000.0

2 2 4000.0

3 I -4000,0

3 3 -2000.0

3 4 -50000,0

-I

I I

0 0

0 0

I I

I 1

I I

62.83

I I I I

0 0 0 0

0 O 0 0

I I I I

I I I I

I I I I

I I

I I

I 1

I I

51
STARS-SOLIDS analysis results:

LORD CRSE HO. 1

HOOE

EHT IHT X-DISPL. Y-OISPL. Z-OISPL, X-ROTH. Y-ROTH. Z-ROTH.

1 1 0.000000E_00 0,000000E*00 0.000000E+00 0.000000E+00 0,000000E÷00 0.000000E+00

2 2 -0.I2528OE+00 0.347953E+00 0.196027E-04 -0.239969E-02 -0.I21545E-02 0.323397E-02

3 3 -0,125397E+00 0,103330E-03 -0,804946E-01 -0,580|22E-03 -0.283265E-03 0.910380E-03

4 4 O.O00000E*O0 O,O00000E*O0 O,O00000E+O0 O,O00000E+O0 O.O00000E+O0 O.O00000E+O0

5 5 0,00000OE+00 0,000000E*00 0.000000E+00 0,000000E+00 0,000000E*00 0,000000E*00

6 6 O.O00000E*O0 O.O00000E+O0 O.O00000E*O0 O,O00000E*O0 O.O00000E÷O0 O.O00000E÷O0

ELEMENT STRESSES

ELEMEHT EHD1 EHD2 EHD3 EHD4 PXI/PX2 PY1/PY2 PZI/PZ2 flX1/MX2 flYI/MY2 flZl/MZ2

NO, SXT SYT SXYT SX8 SYB SXVB

END5 END6 END7 END8 SXX SYY SZ2 SXY SYZ SZX

1 1 2 -,124146E+03 -.931704E+03 ,261767E+04 -,417341E+05 -.193156E+06 -.785077E*05

.124_46E+03 .931704E+03 -.261767E+04 .417341E+05 -.120964E+06 -,332968E+05

2 2 3 -,6g0886E+03 .232402E+03 -,129390E+04 .234814E+05 .397456E+05 ,255976E+05

,690886E+03 -.232402E+03 .129390E*04 -.234814E+05 ,115522E+06 .229060E+04

3 3 4 _,654366E+03 .523180E+03 _.980682E+03 .365547E+04 .437137E+05 .234344E*05

,654366E+03 -,523180E+03 .980682E÷03 -.365547E+04 ,739681E+05 .393472E+05

4 3 5 .654366E,03 .131882E+04 ,249340E+04 -,365547E+04 -.164731E+06 .870857E+05

-.654366E+03 -.131882E +04 ".249340E+04 .365547E+04 -,134477E+06 ,711729E+05

4.1.3 Thick-Wall Cylinder: Plane Strain

A circular cylinder of constant wall thickness 13 subjected to uniformly distributed internal pressures

was analyzed. Figure 10 shows the modeling with triangular and quadrilateral finite elements.

Y

X

_x

A _1_ B

_I_ _I 97o2_

(a) Triangular mesh.

Figure 10. Thick-wall cylinder under internal pressure.

52
y'

Y

A

XX f

B _ 970283

(b) Quadrilateral mesh.

Figure 10. Concluded.

Important data parameters:

Young's modulus, E =

Poisson's ratio, la =

Side lengths, A, B =

Internal pressure, p =

30 x 106

0.3

1.0

300 lbf/in 2

STARS-SOLIDS input data:

Plane Strain analysis of a thick wall cylinder

22, 20, I, 6, O, I, I, O, O,

O, O, 0, O, O, O, O, O, 0

8, O, O, I, I, O, O, 0

2, O, 2, O, I, O, O, I, O,

$ HODRL ORTR

1 1,0000 .0000 .0000 0 1 I 1

II 2.0000 .0000 .0000 0 I 1 1

12 0.0000 .0000 .0000 0 I I I

22 t,O000 ,0000 ,0000 0 1 I 1

$ LOCAL-GLOBAL COOROIHRTE SYSTEM

I I

0,996190 0.00716 0.0 1.99230 0.17432

1.440895 0,30823 O.O

$ ELEMENT CONHECTIVITY COHOITIONS

3 1 I 2 12 0 0 0 0 0

3 10 I0 11 21 0 0 O 0 0

3 11 13 12 2 0 0 0 0 0

3 20 22 21 11 0 0 0 0 0

$ SHELL ELEMENT THICKNESSES

I .I000E+01 .IO00E*OI ,IO00E*OI

$ MATERIAL PROPERTIES

1 11

,3000E+08 .3000E*O0.0000E°OO .O00OE+00 0.0

$ MOOAL LOAD ORTR

I 1 21.8166

12 1 21.7335

12 2 1.9015

-I

I I O 0 0

I I 0 0 1

I I I I 0

I I I I I

0,0

I I 0 0 O O

I I 0 0 0 I

I I 0 0 0 0

I I 0 0 0 I

53
STARS-SOLIDS output summary: table 5 shows the output summary.

Table 5. Radial deformations of a circular cylinder subjected to uniformly

distributed internal pressures.

Deformations

Distance Hand calculation Triangular element Quadrilateral element

r= 1.0 0.3178 × 10 --4 0.3175 x 10-4 0.3174 × 10-4

r = 2.0 0.2022 x 10--4 0.2011 x 10-4 0.2021 × 10 --4

r = 1.5 0.2359 x 10--4 0.2349 x 10-.4 0.2357 x 10-4

4.1.4 Plate Bending: Vibration Analysis

A square cantilever plate was analyzed to yield the natural frequencies and associated mode shapes.

Figure 11 shows the plate with a 4-by-4 finite-element mesh; the bottom edge along the x axis is

clamped.

Y

21 22 i23 24

16 17 18 19

Important data parameters:

11 12 13 14

6 7 8 9

1 10

5

Figure 11. Square cantilever plate.

970284

Young's modulus, E = 10 × 106

Side length, L = 10

Plate thickness, t = 0.1

Poisson's ratio, kt = 0.3

Mass density, p = 0.259 × 10-3

54
STARS-SOLIDS input data:

SOUERE 4 BY 4 PLRTE

25, 16, I, 4, O, I, O, O, 0, 0

O, O, O, 1, O, O, O, O, 0

1, I, 0, 1, 0, 0, 0, 0

2, O, 2, O, I, O, O, 1, O, 0

1, 6, O, 6000.0, 0.0, O, 0.0

$ NODAL DflTR

1 -5.0 0.0

S 5.0 0.0

6 -5.0 2.5

tO S.O 2.5

II -5.0 5.0

15 5.0 5.0

16 -5.0 7.5

20 5.0 7.5

21 -5.0 t0.0

25 5,0 10.0

$ ELEMENT CONNECTIUITY

2 I I 2 7

2 4 4 5 10

2 5 6 7 12

2 B 9 10 15

2 9 11 12 17

2 12 14 15 20

2 13 16 17 22

2 16 19 20 25

NONSPINNING STRUCTURE

0.0 I I I 1 1 I 0 0 0

0.0 I I l 1 1 I 0 0 I

0.0 0 0 0 0 C 0 0 0 0

0.0 0 0 0 0 0 0 0 0 I

0.0 0 0 0 0 0 0 0 0 0

0.0 0 0 0 0 0 0 0 0 I

0.0 0 0 0 0 0 0 0 0 0

0.0 0 0 0 0 0 0 0 0 I

0,0 0 0 0 0 0 0 0 0 0

0,0 0 0 0 0 0 0 0 0 1

6 0 0 0 0

9 0 0 0 0

II 0 0 0 0

14 0 0 0 0

16 0 0 0 0

19 0 0 0 0

21 0 0 0 0

24 0 0 0 0

$ SHELL ELEMENT THICKNESSES

1 0.1

$ ELEMEHT MATERIAL PROPERTIES

I 1

I .OE+07 0,30 0.0 0.259E-3

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

STARS-SOLIDS output summary: table 6 shows the output summary.

Mode

Table 6. Natural frequencies of a square cantilever plate.

Natural frequency (co), Nondimensional parameter ('f),

rad/sec 7 = 0)2 Vf-Pt / D

1 214.02 3.60

2 506.62 8.52

3 1248.40 20.99

4 1538.29 25.87

5 1765.53 29.69

Note: D = plate flexural rigidity

= Et3/12(1 _ p2)

55
4.1.5 General Shell: Vibration Analysis

Figure 12 shows a cantilevered circular cylindrical shell in which quadrilateral shell elements are

used for structural discretization to perform a free-vibration analysis.

/_/_ B _j1"1

/-- 10 19 28 37 46 55 -. /

..'1 "'- -_ _, _ .. __"- *4-_ 73

75

79

8O

R R

970285

X

/-- 10 19_ 28 ....

_ /30 /3,.

/_/_1 /,o

/_;" /32 /41

/ _ 'l,,, /'3,

I__!,_,1,, /,,

•37 ...... 46 .... 55 say /

/50 /_"'/2_ ,_

+ _gS---f,,

'_ X+,! ]/ 4'

_ x,=_z,

Z

(a) Rectangular coordinate system. (b) Random coordinate system.

Figure 12. Finite-element model of cylindrical shell.

Important data parameters:

970266

Side length, A, B = 10

Radius, R = 20

Thickness, t = 0.1

Young's modulus, E = 29.5 × 106

Poisson's ratio, p = 0.3

Mass density, p = 0.733 × 10-3

+

56
STARS-SOLIDSinput data:

SHELL ELEMENT 8 BY 8 CURVED SHELL

81, 64, 1, 4, 0, I, 0, O, 0, 0

0, 0, O, 1, 0, O, 0, O, 0

I, 1, 0, 1, 0, 0, 0, 0

2, O, 2, 0, 1, 0, 0, 1, 0, 0

1, 6, 0, 90000.0, 0.0, 0.0

$ H00RL ORTR

1 0.0 0.0 O.O

2 1.25 0.0 O.O

9 10.0 0.0 0.0

10 0.0 1.25 O, 2803754

I1 1,25 1.25 0,2803754

18 10.0 1.25 0.2803754

19 0.0 2,5 0,478218

20 1.25 2.5 0.478218

27 10.0 2,5 0.478218

28 0.0 3.75 0.5959826

29 1.25 3.75 0.5959826

36 10.0 3.75 0.5959826

37 0.0 5.0 0.6350833

38 1.25 5.0 0.6350833

45 10,0 5,0 0,6350033

46 O.O 6.25 0 _$959826

47 1.25 6.25 0.5959826

54 10.0 6.25 0.5959826

55 0.0 7.5 0.478218

56 1.25 7.5 0.478218

63 10,0 7,5 0.478218

64 0.0 8.75 0,2803754

65 1 .25 8.75 0. 2803754

72 10.0 8.75 0,2803754

73 0.0 10.0 0.0

74 1 .25 10.0 0,0

81 10,0 10.0 0.0

$ ELEMENT CONMECTIUITY

2 I 1 2 11 10 0

2 8 8 9 18 17 0

2 9 10 II 20 19 0

2 16 17 18 27 26 0

2 17 19 20 29 28 0

2 24 26 27 36 35 0

2 25 28 29 38 37 0

2 32 35 36 45 44 0

2 33 37 38 47 46 0

2 40 44 45 54 53 0

2 41 46 47 56 55 0

2 46 53 54 63 62 0

2 49 55 56 65 64 0

2 56 62 63 72 71 0

2 57 64 65 74 73 0

2 64 71 72 81 80 0

$ SHELL ELEMENT THICKNESSES

I 0.1

$ ELEMENT MATERIAL PROPERTIES

1 1

0.2950E+080.3000E+OOO.OOOOE+000.7332E-03

FREE VIBRATION ANALYSTS

I I 1 0

0 0 0 0

0 0 0 0

I I I 0

0 0 0 0 0

0 0 0 0 0

I I 0

0 0 0 0 0

0 0 0 O

I I 0

0 0 0 0 0

0 0 0 0 0

I I 0

O 0 0 0

0 0 0 0

1 1 0

0 0 0 0

0 0 0 0

1 1 0

0 0 0 0

0 0 0

1 I 0

0 0 0

0 0 0

1 t 0

0 0 0

0 0 0

0 0

0 0 0 0

0 0

0 0 0 0

0 0

O 0 0 0

0 0

0 0 0 0

0 0

0 0 0 0

0 0

0 0 0 0

0 0

0 0 0 0

0 0

0 0 0 0

O O

0 0

0 I

0 0

0 0

0 I

O 0

0 0

0 I

0 0

0 0

0 I

0 0

0 0

0 I

0 0

0 0

0 I

0 0

0 0

0 1

0 0

0 0

O I

0 0

0 0

0 I

0 I

0 I

0 I

0 I

0 I

0 l

0 I

0 I

STARS-SOLIDS output summary: table 7 shows the output summary.

57
Table7. Naturalfrequenciesof acylindrical cantilevershell.

Naturalfrequency(e0),

Mode rad/sec

Nondimensionalparameter(y),

_/= coa2_/-pt/ D

1 686.0899 11.30

2 1108.6006 18.26

3 1918.0497 31.60

4 2703.7123 44.54

5 2962.7424 48.81

6 3904.1954 64.32

Alternative curve shell modeling:

Note: X, Y, and Z are the GCS. Xl, Yl, Zl and x2, Y2, z2 are local-global coordinate systems for data

input in a spherical coordinate system, x'l, Y'I, Z'l and x'2, Y'2, z'2 are local-global coordinate systems

for data input in a cylindrical coordinate system.

STARS-SOLIDS alternative input data:

SHELL ELEMENT 8 BY 8 CUHUEO SHELL

81, 64, I, 4, 0, 1, 6, O, O, 0

0, 0, 0, I, 0, 0, 0, 0, 0

1, 1, O, I, O, O, O, 0

2, 0, 2, 0, 1, 1, 0, I, 0, 0

1, 12, 0, 90000.0, 0.0, 0.0

$ HODE DESCRtPTIOM

I 20.00000 .25268025

73 20.00000 -0.25268025

2 20.00000 .25268025

74 20.00000 -0.25268025

3 20,00000 .25268025

?5 20,00000 -0.25268025

4 20.00000 .25268025

13 20.00000 .18951019

22 20,00000 ,12634013

31 20.00000 .06317006

40 20.00000 ,00000

49 20.00000 -0.06317006

50 20.00000 -0.12634013

67 20.00000 -0.18951019

76 20.00000 -0,25268025

6 20.00000 .25268025

9 20.00000 .25268025

15 20.00000 .18951019

18 20.00000 .18951019

24 20,00000 .12634013

27 20,00000 ,12634013

33 20.00000 .06317006

36 20.00000 .06317006

42 20,00000 .00000

45 20.00000 .00000

51 20.00000 -0.06317006

54 20,00000 -0.06317006

60 20,00000 -0.12634013

63 20,00000 -0.12634013

69 20.00000 -0.18951019

72 20.00000 -0.18951019

78 20.00000 -0.25268025

81 20.00000 -0.25268025

5 19,36491170 5.0

14 20.00000 .18951019

32 20,00000 .06317006

41 20,0 0.0

50 20.00000 -0.06317006

59 20.00000 -0.12634013

68 20,00000 -0,18951019

77 19.36491170 -5.0

FREE-UIBRATION ANALYSIS

1.57079633 I I I I I 120000

1,57079633 I I I I I 120000 0 9

1.57079633 0 0 0 0 0 020001

1,57079633 0 0 0 0 0 020001 0 9

1.57079633 0 0 0 0 0 020002

1.570?9633 0 0 0 0 0 020002 0 9

0,0 0 0 0 0 0 010001

0.0 0 0 0 0 0 010001

0,0 0 0 0 0 0 010001

0.0 0 0 0 0 0 010001

0,0 0 0 0 0 0 010001

0,0 0 0 0 0 0 010001

0.0 0 0 0 0 0 010001

0.0 0 0 0 0 0 010001

0.0 0 0 0 0 0 010001

6.25000 0 D 0 0 0 010000

I0.00000 0 0 0 0 00lO000 0 I

6.25000 0 0 0 0 0 010000

10.00000 0 0 0 0 0 010000 0 I

6.25000 0 0 0 0 0 010000

I0.00000 0 0 0 0 0 010000 0 l

6.25000 0 0 0 0 0 010000

I0.00000 0 0 0 0 0 010000 0 l

6.25000 0 0 0 0 0 010000

10.00000 0 0 0 0 0 010000 0 I

6.25000 0 0 0 0 0 010000

tO.O0000 0 0 0 0 0 010000 0 I

6.25000 0 0 0 0 0 010000

I0.00000 0 0 0 0 0 010000 0 I

6.25000 0 0 0 0 0 010000

10.00000 0 0 0 0 0 010000 0 l

6,25000 0 0 0 0 0 010000

10,00000 0 0 0 0 0 010000 0 1

5.0 000000 0

0.00000 0 0 0 0 0 010002

0,00000 0 0 0 0 0 010002 0 9

5.0 000000 0

0.00000 0 0 0 0 0 010002

0.00000 0 0 0 0 0 010002

0.00000 0 0 D 0 0 010002

5.0 000 000 0

58
$ LOCRL-GLOBRL COORDINRTE SYSTEM DRTR

20000 2

0,0 0.0 0.00

0.0 1.0 0.00

20001 2

0.0 0,0 I .25

0.0 I .0 I .25

20002 2

0.0 0.0 2.50

0.0 I .0 2,50

10000 I

0.0 0.0 0.00

0.0 1,0 0.00

10001 1

0.0 0.0 3,75

0.0 1.0 3.75

10002 1

0,0 0.0 5.00

0.0 1 .0 5.00

$ ELEMEHT CONHECTIUITY

2 I I 2 11 10 0

2 O 8 9 18 17 0

2 9 I0 11 20 19 0

2 16 17 18 27 26 0

2 17 Ig 20 29 28 0

2 24 26 27 36 35 0

2 25 28 29 38 37 0

2 32 35 36 45 44 0

2 33 37 38 47 46 0

2 40 44 45 54 53 0

2 41 46 47 56 55 0

2 48 53 54 63 62 0

2 49 55 56 65 64 0

2 56 62 63 72 71 0

2 57 64 65 74 73 0

2 64 71 72 81 00 0

$ SHELL ELEMENT THICKNESSES

t 0,1

$ ELEMENT MATERIAL PROPERTIES

I I

0.2950E+OBO,3000E+OOO,OOOOE+OOO,7332E-03

0,0

0.0

0.0

0,0

0,0

0.0

0 0 0 1

0 0 0 1

0 0 0 1

0 0 0 1

0 0 0 1

0 0 0 1

0 0 0 1

0 0 0 1

0 0 0 1

0 0 0 1

0 0 0 1

0 0 0 1

0 0 0 l

0 0 0 1

0 0 0 I

0 0 0 I

0.00

1 ,25

2.50

0.00

3.75

5.00

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

4.1.6 General Solid: Vibration Analysis

Figure 13 shows a cube idealized by hexahedral solid elements. The nodes lying in the X-Y plane are

assumed to be fixed. Details of the natural frequency analysis of the cube are presented herein.

Z

l,

//

/Y

970287

Figure 13. Cube discretized by hexahedral elements.

Important data parameters:

Side length, L = 10

Young's modulus, E = 10 x 106

Poisson's ratio, la = 0.3

Mass density, p = 2.349 x 10-4

59
STARS-SOLIDS input data:

HEXRHEDROM CRSE - 2 BY 2

2?,8,1,4,0,0,0,0,0,0

O,O,O,l,O,O,O,O,O

1,1,0,I,0,0,0,0

2,0,2,0,1,0,0_1,0,0

1,6,0,150000.0,0.0,0.0

$ MODAL ORTR

I O0.O O0.O 00.0

2 S.O 00.0 00,0

3 10.0 00,0 00,0

4 10.0 S.O 00.0

S 10.0 10,0 O0.O

6 S.O 10,0 00.0

7 00.0 10.0 00.0

8 00.0 S.0 00.0

9 S.O S,O 00.0

I0 00.0 00.0 5.0

I1 S.O 00.0 S_O

12 I0,0 00.0 S.O

13 I0,0 5.0 5,0

14 10.0 10,0 5.0

15 5.0 I0.0 S.O

16 00.0 I0.0 S.O

17 00.0 5.0 S.O

18 5.0 S.O S.0

19 00.0 00.0 I0.0

20 S .0 00.0 10.0

21 lO.O 00.0 10,0

22 10.0 5.0 10.0

23 10.0 10.0 10.0

24 S.O 10,0 I0.0

25 00.0 I0.0 I0.0

26 00.0 S.O 10.0

27 S.O S.O IO.O

$ ELEMENT COMNECTIUITY

4 1 I 2 9 8 10 II 18 17 I

4 2 2 3 4 9 11 12 13 18 I

4 3 9 4 S 6 18 13 14 IS I

4 4 8 9 6 ? 17 18 IS 16 I

4 S I0 11 18 I? 19 20 27 26 1

4 6 II 12 13 18 20 21 22 27 I

4 7 18 13 14 IS 27 22 23 24 I

4 8 17 18 IS 16 26 27 24 2S I

$ ELEMEHT MATERIRL PROPERTIES

I 1

I.OE*? 0.3 0.0 2.349E-4

STARS-SOLIDS output summary: table 8 shows the output summary.

Mode

Table 8. Natural frequencies of a solid cube.

Natural frequency parameter (6_),

6) = co / _/(E/o], rad/sec

Mesh size

2 by 2 4 by 4 6 by 6

1 0.07975 0.07195 0.06958

2 0.07975 0.07195 0.06958

3 0.13149 0.10428 0.09762

4 0.17200 0.16453 0.16234

5 0.22798 0.19330 0.18504

6 0.22798 0.19330 0.18504

Exact solution

&

0.06801

0.06801

0.09288

0.16110

0.18190

0.18190

60
4.1.7 Cantilever Beam (Spinning and Nonspinning Cases): Vibration Analysis

Figure 14 shows a cantilever beam spinning about the Y axis.

Y

5 6 7 8 9 10 11

L = 10,_ _1v I

970288

Figure 14. Spinning cantilever beam.

Important data parameters: The structure is assumed to possess both viscous and structural damping.

Young's modulus, E = 30 x 106

Cross-sectional area, A = 1.0

Moment of inertia:

About y axis = 1/12

About z axis = 1/24

Element length, £ = 6

Nodal translational mass = 1

Nodal mass moment of inertia = 1/35

Scalar viscous damping = 0.628318

Structural damping coefficient = 0.01

Spin rate, Hz = 0.1

STARS-SOLIDS input data:

SPINNING CRNTILEUER BEAM - IO-ELEMEHT IDEALIZATION - UI$C AND STRUCT DRMPING

12,10,1,4,1,0,0,0,0,0

0,0,1,1,0,0,0,0,0

5,0,0,0,0,1,0,0

2,0,2,0,1,0,0,1,0,0

1,6,0,500.0,0.0,0.0

0,01

$ NODAL DATA

1 0,0 0.0 0.0 1 1

2 6.0 0.0 0,0 0 0

3 12.0 0.0 0,0 0 0

4 18.0 0.0 0,0 0 0

5 24.0 0,0 0.0 0 0

6 30,0 0,0 0,0 0 0

? 36,0 0,0 0,0 0 0

8 42.0 0.0 0,0 0 0

9 48,0 0,0 0.0 0 0

10 54.0 0.0 0,0 0 0

II 60,0 0,0 0.0 0 0

12 25,0 15.0 0.0 1 l

$ ELEMENT CONNECTIVITY

I I I 2 12 0 0 0 0

I 10 10 11 12 0 0 0 0

$ LINE ELEMENT BASIC PROPERTIES

I 1,0 D.125000.083333330.04166667

I I I I

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

I I 1 I

0 I I 0 0 I 0

0 1 I 0 0 I I

61
$ ELEMENT MATERIAL PROPERTIES

I I

3O.OE+O6 0.30

$ ELEMENT SPiN RATE DATA

t 0.0 0.628318

$ NODAL MASS DATA

2 1.0

3 1.0

4 1.0

5 1.0

6 l.O

7 1.0

O t.0

9 1.0

IO 1,0

II I.O

2 4 0.0285714

3 4 0,0285714

4 4 0,0285714

5 4 0.0285714

6 4 0.0205714

7 4 0.0285714

8 4 0,0285714

9 4 0,0285714

I0 4 0.0205714

11 4 0.0285714

°I

$ VISCOUS DAMPING DATA

0.0

O.O000E÷OOO.OOOOE÷OOO,OOOOE+OOO,OOOOE*OOO.OOOOE+OOO.OOOOE+O0

0.628318000.628318000.628318000,628318000.620318000.62831800

0,628318000.628318000.628318000.628318000.620318000.62831800

0.628318000.628316000,628318000,628318000.628318000.62831800

0.628310000,628318000.628318000,628318000,620318000.62831800

0.628318000.628318000.628318000.628318000.628318000.62831800

0.628318000,628310000,628318000,628318000.628318000.62831000

0,628318000.628318000.628310000,628318000,628318000.62831800

0,628318000.628318000,620318000.628318000.628318000,62831000

0,628318000.628318000,628310000,628318000.628318000.62831800

0.628318000.628318000,628318000.628318000.628318000.62831800

O,O000E+OOO.OOOOE+OOO,OOOOE÷OOO.OOOOE+OOO.OOOOE+OOO,OOOOE*O0

V

STARS-SOLIDS output summary: table 9 shows the output summary. v

Table 9. Natural frequencies of a spinning cantilever beam.

Mode

Structure without

damping,

IPROB = 2

Structure with

viscous damping,

IPROB = 4

Structure with viscous

and structural damping,

IPROB = 5

2.526 -0.3107 + 2.4885i* -0.3195 + 2.4820i*

3.449 -0.3116 + 3.4207i* -0.3255+ 3.4132i*

15.397 -0.3166 + 15.3900i* -0.3930+ 15.3831i*

21.706 --0.3166 + 21.7015i* -0.4243 + 21.6914i*

43.161 -0.3202 + 43.1551i* -0.4849+43.0627i*

60.951 -0.3202 + 60.9495i* -0.6246 + 60.9391i*

Notes: Natural frequencies

(0.6283 rad/sec).

for various problem types

i, = 4-Si.

are caused by a spin rate of E2 = 0.1 Hz

62
Additionally, table 10showsaparametricstudyof vibrationanalysisof thenonspinningbeamusing

both the IPROB - 1 and IPROB = 3 (dynamic element) cases using consistent mass formulation

(density, p = 0.1666).

Table 10. Natural frequencies of a nonspinning cantilever beam.

Number Natural frequencies (03),

of rad/sec

elements IPROB 031 0)2 033 034 035 036

1 2.676 3.784 16.901 23.897 57.144 80.770

2

3 2.675 3.782 16.766 23.707 49.864 70.494

1 2.675 3.783 16.779 23.724 47.277 66.829

4

3 2.675 3.782 16.759 23.697 46.924 66.332

1 2.675 3.782 16.763 23.702 46.999 66.438

6

3 2.675 3.782 16.759 23.696 46.914 66.317

1 2.675 3.782 16.760 23.698 46.942 66.357

8

3 2.675 3.782 16.759 23.696 46.914 66.317

1 2.675 3.782 16.760 23.697 46.926 66.333

10

3 2.675 3.782 16.759 23.696 46.914 66.317

4.1.8 Spinning Cantilever Plate: Vibration Analysis

The cantilever plate model described in section 4.1.4 is used for this sample problem. The plate is

1 1

spun along the Z axis with a uniform spin rate of f_ Z = 0. 8 x 03n, 03n being the first natural frequency

of vibration of the nonrotating plate. Table 11 shows the first few natural frequencies of the plate in

nondimensional form, 03 being the natural frequencies. Also shown in the table are the results of the free1 with vibration analysis of the plate rotating along an arbitrary axis, the spin rate being _'-_R = 0. 8 × 03n,

components _X = _Y = _z = 0. 8 × (On

STARS-" SOLIDS input data:

SQUARE 4 BY 4 PLATE SPINNING STRUCTURE

25,16,1,4,0,1,0,0,0,0

O,0,1,1,0,0,0,0,0

2,0,0,1,0,0,0,0

2,0,2,0,1,0,0,1,0,0

1,6,0,6000.0,0.0,0.0

$ NODAL DRTA

1 -5,0 0.0 0.0 l I 1 I 1 1 O 0 0

5 5,0 0.0 0.0 I I I I I I 0 0 I

6 -5.0 2.5 0.0 O 0 0 O 0 0 0 0 0

tO 5.0 2.5 0.0 0 0 0 0 0 O 0 0 1

11 -5,0 5.0 0.0 0 0 0 0 0 0 0 0 0

15 5,0 5.0 O.O 0 0 O 0 0 O 0 0 I

16 -5.0 7.5 0,0 0 0 0 0 0 0 0 0 O

20 5.0 7.5 0.0 0 0 0 0 0 0 0 0 1

21 -5.0 I0.0 0,0 0 0 0 0 0 0 0 0 0

25 5.0 lO.O 0,0 0 O 0 0 0 0 0 0 1

63
$ ELEMENT CONNECTIUITV

2 I I 2 7 6 0 0 0 0

2 4 4 5 I0 9 0 0 0 0

2 5 6 7 12 11 0 0 0 0

2 8 9 10 IS 14 0 0 0 0

2 9 11 12 17 16 0 0 0 0

2 12 14 15 20 19 0 0 0 0

2 13 16 17 22 21 0 0 0 0

2 16 19 20 25 24 0 0 0 0

$ SHELL ELEMENT THICKNESSES

I 0.1

$ ELEMENT MHTERIRL PROPERTIES

! !

1.OE*07 0.30 0.0 0.259E-3

$ ELEMENT SPiN RATE DATA

I O. O, I00.0

0 0 I

0 0 I I

0 0 I

0 0 I I

0 0 1

0 0 I I

0 0 I

0 0 I I

STARS-SOLIDS output summary: table 11 shows the output.

Table 11. Natural frequency parameters of a spinning square cantilever plate.

Natural frequency parameter (T),

T = coL2 _/pt / D

fiz = 0-8o)1 fiR = 100.00 rad/sec,

= 100.00 rad/sec fix = fiY = fiz =57.735 rad/sec

Mode co T to T

1 242.32 4.0752 155.48 2.6148

2 526.82 8.8598 489.05 8.2246

3 1271.00 21.3750 1250.40 21.0286

4 1551.90 26.0991 1536.40 25.8384

5 1784.50 30.0108 1768.60 29.7434

6 2902.60 48.8144 2891.60 48.6295

4.1.9 Helicopter Structure: Vibration Analysis

Figure 15 shows a coupled helicopter rotor/fuselage system 14 and the relevant stiffness and mass

distributions, which are suitably approximated for the discrete element modeling of the structure.

Numerical free-vibration analysis was performed for the structure with the rotor spinning at 10 rad/sec

(g2y = 10). Table 12 shows the results, along with the results for the corresponding nonspinning case.

64
Point mess (node 9) = 16 slug

16 --

1 2

I I

3 4

I I

Y

5 6 7 8 9 10 11 12 13 14 15 16 17

i , , ,,-_i , , .....

Hu'b"_'_ ° ' Rotor ' '-y' '

_k ./j Fu.elege

I J I >x

18 19 20 21 22 23 24 25 26 27 28 29 30

(a) Discrete element model.

970289

Mass,

slug/ft

12

FT-T t I I

_ Fuselage

Rotor

-20 - 10 0 10 20

Length, !I

970290

(b) Structural mass distribution.

Stiffness

Ib/ft 2

16 10 6

12 -- _S

8 Fuselage

4

o

-20 -10 0 10 20

Length, ft

970291

(c) Structural stiffness distribution.

Figure 15. Coupled helicopter rotor/fuselage system.

STARS-SOLIDS input data:

HELICOPTER STRUCTURE, JOURHRL CRSE, SPIH - 10.0 (FIXED UZ, UXR, UVR)

31,29,7,4,2,0,0,0,0,0

0,0,1,0,0,0,0,0,0

2,0,0,1,0,1,0,0

2,0,2,0,1,0,0,1,0,0

1,12,0,53.15,0.0,0.0

$ HODRL DRTA

I -25.00000 1,0 0.0 0 0 1

8 -3,12500 1.0 0,0 0 0 1

g 0.00000 1,0 0.0 0 0 1

I0 3.12500 1.0 0.0 0 0 1

17 25.00000 1.0 0.0 0 0 I

18 -20.00000 0.0 0.0 0 0 1

23 -3.33333 0.0 0.0 0 0 I

24 0.00000 0,0 0.0 0 0 I

25 3,33333 0.0 0.0 0 0 I

30 20.00000 0,0 0.0 0 0 I

31 I0.00000 0,5 0.0 I 1 I

65
$ ELEMENT COHNECTIUITY

I 1 2

16 16 17

17 1e 19

|a 19 20

19 20 21

20 21 22

21 22 23

22 23 24

23 24 25

24 25 26

25 26 27

26 27 28

27 28 29

28 29 30

29 9 24

$ LINE ELEMENT BASIC

1 1.

2 I00.

24

24

9

9

9

9

9

9

9

9

9

9

9

9

31

PROPERTIES

I.

I.

$ ELEMENT MATERIAL PROPERTIES

1 |

2.0EOS 0.3

2

1.53E06 0.3

3

2,E06 0,3

4

4.BE06 0.3

S

7.8E06 0.3

6

11,E06 0.3

?

I,EO8 0.3

$ ELEMEHT SPIN AATE DATA

T 0.0 I0.0

$ HOORL MESS DATA

9 I 16, 3

-1

0

0

0

0

0

0

O,

0.3

1.23

1.23

8.6

16.

16.

O.

0.0

0 0 I 0

0 0 I I

STARS-SOLIDS output summary: table 12 shows the output summary.

Table 12. Natural frequencies of a helicopter structure.

Natural frequencies (co),

Mode rad/sec

number k'_y = 0 f2y = 10 Mode shape

2,3 0 0

4 4.640 11.791

5 5.041 11.791

6 22.134 22.219

7 27.892 36.199

8 28.278 37.800

9 37.176 38.478

Rigid body

Rotor first symmetric bending

Rotor first antisymmetric bending

Fuselage first bending

Rotor second antisymmetric bending

Rotor second symmetric bending

Rotor third antisymmetric bending

4.1.10 Rocket Structure: Dynamic-Response Analysis

A rocket idealized by four line elements, as shown in figure 16, 5 is subjected to a pulse loading

function at the base. Figures 17 and 18 show results of the dynamic-response analysis.

66
X

5

4

3

2

y -.9[---_ 1

I Pl = Pl (t)

970292

(a) Rocket structure.

Pl(t)

PO

t o

(b) Pulse loading.

Figure 16. Rocket subjected to dynamic loading.

Important data parameters: arbitrary element and material properties data are

analysis to correlate results with available ones expressed in parametric form.

Young's modulus, E = 1043

Poisson's ratio, l.t = 0.3

Cross-sectional area, A = 1.0

Mass density, p = 1.0

Member length, _ = 2.5

Pulse load intensity, P0 = 10.0

Duration of load, sec = 1.0

Total time period for

response evaluation = 2.0

r

t

970293

assumed for the

STARS-SOLIDS input data:

DYNAMIC RESPONSE CASE - PRZEMIENIECKI

6,4,1,4,1,0,0,0,0,0

O,O,O,O,O,O,O,O,O

1,0,1,1,O,O,0,0

2,0,2,0,1,0,0,1,0,0

1,3,0,20.0,0.0,0.0

0,1;I,2

$ NODAL DATA

1 0,0 O.O 0.0

5 10.0 0.0 O.O

6 5,0 5.0 0,0

$ ELEMENT COHHECTIUITY

I 1 1 2 6 0 0

I 4 4 5 6 0 0

$ LIHE ELEMENT BASIC PROPERTIES

I 1.0 0.0 0,0

$ ELEMENT MATERIAL PROPERTIES

I I

100.0 0.3 0.0

$ OYMAMIC MODAL FORCE DATA

1.0

I l 10.0

-I

0 I I

0 I I

I I I

1,0

0.0

% 1

1 I

I I

I 0

0 0 I

0 0 I

67
$ INCREMENTAL TIME DATA FOR DYNAMIC RESPONSE ANALYSIS

0.10 I0

0.20 5

STARS-SOLIDS analysis results at a typical time step:

DYNAMIC RESPONSE AT TIME = O.7000E+O0

NODE

EXT INT X-DtSPL, Y-DISPL. Z-DISPL. X-ROTN. Y-ROTN, Z-ROTN.

1 0,646322E+00 O.O000O0E+O0 0.OO00O0E+O0 O.O00OO0E+00 O.00O000E+00 0.00000DE+00

2 0.490gggE+OO O.O0O0O0E+O0 0.OO0000E+0O 0.000000E+00 O.0O00O0E+00 O.0O0OOOE+00

3 0.191562E+00 O.00OO00E*00 O,OOO000E+00 0.DO000OE+O0 O.00OOO0E*OO 0,0O0OOOE+O0

4 -0.102987E-02 0,00O00OE+00 0.O00O00E+00 0.000000E*00 0.0000O0E+00 0.0O00O0E+00

5 -0.495080E-01 0,000000E+00 0.000000E+00 0.00000DE+00 0.0O0OO0E+00 0.000000E+00

6 O.OOOO00E+OO O.OOOOOOE+O0 O.O00000E+OO O.O00OOOE+OO O.OOOOOOE+O0 O,OOOOOOE+O0

ELEMENT STRESSES

ELEMENT ENDI END2 END3 END4 PXIIPX2 PYIIPY2 PZIIPZ2 MXIIMX2 MYIIMY2 MZI/MZ2

NO. SXT SYT SXYT SXB SYB SXYB

END5 END6 END? END8 SXX SYY SZZ SXY SYZ SZX

l I 2

2 2 3

3 3 4

4 4 5

0.621289E+01 0.O00O00E*00 O.0000OOE+00 0,0O00O0E÷OO 0.OO0O00E+O0 0.OOO0DOE+0O

-0.621289E+01 0,00000DE*00 0,O00OOOE*0O 0,OOO00OE+O0 0.O000OOE+O0 0.O0O0OOE*0O

0.119775E+02 O.OOOOOOE+O0 O.O00000E+OO O.OOOOOOE+OO O.O00000E+O0 O.OOOOOOE+OO

-0,119775E+02 O.O00000E+O0 O,OOOO00E+O0 O.OO00OOE+O0 O.O00000E+OO O.OO00OOE+O0

0,770366E*01 O.OOOO00E*O0 O.OOOOOOE÷OO O.OO000OE+O0 O.O000OOE+O0 O.O00000E+O0

-0,770366E+01 O.O00OOOE+O0 O,OOOOOOE+OO O.O00OOOE*O0 O.OOOOOOE+OO O.O00OOOE+OO

0,193913E+01 O.0OO000E+0O 0.O00000E÷00 0,0000O0E+00 O.000O00E+00 0,0OO00OE*00

-0,193913E+01 O.00O000E+00 0.O0O000E+00 0.0000O0E+00 0,O00O00E+00 0.0000ODE*00

,.00DF

,s°I- J

Displacement .50D _--

| f T = 2.000

"25D _-_1 I J DI= 1"10_

0 .2T .4T .6T .8T 1.0T

Time, aec

970294

Figure 17. Rocket nodal displacement as a function of time, node 1.

1.00F

.75F

.50F

.25F

Force 0

-.25F "_

-.50F I F = maximum element \

-1.00F i-- force (Px1 = 6.264)

I ] I J I \1

0 .2T .4T .6T .8T 1.0T

Time, sec

970295

Figure 18. Rocket element force as a function of time, element 4.

68
4.1.11 Plate, Beam, and Truss Structures: Buckling Analysis

4.1.11.1 Simply-Supported Square Plate

A buckling analysis was performed for a simply-supported square plate model, described in

section 4.1.4, that was subjected to a uniform unit stress acting along the two edges parallel to the

Y axis. Relevant input data and analysis results are as follows:

STARS-SOLIDS input data:

SQUARE 4 BY 4 PLRTE,BC W-O, lidllne x-O,Y(13)-5.0, BUCKLIHG ANALYSIS

25, 16, I ,4,0, 1,0,0,0,0

0,0, O, 1,0,0, O, 0,0

9, 1,0, I , 1,0,0,0

2,0,2,0,1,0,0, 1,0,0

1,I,0,20000,0,0,0,0.0

$ HODRL ORTR

1 -5,00 0.0 0.0 0

2 -2.50 0.0 0.0 0

3 0.0 0,0 0,0 1

4 2.50 0.0 0,0 0

5 5.00 0.0 0.0 0

6 -5.00 2.50 0,0 0

7 -2.50 2.50 0.0 0

B 0.0 2.5 0,0 I

g 2.50 2,50 0.0 0

10 5.00 2,50 0.0 0

II -5,00 5.00 0.0 0

12 -2,50 5.00 0,0 0

13 0,0 5.00 0.0 I

14 2.50 5,00 0,0 0

15 5,00 5.00 0,0 0

16 -5.00 7.50 0.0 0

17 -2,50 7.50 0.0 0

18 0,0 7,5 0.0 I

Ig 2.50 7.50 0.0 0

20 5,00 7,50 0,0 0

2t -5,00 10,00 0.0 0

22 -2.50 10,00 0,0 0

23 0,0 I0.0 0,0 I

24 2,50 10.00 0.0 0

25 5,00 I0.00 0.0 0

$ ELEMENT COHNECTIUITY

2 I I 2 7 6 0 0

2 4 4 5 10 9 0 0

2 5 6 ? 12 11 0 0

2 8 9 10 15 14 0 0

2 9 11 12 17 16 0 0

2 12 14 15 20 Ig 0 0

2 13 16 17 22 21 0 0

2 16 19 20 25 24 0 0

$ SHELL ELEMENT THICKNESSES

I 0.1

$ ELEMENT MATERIAL PROPERTIES

I I

I ,OE*07 0.30

$ NODAL

I

6

II

16

21

5

10

_5

20

25

-I

ORD DATA

.125

.250

.250

.250

.125

-,125

-.250

-.250

-,250

-,125

0

0

0

0

0

0

0 0

0 0

0 0

0 I

I 1

I 0

I 0

I 0

I I

0 I

0 0

0 0

0 0

0 I

0 I

0 I

0 I

0 1

0 I

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 I

0 0

0 0

0 0

0 0

0 I

0 0

0 0

I D

I 0

I I

I O

I 0

0 0

0 0

0 I

O 0

0 0

0 0

0 0

0 I

0 0

0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

1 0 0 0

1 0 0 0

1 0 0 0

1 0 0 0

1 0 0 0

I 0 0 0

I O 0 0

I 0 0 0

69
STARS-SOLIDS analytical results: table 13 shows the analytical results pertaining to the buckling load.

Table 13. Critical load of a simply-supported square plate.

Bucking load parameter for Mode 1

STARS solution Exact solution

4 by4 8 by 8 14by 14

3530.695 3552.620 3570.561 3615.240

v

4.1.11.2 Cantilever Beam

The cantilever beam described in section 4.1.7 is the subject of a buckling analysis; the relevant

details are given below.

STARS-SOLIDS input data:

CANTILEUER BEAM - IO-ELEMEHT IDEALIZATION - BUCKLING ANALYSIS

C

C TEMPERATURE LOADING ADDED

C

12, 10, ! , 4,1,0,0,0, O, O

1,0,0, 1,0,0,0,0_0

9, 1,0, I, 1,0,0,0

2,0,2,0,1,0,0, 1,0,0

1,1,0,12000.0,0.0,0.0

$ NODAL DATA

1 O.O 0.0

2 6.0 0.0

3 12.0 0.0

4 18,0 O.O

5 24.0 0.0

6 30,0 O.O

7 36.0 0,0

8 42.0 0,0

9 48.0 0.0

I0 54.0 O,O

II 60.0 0,0

12 25.0 15.0

$ ELEMENT COMMECTIUITY

I I 1 2 12 0

I 10 10 II 12 0

$ LINE ELEflEHT BASIC PROPERTIES

I 1,0 0.125 0.083333

$ ELEMENT MATERIAL PROPERTIES

I 1

30.0E+06 0.30 6.6E-06

$ ELEMENT TEMPERATURE DATA

1 -I .0

$ NODAL LOAD DATA

11 I -I ,0

-I

0.0 I I I

O,O 0 0 I

0.0 0 0 I

0.0 0 0 I

O.O 0 0 I

0,0 0 0 I

0.0 0 0 I

0.0 O 0 1

0,0 0 0 I

0.0 O 0 1

0.0 0 I l

0.0 1 I I

0 0 0 0 I 1 I 0 0 0

0 0 0 0 1 1 1 O 0 1

0,041667

STARS-SOLIDS analytical results: table 14 shows the analytical results.

Table 14. Critical load of a cantilever beam.

Buckling load parameter

Mode STARS solution Exact solution

1 7011.14 7010.42

70
4.1.11.3 Truss Problem

The simple truss of figure 195 has also been analyzed to determine the critical loads. The associated

input data and analytical results are given below.

2

Figure 19. Truss structure.

STARS-SOLIDS input data:

PRZ - TRUSS BUCKLIHG ANALYSIS

4,2,1,4,1,0,0,0,0,0

O,O,O,l,O,O,O,O,O

9,0,0,I,1,0,0,0

2,0,2,0,1,0,0,1,0,0

1,2,0,20000,0,0,0,0,0

$ NODAL ORTR

I I00,0 100.0

2 I00.0 0.0

3 0.0 0,0

4 0,0 50,0

$ ELEMENT CONNECTIUITY

I I 3 I 4 1

I 2 2 I 4 1

$ LIHE ELEMENT BASIC PROPERTIES

1 0,1

$ ELEMENT MATERIAL PROPERTIES

1 1

I0.0E03 0.2

$ NODAL LORD DRTA

I 2 -I,0

-I

0,0 0 O I

0,0 I I I

0.0 I I 1

0.0 I I I

I 0 0 O

I 0 0 0

STARS-SOLIDS analytical results: table 15 shows the analytical results.

Table 15. Critical load of a simple truss.

Buckling load parameter

Mode STARS solution Exact solution

1 261.20387 261.20387

71
4.1.12 Composite Plate Bending: Vibration Analysis

To illustrate the use of multiple material angles (as in layered elements) and the diverse coordinate

system capabilities, a square composite plate (fig. 20) similar to that in section 4.1.4 is considered

for vibration analysis. The plate, fixed along two opposite edges, is analyzed for uniform

temperature loading.

///

Important data parameters:

x

r

1 2

yl

"// //.

5 _-_

,o\

__ direction

Figure 20. Square composite plate.

Side length, L = 10

Plate thickness, t = 0.063

Mass density, p = 0.259 x 10-3

Material properties: anisotropic, as shown in input data.

STARS-SOLIDS input data:

TRIAHGULRR 4 BY 4 PLATE / COMPOSITE LAYERS

25, 32, 1, 13j O, O, 2, 8, IO, 2

1, O, O, O, O, 0, O, O, 0

1, 1, O, I, O, 0, O, 0

2, O, 2, O, I, O, O, I, O, 0

1, I0, O, 6000.0, 0,0, 0.0

$ HOORL DATA

1 -5.0 0.0 0.0 1

5 S.O 0.0 0.0 1

6 -2.5 -I0.0 0.0 0

10 -2.5 0.0 0.0 0

11 -S.O 5.0 0.0 0

1S S.O 5.0 0.0 0

16 -2.5 0.0 0.0 0

20 -2.5 -10.0 0.0 0

21 -5.0 I0.0 0,0 I

25 S.O I0.0 0,0 I

ILGCS TEST CASE / HMAHGL TEST CASE

I I I I I 0 0

I I I I I 0 I

0 0 0 0 2 0 0

0 0 0 0 2 0 I

0 0 0 0 I 0 0

0 0 0 0 I 0 I

0 0 0 0 0 0 0

0 0 0 0 0 0 1

I I 1 I I 0 0

1 I 1 I I 0 1

72
$ LOCAL-GLOBAL COORDINATE SYSTEM DRTR 1 2

-10.0 -5,0 0,0 0.0 -1.0

1.0 0.0 0.0 O.O O.O

2I

-10.0 -10.0 0.0 -15.0 -10.0

-15.0 -15,0 O,O

$ ELEMEHT COMHECTIUITY ? I I 2

70000I

7445 10O000l

7567 12000O2

?89 IO 15000O2

?9 11 12 1700003

? 10 12 13 18000O3

7 11 13 14 1900004

? 12 t4 15 2000O04

7 13 16 17 2200005

7 16 19 20 2500005

7 1776I00006

7 20 109400006

7 21 12 I160000?

7 24 15 149O0007

7 25 17 16 I100008

7 26 18 17 1200O08

7 27 19 18 1300O09

7 28 20 19 1400009

7 29 22 21 160000 10

7 32 25 24 1900OO 10

$ COMPOSITE SHELL ELEMENT STACK DESCRIPTION DATA 1 2 I .0315 3 I .0315 I 2 2 I .0315 3 I .0315 3 3 2 I ,0315 4 1 ,0315 4 4 2 I ,0315 2 I ,0315 2 5 2 1 .0315 1 I _0315 I 6 2 I ,0315 6 I .0315 5 7 2 I ,0315 6 I .0315 6 8 2 1 .0315 7 I .0315 7 9 2 I .0315 8 1 .0315 8

102

1 ,0315 I ,0315

$ SPECIFICRTIOH I 2

0

0,0

220

0.7854 3

20

1,5708 4

20

2,3562 5

20

3,1416 6

20

4,7120 7

20

5.4980 B

2O

3,9260

$ ELEMENT MATERIAL PROPERTIES 2

,7966E+D7 .6638E*06 0,0 .2566E*07

O.O .I042E_07 .35e-5 .114e-4

$ ELEMENT TEMPERATURE DATA I I0. 55

FOR MATERIAL AXIS ORIENTATION

O.O

1.0

0.0

0.0 0,125E÷7

0.0 0,259E-3

.I042E+7O

O

00

00

00

00

00

00

0O

00

00

00

0O

00

00

00

00

00

O0

00

00

?3
STARS-SOLIDS output summary: table 16 shows the results.

Table 16. Natural frequencies of a square

composite plate.

Mode

Natural frequency (co),

rad/sec

T=0 T= 10

1 505.41 373.38

2 611.98 486.79

3 967.78 851.04

4 1434.66 1275.97

5 1523.71 1361.70

6 1765.22 1641.70

4.1.13 Thermally Prestressed Rectangular Plate: Vibration Analysis

To illustrate the thermal prestress vibration analysis capability, a free-free rectangular plate (fig. 21)

subjected to varying temperature loading and having varying material properties has been analyzed to

obtain natural frequencies and modes.

Y

2

3

4

5

6

7

Important data parameters:

Rectangular Plate

Plate thickness, t

Mass density, p

Temperature

5O

Figure 21. Rectangular plate.

= 12×50

=0.19

= 2.614 × 10 -4

= varying along the X axis

179 12

180 __

181

182 X

970298

74
STARS-SOLIDS input data:

50"x 12" Riumtnum Plate; NON-UNIFORM HERT; Free-free

182, 150, 15, 4, 0, 1, O, O, O,0

15, O, O, O, O, O, O, O,0

I, O, O, O, O, I, O,0

2, O, 2, 0, 1, O, O, 1, O,0

1, 20, O, 2000.0, 0.0, I.OE+O5

$ HODRL DRTR I 0.0000 12.0000 0.0000

000000000

7 0.0000 0.0000 0.0000000000001

8 2.0000 12,0000 0.0000000000000

14 2.0000 0.0000 0.000000000000 I

15 4.0000 12.0000 0.0000000000000

21 4,0000 0.0000 0.000000000000 I

22 6.0000 12.0000 0.0000000000000

28 6.0000 0.0000 0.0000000000001

29 8.0000 12.0000 0.0000000000000

35 8.0000 0.0000 0.000000000000I

36 10.0000 12,0000 0.0000000000000

42 10.0000 0,0000 0.000000000000I

43 12.0000 12.0000 0.0000000000000

49 12.0000 0.0000 0.000000000000I

50 14.0000 12.0000 0.0000000000000

56 14.0000 0,0000 0,00000000000'01

57 16.0000 12,0000 0.0000000000000

63 16,0000 0.0000 0.000000000000 I

64 18,0000 12.0000 0.0000000000000

70 18.0000 0.0000 0.000000000000 I

71 20.0000 12.0000 0.0000000000000

77 20.0000 0.0000 0.0000000000001

78 22.0000 12.0000 0,0000000000000

84 22.0000 0.0000 0.000000000000I

85 24.0000 12.0000 0.0000000000000

91 24.0000 0.0000 0.000000000000

92 26.0000 12.0000 0.000000000000

98 26,0000 0,0000 0.000000000000

99 28,0000 12,0000 0.000000000000

105 28.0000 0.0000 0.000000000000

106 30.0000 12.0000 0.000000000000

112 30.0000 0.0000 0.000000000000

113 32.0000 12.0000 0.000000000000

119 32.0000 0,0000 0.000000000000

120 34.0000 12.0000 0.000000000000

126 34.0000 0.0000 0.000000000000

127 36.0000 12.0000 0.000000000000

133 36,0000 0,0000 0.000000000000

134 38.0000 12,0000 0,0000000000000

140 38.0000 0.0000 0.000000000000

141 40.0000 12.0000 0.0000000000000

147 40.0000 0.0000 0,000000000000

148 42,0000 12,0000 0.0000000000000

154 42,0000 0,0000 0.000000000000

ISS 44.0000 12.0000 0.0000000000000

161 44.0000 0.0000 0,000000000000

162 46.0000 12.0000 0.0000000000000

168 46.0000 0.0000 0,000000000000

169 48.0000 12.0000 0.0000000000000

175 48,0000 0.0000 0.000000000000

176 50.0000 12.0000 0,0000000000000

182 50.0000 0,0000 0.000000000000

$ ELEMENT COHNECTIUITY CONDITIONS 2 I I 2 9 8

0000

266? 14 130000

2?89 16 150000

2 12 13 t4 21 200000

2 13 15 16 23 220000

2 18 20 21 28 270000

2I9 22 23 30 290000

2 24 27 28 35 3400002

2 25 29 30 37 3600003

2 30 34 35 42 4100003

2 31 36 37 44 4300004

2 36 41 42 49 480D004

2 37 43 44 51 500000S

2 42 48 49 56 550000S

2 43 50 51 58 5700006

2 48 55 56 63 6200006

2 49 57 58 65 6400006

2 54 62 63 70 6900006

2 55 64 65 72 7100006

2 60 69 70 77 7600006

2 61 71 72 79 780000?

2 66 76 77 84 8300007

2 67 78 79 86 8500007

2 72 83 84 91 9000007

2 73 85 86 g3 9200008

2 78 90 91 98 9700008

2 79 92 93 I00 9900009

2 84 g? 98 105 10400009

2 85 gg 100 107 10600009

I000

I00I

I000

I00I

I000

I00I

2000

200I

3000

300I

4000

400I

S000

500I

6000

600I

6000

600I

6000

600I

7000

700I

?000

?001

8000

800I

9000

900I

9000

75
2 90 104 105 112 111

00009t900

2 91 106 107 114 1130000 101 10000

2 96 111 112 119 1180000 I01 I000

2 97 113 114 121 1200000 I01 10000

2 102 110 119 126 1250000 I01 1000

2 103 120 121 128 1270000 10t 10000

2 108 125 126 133 1320000 I01 1000

2 109 127 128 135 1340000 I11 11000

2 114 132 133 140 1390000 ItI 1100

2 115 134 135 142 1410000 12I 12000

2 120 139 140 147 1460000 12I 1200

2 121 141 142 14g 1480000 13I 13000

2 126 146 147 154 1530000 13I 1300

2 127 148 149 156 1550000 14I 14000

2 132 153 154 161 1600000 14I 1400

2 133 155 156 163 1620000 15I 15000

2 138 160 161 168 16700O0 15I 1500

2 139 162 163 170 1690000 15I 15000

2 144 167 168 175 1740000 15I 1500

2 145 169 170 177 1760000 15I 15000

2 150 174 175 182 18t0000 151 IS00

S SHELL ELEMENT THICKNESSES 1 0.1900 0.0000 0,0000 $ MATERIAL PROPERTIES I 1

9,909e+06 0.3205 12.9e-06 2.614e-04 2 1

9.895e+06 0.3205 12.9e-06 2.614e-04 3 I

9_872e+06 0,3205 12,9e-06 2.614e-04 4

9.848e+06 0.3205 12,9e-06 2.614e-04 5

9.832e+06 0,3205 12,9e-06 2.614e-04 6

9,825e+06 0.3205 12,9e-06 2,614e-04 7

g_O13e+06 0.3205 12.9e-06 2,614e-04 8

9.796e+06 0.3205 12.9e-06 2,614e-04 9

9,793e+06 0,3205 12.9e-06 2,614e-04

10

9.789e+06 0,3205 12.9e-06 2.614e-04

11

9,780e*06 0,3205 12,9e-06 2.514e-04

121

9.741e+06 0,3205 12,9e-06 2.614e-04

13I

9,677e+06 0.3205 12,9e-06 2.614e-04

14I

9.518e+06 0.3205 12.9e-06 2.614e-04

15I

9.565e*06 0,3205 12.9e-06 2.514e-04

$ TEMPERATURE DATA I 37,4490 0,0 3 62,4640 0,0 5 89,9840 0.0 7 101,8660 0.0 9 111,3230 0_0

11 117.2770 0.0

13 164,4520 0,0

15 205.9110 0,0

$ NODRL MflSS ORTR I47

36

39

42

71

74

77

106

109

112

141

144

147

176

179

182

-I

1,792E-043

1,792E-043

1.792E-043

1,792E-043

1,792E-043

I,?g2E-043

1,792E-043

1.792E-043

1.702E-043

1,792E-043

t,792E-043

1,792E-043

I_792E-043

I_792E-043

1.792E-043

1.792E-043

1.792E-043

1.792E-043

0.02 46,6570 0.0 0.0

0.04 79.2340 0,0 0.0

0.06 94.7030 0.0 0.0

0.08 109,8280 0.0 0.0

0.0 I0 113.2400 0.0 0.0

0.0 12 135,4120 0,0 0.0

0.0 14 191 ,7370 0,0 0.0

0.0

v

76
STARS-SOLIDS output summary: table 17 shows the results.

Table 17. Natural frequencies of a rectangular free-free plate.

Natural frequencies (co),

rad/sec

Mode Quadrilateral element Triangular element

number Zero temperature Varying temperature Zero temperature Varying temperature

1--6 0.00 0.00 0.00 0.00

7 91.11 90.42 87.60 87.17

8 217.28 213.98 211.08 208.83

9 250.38 248.31 241.37 239.56

10 445.35 440.89 433.49 428.85

11 488.57 487.77 472.26 471.35

12 693.44 695.54 677.19 678.29

4.1.14 Thermally Prestressed Composite Square Plate: Vibration Analysis

A composite square plate (fig. 22) subjected to temperature varying along the X axis was analyzed to

yield natural frequencies and modes. Table 18 shows the results of the vibration analysis.

STARS-SOLIDS output summary: table 18 shows the results.

Table 18. Natural frequencies of a free-free square composite plate.

Natural frequencies if.0),

rad/sec

Mode Quadrilateral element Triangular element

number Zero temperature Varying temperature Zero temperature Varying temperature

1-6 0.00 0.00 0.00 0.00

7 1368.08 1566.65 1320.18 1503.57

8 1654.79 1762.14 1584.41 1683.26

9 3631.85 3749.15 3506.99 3610.58

10 3856.04 3857.21 3702.82 3705.50

11 3968.35 4192.31 3858.03 4074.09

12 5838.15 5888.37 5630.24 5673.17

77
Y

i

Important data parameters:

Side length, L

Plate thickness, t

Mass density, p

Composite stacking

1

- I_-X

1 2 3 4 5 6 7 8 9 10 11 12 13

I_ r I 97O299

Figure 22. Free-free composite square plate.

=12

= 0.24

= 0.1475 x 10-3

= [30°/-30o/-30°/30 °]

STARS-SOLIDS input data:

TRIANGULAR 12-BY-t2 PLATE

169, 144, I, 13, O, O, O, 2, 1, 4

/ COMPOSITE LAYERS / temperature I case,

12, O, O, O, O, O, O, O, 0

I, I, O, 1, O, O, O, 0

2, O, 2, O, 1, O, O, 1, O, 0

1, 12, O, 6000.0, 0.0, 0.0

$ NODAL DATA

1 0.0000 0.0000 0.0000

13 12.0000 0.0000 0.0000

14 0.0000 1.0000 0.0000

26 12.0000 1.0000 0,0000

27 0.0000 2.0000 0.0000

39 12,0000 2,0000 0,0000

40 0.0000 3,0000 0,0000

52 12.0000 3.0000 0.0000

53 0.0000 4,0000 0.0000

65 12.0000 4.0000 O,O00O

66 0.0000 5.0000 0.0000

78 12.0000 5,0000 0,0000

79 0.0000 6.0000 0.0000

gl 12.0000 6.0000 0.0000

92 0,0000 7.0000 0.0000

104 12.0000 7.0000 0.0000

105 0.0000 8,0000 0.0000

117 12.0000 8.0000 0.0000

118 0.0000 9.0000 0,0000

130 12.0000 9.0000 0.0000

131 0.0000 10.0000 0.0000

143 12.0000 10.0000 0,0000

144 0.0000 ll.O000 0.0000

156 12.0000 ll.O000 0.0000

157 0.0000 12.0000 0,0000

169 12.0000 12.0000 0.0000

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

78
$ ELEI1EMT COMNECTIUITY 6 1 1 2 15 14

000

6223 16 15000

6334 17 16000

6445 18 17000

6556 19 18000

6667 20 19000

6778 21 2000O

6889 22 2100O

699 I0 23 22000

6 I0 10 tl 24 23000

6 11 11 12 25 24000

6 12 12 13 26 25000

6 13 14 15 28 27000

6 14 15 16 29 28000

6 15 16 17 30 29000

6 16 17 18 31 30000

6 17 18 19 32 31000

6 18 19 20 33 320O0

6 19 20 21 34 33000

6 20 21 22 35 34000

6 21 22 23 36 35000

6 22 23 24 37 36000

6 23 24 25 38 37000

6 24 25 26 39 38000

6 25 27 28 41 40000

6 26 28 29 42 4t000

6 27 29 30 43 42000

6 28 30 31 44 43000

6 29 31 32 45 44000

6 30 32 33 46 45000

6 31 33 34 47 46000

6 32 34 35 48 47000

6 33 35 36 49 48000

6 34 36 37 50 49000

6 35 37 38 51 50000

6 36 38 39 52 51000

6 37 40 41 54 53000

6 38 41 42 55 54000

6 39 42 43 56 55000

6 40 43 44 57 56000

6 41 44 45 58 57000

6 42 45 46 59 58000

6 43 46 47 60 59000

6 44 47 415 61 60000

6 45 48 49 62 6_000

6 46 49 50 63 62000

6 47 50 51 64 63000

6 48 51 52 65 64000

6 49 53 54 67 66000

6 50 54 55 68 67000

6 51 55 56 69 68000

6 52 56 57 70 69000

6 53 57 58 71 70000

6 54 58 59 72 71000

6 55 59 60 73 72000

6 56 60 61 ?4 ?3000

6 5? 61 62 75 74000

6 58 62 63 76 75000

6 59 63 64 77 76000

6 60 64 65 78 77000

6 61 66 67 80 79000

6 62 67 68 81 80000

6 63 68 69 82 81000

6 64 69 70 83 82000

6 65 70 71 84 8300O

6 66 71 72 85 84000

6 67 72 73 86 85000

6 68 73 74 8? 86000

6 69 74 75 88 87000

6 70 75 76 89 88000

6 71 76 77 90 89000

6 72 77 78 91 90000

6 73 79 80 93 9200C

6 74 80 81 94 93000

6 75 81 82 95 94000

6 76 152 83 96 95000

6 77 83 84 97 96000

6 78 84 85 98 97000

6 79 85 86 99 98000

6 60 86 87 100 990O0

6 81 87 88 101 100000

6 82 88 8g 102 101000

6 83 89 90 103 102000

6 84 90 91 104 103000

6 85 g2 93 I06 105000

6 86 93 94 107 106000

6 87 94 95 108 107000

6 88 g5 96 109 108000

6 89 96 97 110 109000

6 90 97 98 III 110000

6 91 98 99 112 111000

6 92 99 100 113 112000

0I000

02000

03000

04000

05000

06000

0?000

08000

09000

0 10000

0 tl000

0 12000

01000

02000

03000

04000

05000

06000

07000

08000

09000

C 10000

0 11000

0 12000

0I000

02000

03000

04000

05000

06000

07000

08000

0g000

0 10000

0 11000

0 12000

01000

02000

03000

04000

05000

06000

07000

08000

09000

0 10000

0 11000

0 12000

0I000

02000

03000

04000

05000

06000

0?000

08000

0g000

0 I0000

0 II000

0 12000

0I000

02000

03000

04000

05000

06000

07000

08000

0g000

0 10000

0 II000

0 12000

0I000

02000

03000

04000

05000

06000

07000

08000

09000

0 10000

0 11000

O 12000

0I000

0200O

030O0

040O0

05000

06000

0?000

08000

79
6 93 lOO 101 114 113

6 94 I01 102 115 114

6 95 102 103 116 115

6 96 103 104 117 116

6 97 105 106 119 I18

6 98 106 I07 120 119

6 99 107 108 121 120

6 100 108 109 122 121

6 101 109 110 123 122

6 102 I0 111 124 123

6 103 It 112 125 124

6 104 12 113 126 125

6 105 13 114 127 126

6 106 14 115 120 127

6 107 15 116 129 120

6 100 16 117 130 129

6 109 10 119 132 131

6 110 19 120 133 132

6 111 120 121 134 133

6 112 121 122 135 134

6 113 122 123 136 135

6 114 123 124 137 136

6 115 124 125 130 137

6 116 125 126 139 138

6 117 126 127 140 139

6 118 127 128 141 140

6 119 120 129 142 141

6 120 129 130 143 142

6 121 131 132 145 144

6 122 132 133 146 145

6 123 133 134 147 146

6 124 134 135 140 147

6 125 135 136 149 148

6 126 136 13? 150 149

6 127 137 138 151 150

6 128 138 139 152 151

6 129 139 140 153 152

6 130 140 141 154 153

6 131 141 142 155 154

6 132 142 143 156 155

6 33 144 145 158 157

6 34 145 146 159 158

6 35 146 147 160 159

6 36 147 148 161 160

6 37 148 149 162 161

6 38 149 150 163 162

6 39 150 151 164 163

6 140 151 152 165 164

6 141 152 153 166 165

6 142 153 154 167 166

6 143 154 155 160 167

6 144 155 156 169 168

O O

O 0

O 0

O 0

O 0

O 0

O 0

0 0

O 0

0 0

O 0

O 0

O 0

O O

O 0

0 O

0 0

0 0

0 0

O 0

0 0

0 O

0 O

O O

O 0

0 0

0 0 0

O 0 0

O 0 0

O O 0

0 0 0

0 0 0

0 0 0

0 O 0

0 O D

0 O O

0 O O

0 0 0

0 0 O

O 0 O

O 0 0

0 0 0

O 0 0

0 O 0

O O 0

0 0 0

O 0 0

0 0 0

0 O 0

0 0 0

0 O O

0 O O

0 0 9

0 0 10

0 0 11

0 0 12

0 0 I

0 0 2

0 0 3

0 0 4

0 0 5

0 0 6

0 0 ?

0 0 8

0 0 9

0 0 10

0 0 II

0 0 12

0 0 I

0 0 2

0 0 3

0 0 4

0 0 5

0 0 6

0 0 ",'

0 0 8

0 0 9

0 0 10

O 11

0 12

0 1

0 2

0 3

0 4

0 5

0 6 0

0 ? O

0 8 0

0 9 0

O I0 0

0 11 O

0 12 0

0 I 0

0 2 O

0 3 0

0 4 0

0 5 0

0 6 O

0 ? O

0 8 0

0 9 O

0 10 0

0 11 0

O 12 0

$ COMPOSITE SHELL ELEMENT STACK DESCRIPTION DATA

I 4

I .0600 I

I ,0600 2

I ,0600 2

I .0600 I

$ SPECIFICATION FOR MATERIAL AXIS ORIENTATION

I 2 0

0.5236

2 2 0

2,61799

$ MATERIAL PROPERTIES

I 2

30.1169E+65,56559E+50.OOOOE+OO2.65029e+60.OOOOE+OOT,8400e+O57.B400E+05

O.O000E÷OO7,840DE+OSO.2420E-O5O.13?OE-O40.OOOOE+OOO,1475E-03

$ ELEMENT TEMPERATURE DATA

1 29.0278 O.OOOO 0.0000 2 81.8056 0.0000 0,0000

3 124.0278 O,OOOO 0.0000 4 155.6945 0.0000 0.0000

5 176.8056 O.OOO0 O.OOO0 6 187.3611 0.0000 O,OOO0

7 187,3611 0,0000 O,O000 8 176.0056 O,OOOO O.OOO0

9 155.6944 0.0000 O.OOO0 I0 124.0278 O,OOOO O.O000

11 81,8056 0,0000 O,OOO0 12 29.0278 0.0000 0.0000

0 0 0

0 0 0

0 0 O

0 0 O

0 0 O

0 0 0

0 0 0

0 0 0

O 0 0

O 0 0

O 0 0

O 0 0

0 0 0

0 O 0

0 0 0

0 0 0

0 0 0

0 O 0

0 0 0

0 0 0

O 0 O

0 0 0

0 O 0

0 O 0

0 0 0

0 0 0

O 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 O

0 O

0 0

0 0

0 0

0 0

0 0

0 0

0 0

C 0

0 O

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

8O
4.2. STARS-SOLIDS (Nonlinear Analysis)

In this section, the input data, as well as relevant outputs, of several typical nonlinear test cases are

provided in some detail. The input data are prepared in accordance with the procedures described in

section 3 and are defined in consistent unit form.

4.2.1 Clamped Square Plate: Uniform Load

Figure 23 shows a square plate with all edges fixed under uniform load. The results of the geometric

nonlinearity analysis involving large displacement and rotation are presented herein.

Important data parameters:

970300

Figure 23. Clamped plate with uniform load.

Thickness, h

Young's modulus, E

Poisson's ratio, la

Length, a = b

Uniform pressure, q

= 1.0

= 2.0 × 1011

= 0.3

= 50

= 6.0 x 104, in 30 equal increments ofAq = 2000.0

A symmetric, one-quarter plate was modeled using a 5-by-5 mesh.

STARS-SOLIDS input data:

Large deflection analysis of a quarter plate

36, 25, I, 4, O, I, O, 0, O, O

O, O, O, O, 0, O, 0

O, I, O, O, O, O, O, 0

2, O, I, O, O, O, 0, 30

Oi I,

11, O,

2, O,

$ HOORL OflTA

I .0000

2 20,0000

3 40.0000

4 60.0000

5 80,0000

6 100.0000

7 .0000

8 20_0000

.0000 .0000

.0000 ,0000

.0000 .0000

.OOOO .0000

,0000 .0000

,0000 ,0000

20.0000 .0000

20.0000 .0000

I

I

I

I

I

I

I

0 0

81
g 40.0000 20.0000 .0000 0 0 0

I0 60.0000 20.0000 .0000 0 0 0

11 80.0000 20.0000 .0000 0 0 0

12 iO0.O000 20.0000 .0000 I 0 0

13 .0000 40.0000 ,0000 I I I

14 20.0000 40,0000 .0000 0 0 0

15 40.0000 40.0000 .0000 0 0 0

16 60.0000 40.0000 ,0000 0 0 0

17 00.0000 40.0000 .0000 0 0 0

18 100.0000 40,0000 ,0000 1 0 0

19 .0000 60.0000 ,0000 I I I

20 20.0000 60,0000 .0000 0 0 0

21 40.0000 60.0000 .0000 0 0 0

22 60,0000 60.0000 ,0000 0 0 0

23 80.0000 60,0000 .0000 0 0 0

24 I00.0000 60.0000 .0000 I 0 0

25 .0000 00,0000 .0000 I I I

26 20,0000 80,0000 .0000 0 0 0

27 40.0000 80.0000 .0000 0 0 0

28 60.0000 80,0000 ,0000 0 0 0

29 80,0000 80,0000 ,0000 0 0 0

30 100.0000 80.0000 .0000 I 0 0

31 .0000 100.0000 .0000 I I I

32 20,0000 100_0000 ,0000 0 I 0

33 40,0000 I00.0000 .0000 0 I 0

34 60.0000 I00.0000 .0000 0 I 0

35 80.0000 100.0000 .0000 0 I 0

36 I00.0000 I00.0000 .0000 I I 0

$ ELEMENT CONNECTIUtTY CONDITIONS

2 I 1 2 8 7 0 0 0 0

2 2 2 3 9 8 0 0 0 0

2 3 3 4 10 9 0 0 0 0

2 4 4 5 11 10 0 0 0 0

2 S S 6 12 11 0 0 0 0

2 6 7 8 14 13 0 0 0 0

2 7 8 9 15 14 0 0 0 0

2 8 g 10 16 15 0 0 0 0

2 9 I0 11 17 16 0 0 0 0

2 10 11 12 18 17 0 0 0 0

2 li 13 14 20 19 0 0 0 0

2 12 14 lS 21 20 0 0 0 0

2 13 15 16 22 21 0 0 0 O

2 14 16 17 23 22 0 0 0 0

2 15 17 18 24 23 0 0 0 0

2 16 19 20 26 25 0 0 0 0

2 17 20 21 27 26 0 0 0 0

2 18 21 22 28 27 0 0 0 0

2 19 22 23 29 28 0 0 0 0

2 20 23 24 30 29 0 0 0 0

2 21 25 26 32 31 0 0 0 0

2 22 26 27 33 32 0 0 0 0

2 23 27 28 34 33 0 0 0 0

2 24 28 29 35 34 0 0 0 0

2 25 29 30 36 35 0 0 0 C

$ SHELL ELEMENT THICKNESSES

I ,I000E*01 ,IO00E*01 ,I000E+01

$ MATERIAL PROPERTIES

I 1

.2000E-12 ,3000E+O0 ,O000E*O0,0000E+O0

$ ELEMENT PRESSURE DATA

1 -2000.000

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

STARS-SOLIDS output summary: table 19 shows the results. Figure 24 shows the maximum plate

displacement (Wmax) as a function of the load plot.

• J

Table 19. Center deflection for a clamped square plate

with a uniform load.

Wmax

qa4 Theory Difference,

Dh (plot) STARS percent

109.3 (P) 1.20 1.21 0.8

218.6 (2P) 1.66 1.70 2.4

327.9 (3P) 2.00 2.03 1.5

82
3.0

2.5

2.0

(qa4/Dh)/p 1.5

1.0

.5

m Solution /

_ Nonlinear /

------ Linear _.....

-- """""/""- L

.5 1,0 1.5 2.0

Wma x

I

2.5

970301

Figure 24. Clamped plate center displacement as a function of load curve.

4.2.2 Cantilever Beam: Moment at Tip

A static, nonlinear analysis of a cantilever beam (fig. 25) was performed using line elements. The

results are given below.

Important data parameters:

Young's modulus, E

Cross-sectional area, A

Moment of inertia:

About y axis

About z axis

Member length, g

Tip moment, M

1 2 3 4 5 6 7 8

M

9 10 11 12 13---J

-_ L = 12,_ _1

_-X

97_02

Figure 25. Cantilever beam with moment at tip.

= 2.0 × 107

= 0.15

= 2.813 × 10-4

= 2.813 × 10 -4

= 1.0

= 3000.0, in 600 equal increments of zLM = 5.0

STARS-SOLIDS input data:

LRRGE ROTATION ANALYSIS OF CRHTILEUEA BERM WITH MOMENT AT TiP

14, 12, I, 4, I, O, O, O, O, 0

O, O, O, O, O, O, O,

11, O, O, I, I, O, O,

2, O, 2, O, I, O, O,

$ NODAL DATA

1 .0000 .0000 .0000 1 1

2 1.0000 .0000 .0000 0 O

3 2.0000 .0000 .0000 0 0

4 3,0000 .0000 .0000 0 0

S 4,0000 .0000 .0000 0 0

6 5.0000 .DO00 .0000 0 0

? 6.0000 ,0000 .0000 0 0

8 7.0000 .0000 .0000 0 0

9 8,0000 ,0000 ,0000 0 0

O, 0

0

O, O, 600

83
10 9.0000 .0000 .0000 0 0

II 10.0000 ,0000 .0000 0 0

12 11,0000 .0000 .0000 0 0

13 12.0000 .0000 _0000 0 0

14 .0000 3,0000 .0000 1 1

$ ELEMEHT COMHECTIUITY COMDITIOMS

I 1 I 2 14 0 0 0 0

I 12 12 13 14 0 0 0 0

$ LIHE ELEMEHT BASIC PROPERTIES

I ,1500E+00 ,IO00E*OI .28125E-3 ,28125E-3

$ MATERIAL PROPERTIES

1 I

,2000E÷08 .3000E+O0

$ HODRL LOAD ORTR

13 6 5,0

-I

I I I 0

I I I 0

I I I 0

I I I 0

I I I I

0 I I 0 0 0 0

0 I I 0 0 0 I

STARS-SOLIDS output summary: table 20 shows the output summary, and figures 26 and 27 show

deflection curves.

Table 20. Tip displacement, v, for a

cantilever beam with end moment.

Tip Y displacement (v)

M STARS Theory

300 3.7048 3.7107

600 6.6675 6.6860

900 8.3599 8.3884

1200 8.5825 8.6043

1500 7.4971 7.4936

1800 5.5581 5.5183

2100 3.3671 3.2954

2400 1.4980 1.4146

2700 0.3452 0.2787

3000 0.0385 0.0128

y4

F

-2 0 2 4 6 8 10 12

X

970303

Figure 26. Deflection curves for cantilever beam with end moment.

84
3000

2500

200O

Moment 1500

1000

5OO

Displacement

O Tip X, (u), STARS

[] Tip Y, (v), STARS

Tip Y, (v), Theory

0 2 4 6 8 10 12 14

Displacement

970304

Figure 27. Cantilever tip deflection as a function of moment curve.

I

16

4.2.3 Clamped Cylindrical Shell: Uniform Load

A nonlinear analysis of a clamped cylindrical shell under uniform load (fig. 28) was performed. An

8-by-8 mesh was employed for one-quarter of the panel, and the results are presented herein.

! /_--- Symmetry

/ \ plane

_ --_ 70 71 72

Y Is

21 _ [1 -- 16 117 1_.__

_._ A -_/_-_ -------_" X

970305

Figure 28. Clamped cylindrical shell with uniform load.

Important data parameters:

Thickness, h = 0.125

Young's modulus, E = 450,000

Poisson's ratio, _t = 0.3

Length, A = B = 10

R = 100

Total q = 0.3, in 30 equal increments ofAq = 0.01

85
STARS-SOLIDS input data:

Large deflection analysis ofa quarter shel

01, 64, 1,

O, 1, O,

II, O, O,

2, O, 2,

$ NODE DESCAIPTION 1 .00000 2 1.25000 3 2,50000 4 3,75000 5 5.00000 6 6.25000 7 7.50000 8 8.75000 9 10.00000

I0 .00000

11 1,25000

12 2,50000

13 3.75000

14 5,00000

15 6.25000

16 7.50000

17 8.75000

18 10.00000

19 .00000

20 1.25000

21 2,50000

22 3.?5000

23 5.00000

24 6.25000

25 7.50000

26 8,75000

27 10,00000

28 .00000

29 1.25000

30 2.50000

31 3.75000

32 5.00000

33 6.25000

34 7.50000

35 8.75000

36 I0.00000

37 .00000

38 1.25000

39 2.50000

40 3.75000

41 5.00000

42 6.25000

43 7.50000

44 8,75000

45 I0.00000

46 .00000

47 1.25000

48 2.50000

49 3,75000

SO 5.00000

51 6.25000

52 7.50000

53 8,75000

54 10,00000

55 .00000

56 1.25000

57 2.50000

58 3,75000

59 5,00000

60 6.25000

61 7.50000

62 8.75000

63 I0,00000

64 .00000

65 1.25000

66 2.50000

67 3,75000

68 5.00000

69 6.25000

70 7.50000

71 8.75000

72 I0.00000

73 .00000

74 1.25000

4, O, I, O, O, O,0

O, O, O, O, O,0

I, O, O, O,0

O, I, O, O, O, O, 30

.00000 .00000

.00000 .11771

.00000 .21961

.00000 .30575

.00000 ,37618

.00000 .43072

.00000 .47000

.00000 .49344

.00000 ,50126

.25000 .00000

.25000 .11771

.25000 ,21961

.25000 .30575

,25000 .37618

,25000 .43072

,25000 .47000

.25000 .49344

_25000 .50126

2,50000 .00000

2,50000 ,11771

2.50000 .21961

2.50000 .30575

2.50000 .37618

2,50000 .43072

2.50000 .47000

2.50000 .49344

2.50000 .50126

3.75000 .00000

3.75000 .11771

3.75000 .21961

3.75000 .30575

3.75000 .37618

3.?S000 ,43072

3,75000 ,47000

3.75000 ,49344

3,75000 ,50126

5,00000 ,00000

5,00000 .11771

5.00000 .21961

5,00000 .30575

5.00000 .37618

5.00000 .43072

5.00000 .47000

5.00000 ,49344

5.00000 .50126

6.25000 .00000

6.25000 .I1771

6.25000 .21961

6,25000 .30575

6,25000 .37618

6.25000 .43072

6.25000 .47000

6.25000 .49344

6.25000 .50126

7.50000 .00000

7.50000 .11771

7,50000 ,21961

7.50000 ,30575

7,50000 ,37618

7.50000 .43072

7,50000 .47000

?,50000 .49344

?.SO000 .50126

8.75000 .00000

8.75000 .11771

8.75000 .21961

8,75000 .30575

8.75000 .37618

8.75000 _43072

8.75000 .47000

8,75000 ,49344

8,75000 .50126

10.00000 .00000

I0.00000 .11771

_j

86
75 2.50000 10,00000 ,21961

001

76 3.75000 IO.O0000 .305?5001

77 5,00000 I0.00000 .3761800I

78 6.25000 10.00000 ,43072001

79 7.50000 10.00000 .4700000I

80 8.75000 10.00000 .4934400 I

01 I0,00000 10.00000 ,50126101

$ ELEMENT CONNECTIVITY 2 I 1 2 11 I0

0000

2223 12 110000

2334 13 120000

2445 14 130000

2SS6 IS 140000

2667 16 150000

2?78 17 160000

2889 18 170000

29 10 11 20 190000

2 I0 11 12 21 200000

2 11 12 13 22 210000

2 12 13 14 23 220000

2 13 14 15 24 230000

2 14 15 16 25 240000

2 15 16 17 26 250000

2 16 17 18 27 260000

2 17 19 20 29 280000

2 18 20 21 30 290000

2 19 21 22 31 300000

2 20 22 23 32 310000

2 21 23 24 33 320000

2 22 24 25 34 330000

2 23 25 26 35 340000

2 24 26 27 36 350000

2 25 28 29 38 37000O

2 26 29 30 39 380000

2 27 30 31 40 390000

2 28 31 32 41 400000

2 29 32 33 42 410000

2 30 33 34 43 420000

2 31 34 35 44 430000

2 32 35 36 45 440000

2 33 37 38 47 460000

2 34 38 39 48 470000

2 35 39 40 49 480000

2 36 40 41 50 490000

2 37 41 42 Sl SO0000

2 38 42 43 52 5100OC

2 39 43 44 53 5200O0

2 40 44 45 54 530000

2 41 46 47 56 550000

2 42 47 48 ST 560000

2 43 48 49 58 570000

2 44 49 50 59 580000

2 45 SO 51 60 590000

2 46 51 52 61 600000

2 47 52 53 62 610000

2 48 53 54 63 620000

2 49 $5 56 65 640000

2 SO 56 57 66 650000

2 51 57 58 67 660000

2 52 58 59 68 670000

2 53 59 60 69 680000

2 54 60 61 70 690000

2 55 61 62 71 700000

2 56 62 63 72 7100O0

2 57 64 65 74 730000

2 58 65 66 75 740000

2 59 66 67 76 750000

2 60 67 68 77 760000

2 61 68 69 78 770000

2 62 69 70 79 780000

2 63 70 71 80 790000

2 64 71 72 81 800000

$ SHELL ELEMEHT THICKNESSES 1 ,1250E+00 .12SOE+O0 .12SOE+O0 $ MATERIAL PROPERTIES 1 1 • 4500E+06 ,3000E+O0.0000E+O0.0000E+O0 $ ELEMENT PRESSURE DATA 1 -0.01

000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000o0000000000000000000

87
STARS-SOLIDS output summary: table 21 shows the results, and figure 29 shows the load deflection

curve.

Table 21. Center deflection for a clamped

cylindrical shell under uniform load.

Pressure (q) Center deflection (w)

0.01 0.00289

0.02 0.00586

0.03 0.00891

0.04 0.01206

0.05 0.01531

0.06 0.01868

0.07 0.02217

0.08 0.02580

0.09 0.02958

0.10 0.03354

0.11 0.03771

0.12 0.04211

0.13 0.04680

0.14 0.05181

0.15 0.05724

0.16 0.06318

0.17 0.06979

0.18 0.07729

0.19 0.08606

0.20 0.09672

0.21 0.11043

0.22 0.12921

0.23 0.15481

0.24 0.18135

0.25 0.20372

0.26 0.22284

0.27 0.23953

0.28 0.25427

0.29 0.26749

0.30 0.27951

88
.30

.25

.20

Pressure,

q .15

.10

.05

j/

D /

-- I I

I

/f

.05 .10 .15

Deflection, W

J

Solution

Nonlinear

----- Linear

I t I

.20 .25 .30

970306

Figure 29. Center deflection of a clamped cylindrical shell under uniform load.

4.2.4 Clamped Beam: Dynamic-Response Analysis

Figure 30 shows a beam with both ends clamped under concentrated load. The results of a nonlinear

static and response analysis involving large displacement and rotation are presented herein.

P(t)

;ill, "J''i "°

Figure 30. Clamped beam with concentrated load.

_ t

970313

Important data parameters:

Young's modulus, E = 3.0 × 107

Length, L = 20.0

Width, B = 1.0

Thickness, h = 0.125

Mass density, p = 2.5389 x 10-4

Static load, P = 700

Ap = 10

= 640 Dynamic load, Po

At = 2.0 _ts

Ten ideal beam elements were used.

89
STARS-SOLIDSinputdata:

NONLINEAR RESPONSE OF CLAMPED BEAM WITH CONCEHTRRTED LOAD

12, IO, 1, 4, I, O, O,

O, O, O, O, O, O, O,

11, O, 1, 1, O, O, O,

2, O, 2, O, I, O, O,

O, I, 1, 1

$ HODRL DATA

1 .0000 .OOOO .DO00 1

2 2.OOOO ,0000 .0000 0

3 4.0000 .0000 .O00O 0

4 6.0000 .ODD0 .OOO0 0

S 8.0000 .OOOO .OOO0 0

6 IO.ODO0 .0000 .OOO0 0

7 12.00QO .0000 .0000 0

8 14,0000 .OOO0 .OOO0 0

9 I6,OOO0 ,O00O .OOOO 0

10 18.0000 .0000 .DO00 0

11 20.0000 ,0000 ,0000 I

12 I0.0000 15.0000 .0000 I

$ ELEMEHT COMNECTiUITY CONDITIONS

1 I 1 2 12 0 0 0 0

I I0 10 11 12 0 0 0 0

$ LINE ELEMEHT BASIC PROPERTIES

I ,1250E+00 .16276E-3 .16276E-3 .16276E-3

$ MATERIAL PROPERTIES

1 I

O, O, 0

O, O

0

O, O, 1

1

0

0

0

0

0

0

0

0

0

1

I

0 1

0 1

,30ODE÷08 .OO00E+O0.000OE+O0 .25389E-3

$ DYNAMIC NODAL LORD DATA

S,O

6 3 -640.000

-I

$ INCREMENTAL TIME DATA FOR DYHAMIC RESPONSE RMALYSIS

2,0E-6 2500

0 O 0 0

0 0 0 I

STARS-SOLIDS output summary: table 22 shows the results for a nonlinear static solution. Figure 31

shows the displacement as a function of the load plot. Figure 32 shows the displacement as a function of

the time plot for the nonlinear response solution.

Table 22. Center displacement for a

clamped beam with concentrated load.

Load

increment Displacement

10 0.03128

20 0.06983

30 0.10049

40 0.12539

50 0.14623

60 0.16420

70 0.18004

80 0.19425

90 0.20719

100 0.21908

200 0.30605

300 0.36525

400 0.41177

500 0.45075

600 0.48465

700 0.51485

90
800

600

Lo_d, 400

200

-- Solution

Nonlinear /

_ - i

.1 .2 .3 .4 .5

Displacement, W

I

.6

970314

Figure 31. Center displacement: load curve of a clamped beam.

Nonlinear

Dynamic response A t = 2 _teec

------ Static solution

1.0

Displacement, .6

W .4

.2

0 I 2 3 4 5x10 -3

Time, sec g7o315

Figure 32. Center displacement: time curve of a clamped beam.

4.2.5 Shallow Spherical Cap: Dynamic-Response Analysis

Figure 33 shows a clamped spherical cap under apex load. Both triangular and quadrilateral element

meshes (fig. 34) were used for modeling one-quarter of the cap for the nonlinear static analysis. The

triangular element mesh was also used for the nonlinear response analysis. The results are presented

herein.

P(t)

P(t)

'°l

Figure 33. Clamped spherical cap with apex load.

Important data parameters:

Young's modulus, E

Poisson's ratio, p

= 1.0 x 107

= 0.3

_---t

970316

91
Thickness,

t

Radius,R

Height,H

Length,a

Mass density,p

Static load,P

Ap

Dynamic load,P

O

At

= 0.01576 = 4.76 = 0.08589 = 0.9 = 2.45 x 10-4 = 100 = 1 = 100 = 0.5 p.s

STARS-SOLIDS input data:

Hanlineor response

37, 54, I,

O, O, O,

I1, O, I,

2, O, 2,

O, l, I,

$ HOORL OATR 1 4.7600 .0000 .0000

1

2 4.7600 0.0000 0.02620

3 4.7600 0.7854 0.03320

4 4.7600 1.5?07 0.0262I

5 4.7600 0.0000 0.05240

6 4.7600 0,3927 0,05590

7 4.7600 0,7854 0,06460

8 4.7600 1,1700 0.05590

9 4.7600 1.5707 0.0524 I

10 4.7600 0.0000 0.07850

11 4,7600 0.2618 0.07850

12 4,7600 0.5239 0.08200

13 4,7600 0.7854 0.08900

14 4.7600 1.0472 0.08200

15 4,7600 1.3090 0.07850

16 4.7600 1.5707 0.07851

17 4.7600 0.0000 0.11520

18 4.7600 0.2618 0.I1520

19 4.7600 0.5239 0.11520

20 4.7600 0.7854 0.11520

21 4.7600 1.0472 0.11520

22 4.7600 1.3090 0.t1520

23 4.7600 1.5707 0,11521

24 4.7600 0.0000 0.15180

25 4.7600 0.2610 0,15180

26 4.7600 0.5239 0.15180

27 4.7600 0.7854 0.15180

28 4.7600 1,0472 0.15180

29 4.7600 1.3090 0.15180

30 4.7600 1.5707 0.1510I

31 4,7600 0,0000 0.1902I

32 4.7600 0.2610 0,t9021

33 4.7600 .5239 0.1902I

34 4.7600 .7854 0.19021

35 4.7600 1.0472 0.19021

36 4.7600 1.3090 0.19021

37 4,7600 1,5707 0.19021

$ LOCRL-GLOBRL COORDINATE SYSTEM DATA

20000I2

0.0 0.0 0,0 1.0

0.0 1.0 0.0

of spherical cop under apex load (Triangular mesh)

4, O, 1, 1, O, O,0

O, O, O, O, O,0

1, O, O, O,0

0, 1, O, O, O, O,1 I

0,0

1 12000000

0 12000000

0 12000000

1 12000000

0 12000000

0 12000000

0 12000000

0 12000000

1 12000000

0 12000000

0 12000000

0 12000000

0 12000000

0 12000000

0 12000000

I 12000000

0 12000000

0 12000000

0 12000000

0 12000000

0 12000000

0 12000000

I 12000000

0 12000000

0 12000000

0 12000000

0 12000000

0 12000000

0 12000000

I 12000000

1 12000000

I 12000000

1 12000000

I 12000000

1 12000000

1 12000000

1 12000000

0.0

$ ELEMENT CONNECTIUITY CONDITIONS 3 I 1 2 3 0

0000

3213400000

3325300000

3456300000

3567300000

3678300000

3789300000

3894300000

39 I06500000

3 10 10 II600000

3 II 117600000

3 12 II 12700000

3 13 12 13700000

3 14 13 14700000

3 15 14 15700000

3 16 156700000

3 17 15 16800000

3 18 169800000

3 19 I0 17 1100000

3 20 17 18 1100000

3 21 10 12 II00000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

-.j

92
3 22 18 19 12 0 0 0 0 0

3 23 19 13 12 0 O 0 0 O.

3 24 19 20 13 O D O 0 0

3 25 20 2t 13 0 0 0 O 0

3 26 21 14 13 O 0 0 0 0

3 27 21 22 14 0 O 0 O 0

3 28 22 15 14 O 0 O 0 0

3 29 22 23 15 O 0 0 O 0

3 30 23 16 15 0 0 0 0 0

3 31 24 18 17 0 0 O O 0

3 32 24 25 18 0 0 0 0 0

3 33 25 t9 18 O O 0 O 0

3 34 25 ;)6 19 0 0 O O 0

3 35 26 20 19 0 0 0 O 0

3 36 26 2T 20 O 0 0 O 0

3 3T 27 28 20 0 O 0 0 0

3 38 28 21 20 0 0 0 0 0

3 39 28 29 21 0 0 0 0 0

3 40 29 22 21 0 0 0 0 0

3 41 29 30 22 O O 0 O 0

3 42 30 23 22 0 O 0 0 0

3 43 31 25 24 0 0 O O O

3 44 31 32 25 0 0 0 0 0

3 45 32 26 25 O 0 O 0 0

3 46 32 33 26 O 0 O 0 0

3 47 33 27 26 0 0 O 0 0

3 48 33 34 27 0 0 O 0 0

3 49 34 35 27 0 O O 0 O

3 50 35 28 27 0 0 0 0 0

3 51 35 36 28 0 0 0 0 0

3 52 36 2g 28 0 0 O 0 0

3 53 36 37 29 0 0 O 0 0

3 54 37 30 29 0 O 0 O 0

$ SHELL ELEMENT THICKNESSES

1 ,01576 .01576 .01576

$ NRTERIRL PROPERTIES

1 I

1D.E"06 .3000E*O0,0000E"O0 2,450E-04

$ DYNAMIC MODAL FORCE DRTR

0,5

1 3 -25,0

-1

$ INCREMENTAL TiME DATA FOR DYMRMIC RESPONSE ANALYSIS

2, OE-06 250

0 0 0 0

0 0 O 0

0 0 0 0

0 0 O O

O O O 0

0 0 0 O

O 0 O 0

O 0 0 O

O O 0 O

O 0 O 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 O

0 0 0 0

O 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

970317

(a) Triangular mesh.

Figure 34. One-quarter cap model.

(b) Quadrilateral mesh.

970318

93
STARS-SOLIDS output summary: table 23 shows the results for the nonlinear static solution.

Figure 35 shows the displacement as a function of the load plot. Figure 36 shows the displacement as a

function of the time plot for the nonlinear response solution.

Table 23. Center deflection for a clamped spherical cap

under apex load.

Load Displacement,

W/H

increment Quadrilateral mesh Triangular mesh

4 0.0384 0.03694

12 0.1601 0.15374

20 0.4542 0.41541

24 0.5859 0.56075

28 0.7007 0.69837

32 0.8103 0.82891

36 0.9186 0.9522

40 1.0308 1.0753

44 1.1575 1.2173

48 1.3470 1.4091

52 1.5054 1.5400

56 1.6313 1.6211

60 1.7058 1.6794

70 1.8159 1.7827

80 1.8882 1.8576

90 1.9444 1.9179

100 1.9891 1.9689

Load,

P

100

80

60

40

20

-- Mesh r'_

.5 1.0 1.5 2.0

Displacement, W/H

970319

Figure 35. Cap center displacement as a function of load.

94
Nonlinear response

A t = 0.5 Hsec

---- Linear static solution

----- Nonlinear static solution

3.0 --

2.5 --

Displacement,w/H2.011.0.5.5 _

0 100 200 300 400 500 x 10 -6

Time, sec

970320

Figure 36. Cap center displacement as a function of time.

4.2.6 Clamped Beam: Elastoplastic Analysis

Figure 37 shows a clamped beam under uniformly distributed load. A triangular shell-element mesh

was used for modeling; the beam is considered to consist of several layers of elements. Table 24 and

figure 38 show the results.

±

t=0.1

L=IO

(a) Uniform distributed load on the beam.

970321

/

/

/

/

/

/=

\\\\_\\\\_\\\\\\\\\\/////////////// ////

/////////////////! //\\ \ _\\\ \ \\ \ \\_ \\\\\

970322

(b) Finite element model of the beam.

Figure 37. Clamped beam under uniformly distributed load.

/

/

/

/

/

/

95
Important data parameters:

Young's modulus, E

Poisson's ratio, IX

Thickness, t

Length, L

Width, B

Yield stress, Gy

Hardening, H'

t=0.1

8 layers

@ 0.0125

970323

(c) Cross section.

Figure 37. Concluded.

= 1.0 x 107

= 0.3

= 0.1

= 10.0

= 1.0

= 35,000

=0

STARS-SOLIDS input data:

Elosto-Plostic analysis of o strip with both ends fixed

12316016000118

0101000000

11001000000

20201001018

$ HODE OESCRIPTIOH

1 .00000 ,00000 .00000 1

2 .00000 ,50000 .00000 1

3 .00000 1.00000 .00000 I

4 .25000 .00000 ,00000 0

118 9.75000 .00000 ,00000 0

S .25000 .SO000 .00000 0

119 9.75000 .50000 ,00000 0

6 ,25000 1.00000 ,00000 0

120 9.75000 1.00000 .00000 0

121 t0.00000 .00000 .00000 1

122 10.00000 ,50000 .00000 I

123 10.00000 1,00000 .00000 1 1

$ ELEMEHT COHNECTIUITY

? I I 4 5 0 0 0 0

7 20 58 61 62 0 0 0 0

7 21 5 2 1 0 0 0 0

7 40 62 59 58 0 0 0 0

7 41 2 5 3 0 0 0 0

7 60 59 62 GO 0 0 0 0

7 61 6 3 5 0 0 0 0

7 80 63 60 62 0 0 0 0

? 61 61 64 62 0 0 0 0

? 100 110 121 I19 0 0 0 0

? 101 65 62 64 0 0 0 0

7 120 122 119 12t 0 0 0 0

? 121 62 G5 66 O 0 0 0

? 140 119 122 123 0 0 0 0

? 141 65 53 62 0 0 0 0

7 160 123 120 119 0 0 0 0

$ COMPOSITE SHELL ELEflENT STRCK DESCRIPTIOH DRTR

8

0,0125

0,0125

0.0125

0,0125

0,0125

0.0125

0.0125

0,0125

I I 1 1 1

I 1 1 1 I

1 1 1 I I

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

1 I 1 1 1

I 1 I I I

I 1 1 I

0

0 3

0

0 3

0

0 3

0

0 3

0

0 3

0

0 3

0

0 3

0

0 3

96
$ SPECIFICRTIOH FOR I1RTERIRL RXIS ORIEHTRTtOH

1 2 0

0.0

$ ELEMEHT MRTERIRL PROPERTIES

1 1

IO.OE*6 0,3 0.0 0,0 35.0E*3

$ PRESSURE DATA

1 0.875

0.0

STARS-SOLIDS output summary: table 24 shows the results for the elastoplastic analysis. Figure 38

shows the displacement as a function of load plot.

Table 24. Maximum uniformly distributed

load for a clamped beam.

qmax

Difference,

STARS Theory percent

14.875 14.0 6.25

Load

16--

14

12

10

8

6

4

2

T_FII ............

I []'7"'°'n'TS'''r'l

.2 .4 .6 .8 1.0

Deflection

970324

Figure 38. Load-deflection curve for a clamped beam.

4.3 STARS-SOLIDS Heat Transfer (Linear Analysis)

In this section, the input data and relevant outputs of typical heat-transfer test cases are provided in

detail. The input data are prepared in accordance with the procedures described in section 3 and are

defined in consistent unit form.

4.3.1 Cooling Fin: Convection Boundary Condition

A linear steady-state heat-transfer analysis of a cooling fin (fig. 39) was performed using heattransfer line elements. The results are given below.

97
Y

f

Wall, Tw _ 1

1

Tf, hf

-_I_X

2 3 4 5 6 7 8 9

Figure 39. Cooling fin with convection.

970325

Important data parameters: arbitrary available element and material properties data are used for the

analysis to correlate results with existing ones expressed in parametric form.

Coefficient of conductivity, k = 132.0

Convective heat transfer coefficient, hf = 1.6

Fluid temperature, Tf = 70

Wall temperature, Tw = 250

Length, L = 1

Area, A = 0.001365

Perimeter, P = 0.13091

specific heat, Cp = 0.2

STARS-SOLIDS HEAT-TRANSFER input data:

HEAT TRANSFER - TRUSS

10,8,1,11,1,0,0,0,0,0

0,0,0,1,1,0,0,0,0

10,0,0,1,0,0,0,0

2,0,1,0,0,0,0,1,0,0

$ NODAL DRTR

1 0.0 0.0 0.0 0

2 0.125 0.0 0.0 0

3 0.250 0.0 0.0 0

4 0.375 0.0 0.0 0

5 0.500 0.0 0.0 I

6 0.625 0.0 0.0 0

7 0.750 0.0 0.0 0

8 0.8T5 0,0 0,0 0

9 1.000 0.0 0.0 0

I0 0.0 50.0 0.0 I

$ ELEMENT CONNECTIVITY

I I I 2 I0 0 0 0

1 2 2 3 10 0 0 0

I 3 3 4 10 0 0 0

I 4 4 5 10 0 0 0

1 5 5 6 10 0 0 0

I 6 6 ? I0 0 0 0

I 7 7 8 10 0 0 0

I O 8 9 10 0 0 0

$ LINE ELEMENT BASIC PROPERTIES

I 0.001365 O, 13091

$ ELEMENT MATERIAL PROPERTIES

t 6

13.2E01 1.6 0 0.0

0.0 0.0 0 0,0

$ TEMPERATURE BOUNDARY CONDITION DATA

1 I 1 1 250.

0 0 I I

0 0 I I

0 0 I I

0 0 I I

0 0 I I

0 0 I I

0 0 I I

0 0 I I

70.0 0,0 0.0

98
STARS-SOLIDS HEAT-TRANSFER analysis results:

NOOE

EXT INT TEM-SUR 1 TEM-SUR 2 TEM-SUR 3 TEM-SUR 4 TEM-SUR 5 TEM-SUR 6

t 1 0.250000E+03 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0

2 2 0.232333E*03 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0

3 3 0.217624E+03 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0

4 4 0.205605E+03 O.O00000E+O0 O.O00000E+O0 O.O00000E*O0 O.O00000E+O0 O.O00000E*O0

5 5 0.196056E+03 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0

6 6 O.IBBBO3E*03 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E*O0 O.O00000E+O0

7 7 0.183715E+03 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E*O0 O.O00000E+O0

8 8 0.18069gE+03 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E*O0 O.O00000E+O0

9 9 0.179700E+03 O.O00000E+O0 O.O00000E*O0 O.O00000E+O0 O.O00000E+O0 O.O00000E,O0

I0 I0 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0 O.O00000E*O0 O.O00000E+O0 O.O00000E+O0

4.3.2 Three-Dimensional Box: Specified Nodal Temperature

Figure 40 shows a three-dimensional box that is characterized by orthotropic material. The results of

a linear steady-state heat-transfer analysis of the problem are presented herein.

Z y

/

L t Material 2

__ Zga%r-raTV

T1, 1_11< L _ 07o326

Figure 40. Three-dimensional box with conduction.

Important data parameters:

Length, L

Node temperature, T 1,1

Node temperature, T9,4

Material 1:

Coefficients of conductivity, k

kxx

kyy

kzz

Thickness, t

Material 2:

Coefficients of conductivity, k

kxx

kyy

kzz

Thickness, t

= 1.0

= 500

=0

= 3.0

= 1.0

= 1.0

= 0.3

= 1.0

= 3.0

= 3.0

= 0.4

99
STARS-SOLIDSHEAT-TRANSFERinputdata:

R UNIT LENGTH FIRECLAY BRICK - 2X2 TRIANGLE MESH - HEAT TRANSFER - C2

9,8,2,44,0,0,0,2,1,6

0,0,0,1,2,0,0,0,0

10,0,0,1,0,0,0,0

2,0,2,0,1,0,0,1,0,0

$ NODAL DATA

I 0.0000 O.OOO0 O.O000 0 0

2 0.5000 0.0000 O.O000 0 0

3 1,0000 O.O000 0.0000 0 0

4 0.0000 0.5000 O.OOO0 0 0

5 0.5000 0.5000 O.OOO0 0 0

6 1.0000 0.5000 0.0000 0 0

7 0.0000 1.0000 0.0000 0 0

8 0.5000 1.0000 0.0000 0 0

9 1.0000 1.0000 0.0000 0 0

$ ELEMEHT COHNECTIUITY

7 t I 2 5 0 0 0 0

? 2 5 4 I O 0 0 0

7 3 2 3 6 O 0 0 0

? 4 6 5 2 0 0 0 0

7 5 4 5 8 0 0 0 0

7 6 8 7 4 0 0 0 0

7 7 5 6 9 0 0 0 0

? 8 9 8 5 0 0 0 0

0 0 1

O 0 1

0 0 1

0 0 1

0 0 1

0 0 1

0 0 1

0 0 1

O 0 1

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

$ COMPOSITE SHELL ELEMEHENT, STACKS AND 5UBSTRCKS OEFIHITION

I 6 3 3 I 2 0 0

I .15000 2

I .15000 I

2 .40000 I

1 .10000 I

,I0000 2

I ,10000 I

$ SPECIFICATION FOR MATERIAL AXES ORIENTATION

1 2 0

0.0

2 2 0

1.5700

$ ELEMENT MATERIAL PROPERTIES

I 8

O, I. I. O. O.

O, O, O, O. O,

O, O, O, O, O,

O. O, O. O, O,

O. O. 0. O_ O.

O. O. O. O, O,

O,

3,

O.

O.

O.

O,

O.

O.

2 8

I, O, 3. 3, O, O, O,

O. O, O, O, O, O. O,

O, O, O, O. O, O, O.

O, O. O. O. 0, O, O.

O, O, O. O. O, O. O,

0, O, O, O, O. O, 0.

$ TEMPERATURE BOUNDARY CONDITION DATA

I I 1 I 500.

9 4 9 4 O,

O.

O,

O,

O.

O.

O.

STARS-SOLIDS HEAT-TRANSFER analysis results:

NOOE

EXT INT TEM-SUR 1 TEM-SUR 2 TEM-SUR 3 TEM-SUR 4 TEM-SUR 5 TEfl-SUR 6

I 0.500000E*03 0.224?75E*03 0.212283E*03 0.200333E+03 O.O00000E+O0 O.O00000E+OO

2 0,267260E+03 0.223166E+03 0.207237E+03 0.199651E*03 O.O00000E+O0 O,OOOO00E+O0

3 0.23239BE+03 0.211402E+03 0.203162E+03 0.197953E+03 O.O00000E*O0 O,OO000OE+O0

4 0.205148E+03 0.208393E+03 0.196695E*03 0,196979E*03 O.O00OOOE÷O0 O,O00000E+O0

5 O.IB5295E+03 0.202975E+03 0.188997E÷03 0.199701E÷03 O.000000E÷O0 O.O00000E+O0

6 0,189?22E+03 O,Ig3493E*03 0,185473E+03 O,IB7941E*03 O,O00000E÷O0 O.O00000E+O0

7 0.193992E+03 0,186909E+03 O,17BB82E+03 0,164663E+03 O.O00000E+O0 O.O00000E+O0

8 0,191341E*03 0.181805E+03 0,169013E+03 0.142837E+03 O.O00000E*O0 O.O00000E+O0

9 O.190919E+03 0.176588E+03 0.169369E+03 O.O00000E+O0 O.O00000E+O0 O.O00000E+O0

100
4.3.3 Square Plate: Transient Heating

A heat-transfer analysis of a square plate (fig. 41) with transient internal heating, heat flow, and

convective heating was performed. The results are presented here.

1

Y

I Ta ' ha _y

//;/7

y/Z/'o

4 5 "-_" x

1

lnsulated 2 Tedg e

L v I 970327

(a) Plate model.

T a

201 _

I

t=l

Q qs

1C

(b) Pulse heating.

Figure 41. Square plate with transient heating.

-__t

t=l

970328

Important data parameters:

Coefficient of conductivity, k = 1.0

Internal heat generation rate, Q = 1.0

Surface heat flow rate, qs = 10.0

Convective heat-transfer coefficient, ha = 3.0

Air temperature, Ta = 20

Edge temperature, Tedge = 10

Length, L = 1

Thickness, t = 0.1

Time step, At = 0.05

Total time period for response = 4.0

101
STARS-SOLIDSHEAT-TRANSFERinput data:

SHELL -4x4- Isotroptc plate- Teanslent heat loading

25,32,2,44,0,0,0,1,2,1

0,0,0,2,10,0,0,0,0

10,0,1,1,0,0,0,0

2,0,2,0,1,0,0,1,0,0

1,20,0,1675.,3.0,0.0

0,1,1,2 $ NOORL DATA 1 0.000 0.000 0.000

00

2 0.250 0.000 0.00000

3 0.500 0.000 0.00000

4 0.750 0.000 0.00000

5 1.000 0.000 0.00000

6 0.000 0.250 0.00000

7 0.250 0.250 0.00000

8 0.500 0.250 0_00000

9 0.750 0.250 0.00000

10 1.000 0.250 0.00000

I1 0.000 O.SO0 0.00000

12 0.250 0.500 0.00000

13 0.500 0.500 0.00000

14 0.750 0.500 0.00000

15 1.000 0.500 0.00000

1G 0.000 0.750 0.00000

17 0.250 0.750 0.00000

18 0.500 0.750 0.00000

19 0.750 0.750 0.00000

20 1.000 0.750 0.00000

21 0.000 1.000 0.00000

22 0.250 1.000 0.00000

23 0_500 1.000 0.00000

24 0.750 1.000 0.00000

25 1.000 1.000 0.00000

$ ELEMENT CONNECTIVITY CONDITIONS 7 I I 7 6 0

000

72?I20000

732870000

748230000

753980000

769340000

774 t090000

78 10450000

796 12 110000

7 10 12670000

7 117 13 120000

7 12 137O0000

7 138 14 130000

7 14 14890000

7 159 15 T40000

7 16 15g I00000

7 17 11 17 160000

7 10 17 II 120000

7 19 12 18 170000

? 20 18 12 130000

7 21 13 19 180000

7 22 19 13 140000

7 23 14 20 190000

7 24 20 14 150000

7 25 16 22 210000

7 26 22 16 170000

7 27 17 23 220000

7 28 23 17 180000

7 29 10 24 230000

7 30 24 18 lg0000

7 31 19 25 240000

7 32 25 19 200000

$ COMPOSITE SHELL ELEMEHENT 1 1 1 I 0

000

I 0.10001

2III0000

2 0.1000I

$ SPECIFICATION FOR MATERIAL AXES ORIENTATION 1 2 0

0.0

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

"V"

102
$ ELEMENT 1

8

I.

O.

O,

O.

O,

O.

1.

28

1.

O.

O.

O.

O.

O.

1.

MATERIAL PROPERTIES

O. 1. I. O, O.0

O. O. O. O, O.0

O. O. O. O. O.0

O. O. O. O, O.0

O, O. O, O, O.0

O, O, O. O. O.0

1. O 1, O O, 0 O. 0 O, 0 O. 0 O.

I.

$ TEMPERATURE BOUNDARY CONDITION DATA 1 I 1 I I0, 1 2 1 2 I0, 2 t 2 I I0, 2 2 2 2 10. 3 I 3 I 10. 3 2 3 2 10. 4 I 4 1 I0. 4 2 4 2 I0. 5 I 5 I I0. 5 2 S 2 10. $ NODAL FORCE RCCELERRTIOH/ELEMEHT HEAT 56789

10

11

12

13

14

15

16

17

18

19

2O

21

22

23

24

25

26

27

28

29

30

31

32

-I

I.O

I .O 2 .O 3 .0 4 .O

.0

.0

.0

.0

.0

.0

.0

.0

.0

.O

.0

.0

.0

.0

.0

.0

.0

.O

.0

.0

.O

.0

.0

.0

.0

1.0

1.0

1.0

1, O. 3.0

O, O. O,0

O. O. O,0

O. O. O,O

O, O. O.O

O, O. O. O.

TRANSFER DATA

0.0 O,O

0.0 0,0

0.0 0.0

0.0 0_0

0.0 0.0

O.O O.O

O,O 0.0

10.0 O.O

0.0 0.0

0.0 0.0

0.0 0.0

O.O O.O

0.0 0.0

0.0 0.0

0.0 0.0

10,0 O,O

0,0 0,0

0,0 0,0

0,0 0,0

0,0 O,O

0,0 O.O

0,0 0,0

O,O 0,0

10,0 0.0

O,O 20,0

O,O 0,0

0,0 20,0

0,0 0.0

0,0 20.0

0,0 0.0

0.0 20.0

10,0 0,0

$ INCREMENTAL TIME DATA FOR DYNAMIC RESPONSE ANALYSIS

0.05 20

0,05 60

103
STARS-SOLIDSHEAT-TRANSFERoutputsummary:table25showstheresults.

Table25.Heat-transferanalysisresultsof a square

platewith transientheating.

Temperature

Node Time = 1.0 Time = 4.0

1 10.0000 10.0000

2 10.0000 10.0000

3 10.0000 10.0000

4 10.0000 t0.0000

5 10.0000 10.0000

6 12.4740 8.1250

7 12.5685 8.1250

8 12.9048 8.1250

9 13.6278 8.1250

10 15.1516 8.1250

11 14.6934 6.2500

12 14.8553 6.2500

13 15.3559 6.2500

14 16.4015 6.2500

15 18.3025 6.2500

16 16.5866 4.3750

17 16.7153 4.3750

18 17.2313 4.3750

19 18.2784 4.3750

20 20.1826 4.3750

21 18.0622 2.5000

22 18.1970 2.5000

23 18.5183 2.5000

24 19.2186 2.5000

25 20.8599 2.5000

104
4.3.4 Composite Square Plate: Transient Heating

This problem repeats the problem in section 4.3.3 with composite material (fig. 42), and the solution

results are given below.

X Ta, h a

 4)4)4)4

_ _ __ 15_2 ._1

1 2 3 4

_lnsulated

Tedge _--_1 x 2 970329

L

(a) Plate model.

2O

T a

L

_- t

t=l

Q qs

10

(b) Pulse heating.

Figure 42. Composite square plate with transient heating.

"__ t

t=l

970330

Important data parameters:

Coefficient of conductivity, kx = 3.0

Coefficient of conductivity, ky = 1.0

Coefficient of conductivity, kz = 1.0

Internal heat generation rate, Q = 1.0

Heat flow rate, qs = 10.0

Convective heat transfer coefficient, ha = 3.0

Air temperature, Ta = 20

Edge temperature, Tedge = 10

Length, L = 1

Thickness, t of each layer = 0.0315

Time step, At = 0.05

Total time period for response = 4.0

105
STARS-SOLIDS HEAT-TRANSFER input data:

SHELL -4x4- composite eleient - Transient heat loading

25,32,2,44,0,0,2,4,6,2

0,0,0,2,10,0,0,0,0

|0,0,1,1,0,0,0,0

2,0,2,0,1,0,0,1,0,0

2,20,0,1675.,3.0,0,0

0,1,1,2

$ NODAL ORTR

1 -0.5 0.0 0.0 0 0 0 0

5 0.5 0.0 0.0 0 0 0 0

6 -0.25 -1.0 0.0 0 0 0 0

10 -0.25 0.0 0.0 0 0 0 0

11 -0.5 0.5 0.0 0 0 0 0

15 0.5 0,5 0.0 0 0 0 0

16 -0.25 0.0 0.0 0 0 0 0

20 -0.25 -1.0 0.0 0 0 O 0

21 -0.5 1 .0 0.0 0 0 O 0

25 0.5 1 .0 0.0 0 0 0 0

$ LOCAL-GLOBAL COORDINATE SYSTEM DATA

I 2

-1.0 -0.5 0.0 0.0

1,0 0.0 0.0 0.0

2 1

-1.0 -1.0 0.0 -1.5

-1.5 -1.5 0.0

$ ELEMENT CONNECTIUITY CONDITIONS

7 1 7 6 I 0 O 0

7 2 1 2 7 0 0 0

7 3 8 T 2 0 0 0

7 4 2 3 8 0 0 0

7 5 9 8 3 0 D 0

7 6 3 4 9 0 0 0

7 7 I0 9 4 0 0 O

7 8 4 5 10 0 0 O

7 g 12 II 6 0 0 0

7 I0 6 7 12 0 0 0

7 11 13 12 7 0 0 0

? 12 7 8 13 0 0 0

T 13 14 13 O 0 0 0

7 14 8 9 14 0 0 0

7 15 15 14 9 0 0 0

7 16 9 10 15 0 O 0

7 17 17 16 II 0 O 0

7 18 11 12 17 0 0 0

7 19 18 17 12 0 0 0

7 20 12 13 18 0 0 0

7 21 19 18 13 0 0 0

7 22 13 14 19 0 0 0

7 23 20 19 14 0 0 0

T 24 14 15 20 0 0 0

7 25 22 21 16 0 0 0

7 26 16 17 22 0 0 O

7 27 23 22 17 O 0 O

7 28 17 18 23 0 0 O

7 29 24 23 18 0 0 0

7 30 18 19 24 0 0 0

? 31 25 24 19 0 0 0

T 32 19 20 25 0 0 0

$ COMPOSITE SHELL ELEMEflEHT

I 2 I 2 0 0 0 0

I 0.0315 3

l 0.0315 I

2 2 t 2 0 0 0 0

I 0.0315 3

I 0.0315 3

3 2 I 2 0 0 0 0

I 0,0315 4

I 0.0315 4

4 2 I 2 0 0 0 0

1 0.0315 2

1 0.0315 2

5 2 I 2 0 0 0 0

2 0.0315 I

2 0.0315 I

6 2 I 2 0 0 0 0

I 0,0315 I

I 0.0315 I

-I .0

O,O

-I ,0

0 I

0 I

0 I

0 I

0 I

0 I

0 I

0 I

0 2

O 2

0 2

0 2

0 2

0 2

0 2

0 2

0 3

0 3

0 3

0 3

0 4

0 4

0 4

0 4

0 5

0 6

0 5

0 6

0 5

0 6

O 5

0 6

0 0 I 0 0

0 0 1 0 1

0 0 2 0 0

0 0 2 0 1

O 0 I 0 0

0 0 I 0 1

0 0 0 0 0

0 0 0 0 I

0 0 I 0 0

O 0 I 0 I

0.0

1_0

0.0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

O 0 0 0 0

0 0 0 0 O

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

O 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

106
$ SPECIFICATION FOR MATERIAL AXIS ORIENTATION 1 2 0

0.0

220

0.7854 3

20

1.5708 4

20

2,3562

$ ELEMENT MATERIAL PROPERTIES t 8

3. O. 1. I.

O_ O. O. O.

O. O. O. O.

O. O, O. O,

O. O, O. O,

O, O. O. O.

1, 1,

20

3.

O.

O.

O,

O.

O,

1.

O, 1, 1.

O, O. O.

O, O. O,

O. O. O.

O. O. O.

O. O, O.

1,

$ TEMPEARTURE OOUHDARY CONDITION DATA I I I I 10. I 2 I 2 10. 2 I 2 I 10. 2 2 2 2 10. 3 I 3 I 10. 3 2 3 2 I0. 4 I 4 I I0. 4 2 4 2 I0. S I 5 I I0. S 2 S 2 10. $ MODAL FORCE ACCELERATION/ELEMENT HEAT TRAMSFER OATR

1.0

I23456?89

I0

11

12

13

14

15

16

17

18

19

2O

21

22

23

242

25

26

27

28

29

3O

31

32

-I

$

.0 0.0 0.0

.0 0,0 0,0

.0 0.0 0,0

.0 0,0 0,0

.0 0,0 0,0

.0 0.0 0.0

.0 0.0 0,0

.O 10.0 0.0

.0 0,0 0.0

.0 0.0 0.0

.0 0,0 0,0

.0 0,0 0,0

.O 0.0 O,O

.0 0.0 0.0

.0 0,0 0.0

1.0 I0.0 0.0

1.0 0.0 0.0

1,0 0.0 0.0

1.0 0.0 0,0

1,0 0,0 0,0

1.0 0.0 0.0

1,0 O.O O.O

1.0 O.O 0.0

1,0 I0,0 0.0

1.0 0,0 20.0

1.0 0,0 0.0

1,0 0_0 20,0

1.0 0,0 0.0

1.0 0.0 20,0

1.0 0,0 0,0

1,0 0,0 20.0

1.0 10,0 0.0

INCREMENTAL TIME ORTR FOR OYflRMIC

O,OS 20

0,05 60

RESPONSE ANALYSIS

O.

O.

O.

O.

O,

O,

O.

O,

O.

O.

Q,

O.

00000O

O,

O,

O.

O.

O,

O,

107
STARS-SOLIDS HEAT-TRANSFER output summary: table 26 shows the results.

Table 26. Heat-transfer analysis results of a composite square plate with

transient heating.

Temperature

Time = 1.0 Time = 4.0

Node Top Bottom Top Bottom

1 10.0000 10.0000 10.0000 10.0000

2 10.0000 10.0000 10.0000 10.0000

3 10.0000 10.0000 10.0000 10.0000

4 10.0000 10.0000 10.0000 10.0000

5 10.0000 10.0000 10.0000 10.0000

6 12.5207 12.5276 8.0513 8.1142

7 12.5298 12.3328 8.2472 8.1142

8 12.6465 12.4670 8.3308 8.2436

9 13.0094 12.8265 8.4126 8.3416

10 13.8595 13.4883 8.5948 8.3604

11 13.8247 13.8107 6.9806 6.9805

12 13.7669 13.8069 7.1627 7.1480

13 13.9385 14.0073 7.2813 7.2948

14 14.4600 14.5245 7.4240 7.4280

15 15.4611 15.5969 7.5932 7.6121

16 15.3499 15.3530 5.5599 5.5594

17 15.1669 15.1641 5.7781 5.7804

18 15.2786 15.2635 5.9394 5.9396

19 16.6615 15.6458 6.0931 6.0905

20 16.3046 16.2685 6.2944 6.2907

21 17.2782 17.2771 3.2639 3.2643

22 17.3640 17.3634 3.3176 3.3171

23 17.4679 17.4722 3.3927 3.3919

24 17.7457 17.7525 3.4643 3.4648

25 18.3890 18.4030 3.5143 3.5162

4.4. STARS-SOLIDS Heat-Transfer (Nonlinear Analysis)

In this section, the input data and relevant outputs of typical nonlinear heat-transfer test cases are

provided in detail. The input data are prepared in accordance with the procedures described in section 3

and are defined in consistent unit form.

108
4.4.1 Cooling Fin: Radiation Boundary Condition

A nonlinear steady-state radiation analysis of a cooling fin (fig. 43) was performed using heattransfer line elements. The results are given below.

y Radiation

w../_l 2 3 4 s s T . 9

Tw '_

Figure 43. Cooling fin with radiation.

_X

970331

Important data parameters:

Coefficient of conductivity, k = 132.0

Wall temperature, Tw = 1500

Length, L = 1

Area, A = 0.001365

Stefan-Boltzmann constant, o = 0.1713 x 10-8

Emissivety, E = 0.6

STARS-SOLIDS HEAT-TRANSFER input data:

RADIRTION HEAT TRANSFER - TRUSS

10,8,1,11,1,0,0,0,0,0

0,0,0,1,1,0,0,0,0

10,0,0,1,0,0,0,0

2,0,1 ,0,0,0,0, 1,0,0

$ NODAL DATA

I 0.0

2 0,125

3 0.250

4 0,375

5 0.500

6 0.625

7 0,750

8 0.875

9 I ,000

10 0,0

$ ELEMENT CONNECTIVITY

I

2

3

4

5

6

7

8

0,0 0.0 0

0.0 0.0 0

0.0 0,0 0

0.0 0,0 0

0,0 0.0 0

0,0 0,0 0

0.0 0,0 0

0,0 0.0 0

0,0 0,0 0

50,0 0,0 1

1 2 10 0 0 0 0 0

2 3 10 0 0 0 0 0

3 4 I0 0 0 0 0 0

4 5 10 0 0 0 0 0

5 6 10 0 0 0 0 0

6 7 10 0 0 0 0 0

7 8 I0 0 0 0 0 0

8 9 I0 0 0 0 0 0

$ LINE ELEMEHT BASIC PROPERTIES

I 0.001365 0. 13091

$ ELEMENT MATERIAL PROPERTIES

I 6

10,5 0,0 0

0,6 0.0 0

$ TEMPERATURE BOUNDARY COHDITION DATA

1 I t I 1500

O,O 0.0

0.0

0.0 0,1713E-8

109
STARS-SOLIDSHEAT-TRANSFERanalysisresults:

HOORL TEMPERflTURE

NODE

EXT INT TEM-SUR ! TEM-SUR 2 TEM-SUR 3 TEM-SUR 4 TEM-SUR 5 TEM-SUR 6

1 I .150000E+04 .O00000E+O0 .OOO000E+O0 .OOOOOOE+DO ,O00000E+O0 .OOOOOOE+O0

2 2 .105848E+04 ,OOOO00E+O0 .OOO00OE*OO .OOO00OE+O0 .DOOOOOE+OO .OOOOOOE+O0

3 3 ,850319E+03 .OOOOOOE+O0 .OOOO00E+O0 .O000OOE+OO .OO000OE+OO .O00OOOE+O0

4 4 ,727245E÷03 .O0000OE+O0 .ODOOOOE*OO ,OOO000E*O0 ,OOOO00E+O0 .OO0000E+OO

5 5 .647702E+03 .OOOO00E+OO .OOOO00E+OO O00OOOE+O0 .O00OOOE*O0 ,OOO000E+O0

6 6 .594974E+03 .OO0000E+O0 .OOOOOOE+OO O00000E*OD .O000OOE+OO .OO0000E+OO

7 7 .561119E.03 ,OOO00OE+O0 .OOOOOOE+O0 O00OOOE+O0 ,O000OOE+OO .OOO00OE*OO

O O .542098E+03 .O00000E*O0 .OO00OOE*O0 O00000E+O0 .O0000OE*OO .OOOOOOE÷OO

9 9 ,535953E*03 ,O0000OE+O0 ,OOOOOOE*OO OOOOOOE*OO ,OOO000E+O0 .OOOOOOE*OO

10 10 .OOOOOOE+OO .O000OOE+O0 .OOOOOOE+O0 OOOOOOE+OO .O000OOE*O0 .OOO00OE*OO

v

4.4.2 Three-Dimensional Box: Radiation Boundary Condition

Figure 44 shows a three-dimensional box that is characterized by orthotropic material. The results of

a nonlinear steady-state radiation heat-transfer analysis of the problem are presented herein.

Z

?

Radiation

±

0.5

i

0.5

T

L

970332

Figure 44. Three-dimensional box with radiation.

Important data parameters:

Length, L = 1.0

Stefan-Boltzmann constant, a = 0.1713 x 10--8

Emissivity, e = 0.6

Material 1:

Coefficient of conductivity, k

kxx = 10.5

kyy = 10.5

kzz = 10.5

thickness, t = 0.5

Material 2:

Coefficient of conductivity, k

kxx = 2.1

kyy = 2.1

kzz = 2.1

thickness, t = 1.0

110
STARS-SOLIDSHEAT-TRANSFERinput data

RADIATION HEAT TRANSFER - COMPOSITE BOX

4,2,3,44,0,0,0,1,1,3

1,0,0,1,0,0,0,0,0

10,0,0,1,0,0,0,0

2,0,2,0,1,0,0,1,0,0

$ NODAL DATA

1 O.OO00 O.OOO0 O,OOOO 0

2 2.0000 0.0000 O.OOOO 0

3 O.OOO0 2.0000 O.OOO0 0

4 2.0000 2.0000 O.OOO0 0 0

$ ELEMENT CONNECTIUITY

? I 1 2 3 0 0 0 0

7 2 4 3 2 0 O 0 0

$ COMPOSITE SHELL ELEMENENT

1 3 3 1 I 0 0

3 ,50000

2 1.0000

I .50000

$ SPECIFICATION FOR MATERIAL AXES ORIENTATION

1 2 0

0.0

$ ELEMEHT MATERIAL PROPERTIES

I 8

10,5 0

O. 0

O. 0

O.

O.

O.

O,

2 8

2,1

O.

O,

O,

O,

O,

O,

3 8

10,5

O,

O.

O,

O,

O,

O,

10.5

O,

I000,

0 O.

0 O.

0 O,

0

0, 2,1

0, O,

0, O,

0, O.

0. 0,

0, 0.

0,

O, 10.5

O. O,

O. O.

O. O,

O. O,

0, O.

O,

$ INITIAL HODRL TEMPERATURE DATA

I 4 800.0

2 4 800.0

3 4 800.0

4 4 800.0

-I

0 0 0 I I 0 0 O

0 0 O I I 0 0 0

O 0 0 I I 0 0 0

0 0 I I 0 0 0

t I 0 0 O 0

I I 0 0 O 0

10.5 0. 0, 0,

0. 0, 0. 0,

0, O, 0, 0,

0. O. 0, 0,

O. O. 0, O,

O. O, 0. O,

2.1 O, O, O,

O, O, O, O.

O, O, O, O.

O, O, O, O.

O, O. O, O.

O, O. O, O.

10,5 O. O, O.

O, O, O, O.

O. O, O, O,

O, O, O. O,

O, O, 0.1713E-8 O,

O. 0,6 O. O,

STARS-SOLIDS HEAT-TRANSFER analysis results:

NODE

EXT INT TEM-SUR I TEM-SUR 2 TEM-SUR 3 TEM-SUR 4 TEM-SUR 5 TEM-SUR 6

I I ,156460E,04 ,151698E÷04 .I04079E+04 .99316AE+03 ,0OOOOOE+00 ,OO00OOE*O0

2 2 ,156460E+04 ,151698E÷04 .I0407gE+04 .993168E+03 ,O00000E*O0 ,O00000E+O0

3 3 ,156460E+04 ,151698E+04 .I04079E+04 .993168E÷03 .O00000E÷O0 ,ODOOOOE+00

4 4 .156460E+04 .151698E+04 .104079E+04 .093168E÷03 .O00000E+O0 .OOOOOOE+O0

4.4.3 Composite Square Plate: Radiation Boundary Condition

A radiation heat-transfer analysis of a composite square plate (fig. 45) with a specified temperature

was performed. Table 27 shows the results.

111
X

-F

L

_yl _-- Insulated

25

/: "_ '!i !i'_ii , ,ii i _'

-_=1000 _ insulated I x 2

Radiation

10

970333

Figure 45. Composite square plate with radiation.

Important data parameters:

Coefficient of conductivity, kx

Coefficient of conductivity, ky

Coefficient of conductivity, kz

Length, L

Thickness of each layer, t

Temperature, T

Emissivity, e

Stefan-Boltzmann constant, (_

= 3.0

= 1.0

= 1.0

= 1

= 0.0315

= 1000

= 0.6

= 0.1713 x 10-8

v

STARS-SOLIDS HEAT-TRANSFER input data:

SHELL -4x4- composite element - Rodiotion

25,32,2,44,0,0,2,8,9,2

O,O,O,l,lO,O,O,O,O

10,0,0,1,0,0,0,0

2,0,2,0,1,0,0,1,0,0

$ NODAL DATA

I -0.5 0,0 0.0 0 0 0 0 0 O 1

5 0.5 0,0 0.0 0 0 0 0 0 0 I

6 -0.25 -I .0 0,0 0 0 0 0 0 0 2

10 -0.25 O.O O.O 0 0 0 0 0 0 2

11 -0.5 0.5 O.O 0 0 O 0 0 0 1

15 0.5 0.5 O.O 0 0 0 0 0 0 1

16 -0.25 O.O O.O 0 0 0 0 O 0 0

20 -0.25 -I .0 0.0 O O 0 0 O 0 O

21 -0.5 1.0 0.0 0 0 0 0 0 0 1

25 0.5 1.0 0.0 0 0 0 0 0 0 I

$ LOCAL-GLOBAL COORDINATE SYSTEM DATA

I 2

-I .O -0.5 0.0 O.O -I .0 0.0

1.0 O.O 0.0 0.0 O.O 1.0

2 I

-I .0 -1,0 0,0 -1 ,5 -I ,0 0.0

-I .5 -I ,5 0.0

$ ELEMENT CONNECTIVITY CONDITIONS

7 1 I ? 6 0 0 0 0 I I 0

7 2 7 I 2 0 0 0 0 1 I 0

7 3 2 8 7 0 0 0 O I I 0

T 4 8 2 3 0 0 0 O 1 I 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

112
7

53

7G9

774

?8 10

796

7 10 12 7 11 7 ? 12 13 7 13 8 7 14 14 7 15 9 7 16 15 7 17 11 7 18 17 ? 19 12 7 20 18 7 21 13 7 22 19 7 23 14 7 24 20 7 25 16 7 26 22 7 27 17 7 28 23 7 29 18 T 30 24 7 31 19 7 32 25

$ COMPOSITE SHELL I 2 I 0.0315 I 0,0315 2 2 2 0.0315 2 0,0315 3 2 I 0.0315 I 0.0315 4 2 2 0,0315 2 0,0315 5 2 I 0,0315 I 0,0315 6 2 I 0.0315 I 0.0315 7 2 2 0,0315 2 0,0315 8 2 l 0,0315 1 0,0315 9 2 2 0.0315 2 0.0315 $ SPECIFICATION I 2 0

0.0

220

O, 7854 3

20

I ,5708 4 2

0

2.3562 5

20

3,1416 6

20

4.7120 7

20

5.4980 8

20

3.g260

$ ELEMENT MATERIAL I 8

3,

O,

O,

O.

O.

O.

I,

28

3,

0,

O.

O.

O.

O.

I.

98000

34000

109000

45000

12 110O0

67000

13 12000

78000

14 13000

89000

IS 14000

9 10000

17 16000

tl 12000

18 17000

12 13000

19 10000

13 14000

20 19000

14 15000

22 210O0

16 17000

23 22000

17 18000

24 23000

18 19000

25 24000

19 20000

ELEMENEHT 2 0

000

272

0000

2?2

0000

222

0000

222

0000

332

0000

II2

0000

20000

772

0000

77

FOR MATERIAL AXIS ORIENTATION

PROPERTIES

O. I. I. O,0 O,

O. O. O. O, O. O.

O. O, O. O, O. O.

O. O, O, O, O. O.

O. O, 0, O. O, O.

O. O. O, O. O, O,

I, 0 I, 0 O, 0 O, 0 O, 0 O, 0 0.6 I

I,

O,

O,

O,

0.1713E-8

O,

O,

O.

O,

O.

O,

O.

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

I13
$ TEflPEAATUAE BOUHDRRY COHOITION DATA

I I I I 1000.

I 2 I 2 1000,

6 I 6 I 1000.

6 2 6 2 1000.

11 I 11 I I000,

11 2 11 2 1000.

16 I 16 I 1000.

16 2 16 2 I000.

21 I 21 I 1000.

21 2 21 2 1000,

k

STARS-SOLIDS HEAT-TRANSFER output summary: table 27 shows the results.

Table 27. Heat-transfer analysis results for a

composite plate with a radiation boundary

condition.

Node Top

Temperature

Bottom

1 1000.00 1000.00

2 928.91 930.53

3 866.21 867.33

4 805.83 806.62

5 769.79 771.48

6 1000.00 1000.00

7 940.31 941.10

8 878.29 878.84

9 816.77 818.55

10 762.80 759.63

11 1000.00 1000.00

12 939.80 938.08

13 877.30 875.68

14 814.73 812.71

15 754.18 754.65

16 1000.00 1000.00

17 938.23 938.40

18 875.09 875.52

19 808.93 809.36

20 746.37 746.86

21 1000.00 1000.00

22 938.15 938.12

23 875.23 875.10

24 811.48 811.30

25 761.17 760.90

114
4.4.4 Three-Dimensional Box: Transient Heating with a Radiation Boundary Condition

The three-dimensional box described in section 4.4.2 is used for this sample problem and is

subjected to transient loading (fig. 46). The results of a nonlinear transient heat-transfer analysis for a

composite box with radiation at the top and transient heat flow at the bottom are presented herein.

q$

1000_

t=60

97033.4

Figure 46. Three-dimensional box pulse heat flow.

STARS-SOLIDS HEAT-TRANSFER input data:

RADIATION HEAT TRANSFER - COMPOSITE BOX

4,2,3,44,0,0,0,1,1,3

0,0,0,I,0,0,0,0,0

10,0,1,1,0,0,0,0

2,0,2,0,1,0,0,1,0,0

1,10,0,1300.0,0.0,0

0,1,1,2

$ HODAL DATA

I 0.0000 0.0000 0.0000 0 0

2 2.0000 0.0000 0.0000 0 0

3 0.0000 2.0000 0.0000 0 0

4 2.0000 2.0000 0.0000 0 0

$ ELEMEHT CONNECTIUITY

? 1 I 2 3 0 0 0 0

? 2 4 3 2 0 0 0 0

$ COMPOSITE SHELL ELEMENENT

I 3 3 I I I 0 0

3 .50000 1

2 1.0000 1

I .50000 I

$ SPECIFICATION FOR MATERIAL AXES ORIENTATION

1 2 0

0.0

$ ELEMENT MATERIAL PROPERTIES

1 B

10.5 O.

O. O.

O. O.

O. 0

O. 0

O. 0

0.038 658

2 0

2.1 0

O. 0

O. O.

O. O.

O. O.

O. O.

0,038 658.

10.5 10.5 O.

O. O. O.

O. O. O.

O, O. O.

O. O. 0

O. O. 0

2.1

O.

0

0,

0,

O.

2,1

0,

0,

0.

0,

0,

0 0

0 0

o 0

0 0

I 1

t 1

0

O.

O.

O.

O.

O.

1 I 0 0 0

I I 0 0 0

I I 0 0 0

I I 0 0 0

0 0 0 0

0 0 0 0

O. O.

O. O.

0. O,

O. O.

O, O,

O. O.

115
:3 8

10.5 O. 10.5 10.5 O. O.

O. O, O. O. O. O.

O, O. O. O. O. O.

O. O. O. O. O. O.

O, O, O. O. O.O. 1713E-8

O, O. O, O, 0,6 O.

0.038 656.

$ ELEMEHT HEAT TRANSFER DATA

60.0

t 6 0.0 I000.0 0.0

2 6 0.0 I000.0 0.0

-1

$ INCREMENTAl TIME DATA FOR RESPONSE CALCULATION

1 .0 60

1 .0 200

O,

O,

O.

O.

O.

O.

STARS-SOLIDS HEAT-TRANSFER output summary: table 28 shows the results.

Table 28. Nonlinear transient heat-transfer analysis

results for a composite box with a radiation

boundary condition.

Temperature

Surface Time = 60 Time = 260

1 1255.12 447.864

2 1211.06 447.632

3 868.263 438.458

4 841.579 436.887

4.4.5 Two-Dimensional Strip: Transient Heating with a Radiation Boundary Condition

A radiation heat-transfer analysis of a two-dimensional strip (fig. 47) with a transient heat flow was

performed. Table 29 shows the results.

12 13 14 15 16 17 18 19 20 21 22

__-

1 2 3 4 5 6 7 8 9 10 11

J_ L _I

(a) Strip model.

Radiation

970335

Figure 47. Two-dimensional strip with transient heat flow and radiation boundary condition.

116
qll

1000

Important data parameters:

t= 20

(b) Pulse heat flow.

Figure 47. Concluded.

Coefficient of conductivity, k = 10.5

Length, L = 1.0

Thickness, t = 0.1

Emissivity, E = 0.6

Stefan-Boltzmann constant, o = 0.1713 x 10-8

Density, p = 658

Capacity, c = 0.038

r

970336

STARS-SOLIDS HEAT-TRANSFER input data:

TRANSIENT HOHLIHEAR (RROIATION) HEAT TRANSFER - 2-D STRIP

22,20,2,44,0,0,0,1,2,1

0,0,0,1,0,0,0,0,0

10,0,1,1,0,0,0,0

2,0,2,0,1,0,0,1,0,0

1,10,0,1300,0.0,0

0,I,1,2

$ HODAL DATA

I 0.0000 0,0000 0.0000 0 0

2 0,1000 0,0000 0,0000 0 0

3 0.2000 0.0000 0.0000 0 0

4 0.3000 0.0000 0,0000 0 0

5 0.4000 0.0000 0,0000 0 0

6 0.5000 0.0000 0,0000 0 0

7 0.6000 0.0000 0.0000 0 0

8 0.7000 0,0000 0,0000 0 0

9 0,8000 0,0000 0,0000 0 0

10 0,9000 0,0000 0,0000 0 0

11 1,0000 0,0000 0,0000 0 0

12 0.0000 0.1000 0,0000 0 0

13 0.I000 0.1000 0.0000 0 0

14 0.2000 0.1000 0,0000 0 0

15 0.3000 0.1000 0.0000 0 0

16 0.4000 0.1000 0.0000 0 0

17 0.5000 0.1000 0,0000 0 0

18 0.6000 0,1000 0.0000 0 0

19 0.7000 0.1000 0.0000 0 0

20 0.8000 0.1000 0.0000 0 0

21 0,9000 O,lODD 0,0000 0 0

22 1.0000 0.1000 0,0000 0 0

117
$ ELEMENT CONNECTIVITY

7 I I 2 13

7 Z 2 3 14

7 3 3 4 15

? 4 4 5 16

? 5 5 6 17

? 6 6 ? 18

? ? ? 8 Ig

? 8 8 9 20

? 9 9 I0 21

7 I0 10 II 22

7 11 13 12 I

7 12 14 13 2

7 13 15 14 3

7 14 16 15 4

? 15 17 16 5

7 16 18 17 6

7 17 19 18 ?

7 18 20 19 8

7 19 21 20 9

7 20 22 21 10

$ COMPOSITE SHELL ELEMENT

I 1 I 1 0

I ,10000 1

2 I I I 0

2 .I0000 1

$ SPECIFICATION FOR MATERIAL

I 2 0

0.0

$ ELEMENT MATERIAL PROPERTIES

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

O 0 0 0

0 0 0 0

O 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0

0 0 0

AXES ORIENTATION

I 8

10.5 O, 10.5 10,5 O.

O. O, O, O, O.

O. O, O, O. O.

O, O, O, O, O.

O. O, O, O. O.

O, O, 0, O, O.

0.038 658

2 8

10.5 O, 10.5 10.5 0,

O. O, O, O, O,

O. O, O, O, O,

O, O. O, O, O,

O. O, 0.1713E-8 0, O,

O. 0,6 O, O, O.

O,03B 658

$ ELEMENT HEAT TRANSFER DATA

20,0

II 2 0.0

-I

I000.0

$ INCREMENTAL TIME DATA FOR RESPONSE CALCULATION

0.2 I00

0,2 500

0.0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

O 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

O,

O.

O,

O,

O,

O,

O_

O,

O.

O,

O,

O,

118
STARS-SOLIDSHEAT-TRANSFERoutputsummary:table29showstheresults.

Table29.Nonlineartransientheat-transferanalysis

resultsfor atwo-dimensionalstripwith a radiation

boundarycondition.

Node

Temperature

Time = 20 Time = 120

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

785.204

775.962

767.581

759.767

752.689

746.294

740.585

735.559

731.208

727.530

724.538

785.072

776.128

767.529

759.777

752.687

746.294

740.585

735.558

731.205

727.516

724.461

410.808

410.793

410.751

410.682

410.586

410.461

410.310

410.130

409.924

409.689

409.427

410.805

410.792

410.751

410.682

410.586

410.461

410.310

410.130

409.924

409.690

409.430

119
5. STARS-AEROS AND STARS-ASE MODULE DESCRIPTIONS: LINEAR

AEROELASTIC AND AEROSERVOELASTIC ANALYSIS

The aeroelastic and aeroservoelastic modules (fig. 2) are recent additions to the original STARS

program 1 that are capable of predicting related stability of such structures as aircraft and spacecraft.

Thus, when the vibration analysis is performed using the STARS-SOLIDS module, the program continues to determine flutter and divergence characteristics as well as open- and closed-loop stability analyses, as desired. Figure 48 shows a typical feedback control system. Some details of the current analysis

techniques have previously been provided. 15,16

Section 5.1 gives the detailed numerical formulation in connection with the present aero-structuralcontrol analysis. The unsteady aerodynamic forces for supersonic flow are computed by a constant

pressure method, 17 and the doublet lattice method 18,19 is used for the subsonic case. Both k and p-k

stability (flutter and divergence) solution procedures are available to the user.

For the ASE analysis, the aerostructural problem is recast in the Laplace domain when the generalized aerodynamic forces are curve-fitted using Pad6 and least-squares approximations, thereby yielding

the state-space matrices. 20 Such matrices can then be augmented by analog elements such as actuators,

sensors, prefilters, and notch filters and by the analog controller. The associated equivalent-open-loop

(loop-gain) or open-loop transfer function is obtained by standard procedure. The closed-loop

formulation is similarly derived by appropriately taking into account the feedback equation. The system

frequency responses are obtained from the appropriate transfer matrices. Associated modal damping and

frequency values can also be derived by solving the eigenvalue problem of the augmented state-space

plant dynamics matrix.

In the case of a digital controller, a hybrid equivalent open-loop or closed-loop transfer function is

achieved by suitably combining the controller, the open-loop transfer function of the original analog

system of the plant, and other analog elements. Frequency responses are then obtained in a routine manner. The modal damping and frequency values are obtained by transferring the augmented analog statespace plant dynamics matrix from its usual Laplace (s) plane to the digital z plane, adding the same to

the corresponding matrix for the controller, and solving the associated eigenvalue problem.

Furthermore, the open-loop stability analyses (flutter and divergence) can also be effected with or

without the controller (analog or digital). Effecting the analyses is achieved by solving eigenvalue

problems of the appropriately augmented and transformed, as the case may be, plant dynamics matrix

for a number of reduced frequency values and noting the change in sign of the real part of the

eigenvalues. Such a solution without a controller can be compared with the aeroelastic analysis using

the k and p-k methods, whereas the relevant solution in the presence of a controller is useful for

comparing relevant flight test results of modern, high-performance, unstable aircraft.

120
DM

Gy

Figure 48. Feedback control system

Summing junction outputs :

u - r-Gy

X - AX+Bu

y -- CX+Du

970337

5.1 Numerical Formulation for Linear Aeroelastic and Aeroservoelastic Analysis

In the numerical formulation presented here, structural discretization is based on the finite-element

method, whereas the panel methods are adopted for computation of unsteady aerodynamic forces. The

more specialized matrix equation of motion of such structures relevant to the current analysis has the

form

Mq + Cq + Kq + qAe(k)q = P(t) (36)

in which the relevant terms are defined as follows:

M = inertia matrix

C - damping matrix

K - elastic stiffness matrix

= dynamic pressure 1/2pV 2 (p and V are the air density and true airspeed, respectively)

k = reduced frequency 03b/V (03 and b are the natural frequency and wing semichord length,

respectively)

Ae(k) = aerodynamic influence-coefficient matrix for a given Mach number (Moo) and a set of ki

values

q -- displacement vector

P(t) = external forcing function

s = Laplace variable (= "*1 03, i* being .¢C-i-)

A solution 1 of the related free-vibration problem

I_rl + qQ(k)rl = P(t)

M/I + kq = 0 (37)

yields the desired roots, 03, and vectors, _. Next, by applying a transformation

121
q = a,n (38)

to equation (36) and premultiplying both sides by (pT, the generalized equation of motion is derived as

1VIfl+ C/1 + I_B + qQ(k)B = P(t) (39)

in which 1VI=oTM_, and so forth. The modal matrix _=[(Pr _e _8] and the generalized

coordinate rl = [_r Be rib ] incorporate rigid-body, elastic, and control-surface motions, respectively.

By expressing the generalized aerodynamic force matrix Q(k) as Pad6 polynomials 15 in

i*k (=i* o_b/V = sb/V), equation (39) results in

i*k i*k

i,k+_l A 3-t i*k + _2 A 4 +

Q(k) =A 0 +1 kA 1 + (i*k)2A2 + --

where 13j are the aerodynamic lag terms (assuming j = 1, 2), and

i*k k 2 i*k_j

i*k +_3j - k 2 +[3 2 + k 2 +_2

(40)

(40(a))

Further, separation of the real and imaginary parts in equation (40) yields

{_R(k) = (QR (k)- A0)

= -k2I +-----------_ I I A 3

A4

= SR (k),_

Qi(k)= QI(k) A1

k

_1 _2 I A 3

= 0 k2+_l 2I k2+_2 2 A4

= SI (k)._

in which for a small value of k = kl, the coefficients assume the following form:

A0 = QR (kl)

(41)

(41(a))

(42)

122
A1 = QI(kl) A3 A---&4 (42(a))

kl [_1 1_2

By substituting equation (42(a)) in equation (41(a)), the unknown coefficients A3 and A4 can be

determined; however, the resulting solution will be sensitive to the choice of _j. Conversely, if the

elements of the A1 matrix are replaced by measured damping coefficients without any lag terms, then

the solution will be insensitive to the 13jvalues.

Equations (41) and (41(a)), computed for a number of values of reduced frequencies ki, can be

combined as

QR(k2)

(_I(k2) SI(k2)

SR(kNF-1)

SI(kNF-I)

[A2] A3

A4

(43)

or

and a least-square solution

Q = sA, (44)

A = [S';SI-IsTQ (45)

yields the required coefficients A2, A3, and A4. This procedure may be easily extended for a larger

number of lag terms, if desired. Equation (39) may be rewritten as

I¢lq+c:/l+Rn+q[Aorl+& (sb) V

and collectinglikcterms givcs

q+A2_,-_- . [sb) ) 2 n+A3X I+A4X z+... ] = 0

+q[-Q-b)21 A 2 1]+qA3XI+qA4X2+... = 0

(46)

(47)

or

Also

Krl + C_ + Mf_ + qA3X 1 + qA4X 2 + . . . = 0 (48)

123
from which

Equations (48), (49), and (50) can be rewritten as one set of matrix equations,

or

from which

I' I! ° °

M -C -qA 3 -qA 4

I Xl = I -VI311 0

V

I X 2 I 0 --_- 1121

M'X' = K'X'

X' = (i_')-I K_K '

=RX'

Also, the state-space vector X' may be rearranged as

X"=[(1]r Tie l_r Tie

o]

and equation (53) may be partitioned as

Xl X2)(TI8 _8)]

[_]=[RI,, RI,,I] [uX] kRit,i RII,II

(49)

(50)

[:] Xl

X2

(51)

(52)

(53)

(54)

55)

where the first set of matrix equations denotes the plant dynamics, and the second set represents the

dynamics of control modes. In the case of plant dynamics, the state-space equations become

X = _,X + l_u (56)

in which the relevant matrices and vectors are defined as

,_, = plant dynamics matrix

124
U _

control-surface influence matrix

generalized coordinates in inertial frame

control-surface motion input into plant

and where the terms ._,X and 13u represent, for example, the airplane dynamics and the forcing function

on the airplane caused by control-surface motion, respectively.

Coordinate Transformation

To incorporate control laws and feedback, it is necessary to transform equation (56) from the Earthfixed (inertial) to the body-fixed coordinate system. Because no transformations are applied to elastic

and aerodynamic lag state vectors, a transformation of the form

X = "r21 (A'r 1 -'r3)x + "r2ll_u

= AX + Bu

in which

(57)

and so forth. T1 is the coordinate transformation matrix on order of 12 and yields the required statespace equation in the body-fixed coordinate system.

Determination of Sensor Outputs

The structural nodal displacements are related to the generalized coordinates by equation (38), and

the related sensor motion can be expressed as

qs = TsOrl

= CoX

(58)

where C O = [TsO 0 0 0] and in which Ts is an interpolation matrix. Similar relations can be derived

for sensor velocities and accelerations as

= ClX

(59)

where

CI = TsO 0

125
Equation (57) is next premultiplied by C1 to yield

c1X = C1AX + C1Bu

= C2X + D2u

and by adjoining equations (58) and (60), the following expression is obtained:

[qs]rcc [ ]

y =qs = o X+ 0 u

qs L 21 D2

or

(60)

y = CX + Du (61)

which is the required sensor output relationship. The matrices C and D signify output at the sensor

caused by body and control-surface motions, respectively.

Augmentation of Analog Elements and Controller

The complete state-space formulation for an aircraft incorporating structural and aeroelastic effects

is represented by equations (57) and (61). To conduct an aeroservoelastic analysis, it is essential to

augment such a formulation with associated analog elements (for example, actuators, sensors, notch

filters, and prefilters) along with the controller. Thus, the state-space equations of one such element can

be expressed as

X (62) (i) = A(i)x (i) + B(i)u (i)

y(i) = c(i)x(i) + D(i)u(i) (63)

which can be augmented to the original equations (57) and (61), as appropriate. Typically, for the case of

a connection from the plant output to the external input, the relevant formulation is as follows:

or

noting that U (1) = y. Also

[x]I X(i) = B(i)AC A(i)°lExl x(i) +E"I B(i) D [tl]

X(i ) = A(i)X(i ) + B(i)u

D

[y(Yi)l=[D(iC)c c(0i)][x(X)]+[o(i)D][ u]

(64)

(65)

or

126
Y(i) = C(i)X(i) + D(i)u

which is the new sensor output expression.

Any analog element, including a controller, can be augmented in a similar manner.

a typical feedback control system.

(66)

Figure 48 shows

For such a system, the three sets of relevant matrix equations are

X = AX + Bu (67)

y = CX + Du (67(a))

u = r - Gy (67(b))

where equation (67(b)) is the feedback equation.

(67(a)), and (67(b)), the following relationships are obtained:

Further, from equation (68)

By applying Laplace transformations to equations (67),

sX(s) = AX(s) + Bu(s)

y(s) = CX(s) + Du(s)

u(s) = r(s) - G(s)y(s)

X(s) = [sI - A]-IBu(s)

(68)

(68(a))

(68(b))

(69)

and the substitution of equation (69) into equation (68(a)) yields the required open-loop frequencyresponse relationship

y(s) = [C(sI- A)-IB + D]u(s) (70)

= H(s)u(s)

H(s) is the equivalent open-loop (loop-gain) transfer function with the analog controller, or the openloop transfer function without the controller. To obtain the closed-loop frequency-response relationship,

equation (70) is substituted in equation (68(b)), resulting in

u(s) = r(s) - G(s)H(s)u(s) (71)

or

u(s) = [I + G(s)H(s)] -1 r(s)

Again, substitution of equation (70) yields

(71(a))

127
y(s) = (I'I(s)[I + G(s)H(s)] -1)r(s) (71(b))

= I_I(s)r(s) (72)

in which l_I(s)is the desired closed-loop transfer function. The frequency-responses plots can be

A

obtained from the transfer matrices H(s) or H(s), as appropriate. Associated damping and frequency

values for the system for the loop-gain or open-loop case can also be calculated by solving the

eigenvalue problem of the relevant A matrix for various ki values and observing the changes in sign of

the real part of an eigenvalue.

In the presence of a digital controller, a hybrid approach 15 is adopted for the frequency-response

solution. Thus, if A', B', C', and D' are the state-space matrices associated with the controller, the

related transfer function is given by

G(z) = C'[zI-A']-IB ' +D' (73)

The frequency-response relationship for the hybrid analog/digital system can be written as

(74)

= G(s,T)H*(s,x,T)u(s) (74(a))

in which H(s) is the open-loop transfer function for the plant and other analog elements, [ZOH] is the

zero-order hold complex expression

r

and where H*(s) is now the equivalent open-loop (loop-gain) transfer function of the hybrid system. The

closed-loop frequency-response relationship can be obtained as before by using equations (74(a))

and (68(b)):

y(s) = {H*(s,x,T)[I+ G(s,T)H*(s,x,T)] -1 }r(s)

= I?/*(s,z,T)r(s) (75)

To compute the damping and frequencies, the analog plant dynamics matrix A is transformed into

the z plane by the standard discretization procedure, which is then augmented to the A' matrix. The

appropriate eigenproblem solution of the final matrix yields the required results, as before. The STARS

program has been extended to include capabilities representative of formulations presented in

this section.

128
6. DATA INPUT PROCEDURE

(STARS-AEROS and ASE)

Figure 49 shows the data input strategy for the entire ASE analysis procedure; section 3 describes the

input for the STARS-SOLIDS module. In the following, the data pertaining to the other related analyses

are given in the appropriate order, in which the STARS-AEROS module data input is compatible with

the program previously described. 18

FEM

modeling option

Direct data input

(Section 3 data)

Measured mode_ ....

input option /

Data input

to compute

generalized mass

Aerodynamic

data input

Data input

option for

mode selection

Data input for

ASE aerodynamic

curvefitting

Data input to

augment control

system

Data input for

frequency responses

_l PREPROCESSOR I v I

I so,,o,I

Vl AEROL I

[ CONVERT

"_]1 PADE

_-I CONTROL

[ FRESP

POSTPROCESSOR I

970338

Figure 49. ASE analysis data input scheme.

6.1 GENMASS Data (STARS-AEROS-GENMASS)

Purpose: Prepare genmass.dat data file.

Description: Computes a generalized mass matrix.

6.1.1 $ Job Description

Format (FREE)

129
6.1.2

°

2.

6.1.3

6.1.3.1

,.

2.

ISTMN, NLVN, GR

Format (215, El0.4)

Description:

Notes:

ISTMN

NLVN

GR

Generalized mass-matrix generation data.

= integer specifying the starting mode number

= number of laterally vibrating nodes

= gravitational constant

$ Laterally Moving Nodal Numbers Data

Format (FREE)

(LN(I), I = 1, NLVN)

Format (I5)

Description: NLVN number of nodes input data.

Notes:

(Required if NLVN > 0)

Input of a GR value is needed to convert generalized mass data into a generalized weight

acceptable to the AEROS module.

If direct STARS interpolation is used, then the LN refers to the nodes as defined in STARSSOLIDS (that is, the output vector, as defined in section 3.5.10 of the STARS manual).

3. Note:

The data are to be stored in the file genmass.dat.

6.2 AEROL Data (STARS-AEROS-AEROL)

Purpose: Prepare the aerodynamic data file.

Description: Computes unsteady aerodynamic forces by panel methods.

6.2.1 Job Title: 1:6 (six lines of title cards)

Format (FREE)

6.2.2 (LC(1), I = 1, 40)

Format (1015)

1. Description: Basic data parameters.

130
2. Notes:

LC(1)

LC(2)

LC(3)

LC(4)

LC(5)

LC(6)

LC(7)

LC(8)

LC(9)

LC(10)

= integer defining the flutter and divergence solution algorithm

= -1, p-k type of solution

= 0, pressure calculations only

= 1, k and state-space solutions

= 2, divergence analysis

= maximum number of vibration modes to be used in the analysis

0 < LC(2) < 50

= number of lifting surfaces

0 < LC(3) < 30, for the doublet lattice method or constant pressure method

number of reduced velocities (VBOs), used in the analysis

If LC(1) = -1, set LC(4) = 6

If LC(1) = 0 or 1, set 1 < LC(4) < 50

If LC(1) - 2, set LC(4) = 1

LC(4) and LC(13) apply to the reduced velocities described in sections 6.2.5

and 6.2.7

= number of air densities at which flutter and divergence solutions are to be

found

0 < LC(5) < 10

If LC(1) = 0, set LC(5) = 0

= print option for tested aerodynamic forces used to check the aerodynamic

force interpolation

= 1, print

= 0, no print

= print option for aerodynamic pressures

= 1, print data

= 0, no print

= print option for lift and moment coefficients

= 1, print data

= O, no print

= input frequency-independent additions to the aerodynamic matrix

= l, make additions

= O, no additions

= print option for a full set of interpolated generalized forces when used in k

solutions

= 1, print data

= 0, no print

131
LC(11)

LC(12)

LC(13)

LC(14)

LC(15)

LC(16)

LC(17)

LC(18)

LC(19)

indexof themodewhosefrequencyis to beusedin normalizingflutter

determinant

Frequencychosenmustbenonzero

Suggestedindexis 1

indexdefiningtheflutter-determinantformulation

1,for nonzerofrequencies[D = K-1 (M + AE)]

0, in presence of zero frequencies [D = (M + AE) -1 K]

where K = generalized stiffness matrix

M = generalized mass matrix

AE = aerodynamic force matrix

IfLC(1) - 0, set LC(12) = 0

index defining the interpolation of aerodynamic forces

0, no interpolation, compute at each input VBO

1, compute directly at only six VBOs, interpolate to others

IfLC(1) =-1, set LC(13) = 1

If LC(1) = 0 or 2, set LC(13) = 0

If LC(1) = 1, set LC(13) = 0 or 1, as desired

= not used..Set = 0

= index defining the velocity scale in the flutter solution output

= 1, use true airspeed, TAS

= 0, use equivalent airspeed, EAS

= index defining the addition of structural damping to the complex stiffness

matrix

= 1, add a single damping value to all modes

= -1, add an individual damping value to each mode

= 0, no damping added

= print option to display the number of iterations required to find each root in a

p-k solution

= 1, print

= 0, no print

= option for root extrapolation in a p-k solution

= 1, use root values at two previous velocities for initial estimation of a root

= 0, use root value at previous velocity as the root estimate

If LC(1) ;_ -1, set LC(18) = 0

= option for ordering of roots following a p-k solution

= 1, to perform ordering

= 0, no ordering required

If LC(1) _: -1, set LC(19) = 0

132
LC(20)

LC(21)

LC(22)

LC(23)

LC(24)

LC(25)

LC(26)

LC(27)

LC(28)

LC(29)

= print optionfortheiteratedrootsin ap-k analysisor intermediateresultsin a

k analysis

= 1, print

= O, no print

= index for aerodynamics

= 1, use the doublet lattice method or constant pressure method (subsonic and

supersonic Mach numbers, respectively)

= index defining the generation and storage of the aerodynamic influence

coefficients matrix

= O, compute and save

= 1, read precomputed values from a file

= print option for the input modal vector

= 1, print

= O, no print

= print option for the interpolated deflections and slopes of aerodynamic

elements

= 1, print

= O, no print

= number of modal elimination cycles

0 < LC(25) < 25

= index defining the additional flutter analysis

= 0, no additional cycles

> 0, perform additional flutter analysis cycles with stiffness variations applied to

a mode

0 < LC(26) < 20

= index of mode whose frequency and stiffness is to be varied for the LC(26)

cycles

If LC(26) = 0, set LC(27) = 0

print option for the modal eigenvectors

1, print

0, no print

If LC(1) = -1, the eigenvectors for the critical flutter root in a user-chosen

velocity interval are displayed

If LC(1) = 0 or 2, set LC(28) = 0

If LC(1) = 1, the eigenvectors for all roots between user-chosen VBOs and

real frequencies are displayed

= print option for physical vectors corresponding to modal eigenvectors

= 1, print

= 0, no print

133
6.2.3

.

2.

LC(30)

LC(31)

LC(32)

LC(33)

LC(34)

LC(35)

LC(36)

LC(37)

LC(38)

LC(39)

LC(40)

INV

Format (15)

Description:

Notes:

INV

= print option for the k solution flutter-determinant matrix analysis

= 1, print

= 0, no print

If LC(1) = -1 or 0, set LC(30) = 0

= index defining revisions to generalized mass matrix and modal frequencies

= 1, revise

= 0, no change

= index defining revisions to the generalized stiffness matrix

= 1, revise

= 0, no change

= index defining the type of aerodynamics

= 1, steady state

= 0, oscillatory

If LC(1) = 2, set LC(33) = 1

= not used. Set = 0

= not used. Set = 0

= not used. Set = 0

= print option for aerodynamic element geometric data associated with doublet

lattice and constant pressure methods

= 1, print

= 0, no print

If LC(21) _: 1, set LC(37) = 0

tape unit for an ASCII printout of generalized forces and associated

information. Suggest LC(38) = 99

= not used. Set = 0

= not used. Set = 0

Input vibration data location flag.

= integer defining the location of input

generalized masses

= 1, STARS-SOLIDS binary file

= 2, this input file

vectors, modal frequencies, and

_J

134
6.2.3.1 NMDOF

Format (15)

1. Description:

2. Notes:

NMDOF

Input vector degrees of freedom.

6.2.3.2

.

2.

6.2.3.3

I.

2.

6.2.3.4

(Required if INV = 2)

.

2.

6.2.3.5

total number of modal degrees of freedom used to define an input mode shape

0 < NMDOF < 1000

(QZ(I), I = 1, NMDOF)

Format (7E10.0)

Description:

Note:

LC(2) sets of NMDOF input deflections.

QZ(I)

NCARD

Format (I5)

Description:

Note:

NCARD

I, J, ww(I, J)

Format (215, El0.0)

Description:

I

J

WW(I, J)

Notes:

= principal out-of-plane deflection at point I of the input vector

Mass matrix specifications.

= Number of nonzero generalized mass matrix elements

(Required if INV = 2)

(Required if INV = 2)

(Required if INV = 2)

NCARD sets of data specifying nonzero generalized mass matrix elements.

= row index of the generalized mass matrix

= column index of the generalized mass matrix

= generalized mass (weight) matrix value, lbf

(OMG(1), I = LC(2))

Format (7El0.0)

1. Description:

2. Note:

OMG(I)

LC(2) modal frequencies.

(Required if INV = 2)

= modal frequency in proper order, Hz

135
6.2.4 BR, FMACH

Format (2E10.4)

1. Description: Reference values for aerodynamics.

2. Notes:

BR = reference semichord, in.

FMACH = reference freestrearn Mach number

If FMACH < 1.0, the doublet lattice method is used

If FMACH _> 1.0, the constant pressure method is used (LC(13) must equal 0)

6.2.5 (VBO(I), I = 1, LC(4))

Format (7F10.4)

(Required if LC(1) = 1)

1. Description: LC(4) reduced velocities.

2. Notes:

VBO(I) = reduced velocity (V/b0_) for flutter-divergence analysis

If aerodynamic interpolation is chosen, then aerodynamic forces will be interpolated at each

of these VBO(I) values, using the values for the RVBO input in section 6.2.7. If direct

calculation is used, the aerodynamic forces will be calculated at each of these reduced

velocities.

0 < LC(4) < 30

6.2.6 NV, V1, DV

Format (15, 2FI0.0)

(Required if LC(1) =-1)

1. Description: Airspeed velocity specification for p-k analysis.

2. Notes:

NV = number of velocities used in initial analysis, knots

1 < NV < 20

V1 = lowest velocity from which to start analysis, knots

V 1 > 200, suggested

DV = velocity increment to be summed to V 1 during initial analysis, knots

DV < 250, suggested

136
6.2.7 TOLI, (RVBO(I), I = 1, 6)

Format (7El0.0)

(Required if LC(1) = -1 or LC(13) = 1)

1. Description: Aerodynamic forces interpolation data.

2. Notes:

TOLl = tolerance value used for testing the interpolation fit; a nominal value of

1.0E-03 is recommended

RVBO(I) = reduced velocity at which aerodynamic forces will be computed, to be used as

part of the basis in interpolating forces at other reduced velocities

If aerodynamic interpolation is used, the RVBOs should span the entire range of VBOs of

section 6.2.5.

For LC(1) = -1, use the following approximations:

1. RVBO(1) < 1.69 x 12.0 x V1 / (BR x WMAX), where

WMAX = maximum modal frequency, rad/sec.

. RVBO(6) > 1.69 x 12.0 × VMAX / (BR x WMIN), where

VMAX = V 1 + (NV - 1) × DV, and

WMIN = minimum modal frequency, rad/sec.

6.2.8 MADD, IADD, MSYM

Format (315)

(Required if LC(31) = 1)

1. Description: Specifications for changes to mass matrix and modal frequencies.

2. Notes:

MADD = number of changes to mass matrix

IADD = number of changes to modal frequencies

MSYM = integer specifying the symmetry of mass matrix modifications

= 0, changes are symmetric

= 1, changes are nonsymmetric

6.2.8.1 I, J, WW(I, J)

Format (215, F10.0)

(Required if MADD > 0)

1. Description: MADD changes to the mass matrix.

137
2. Notes:

I ._

J =

WW(I, J) =

IfMSYM =

6.2.8.2 I,OMG(1)

Format (15,F10.0)

I. Description:

2. Notes:

I =

OMG(I) =

6.2.9 GDD

Format (El0.4)

1. Description:

2. Note:

GDD =

6.2.10 NCD

Format (15)

1. Description:

2. Note:

6.2.10.1

row index of the mass matrix element

column index of the mass matrix element

value to be substituted for the existing element in mass matrix, Ibm

0, specify only changes to upper triangular elements

(Required if IADD > 0)

IADD changes to modal frequencies.

index of the mode to be changed

new frequency to be substituted for the old, Hz

General structural damping factor.

(Required if LC(16) = 1)

A single value for hysteretic damping to be applied to all modes; the

imaginary term on the diagonal of the complex stiffness matrix will be

multiplied by the term GDD

(Required if LC(16) = -1)

Integer specifying individual structural damping.

NCD = number of individual modes for which hysteretic damping will be specified

(I, GDP(I)) (Required if LC(16) = -1 and NCD _ 0)

Format (I5, El0.0)

1. Description: NCD individual structural damping values.

138
2. Notes:

6.2.11

.

2.

6.2.12

I = mode index

GDP(I) = hysteretic damping applied to mode I

GMAX, GMIN, VMAX, FMAX

Format (4F10.0)

Description:

Notes:

GMAX

GMIN

VMAX

1. Description:

2. Notes:

RHOR(I)

6.2.13

.

2.

(Required if LC(1) _e 2)

Maximum and minimum scales for V-g and V-f print plots.

FMAX =

(RHOR(1), I -- 1, LC(5))

Format (7F10.0)

LC(5) values of air density ratios.

maximum value of damping scales for V-g plots

minimum value of damping scale for V-g plots

maximum value of velocity scale for V-g and V-f plots, knots

maximum value of frequency scale for V-f plots, Hz

(Required if LC(1) ¢ 0)

= density ratio with respect to sea level

0 < RHOR(I) _< 10

A separate flutter and/or divergence analysis is performed at each density ratio in which the

aerodynamic force matrix is multiplied by the square root of the density ratio.

NADDF, NSYM

Format (215)

(Required if LC(9) = 1)

Description:

Notes:

NADDF

NSYM

Specifications for frequency-independent additions to aerodynamic matrix.

= number of following additions to the flutter-determinant aerodynamic matrix

= index defining symmetry of additions

= 0, additions are symmetric; input only upper triangular elements

= 1, additions are not symmetric

139
6.2.13.1 I, J, DETAD(I, J)

Format (215, 2El0.0)

1. Description:

2. Notes:

6.2.14

.

2.

6.2.14.1

.

2.

(Required if LC(9) = 1)

NADDF frequency-independent additions to the aerodynamic matrix.

I = row index of additions

J = column index of additions

DETAD(I, J) = value of addition; DETAD(I,J) is a complex value

Additions to the aerodynamic matrix QBAR are done in the following manner:

DETADREAL .. DETADIMAG

QBAR = QBAR -P k2 + 1 k

where k is the reduced frequency and i* =

NADDS, NSYM

Format (215)

Description: Specifications for changes to the generalized stiffness matrix.

Notes:

NADDS

NSYM

= number of following changes to the stiffness matrix

= index specifying symmetry of changes

= 0, changes are symmetric (B(I,J) = B(J,I))

= 1, changes are not symmetric

I,J, B(I, J)

Format (215, 2El0.0)

NADDS changes to the stiffness matrix.

= row index of changes

= column index of changes

= new value of the complex stiffness matrix element

= 0, only the upper triangular elements are input

Description:

Notes:

I

J

B(I, J)

If NSYM

(Required if LC(32) = 1)

(Required if LC(32) = 1)

140
6.2.15 RATOM(I)

Format (7E10.0)

1. Description: LC(26) values of stiffness variations for an input mode.

2. Note:

6.2.15.1

,

2.

6.2.16

Description:

Notes:

NOTIR

NINZ

(Required if LC(26) > 0)

RATOM(I) = ratio of modal frequency with respect to the original input value, OMG(I)

NOTIR, (NINZ(J), J--l, NOTIR ) (Required if LC(25) ¢ 0)

Format (1015)

LC(25) sets of modal elimination specification for flutter and divergence analysis.

= number of deleted modes in a given modal elimination cycle

= index of the individual deleted mode for a given cycle

It should be noted that the AEROS module always does an initial analysis without modal

deletions before doing any modal elimination analyses as defined in this section.

VA, VB

Format (2El0.0)

1. Description:

2. Notes:

VA

VB

6.2.17

Eigenvector calculation range.

(Required if LC(28) = 1 and LC(1) _ 2)

= lower bound of the range for which the eigenvectors are to be calculated

= upper bound of the range for which the eigenvectors are to be calculated

If LC(1) = -1, the range is for velocity, V, knots

V

If LC(1) = 1, the range is for reduced velocity, --

FLO, FHI

Format (2El0.0)

1. Description:

2. Notes:

FLO

Bo)

(Required if LC(28) = 1 and LC(1) = 1)

Eigenvector display range.

= lower bound of the frequency range for which the eigenvectors are to be

displayed, Hz

141
6.2.18

°

2.

6.2.19

°

2.

FHI = upper bound of the frequency range for which the eigenvectors are to be

displayed, Hz

FL, ACAP

Format (2F10.0)

Description: Reference length and area.

Notes:

FL = reference chord of the model, in. (2.0 x BR, normally)

ACAP = reference area of the model, in 2

NDELT, NP, NB, NCORE, N3, N4, N7

Format (715)

Description: Doublet lattice and constant pressure methods geometrical paneling data.

Notes:

NDELT = index defining aerodynamic symmetry

= 1, aerodynamics are symmetrical about Y = 0

= -1, aerodynamics are antisymmetrical about Y = 0

= 0, no symmetry about Y = 0 (single surface only)

NP = total number of "panels" on all lifting surfaces

NB = body identification flag

= 0, no bodies of any kind

> 0, number of slender bodies used for doublet lattice analysis

= -1, constant pressure method body elements exist

0 < NB < 20 for doublet lattice method

NCORE problem size, N × M, where

N = total number of aerodynamic elements, and

M = number of modes

N3 = print option for pressure influence coefficients

= 1, print

= 0, no print

N4 = print option for influence coefficients relating downwash on lifting surfaces to

body element pressures

= 1, print

= O, no print

V

V j

142
6.2.20

N7 = index specifying the calculation of pressures and generalized forces

= 1, calculate

= 0, cease computations after influence coefficients are determined

If LC(1)=-1 or 1, set N7 = 1

IBOD1, IBOD2

Format (215)

1. Description:

2. Notes:

6.2.21.2

6.2.21.3

6.2.21.4

(Required if NB = -1)

6.2.21.5

Aerodynamic elements defining contiguous panels that describe a supersonic body

for the constant pressure method.

IBOD1 = first aerodynamic element on first panel (lowest index)

IBOD2 = last aerodynamic element on last panel (highest index)

Sections 6.2.21.1 to 6.2.21.5 are Repeated for NP Sets of Surface Paneling Data.

XO, YO, ZO, GGMAS

Format (4F10.0)

X1, X2, X3, X4, Y1, Y2

Format (6F10.0)

Z1, Z2, NEBS, NEBC, COEFF

Format (2F10.0, IX, 213, 3X, F10.0)

(TH(I), I -- 1, NEBC)

Format (6F10.0)

(TAU(1), I = 1, NEBS)

Format (6F10.0)

1. Description: NP sets of data defining aerodynamic panels and their component aerodynamic

elements. Section 6.2.21.1 translates and rotates panels. Such coordinates are in the

global (aircraft) system indicating the position of the origin of the LCS for each

panel. Section 6.2.21.2 contains coordinates of points defining an aerodynamic

panel, and section 6.2.21.3 defines boundaries of "aerodynamic elements" in the

panel. The panel is divided into a number of smaller trapezoids, called "aerodynamic

elements," by lines of a constant-percent panel chord and constant-percent panel

span. Section 6.2.21.4 defines chordwise panel stations, and section 6.2.21.5 defines

spanwise panel stations.

143
2. Notes:

XO

YO

ZO

GGMAS

= translationalvalueto beappliedto x coordinates,in.

= translationalvalueto beappliedto y coordinates,in.

= translationalvalueto beappliedto z coordinates,in.

= paneldihedralor rotationaboutaglobalX axis,deg

GGMAS is in a right-handedcoordinatesystem;anupright panelwould requirea positive

rotationof 90°. Deflectionsareappliedto theaerodynamicpanel,thenthepanelis translated

androtatedinto position.

X 1 = x coordinateof thepanel

X2 = x coordinateof thepanel

X3 = x coordinateof thepanel

X4 = x coordinateof thepanel

Y1 = y coordinateof thepanel

Y2 = y coordinateof thepanel

Z1 = z coordinateof thepanel

Z2 = z coordinateof thepanel

Coordinatesarein theLCS.

NEBS =

NEBC =

COEFF =

TH(I) =

TAU(I) =

inboardleadingedge,in.

inboardtrailingedge,in.

outboardleadingedge,in.

outboardtrailingedge,in.

inboardedge,in.

outboardedge,in.

inboardedge,in.

outboardedge,in.

numberof elementboundariesin thespanwisedirection

2 < NEBS < 50

NEBS must be set = 2 for each body interference panel

number of element boundaries in the chordwise direction

2 < NEBC < 50

entered as 0.0

chordwise element boundaries for the panel in a fraction of the chord

0.0 < TH < 1.0

(TH(1) = 0.0, TH(NEBC) = 1.0)

spanwise element boundaries for the panel in a fraction of the span

0.0 < TAU < 1.0

(TAU(1) = 0.0, TAU(NEBS) = 1.0)

144
6.2.22

6.2.22.1

6.2.22.2

6.2.22.3

6.2.22.4

The data are to be repeated NP times in the following sequence:

1. Vertical panels or a plane of symmetry (Y = 0).

2. Panels on other surfaces.

3. Body interference panels. These panels must be one element wide (that is, NEBS = 2).

There are (NEBS - 1) × (NEBC - 1) aerodynamic elements on a primary or control surface.

Indices for aerodynamic elements start at the inboard leading-edge element and increase

while traveling aft down a strip, then outward strip-by-strip, and ending at the outboard

trailing-edge element.

Sections 6.2.22.1 to 6.2.22.4 are Repeated for NB Sets of Slender-Body Data

(Required if NB > 0)

XBO, YBO, ZBO

Format (3F10.0)

ZSC, YSC, NF, NZ, NY, COEFF, MRK1, MRK2

Format (2F10.0, IX, 312, 3X, 1F10.0, 213)

(F(I), I = 1, NF)

Format (6F10.0)

(RAD(I), I = 1, NF)

Format (6F10.0)

1. Description:

Notes:

XBO

YBO

ZBO

ZSC

YSC

NF

.

NB sets of data defining subsonic slender bodies and their component elements.

Section 6.2.22.1 defines X, Y, and Z global reference coordinates. Section 6.2.22.2

defines slender-body origin, elements, and any related interference panels.

Section 6.2.22.3 defines slender-body element stations, and section 6.2.22.4 defines

slender-body radii.

= translational value to be added to the x coordinate, in.

= translational value to be added to the y coordinate, in.

= translational value to be added to the z coordinate, in.

= local z coordinate of the body axis, in.

= local y coordinate of the body axis, in.

= number of slender-body element boundaries along the axis

2 <NF< 50

145
6.2.23

NZ flag for

1, body

0, body

body vibration in the Z direction

vibrating

not vibrating

NY = flag for

= 1, body

= 0, body

body vibration in the Y direction

vibrating

not vibrating

COEFF = entered as 0.0

MRK1 = index of the first aerodynamic element on the first interference panel

associated with this slender body

MRK2 = index of the last aerodynamic element on the last interference panel associated

with this slender body

F(I) = x coordinate of the body station defining a slender-body element in local

coordinates, in. (starting with the body nose and proceeding aft)

RAD(I) = radii of body elements at the stations F(J), in.

NZ must never equal NY.

Vertically vibrating bodies should be input before laterally vibrating ones. If both vertical and

lateral body vibrations are desired in a single body, two bodies are input at the same location

with corresponding NZ and NY.

A slender body, as defined here, is a frustum of a right-angle cone; there are (NF - 1)

slender-body elements.

NSTRIP, NPR1, JSPECS, NSV, NBV, NYAW

Format (615)

1. Description: General aerodynamics data.

2. Notes:

NSTRIP =

NPR1

number of chordwise strips of panel elements on all panels.

For LC(8) = 0, set NSTRIP = 1

Printouts of lift and moment coefficients for the strips occur for NSTRIP > 1

Never set NSTRIP = 0

= print option for pressures in subroutines QUAS or FUTSOL. Use only for

debugging

= 1, print

= 0, no print

146
6.2.23.1

JSPECS = index describing plane aerodynamic symmetry about Z = 0

= 1, antisymmetrical aerodynamics about Z = 0 (biplane or jet effect)

= -1, symmetrical about Z = 0 (ground effect)

= O, no symmetry about plane Z = 0

NSV = number of strips lying on all vertical panels on the symmetric plane Y = 0

NBV = number of elements on all vertical panels lying on the plane Y = 0

NYAW = symmetry flag

= 0, if NDELT = 1 (symmetric about Y = 0)

= 1, if NDELT = -1 (antisymmetric about Y = 0)

= 0 or 1, if NDELT = 0 (asymmetric about Y = 0)

(LIM(I, 1), LIM(I, 2), LIM(I, 3), I = 1, NSTRIP)

Format (313)

1. Description: NSTRIP sets of data defining chordwise strips for aerodynamic coefficient

calculations.

2. Notes:

LIM(I,1) - index of the first element on each chordwise strip

LIM(I,2) = index of the last element on each chordwise strip

LIM(I,3) = 0

For NSTRIP = 1, a blank card is used.

6.2.24 Sections 6.2.24.1 and 6.2.24.2 are Repeated for LC(3) Sets of Primary Surface Data.

6.2.24.1 KSURF, NBOXS, NCS

Format (1L5, 215)

6.2.24.2 NLINES, NELAXS, NICH, NISP

Format (415)

6.2.25 Sections 6.2.25.1 and 6.2.25.2 are Repeated for NLINES Subsets of Data.

6.2.25.1 NGP, XTERM1, YTERM1, XTERM2, YTERM2

Format (15, 4El0.0)

6.2.25.2 (YGP(I), I = 1, NGP)

Format (8El0.0)

147
6.2.26

6.2.27

6.2.28

6.2.29

6.2.29.1

6.2.29.2

6.2.30

DIST

Format (El0.0)

(XI(I), YI(I), X2(I), Y2(I), I = 1, NCS)

Format (4E10.0)

(Required if NELAXS = 1)

NLINES, NELAXS, NICH, NISP

Format (415)

(Required if KSURF = T)

(Required if KSURF = T)

Sections 6.2.29.1 and 6.2.29.2 are Repeated for NLINES Subsets of Data.

(Required if KSURF = T)

NGP, XTERM1, YTERM1, XTERM2, YTERM2

Format (I5, 4El0.0)

(YGP(I), I = 1, NGP)

Format (BE10.0)

DIST

Format (El0.0)

1. Description:

(Required if NELAXS = 1 and KSURF = T)

2. Notes:

LC(3) sets of input modal vector data to be applied to the interpolation of

deflections for primary and control-surface aerodynamic elements.

KSURF = flag indicating control surfaces on a primary surface

= T, this surface has one or more control surfaces with forward hinge lines

= F, this surface has no control surfaces

NBOXS = number of elements on this surface, including those elements on control

surfaces

NCS = number of control surfaces on primary surface

0 < NCS < 5

NLINES = number of lines along which input modal vector data are prescribed

1 < NLINES < 50

NELAXS = index defining input vector components

= 1, translation and pitch rotation are prescribed at each input point

= 0, only translation is prescribed

NICH = index defining the chordwise interpolation/extrapolation from the input vector

to aerodynamic elements

= 0, linear

= 1, quadratic

= 2, cubic

148
NISP = index defining the spanwise interpolation/extrapolation from the input vector

to aerodynamic elements

= 0, linear

= 1, quadratic

= 2, cubic

NGP = number of points on an input vector line

2 _<NGP < 50

XTERM1 = x coordinate specifying the inboard end of an input vector line in the LCS

YTERM 1 = y coordinate specifying the inboard end of an input vector line in the LCS

XTERM2 = x coordinate specifying the outboard end of an input vector line in the LCS

YTERM2 = y coordinate specifying the outboard end of an input vector line in the LCS

YGP(I) = spanwise coordinate of a point along an input vector line, going inboard to

outboard in the LCS

Xl(I) = x coordinate of the inboard terminus of the Ith control-surface leading edge in

the LCS

YI(I) = y coordinate of the inboard terminus of the Ith control-surface leading edge

in the LCS

X2(I) = x coordinate of the outboard terminus of the Ith control-surface leading edge

in the LCS

Y2(I) = y coordinate of the outboard terminus of the Ith control-surface leading edge

in the LCS

DIST = displacement reference distance

The Following Sets of Data are Repeated NB Times. (Required if NB > 0)

NGP, NSTRIP, IPANEL

Format (315)

6.2.31.2 (XGP(I), I = 1, NGP)

Format (6F10.0)

1. Description: NB sets of data describing the input modal vector to be applied to the slender-body

aerodynamic elements deflection.

149
2. Notes:

NGP =

NSTRIP =

IPANEL =

XGP(I) =

These data are

6.2.32 KLUGLB

Format (15)

1. Description:

2. Notes:

KLUGLB

number of points on a slender-body axis at which input vector data are

prescribed

2 < NGP < 50

number of interference panels (or strips) associated with a slender body

index of the first interference panel associated with a slender body

streamwise coordinate of each point at which input modal data are prescribed

in the LCS

not to be input for a constant pressure method model.

Print option for global geometry.

= print option for aerodynamic elements in the GCS

= 1, print

= 0, no print

6.2.33 Notes On Module Usage

Aerodynamic Modules

The STARS-AEROS-AEROL aerodynamic module consists of two unsteady, linear, inviscid,

aerodynamic codes: the doublet lattice method for subsonic analyses, and the constant pressure

method 17 for supersonic analyses. Flutter and divergence solutions can be obtained by k, p-k, or statespace methods.

Aerodynamic Modeling

The aerodynamic elements on lifting and interfering surfaces consist of trapezoidal elements parallel

to the free stream. The aspect ratio of an element should be, ideally, on the order of unity or less.

The number of elements required for accurate analysis varies with the model and the reduced

frequency values. Increasing the number of elements will increase the computational time. Higher

reduced-frequency values require smaller and, therefore, more elements than lower reduced-frequency

values. A guide for element size in the streamwise direction is k Ax < 0.04, where k is reduced

frequency and Ax is element length.

_j

150
Elementsshouldbeconcentratednearwing tips, leadingandtrailing edges,control-surfacehinges,

andsoforth. As a guide,acosinedistributionof elementsoverthechord andfull spanof the wing can

be adopted.

The surfaceelementcanbeconsideredashavinganunsteadyhorseshoevortexboundalongtheonequarterchord of the elementandtrailing aft to infinity. The downwashfrom the unsteadyvortices is

calculatedat a control point locatedat thethree-quarterchordof thecenterlineof anelement.Because

theinduceddownwashatthecenterof avortexis infinite, nocontrolpoint shouldeverlie on anyvortex

line, suchasalongtheextensionof anyelementedge,eitherupstreamor downstream.

6.3 CONVERT Data (STARS-ASE-CONVERT)

Purpose: Prepare convert.dat data file.

Description: Enables the selection of desired modes.

6.3.1 $ Job Title

Format (FREE)

6.3.2 NM

Format (I5)

1. Description: General data.

2. Note:

NM = total number of desired modes to form reduced generalized matrices

6.3.3 $ Modal Selection and Ordering

Format (FREE)

6.3.3.1 IOLD, INEW

Format (215)

1. Description: Orders the modes to be used for ASE analysis, NM sets of data.

2. Notes:

3. Note:

IOLD = old modal number

INEW = new modal number

Output is the reduced generalized force matrix and is stored in the GFORCE_PADE.DAT

file for subsequent input into the ASE module.

151
6.4 ASE PADI_ Data (STARS-ASE--PADI_)

Purpose: Prepare pade.dat data file.

Description: Performs Pad6 curve fitting of unsteady aerodynamic forces and the state-space matrix

formulation.

6.4.1 $ Job Title

Format (FREE)

6.4.2 NRM, NEM, NCM, NG, NS, NK, NA, RHOR, VEL, CREF, IWNDT, NQD

Format (FREE)

General input data. .

2.

6.4.3

Description:

Notes:

NRM = number of rigid-body modes

NEM = number of elastic modes

NCM = number of control modes

NG = number of gusts

NS = number of sensors

NK = number of sets of input data at discrete reduced frequencies

NA = order of Pad6 equation, 0< NA _<4

RHOR = relative aerodynamic density with respect to sea level

VEL = true airspeed, ft/sec

CREF = reference chord, ft

IWNDT = wind-tunnel correction index

= 0, uses formulation as in reference 16

1, uses wind-tunnel data to modify aerodynamic generalized force matrix as in

reference 16

NQD = number of velocities for flutter and divergence analysis, to be set to 0 for ASE

analysis as in reference 16

$ Tension Coefficients

Format (FREE)

152
6.4.3.1 (BETA(I), I - 1, NA)

Format (FREE)

1. Description:

2. Note:

BETA(I)

6.4.4

6.4.4.1

Pad6 approximation data.

= tension coefficients

$ Generalized Masses

Format (FREE)

((GMASS(I, J), J = I, NM), I = 1, NM)

Format (FREE)

Description: Generalized mass data, upper symmetric one-half, starting with the diagonal element.

NM = total number of modes

= NRM + NEM + NCM

GMASS(I) = generalized mass of mode I, slugs

6.4.5 $ Generalized Damping

Format (FREE)

Notes:

6.4.5.1 (DAMP(I), I = 1, NM)

Format (FREE)

Generalized damping data.

= generalized damping applied to mode I

1. Description:

2. Note:

DAMP(I)

$ Natural Frequencies

Format (FREE)

6.4.6

(OMEGA(I), I = 1, NM)

Format (FREE)

Modal frequency data.

6.4.6.1

1. Description:

2. Note:

OMEGA(I) = natural frequency of mode I, rad/sec

153
6.4.7 (Required if NQD > 1)

6.4.7.1

.

2.

6.4.8

6.4.8.1

°

2.

$ Velocities for Flutter and Divergence Analyses

Format (FREE)

O/EL(I), I = 1, NQD)

Format (FREE)

Description: True airspeed data for flutter and divergence analyses, ft/sec.

Note:

(Required if NQD > 0)

VEL(I) = airspeed values to be used to calculate the frequency and damping

$ Aircraft Angles, Degrees of Freedom

Format (FREE)

(Required if NQD = 0)

PHI, THETA, PSI, US, VS, WS, PS, QS, RS, PHID, THAD, PSID, NDOF

Format (FREE) (Required if NQD = 0)

Description: Data for transformation of Earth- to body-centered coordinate systems.

Notes:

PHI = roll angle, deg

THETA = pitch angle, deg

PSI = yaw angle, deg

US, VS, WS = body axes velocities

PS, QS, RS = angular rates

PHID, THAD, PSID = Euler angle rates

NDOF

6.4.9 $ Sensor Data

Format (FREE)

6.4.9.1 IFLSI

Format (FREE)

= number of aircraft degrees of freedom; a negative sign indicates

antisymmetric case

(Required if NQD = 0 and NS > 0)

1. Description: Flag for identification of sensor interpolation points in the presence of GVS data only.

154
2. Notes:

IFLSI = 1,

-- 0,

for an antisymmetric case

for a symmetric case

for a non-GVS case

6.4.9.2 XS, YS, ZS

Format (FREE)

LX, MY, NZ, THX, THY, THZ

Format (FREE)

.

.

Description:

Notes:

XS

YS

ZS

LX

MY

NZ

THX

THY

THZ

(Required if NQD = 0 and NS > 0)

3. Notes:

Sensor location and orientation; NS sets of data.

= X coordinate of the sensor

= direction

= direction

= direction

= direcUon

= direction

= direction

Y coordinate of the sensor

Z coordinate of the sensor

cosine for an accelerometer normal in X

cosine for an accelerometer normal in Y

cosme for an accelerometer normal in Z

cosine for the pitch axis about X

cosine for the pitch axis about Y

cosine for the pitch axis about Z

For the case IFLSI , 0, the user must modify the file VEC_AND_COORDS.DAT by

defining the appropriate sensor location. This modification is done by setting the fourth

column of the relevant nodes in the nodal coordinates section of the data file to the

appropriate value of IFLSI. Sections 6.4.4 through 6.4.6.1 are generated by STARS-ASECONVERT and can be obtained from the file MDF_PADE.DAT.

6.5 ASE CONTROL Data (STARS-ASE-CONTROL)

Purpose: Prepare controls-related data.

Description: Augments control elements.

155
6.5.1

6.5.2

1. Description:

2. Notes:

NX

6.5.3.1

6.5.3.2

$ Job Title

Format (FREE)

NX, NY, NU, NV, NXC, DELTAT, TDELAY, MAXBC, MAXPO

Format (FREE)

System parameters.

= number of states in the plant

= [2 × (NRM + NEM) + NA × (NRM + NEM + NCM)] (Refer to section 6.4)

NY = number of outputs from the plant

= (number of rows of C matrix)

= (2 × NS × 3)

NU = number of inputs to the plant

= (2 × NCM)

NV = number of external inputs to the system

NXC = total number of continuous states (the plant plus analog elements)

DELTAT = sample time for digital elements

TDELAY = system time delay

MAXBC = maximum number of block connectivity

MAXPO = maximum polynomial order plus one

NB, NYBTUV, IADDRA, IADDCB, IADDRC, NLST, NDRESP, IRP, ITRP

Format (FREE)

MAXA, MAXB, MAXC, NBSS

Format (FREE)

1. Notes:

NB

NYBTUV

IADDRA

= number of blocks of analog and digital elements in the system, including the

summing elements and excluding the plant

= NYTOV + NBTOU (See section 6.5.10.2 for definitions.)

= additional rows of A caused by the augmentation of control elements;

appropriate summation of orders of polynomials of all analog elements for

open- and closed-loop solutions are derived from the block connectivity input

156
6.5.4.1

1. Note:

6.5.4.2

IADDCB

IADDRC

NLST

NDRESP

IRP

ITRP

MAXA

MAXB

MAXC

NBSS

= additional columns of B caused by the augmentation of control elements

= additional rows of C caused by the augmentation of control elements, equal to

the number of connecting links into the block/connecting junction

= total number of frequency-range specifications for frequency-response

computations

= number of times the loops are broken for open-loop response evaluation

= frequency-response problem number to be evaluated

= total number of frequency-response cases

= maximum row dimension of the direct input A matrix

= maximum row dimension of the direct input B matrix

= maximum row dimension of the direct input C matrix

= number of control block state-space matrices as direct input

$ Block Connectivity

Format (FREE)

Analog blocks are to precede digital blocks

IBN, ICN1, ICN2, ICN3, IEXI, IELPCL, ISLPCL

Format (715)

1. Notes:

IBN

ICN 1, ICN2,

ICN3

IEXI

IELPCL

ISLPCL

= integer defining the block number

= connecting block numbers (a maximum of 3)

= integer defining the external input number

= integer defining the closing block (feedback signal) of the closed-loop

system

= integer defining the starting block of the closed-loop system

157
2. Note:

A symbolicgainblock indicatingtheclosingof loop is identifiedby the presenceof starting

andclosingblocks.

The feedbacksignal is assumedto be negative.For positive feedback,set IELPCL to its

negative.

6.5.5.1 $ Transfer Function Description, as Order of Polynomials, for Each Block

Format (FREE)

1. Note:

The polynomial descriptions pertain to either analog or digital elements, as appropriate.

6.5.5.2 IBN, ICNP, ICDP, ICROW

Format (415)

1. Notes:

ICNP integer defining the number of coefficients in the numerator polynomial

NA, row number for the A matrix (for the direct state-space matrix input

option)

ICDP integer defining the number of coefficients in the denominator polynomial

NCB, colunm number for the B matrix (for the direct state-space matrix input

option)

ICROW = integer defining the number of coefficients in the denominator polynomial

= NCR, row number for the C matrix (for the direct state-space matrix input

option)

= 0, for a polynomial input

6.5.6.1 $ Listing of Polynomial Coefficients

Format (FREE)

6.5.6.2 IBN, (POLCON(I), I=1, MAXPO)

Format (15, < MAXPO > (El0.4))

6.5.6.3 IBN, (POLCOD(I), I=1, MAXPO)

Format (15, <MAXPO > (El0.4))

1. Notes:

1. The coefficients are to be listed in increasing order of polynomials.

158
2. The numeratorcoefficients (POLCON) are placedin one row, and the denominator

(POLCOD)coefficientsin thenextrow,for eachblock,oneblock at atime.

3. Datato bepreparedfor eachblock;NB setsof dataaretheinput.

6.5.6.4 $ Listing of State-Space Matrices of Control Blocks as Direct Input

(Required if NBSS ;_ 0)

6.5.6.5 IBN, NA, NCB, NCR

Format(FREE)

6.5.6.6 ((A(I,J),J=l, NA, B(I, J),J=l, NCB), I=1, NA)

Format (FREE)

6.5.6.7 ((C(I,J),J=l, NA, D(I, J),J-I, NCB), I=I, NCR)

Format (FREE)

1. Description: NBSS sets of directly input state-space matrix data.

6.5.7.1 $ Gain Inputs for Each Block

Format (FREE)

6.5.7.2 IBN, Gain

Format (5(15, El0.4))

1. Note:

Gains alternatively can be the input as the multiplier of polynomial coefficients in the

numerator. NB sets of data are the input.

6.5.8.1 $ Specification for System Outputs, NYB = NY + NB Number of Data

Format (FREE)

6.5.8.2 ISO1, ISO2,...ISONYB

Format (1615)

1. Description: These data are needed for closed-loop frequency-response analysis only.

2. Notes:

1. Plant outputs are numbered 1 through NY.

2. Each block output is numbered as NY + IBN.

159
3. Note:

6.5.9.1

6.5.9.2

ISOI = desired output from any sensor (the corresponding row of the C matrix for the

plant) and any control element (augmented thereafter)

$ Specification for System Inputs, NUV = NU + NV Number of Data

Format (FREE)

ISI1, lSI2,..., ISINUV

Format (1615)

1. Notes:

2. Note:

1. Plant input are numbered 1 through NU.

2. Each block input is numbered as NU + IEXI.

ISH = plant input (the corresponding column of the B matrix for the plant) and

external input

6.5.10.1 $ Connection Details From Plant to Blocks

Format (FREE)

6.5.10.2 NYTOV, NBTOU, NBTOK

II

6.5.10.3

1. Notes:

Format (315)

Notes:

NYTOV

NBTOU

= number of connections from plant outputs to external inputs

= number of block outputs connected to plant inputs

NBTOK = number of digital element outputs connected to analog element inputs

IYTOV1, IYTOV2

Format (215)

IYTOV 1

IYTOV2

= row number of the C matrix corresponding to output from the plant to the

feedback control system

= external input number that describes the connection of the plant output to the

control system

160
.

6.5.10.4

Note:

Repeat NYTOV times, ISO to IEXI.

IBTOU1, IBTOU2

Format (215)

1. Notes:

IBTOU1

IBTOU2

= block number to be connected to the plant input

= column of the B matrix to which the block is connected

2. Note:

Output NBTOU times, IBN to ISI.

6.5.10.5 IBTOK1, IBTOK2

Format (215)

Output NBTOK times, IBN (analog) to IBN (digital).

1. Note:

$ Frequency Range Specification

Format (FREE)

FREQI, FREQF, NFREQ

Format (2F10.4,I5)

6.5.11.1

6.5.11.2

Description: NLST sets of frequency data.

Notes:

FREQI

FREQF

NFREQ =

.

2.

initial frequency

final frequency

number of frequencies within the range, logarithmically spaced

6.5.12.1 $ Loop Definitions

Format (FREE)

(Required if NLST ;e 0)

6.5.12.2 ILOOP, IPRINT

Format (FREE)

161
6.5.12.3 NBRAK1, NBRAK2, NOUTBL, NINBL

Format (415)

1. Notes:

2. Note:

.

(Required if ILOOP = 0 or 1)

ILOOP

IPRINT

NBRAK1 =

NBRAK2 =

NOUTBL =

NINBL =

= integer defining the loop type

= 0, for the closed-loop response case

= 1, for the open-loop response case

= 2, for eigensolution of the system

= eigensolution print option for the closed-loop case

= 0, prints eigenvalues only

= 1, prints eigenvalues and vectors

block having the output signal

block having the input signal

output of block NBRAK1

input of block NBRAK2

Data of section 6.5.12.3 are to be repeated NDRESP times.

Additional notes:

Input data for STARS-ASE-FRESP are created from running STARS-ASE-CONTROL. No

additional input data are required from the user.

A transfer function can be obtained between any two blocks in a loop, provided the input

block has an output signal going in the direction of the plant.

v _

162
7. SAMPLE PROBLEMS

(STARS INTEGRATED AERO-STRUCTURAL-CONTROL SYSTEMS ANALYSIS)

A simplified aircraft test model has been selected as a standard problem for the full spectrum of ASE

analyses. In this section, the relevant data (fig. 49) for associated SOLIDS, AEROS, and ASE modules

are presented in detail. Each data set is followed by relevant output of results. The input data are

prepared in accordance with the procedures described in section 6. Details for running the aircraft test

model appear in section 7.7.

Three perfect rigid-body modes (Y translation, X-rotation roll, and Z-rotation yaw about the center

of gravity, OpR), two rigid-control modes (aileron and rudder deflections, OC), eight elastic modes (OE),

and three usual rigid-body modes (O R) are generated in this module, of which the latter are excluded

from consideration as GENMASS data input (O = • R + _ + OpR + OC). The perfect rigid-body modes

(OpR) are moved in the front through data input to the CONVERT submodule for subsequent ASE

analysis (O = OpR + (bE + OC).

7.1 Aircraft Test Model: Free-Vibration Analysis (STARS-SOLIDS)

The input data pertain to the flee-vibration analysis of the finite-element model. The direct modal

interpolation option is used for subsequent flutter and ASE analyses.

The finite-element model (fig. 50) of the symmetric one-half of the aircraft is used for the vibration

analysis. Only the typical antisymmetric case is presented here; figure 51 shows a direct interpolation

scheme for subsequent aeroelastic and ASE analyses.

65

s5

6

18_. _<'_2 __ "_. "_,27

1 121 _ 61 _ 1 0 6 s Fuselage

970339

Figure 50. Aircraft test model symmetric one-half finite-element model with nodes.

163
39

t?.l

Top view,

vertical deflections

/-- Wing Large case, STARS node numbers

/_.__ Smell case, direct interpolation points

/ / I i, i_z _,,_,,t. ,--Horizontal

/ / l IP It 'TIT_.a / trail

/3,,././ .1_2uw¢' _ / / / _. ,f_--.Jg_LZL_

___ Vertical

Fuselage L q _ .i tail

_u'_k, 2z,JJ 44 s7 z_,S

AZ_, "" / /_ss" 1,7

Side view, lateral deflections /J " ILIL /, !

Fuselage ' t,

•-" P..s'" _ m-" mK e_" _ 'm _,_ _.

970340

Figure 51. Aircraft test model antisymmetric case, direct-surface interpolation scheme.

STARS-SOLIDS input data (atm_solids.dat):

AIRCRAFT TEST MODEL

C

C RHTISYMMETRIC HALF MODEL

C IIHTP - I, DIRECT IMTERPOLRTtOH OF MODRL DATA

C

C MCHTRL - 5, FIRST THREE TO GEMERRTE PERFECT RIGID BODY MODES

C Y TRRHSLRTIOH, ROLL RND YRW, PLUS RILEROHS RHD RUDDER COHTROL

C MODES.

C///////////////////////////////////////////////////////////////////////

74, 149, I, 4, 22, 5, O, O, O, O

O, 0, O, O, O, O, 5, 132, 0

I, I, O, O, O, 1, O, I

2, O, 2, O, 1, O, O, 1, O, O

1, I1, O, 7500.0, O.O, 0.0

$ HODRL DRTR

1 300.0000 200.0000 O.OOOO O 0 0 0 0 0 0

2 312.5000 200.0000 O.OOOO O 0 0 O O O O

3 325.0000 200.0000 O.OOOO O O 0 O O 0 O

4 337.5000 20O,OOO0 O.OOOO 0 O D O O O O

5 350.0000 200.0000 O,OOO0 0 0 0 0 O 0 O

6 287.5000 150.0000 O,OOOO 0 0 0 0 0 0 0

? 303.1250 150.0000 0.0000 0 O 0 O O O O

8 318.7500 150.0000 O.OOOO 0 O O O O O 0

9 334.3?50 150.0000 O,OOO0 0 O D 0 0 0 0

10 350.0000 150.0000 O.OOO0 0 0 O O O 0 0

11 335.3750 149.0000 O.OOOO 0 O 0 O O O 0

12 350.0000 149.0000 O.OOOO 0 0 0 O O O O

13 275,0000 lO0,OOOO O.OOOO O O 0 0 0 O O

14 293.7500 100.0000 O.OOOO O 0 D O O O 0

15 312.5000 100.0000 O.OOOO O 0 O 0 0 O O

16 331,2500 lOO.OOO0 0.0000 0 0 O 0 0 0 0

17 332,2500 100.0000 0.0000 O 0 0 0 0 0 O

18 350.0000 IOO,O00O O.OOO0 O 0 O O 0 0 O

19 262.5000 50.0000 0,0000 O 0 0 0 O 0 0

20 284.3750 50,0000 O.OOOO O 0 O 0 O 0 0

21 306.2500 50,0000 O.O000 O O O O 0 0 0

164
22 328.1250 50,0000 0.0000

23 329.1250 51.0000 0,0000

24 350.0000 51.0000 0.0000

25 350.0000 50.0000 0.0000

26 250,0000 0.0000 0.0000

27 275,0000 0.0000 0,0000

28 300_0000 0.0000 0.0000

29 325.0000 0,0000 0.0000

30 350.0000 0.0000 0.0000

31 200.0000 0,0000 0.0000

32 400.0000 0.0000 0.0000

33 150.0000 0.0000 0.0000

34 450.0000 0.0000 0.0000

35 100.0000 0.0000 0,0000

36 500,0000 0.0000 0.0000

37 50.0000 0.0000 0.0000

38 560.0000 0,0000 0.0000

39 0,0000 0.0000 0.0000

40 600.0000 0.0000 0.0000

41 520,0000 0.0000 50.0000

42 580.0000 I00.0000 0.0000

43 555,0000 0,0000 50.0000

44 520.0000 20.0000 0.0000

45 580,0000 0.0000 20.0000

46 560.0000 20.0000 0,0000

47 600.0000 0,0000 20.0000

48 600.0000 20.0000 0.0000

49 540.0000 0.0000 100,0000

50 526.6666 46.6667 0,0000

51 580.0000 0.0000 50,0000

52 560.0000 46.6667 0,0000

53 581,0000 0.0000 21.0000

54 600.0000 46.6667 0.0000

55 600,0000 0.0000 21.0000

56 533,3331 73.3333 0.0000

57 565,0000 0.0000 100.0000

58 560.0000 73,3333 0.0000

59 580.0000 0.0000 80.0000

60 600_0000 73.3333 0.0000

61 581,0000 0,0000 79,0000

62 540,0000 100.0000 0,0000

63 600,0000 0.0000 7g,O000

64 560.0000 100.0000 0.0000

65 600.0000 0.0000 100.0000

66 600.0000 100.0000 0.0000

67 600.0000 0.0000 80.0000

68 580,0000 73.3333 0.0000

69 580,0000 46.6667 0.0000

70 580,0000 20.0000 0,0000

71 581.0000 100,0000 0,0000

72 581,0000 73,3333 0,0000

73 581.0000 46.6667 0,0000

74 581.0000 20.0000 0,0000

$ ELEMENT CONNECTIUITY CONDITIONS I 6 7 2 I 2 7 8 3 2 3 8 9 4 3 4 9 10 5 4 5 13 14 7 6 6 14 15 8 7 7 15 16 9 8 8 19 20 14 13 9 20 21 15 14

10 21 22 16 15

18

19

20

21

22

23

24

25

26

27

28

29 10

II 26 27 20 19

12 27 28 21 20

13 28 29 22 21

14 29 30 25 22

15 17 18 12 11

16 23 24 18 17

1712 390

23 390

34 390

45 390

67 390

78 390

89 390

9 10 390

6I 390

72 390

83 390

94 390

5 390

0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

000

000

000

000

000

000

000000000000

00

00

00

0000000000000000000000

000

000

000

000

000

000

000

000

000

000

0000000

00

00

000000000000000000

110

I10

10

I0

110

II0

10 I 0

110

110

10

10

10

165
166

30 13 14

31 14 15

3:' 15 16

33 136

34 14?

35 158

36 169

37 19 20

38 20 21

39 21 22

40 22 25

41 19 13

42 20 14

43 21 15

44 22 16

45 26 27

46 27 28

47 28 29

48 29 30

49 26 19

50 27 20

51 28 21

52 2g 22

53 30 25

54 II 12

55 17 la

56 23 24

57 23 17

50 1? 11

59 24 18

60 18 12

61 11g

62 16 17

63 22 23

64 56 58

65 58 rio

66 50 52

67 52 69

68 44 46

69 46 ?0

70 62 64

71 64 42

72 56 58

73 58 68

74 56 62

?5 58 64

76 60 66

77 50 52

78 52 69

79 50 56

80 52 58

81 54 60

82 44 46

83 46 ?0

84 44 50

85 46 52

86 48 54

87 36 38

88 36 43

89 41 43

90 38 45

91 43 51

92 38 40

93 59 6?

94 53 55

95 36 41

96 41 49

97 36 43

98 43 57

99 4g 57

IO0 30 43

101 38 45

102 45 51

103 41 43

104 43 51

105 51 59

106 59 57

107 59 67

108 57 65

109 67 65

II0 40 47 I 11 45 4?

112 53 55

39

39

39

39

39

39

3gIIII

39

39

39

39I!I

0

I0

390

390

390

390

390

390

390

390

3g0

390

390

390

390

390

10

64 62

42 64

58 56

68 58

52 50

69 5200000000000000000

430

410

57 49

51 43

59 5?

47 45

65 57

63 61000000000O000000000

0000

00000

00000

00000

00000

00000

0000O

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

II0000

II0000

I0000

II0000

II0000

10000

10000

II0000

II0000

1O000

I0000

110000

110000

I0000

10O00

II0000

110O00

I0000

I0000

110000

110000

I0000

I0000

I0000

20000

20000

20000

20000

20000

20000

20000

50000

50000

50000

30000

30000

30000

30000

30000

30000

30000

30000

30000

30000

30000

30000

20000

30000

30000

30000

30000

20000

30000

30000

30000

30000

20000

40000

40000

40000

40000

40000

40000

40000

50000

40000

40000

40000

40000

40000

40000

40000

40000

40000

40000

40000

40000

40000

4O000

40000

40000

40000

90000
11353 61

114 55 63

115 61 63

116 45 53

117 61 59 I18 38 46

119 36 44

120 39 37

121 37 35

122 35 33

123 33 31

124 31 26

125 26 28

126 28 30

127 30 32

120 32 34

129 34 36

130 36 38

131 38 40

00000

00000

00000

00000

0000O

00000

00000

O000D

00O00

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

132 72 60 66 710000

133 73 54 60 720000

134 74 48 54 730000

135 42 71

136 68 72

137 69 73

130 70 74

139 74 73

140 73 72

141 72 71

142 70 69

143 69 68

144 68 42

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

145 71 66 6500000

146 72 60 6500000

147 73 54 6500000

148 74 48 6500000

149 40 70 6500000

$ LINE ELEMENT BASIC PROPERTIES 1 1,5000 37.5000 10,8000 18.8000 2 0.5300 3.8000 1,9000 1,9000 3 0.?500 19_0000 9,0000 9,0000 4 0.0600 1,5000 0,7500 0.7500 5 0.4000 1,5000 0,7500 0.7500 6 19.0000 750.0000 375.0000 375,0000 8 3.7500 1500.0000 750.0000 750,0000 9 0.0300 0_8000 0,4000 0,4000

10 0.0100 0.4000 0.2000 0.2000

11 1.1250 28.1250 14.0600 14,0600

120 11.2500 675.0 338.0 338_0

121 18.7500 900.0 900,0 900,0

122 18.7500 1050.0 1575,0 1575,0

123 10.7500 1200,0 2250,0 2250,0

124 18.7500 1650.0 2625.0 2625,0

125 18.7500 1875.0 1875.0 1875_0

126 18.7500 2250.0 1125,0 1125,0

127 18.7500 3000.0 1275.0 1275.0

128 18.7500 3000.0 1275_0 1275.0

129 18.7500 3000.0 1275.0 1275.0

130 16.5000 2250.0 975.0 975.0

131 15,0000 1500.0 675.0 675,0

$ SHELL ELEMENT THICKNESSES I 0.1130 2 0,0530 3 0.0900 4 0,0400 5 0.0100 $ MATERIAL PROPERTIES I I

I.OE÷07 0.30 O, ,259E-03

$ NODAL MASS DATA

39

37

35

33

31

26

28

30

32

34

36

38

4O

0.01953

0.03893

0,05843

0,09723

0,19433

0,29153

0.29153

0,29153

0,29153

0.29153

0.29153

0.29153

0,19433

g0000

90000

90000

100000

100000

80000

80000

1200000

1210000

1220000

1230000

1240000

1250000

1260000

1270000

1280000

1290000

1300000

1310000

20000

20000

20000

50000

50000

50000

50000

20000

20000

20000

30000

30000

30000

20000

20000

20000

20000

80000

167
-I

$ OUTPUT POINT SPECIFICRTIOH FOR DIRECT INTERPOLATION OF MODAL ORTR

I 36

2 36 36 41

3 3G 41 41 41

4 41

5 41 49

6 41 49 49

? 49

0 35 38

9 38 38 43

10 36 43 43 43

11 43

12 43 57

13 43 57 5?

14 57

15 38 40

16 45

17 45 51 51

18 51

19 5t 59 59 59

20 59

21 57 65

22 67

23 65

24 53

25 61

26 55

27 63

28 26

29 19 26

30 19

31 13 19 19

32 13 13 19

33 13

34 6 13

35 6

36 1 6 6

37 1 I 6

38 1

39 27

40 20 27

41 20

42 14 20 20

43 14 14 20

44 14

45 7 14

46 ?

47 2 7 7

48 2 2 ?

49 2

50 28

51 21 28

52 21

53 15 21 21

54 15 15 21

55 15

56 O 15

5? 8

58 3 8 8

59 3 3 8

60 3

61 2g

62 22 29

63 22

64 16 22 22

65 16 16 22

66 16

67 9 16

6O 9

69 4 9 g

70 4 4 9

71 4

?2 30

73 25 30

74 25

75 I0

76 5 10 I0

77 5 5 tO

78 5

79 23

80 17 23 23

81 17 17 23

168
82

I '7

03 11 17

84 11

85 24

86 18 24 24

O? 10 1O 24

88 18

89 12 18

90 12

91 44

92 44 50 50 50

93 50 50 56

94 56

95 56 62

96 62

97 46

98 46 52 52 52

99 52 52 58

100 58

101 58 64

102 64

103 ?0

104 69 ?0 70 70

105 6B 68 6g

106 68

107 42 68

10B 42

109 74

110 73 74 74 74 I 11 72 72 73

112 72

113 71 72

114 ?1

115 48

116 48 54 54 54

11? 54 54 60

118 60 I I9 60 66

120 66

121 39

122 35

123 33

124 31

125 26

126 28

127 30

128 32

129 34

130 36

131 3B

132 40

$ RIGID BODY CONTROL MODE DATA I 2 -I.0 74

I <--- RIGID BODYY TRANSLRTION

-I

I2 -0.690B

l3 16.6009

I4 1,0000

22 -0,6908

23 16,6089

24 1.0000

32 -0,6908

33 16,6089

34 I.OOO0

42 -0,6908

43 16.6089

44 1.0000

52 -0.6908

53 16.6089

54 l,OOO0

62 -0.5181

63 12,4567

64 l.OOO0

?2 -0,51BI

?3 12.4567

74 1,0000

82 -0.5181

83 12.4567

84 1.0000

92 -0.5101

93 12,456?

94 1,0000

I02 -0.5181

103 12.4567

<--- RIGID BODYX ROTATION (ROLL)

169
10

11

11

11

12

12

12

13

13

13

14

14

14

15

15

15

16

16

16

17

17

17

10

18

10

19

19

19

20

20

20

21

21

21

22

22

22

23

23

23

24

24

24

25

25

25

26

27

28

29

3O

31

32

33

34

35

36

37

30

39

40

41

4t

41

42

42

42

43

43

43

44

44

44

45

45

45

46

46

46

47

47

47

48

.0000

-0.5147

12.3737

.0000

-0.5147

12.3737

.0000

-0.3454

8.3045

.0000

-0,3454

8.3045

.0000

-0.3454

8.3045

.0000

-0.3454

8.3045

.0000

-0.3454

8.3045

.0000

-0.3454

8.3045

.0000

-0.1727

4.1522

.0000

-0.1727

4.1522

1.0000

-0,1727

4,1522

1.0000

-0.1727

4.1522

l.O000

-0.1762

4.2353

1,0000

-0,1762

4.2353

1.0000

-0,1727

4_1522

.0000

.0000

.0000

.0000

.0000

.0000

.0000

.0000

.0000

,0000

,0000

.0000

.0000

.0000

.0000

,0000

-4.1522

-0.1727

1.0000

-0.3454

8,3045

1,0000

-4.1522

-0.1727

1,0000

-0.0691

1.6609

1.0000

-1.6609

-0,0691

1.0000

-0.0691

1,6609

1.0000

-1.6609

-0.0691

1.0000

-0.0691

170
48

48

4g

49

49

50

50

50

51

51

51

52

52

52

53

53

53

54

54

54

55

55

55

56

56

56

57

57

57

58

58

58

5g

5g

5g

60

60

60

61

61

61

62

62

62

63

63

63

64

64

64

65

65

65

66

66

66

67

67

67

68

68

68

69

6g

69

?0

7O

70

?I

?I

71

?2

72

72

?3

?3

73

74

74

?4

-III

3423423423423423423423423423423423423423423423423423421.6609

1.0000

-8.3045

-0,3454

1.0000

-0.1612

3,8754

1.0000

-4,1522

-0_1727

1.0000

-0.1612

3,8754

1.0000

-1.7439

-0,0725

.0000

-0.1612

3.8754

.0000

-1.7439

-0.0725

.0000

-0.2533

6,0899

.0000

-8,3045

-0,3454

.0000

-0.2533

6,0899

,0000

-6.6436

-0.2763

,0000

-0.2533

6.0899

,0000

-6.5605

-0.2729

,0000

-0,3454

8,3045

1,0000

-6.5605

-0.2729

1.0000

-0.3454

8.3045

1.0000

-8.3045

-0.3454

1,0000

-0,3454

3 8,3045 4 1,0000 2 -6.6436 3 -0.2763 4 1,0000 2 -0.2533 3 6,0899 4 1,0000 2 -0,1612 3 3,8754 4 1.0000 2 -0.0691 3 1.6609 4 1,0000 2 -0.3454 3 8.3045 4 1,0000 2 -0.2533 3 6,0899 4 1.0000 2 -0,1612 3 3,8754 4 1,0000 2 -O,06gl 3 1.6609 4 1.0000 I 16.5227 2 -2.7670

<--- RIGID BODYZ ROTRTIOM (YAW) AT 275 IN.

171
7

7

T

6

8

O

9

9

9

10

10

I0

II

11

II

12

12

12

13

13

13

14

14

14

15

15

15

15

16

16

17

17

17

IO

10

10

19

19

19

20

20

20

21

21

21

22

22

22

23

23

23

24

24

24

25

25

25

26

26

26

27

27

27

28

20

28

29

6 1,0000

16,4795

-3.0050

6 1.0000

16,4364

2 -4,8431

6 1,0000

16.3932

2 -5.8812

6 1,0000

16.3500

2 -5.9192

6 1,0000

12.4137

2 -1.5552

6 1.0000

12.3596

2 -2.8530

5 1,0000

12,3057

2 -4.1514

5 1,0000

12.2517

2 -5,4489

6 1.0000

12,1978

2 -6.7465

6 1,0000

12.1552

2 -5.5205

6 1,0000

1 12.1147

2 -6.7431

6 1.0000

8,3045

-0.3454

1.0000

8,2398

-1,9025

1.0000

8,1750

-3.4595

1.0000

8,1102

-5,0157

1,0000

8.1060

-5.0098

1.0000

8,0455

-5.5738

1,0000

4,1955

0.8654

1.0000

4.1199

-0.9512

1.0000

4,0443

-2,7679

1.0000

3,9688

-4.5845

1,0000

4,0483

-4.6710

I,O000

3,9763

2 -6.4045

6 1,0000

3.8932

2 -6.4011

6 1.0000

0.0863

2 2.0761

6 1.0000

0,0000

2 0.0000

6 1,0000

-0.0864

2 -2,076)

6 1.0000

-0.1727

172
29

29

30

30

30

31

31

31

32

32

32

33

33

33

34

34

34

35

35

35

36

36

36

3?

3?

37

38

38

38

39

39

39

40

40

40

41

41

41

42

42

42

43

43

43

44

44

44

45

45

45

46

46

46

47

47

4?

40

48

48

49

49

49

50

50

50

51

51

51

52

52

52

53

53

53

54

54

54

55

55

55

56

56

56

-4.1523

1.0000

-0.2591

-6.2284

1.0000

0.2591

6.2284

1.0000

-0,4318

-10.3807

1.0000

0.4318

10.3807

1.0000

-0.6045

-14.5330

1,0000

0.6045

14,5330

1,0000

-0.7772

-18.6852

1.0000

0_7772

10.6852

1.0000

-0.9845

-23.6680

1.0000

0.9499

22,8375

1,0000

-1,1227

-26,9898

1.0000

-0.8463

-20.3461

1,0000

?_2510

-25.6743

1.0000

-0.9672

-23.2527

1.0000

0.8146

-20,4152

.0000

-1.0536

-25,3289

.0000

0,6765

-23,7371

_0000

-1.1227

-26.9898

.0000

0.5383

-27,0589

.0000

-0.9154

-22.0071

1.0000

3.0061

-21.0610

1.0000

-1.0536

-25.3289

1.0000

2,8910

-23.0291

1,0000

-I,0570

-25.4119

1.0000

2.?528

-27,1510

1.0000

-I,1227

-26,9898

1,0000

I 5.1977 2 -21.7067 6 1,0000

173
57

57

57

58

58

58

59

59

59

60

60

6O

61

61

61

62

62

62

63

63

63

64

84

84

65

65

65

66

66

66

67

67

67

68

68

68

69

69

69

70

7O

70

71

71

71

72

72

72

73

73

73

74

74

74

-I

11

17

23

24

18

12

II

17

23

24

18

12

-I

53

53

61

61

55

55

63

63

-I

-1.0017

-24.0832

,0000

5.1056

-23.9212

.0000

-I,0536

-25,3289

,ODD0

.9674

-27,2431

.OOO0

-I.0570

-25.4119

.O00O

7.3892

-22.3525

.0000

-1.1227

-26,9898

.OOO0

7,3201

-24,0134

,DO00

-1,1227

-26,9898

.DO00

,1819

-27.3352

.0000

-1.1227

-26,9898

1,0000

5.0365

-25.5822

1.0000

2.8219

-25,4901

1.0000

0.6074

-25,3980

1,0000

7.2475

-25.7573

l,O00O

5,0330

-25.6652

1.0000

2.8185

2 -25.5731

6 1,0000

I 0,6039

2 -25,4810

6 1,0000

3 0.0833

3 0,0833

3 0,0833

3 I. 8229

3 I .5625

3 I, 3020

5 1.0

5 1.0

5 1,0

5 1,0

5 1,0

5 1.0

2 -,08333

6 1.00000

2 -.08333

6 1.00000

2 -I,66667

6 1.00000

2 -1.66667

6 1,00000

<--- AILERON DEFLECTION, T,E. UP

<--- RUDDER DEFLECTION, T,E. NEGATIUE

'v"

Note: k and p-k solutions can be run with or without the rigid-body control-mode data. When the data

are not included, appropriate changes must be made to the above file and subsequent input files.

174
Aircraft TestModel STARS-SOLIDSanalysisresults:

Table 30 showsthe resultsof the free-vibrationanalysis.Figure 52 showsthe eight elastic mode

shapes,and figure 53 showsthe threeperfectrigid-body andtwo control modes.In order to effect a

correctresponsefrom thecontrollers,theperfectrigid-bodyandcontrol modesneedto bedefinedin the

mannershownin table31.

Table30.Aircraft testmodel:Antisymmetricfree-vibrationanalysisresults.

Mode shape Eigenvalue Generalized

SOLIDS AEROS-ASE Hz rad/sec mass,Ibm Mode shape

1 ......... 114.1

2 ......... 2,533

3 ......... 531.8

4 1 10.141 63.715 8.2

5 2 12.450 78.224 235.2

6 3 14.684 92.262 46.51

7 4 28.751 180.649 60.54

8 5 29.809 187.296 204.3

9 6 32.448 203.879 47.87

10 7 35.736 224.535 3.228

11 8 51.137 321.303 239.3

12 9 ...... 2,534

13 10 ...... 151,200

14 11 ...... 589,000

15 12 ...... 128.60

16 13 ...... 14.22

Rigid-bodyX rotation (OR)

Rigid-bodyY translation (tI:DR)

Rigid-body Z rotation (OR)

Vertical fin first bending (_E)

Fuselage first bending (_E)

Wing first bending (OE)

Wing second bending (_E)

Fuselage second bending (OE)

Wing first torsion (OE)

Fin first torsion (_E)

Fuselage third bending (_E)

Rigid-body Y translation (_PR)

Rigid-body roll (_PR)

Rigid-body yaw at 275 in. (OPR)

Flap deflection (Oc)

Rudder deflection (Oc)

175
. __Mode 11, wing 3B

970341

Figure 52. Aircraft test model antisymmetric case, elastic ((I_E) mode shapes.

176
S Rigid-body mode,

X-Y plane motion

/-- Control mode, '

_l _ Rigid-body mode,

_,z_,_c_ ._/ X-rotation motion /_ Control mode,

970342

Figure 53. Aircraft test model antisymmetric case, perfect rigid body (CI)pR) and control (_c) modes.

177
Table 31. Aircraft test model rigid-body and control-mode

generationparameters.

Motion Symmetricanalysis Antisymmetricanalysis

X translation 1.0in X

Y translation 1.0in Y

Z translation -1.0 in Z

X rotation -A in Z

Y rotation -A in Z

Z rotation -A in Y

Flap -A in Z

Aileron A in Z

Elevator -A in Z

Rudder -A in Y

In table31,thetermA is definedas A= (dN- dA)/12,wheredNanddA representhecoordinatesof the

nodeunderconsiderationandtheaxisof rotation,respectively.

7.2 Aircraft Test Model: Generalized Mass Analysis (STARS-AEROS-GENMASS)

This run is made by deleting the first three-rigid body modes so that

cI) = (I)E + (1)pR + (I)C

STARS-AEROS-GENMASS input data (atm__genmass.dat):

$ BERG TEST MODES, ANTISYMMETRIC UERSION

4 39 386.088

$ LATERALLY MOVING direct Interpolation output NODE NUMBERS

I

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

2O

21

22

23

24

25

178
20

21

22

23

25

26

27

121

122

123

t24

125

126

127

128

! 29

130

131

132

Table 30 shows the calculated generalized mass.

7.3 Aircraft Test Model: Aeroelastic Analysis (STARS-AEROS-AEROL)

The input data used for the eventual ASE response analysis axe given in this section. These data also

enable flutter and divergence analysis of the aircraft. For a k method of flutter solution, the number of

reduced frequencies in the data is increased from 10 to 28, and all rigid-body and control modes must be

eliminated. For p-k solution, the number of reduced frequencies is fixed at 6, and all rigid-body and

control modes must also be eliminated. Figures 54 to 56 show the aircraft test model-relevant

aerodynamic model arrangements.

970343

Figure 54. Aircraft test model antisymmetric case, one-half aircraft aerodynamic boxes.

179
Buttline,

in.

200--

150 --

100--

50-

0

Top view

_1

m

7

6

I

4

14

5O

0

Side view

14

15

I I I I I I

0 1O0 200 300 400 500

Fuselage station, In.

Figure 55. Aircraft test model antisymmetric case, aerodynamic panels.

I

600

970344

200

150

Buttllne,

in. 100

50

0

100

Waterline,

in. 50

Top view

I I

IIII

IIII //// I I

/ I

/ I

/ I

/ I

(,

Side view

r

I I I I I I

0 100 200 300 400 500

Fuselage station, in.

(a) Aerodynamic boxes.

Figure 56. Aircraft test model antisymmetric case, aerodynamic boxes.

v

I

6OO

970345

180
-15

I I I I I

0 1O0 200 300 400

Fuselage station, in.

(b) Slender-body definitions.

Figure 56. Concluded.

645

l JJJ

I I

500 600

970346

STARS-AEROS-AEROL input data (atm_aero_ase.dat), ASE flutter analysis:

AIRCRAFT TEST MODEL - ANTISYMMETRIC CASE - flCNTRL = 5

SET UP FOR ASE SOLUTION.

DIRECT SURFACE IHTERPOLRTIOH,

8 ELASTIC MODES FROM 11 SOLIDS (-3 RT GENMRSS) + 3 PERF• RIG. + 2 CONTROL

FILE FOR RSE, FOR FLUTTER USE COHUERT TO EXCLUDE RBC'S, FOR FRESP USE fiLL

MACH NO, - 0.g0 RLTITUDE: SEA LEUEL

I 13 3 10

1 0 0 0

I 0 0 0

0 0 0 0

1

38.89 0.90

11000,0 1000,0

0.667 0,500

• 10 -.40

1,0

77.78 15000.

-I 15 I 1200

508.0 580.0

0.0 0,0

O, 0 O. 3333

O, 0 O. 3333

532.0 600,0

0,0 0,0

O. 0 O. 2353

0,0 1.0

580.0 600.0

0.0 0_0

0,0 1,0

O, 0 0. 3333

255,0 350,0

0.0 O,O

0.0 0.25

0,0 0,5

262,5 328.125

0.0 0.0

0.0 0.3333

0,0 0.34

275,0 331 .25

0.0 0.0

O. 0 0,3333

0.0 0.34

287.5 350.0

0,0 0,0

0,0 0.25

0.0 0.34

328.125 350.0

0.0 0.0

0,0 I .0

0.0 0,34

331.25 350,0

0.0 0.0

0.0 I .0

0.0 0.34

I 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 99 0 0

100,0 50,0

0.25

1400, 80,0

10.0 5.0 1,0

0 0 I

90,0

532,0 580,0 20.0 80,0

4 4 0,0

O. 6666 I,0

O.6666 I,0

90. O

540,0 600,0 80.0 IOO.O

2 5 0,0

O. 4705 0,7059 I .0

90,0

580.0 600.0 20,0 80,0

4 2 0,0

0. 6666 I .0

262,5 350,0 20,0 50.0

3 5 0,0

0.50 0.75 1,0

1.0

275,0 331.25 50.0 I00.0

4 4 0.0

O. 6666 I , 0

0.66 I .0

287.5 334.375 I00,0 150,0

4 4 0,0

0,6666 I ,0

0.66 I ,0

300.0 350.0 150.0 200,0

4 S 0.0

0.50 0.75 1.0

0.66 I .0

331 .25 350.0 50,0 100.0

4 2 0.0

0.66 1.0

334,375 350,0 100.0 150,0

4 2 0,0

0.66 I,0

181
520.0 580.0 527.5 580.0 20.0 50.0

0.0 0,033 0,0

0.0 0,4167 1.0

0.0 0.5 1.0

527.5 580.0 540.0 580.0 50.0 100.0

0.0 0.043 0.0

0.0 0.416? 1.0

0.0 0.34 0.66 1.0

580.0 600.0 580.0 600.0 20.0 50.0

0.0 0.032 0.0

0.0 1.0

0.0 0.5 1.0

580.0 600.0 580.0 600.0 50.0 100.0

0.0 0.042 0,0

0,0 t.O

0.0 0.34 0.66 1.0

-5,0 600.0 -5.0 600.0 0.0 20.0

-20.0 0.02 11 0.0

0.0 0.t074 0.2149 0.3223 0.4298 0.5085

0.5868 0.6777 0.7769 0.8678 1.0000

0.0 1.0

-5.0 600.0 -5.0 600.0 20,0 0.0

0.0 20.02 11 0.0

0.0 0.1074 0.2149 0.3223 0.4298 0.5003

0.5068 0.6777 0.7769 0.8678 1.0000

0,0 l,O

0.0 0.0 140 I 0.0 76 95

-15.000 25.000 85,000 145.000 205,000 245,000

295.000 335.000 365.000 425.000 485.000 565.000

605.000 645.000

0.0 I0.0 20.0

40,0 40.0 40.0

20.0 15.0

1002 161

T 161

401

7 502,0

2.0

7 542.0

2,0 17,0

? 578.0

2.0 17.0

2 598.0

82.0 t00.0

580.0 20.0

20I1

2 582.0

22.0 78,0

2 598.0

22,0 78,0

T 441

6011

11 252.0

2.0 25,0

167.0 183.0 I t 270.0

2.0 25.0

167.0 183.0

II 298,0

2,0 25,0

167.0 183.0

11 323.0

2.0 25.0

167.0 183.0

3 348.0

2,0 25.0

I

2.0 542.0

17.0 37,0

2.0 560.0

37.0

2,0 578.0

40.0

82.0 598,0

580.0

22,0 582.0

22.0 598,0

4

152.0

328.125 2

0

6 330,0

52.0

6 348,0

52.0

T 151

301

6 522.0

20,0

6 550.0

20_0

6 578,0

20.0

580.0

20t

6 582.0

20.0

6 598,0

20.0

20_0 20.0 40.0

30.0 30.0 20,0

100.0

50,0 75.0 85.0

I00.0

50,0 75.0 85,0

100.0

50.0 73.0 82.0

100.0

80,0

78,0

78,0

2.0 302.0 200.0

50.0 67.0 83,0 102.0

200.0

2.0 313.0 200.0

50.0 67.0 83.0 102,0

200,0

2.0 324,0 200.0

50.0 67.0 83.0 102.0

200,0

2,0 336.0 200.0

50.0 67.0 83.0 102,0

200.0

2,0 348.0 48,0

48,0

348.0 152.0 348.0 200.0

167.0 183.0 200.0

50.0 334.375 150.0

11

52,0 336.0 148.0

67.0 83,0 102.0 125.0 148.0

52,0 348,0 148.0

67.0 83.0 102,0 125,0 148.0 I

20.0 542.0 I00.0

40.0 55.0 72,0 87,0 I00,0

20.0 562,0 I00,0

40.0 55,0 72,0 87,0 I00.0

20,0 578.0 IO0.O

40,0 55.0 72,0 87.0 100.0

20.0 580.0 100,0 I

20.0 582_0 100.0

40,0 55,0 72,0 87,0 100.0

20,0 598.0 100.0

40.0 55.0 72.0 87,0 100.0

I00.0

I00.0

I00_0

125,0

125,0

125.0

125.0

150.0

150.0

150.0

150.0

• I

182
12 2 14

O,O IOO.O 150.0 200.0 250.0 300.0

350.0 400.0 450.0 50O,O 560.0 600.0

0

STARS-AEROS-AEROL input data (atm_aero_k.dat), k-type flutter analysis:

The data presented here pertain only to changes required in the corresponding ASE analysis case and

occur within the first 16 lines, which are replaced by these 19 lines.

AERO TEST MODEL - ANTISYMMETRIC CASE

K-FLUTTER SOLUTION

8 ELASTIC FROM 11 IN SOLIDS (-3 AT OENMASS, Ic(2S) = 1, - 3 PERF. RIGID - 2 CONTROL)

DIRECT SURFACE INTERPOLATION /// CORRECTED INTERP FORMAT AND POINTS

STARS STRUCTURAL MODEL, BYPASS RIGID BODY MODES IN GENflRSS

MRCH NO.=O.9O

I 13 3 28

I 1 0 0

I 0 O 0

0 0 O 0

1

38.89 0.90

.350 .745

2. DO0 2. 450

4.150 4,551

Ig.O00 24.070

,10 -,40

1,0

5 9 10 11

ALTITUDE: SEA LEUEL

1 0 O 0 O O

0 0 O 0 0 0

I O O 0 0 0

O 0 O 99 0 0

.940 1,4gl 1.615

2,750 3,150 3.270

5,250 7.000 9.000

50.000 140,000 315.774

1400. 80.0

12 13

1.698 1,864

3.400 3,850

11,110 15.000

616.746 1200,000

STARS-AEROS-AEROL input data (atm_aero_pk.dat), p-k-type flutter analysis:

The data presented here pertain only to changes required in the corresponding ASE analysis case and

occur within the first 16 lines, which are replaced by these 17 lines.

READ TEST MODEL - RHTISYMMETRIC CASE -

PK-FLUTTER SOLUTION

8 ELASTIC FROM I1 IN SOLIDS (-3 AT GENMASS, Ic(25) " I, - 3 PERF. RIGID - 2 CONTROL)

DIRECT SURFACE INTERPDLRTION /// CORRECTED IHTERP FORMAT AND POINTS

STARS STRUCTURAL MODEL, DYPRSS RIGID BODY MODES IN GENMASS

MACH NO.=O.gD

-I 13 3

1 I I

I 0 0

0 0 0

1

38.89

20 200.0

IO. OE-04

.I0

1.0

5 9 I0

0.90

ALTITUDE: SEA LEUEL

6 1 O 0 O 0 0

0 0 O O 0 1 0

O 1 0 0 0 0 0

O 0 0 O 99 O 0

40.0

.21 2.0 4,0 6,0

-.40 1400, 80.0

11 12 13

7,0 8.0

STARS-AEROS-AEROL analysis results:

Table 32 shows the results of flutter analysis by various methods using direct interpolation of modal

data. The flutter solution based on the ASE method using state-space formulation employs a data file (as

in section 6.4) and is presented in sections 7.4 and 7.5. Figures 57 to 59 show the pattern of root location

as a function of velocity for the k, p-k, and ASE methods. In this connection, it should be noted that only

the elastic modes are considered in these analyses. In the ASE method, the real (0t) and imaginary (13)

183
parts of the eigenvalues, termed as damping and frequencies, of the state-space plant dynamics matrix

(A) are plotted against the airspeed. In the k and p-k methods, the damping term is expressed as g' =

2tx13 / w 2 where o3n = _ tx 2 + _2 and is the magnitude of the eigenvalue of the closed-loop control

n'

system A matrix.

Damping, _ 100

g'

- 200

\

\

Frequency,

rad/aec

_,8

300

_'6

">< _ 2oo

3 N _ 100

-200 - 100 0

Damplng, g' - g'

J L

J "_

J

"/ J! "I

.J J -_

4OO

J_ 8

/" _ 300

4

./ e2 100

/I

_'" Mode 3/_ 0

Figure 57. Aircraft test model k flutter analysis -- damping (g'),

antisymmetric case, using direct interpolation where g' = g x 200.

_,8

200

_'6

J

_v

_,5

_-4

_2

_'7

1000 2000

Veloclty, KEAS

970347

frequency (b), velocity (v) plot,

184
Damping,

g, -100

500

h,8

300

Frequency,

rad/sec ,_

I 4_.._5'200

I- _'1

100

__ _, 3 "" """ _.2

- 200

- 200 - 100

Damping, g'

J

40O

Mode 6 /_

Mode 7f/

/- #

,..I

0 _g,

Velocity, KEAS

1000

_.2

__' _,6_,5 _.8

_.3

.4

Mode 8 "

,-_ _ Mode 5.

/. ,'_ _ Mode 1

J _ _-Mode 2 N

Figure 58. Aircraft test model p-k flutter analysis -- damping (g'),

antisymmetric case, using direct interpolation where g' = g x 200.

40O

300

_,8

2oo _ ____4;C5- --

",7 ElL1

100 j _,3--_,2

0 1000 2000

Velocity, KEAS 970348

frequency (b), velocity (v) plot,

185
Frequency,

red/sac

Damping, _ 100

g'

- 200

500

- 200 - 100 0

Damping, (X (_

Y

Velocity, KEAS

_1 1000

_; _7

2000

-_42, _.s, _.e

_ P

A ,

500

_ 400

300 /-'_'6--

• _ _ _. Mode 8

7 _.4

200 _ _ _

de 1 " MlOde5 f

Mode 3 _ _ _

__e_v 0 1000 Velocity, KEAS

970349

Figure 59. Aircraft test model ASE flutter analysis m damping (a), frequency (b), velocity (v) plot,

antisymmetric case, using direct interpolation.

7.4 Aircraft Test Model: Aeroelastic Analysis (STARS-ASE-CONVERT)

The input data presented here enable the appropriate reordering of generalized matrices. For the

flutter analysis, only the eight elastic modes (_E) are used. For the ASE solution, the three perfect rigidbody modes ((1)pR) are placed in the front, followed by eight elastic modes (OE) and two rigid-control

modes (_c).

STARS-ASE-CONVERT input data (atm_aero_convert.dat), ASE flutter solution:

$ COHUERT FILE FOR RSE FLUTTER RRD OIUERGEHCE $OLUTIOH

8

$ rlODRL SELECTIOH RHD ORDERtHG

1,1

2,2

186
3,3

4,4

5,5

6,6

8,15

STARS-ASE-CONVERT input data (atm_ase_convert.dat), ASE frequency response and damping

solution:

CONVERT FILE FOR ASE SOLUTION

t3

MODAL SELECTION RNO ORDERING

9,1

10,2

11,3

1,4

2,5

3,6

4,7

5,8

6,9

7,10

8,It

12,12

13,13

7.5 Aircraft Test Model: Aeroservoelastic Analysis (STARS-ASE-PADE)

The input data presented here effect curve fitting of unsteady aerodynamic forces employing Pad6

polynomials. The state-space matrices are also formed in this module. Version I of the input file pertains

to the ASE flutter solution, whereas version II corresponds to the subsequent ASE frequency-response

and damping solution. The generalized mass, generalized damping, and natural frequencies are output by

STARS-ASE--CONVERT into the file MDF_PADE.DAT, which can then be cut and pasted into the

PADI_ input files.

STARS-ASE-PADt_ input data (atm_aero_pade.dat), ASE flutter solution:

RTM RSE FLUTTER RNRLYSIS, 0.9 MILCH AT SEA LEVEL - VERSION I DATA

O, B, O, O, O, 10, 2, 1.0, 1004.?9, 3.2, O, 69

TENSIOH COEFFICIENTS

0.4 0.2

GENERALIZED MRSS

,2543E*00 0,0 0,0 0.0 0_0 0,0 0.0 0,0

,7310E*01 0,0 0,0 0.0 0.0 O.O O.O

.1446E÷01 0.0 0.0 0.0 0.0 0.0

,t882E+01 O.O 0.0 0.0 0.0

,6351E*01 0,0 0.0 0.0

,1488E*01 0.0 0.0

.1003E*00 0,0

.7438E+01

GEHERRL I ZED DRilP ING

, OOOOOOOOE+OO . OOOOOOOOE+OO .OOOOOOOOE+OO

.OOOOOOOOE+OO .OOOOOOOOE+OO .OOOOOOOOE+OO

Natural Frequenciea (radians)

.63715276E*02 ,7_224005E÷02 ,92261642E+02

. 18729576E+03 .20387943E+03 .22453529E÷03

VELOCITIES FOR FLUTTER AND DIVERGENCE RHRLYSIS

1.0

100.0

200.0

300. O

400.0

500.0

600.0

700,0

.OOO00000E*OO

.O00000OOE+O0

.18064940E+03

.32130318E+03

187
800.0

900.0

1000,0

1100.0

t200.O

]210.0

1220.0

1230.0

1240.0

1250.0

1260.0

1270,0

1280.0

1290.0

1300.0

1400.0

1500.0

1600.0

1TO0.O

1800.0

1900.0

2000.0

2050,0

2100.0

2150_0

2200,0

2250.0

2300,0

2350,0

2400,0

2450.0

2500,0

2550.0

2600.0

2650,0

2700.0

2710.0

2730.0

2740.0

2750.0

2760,0

2780,0

2790,0

2800,0

2850.0

2875.0

2900,0

2950.0

3000.0

3050.0

3100,0

3150,0

3200.0

3250,0

3300.0

3350,0

3400.0

3450.0

3500.0

3550.0

3600,0

STARS-ASE-PADI_ input data (atm_ase_pade.dat), ASE frequency response and damping solution:

$ RTM RSE ANALYSIS, O.g MRCH AT 40K FEET - VERSION II DATA

3_ 8, 2, O_ 2, I0, 2, 0.24708, 871,27, 3.2, O, 0

$ TENSION COEFFICIENTS

0.4 0.2

$ GENERRLIZEO MASS

0.7875E+02 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0,0 0.0 0,0

0.470lE+04 0.0 0,0 0.0 0,0 0.0 0.0 0.0 0,0 0.0 0.0 0,0

0,1831E','05 0.0 0,0 0.0 0,0 0.0 0.0 0.0 0.0 0.0 0,0

0.2543E*00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0,0 0.0

0.7310E+01 0.0 0.0 0.0 0,0 0.0 0.0 0.0 0.0

O.I446E+OI 0,0 0,0 0.0 0.0 0.0 0.0 0,0

0,1882E+01 0,0 0.0 0.0 0.0 0.0 0.0

188
0,6351E+01 O.O O.O O.O 0.0 0.0

0.1488E+01 O,O O,O O.O O.O

0.1003E+00 0.0 0.0 O.O

0.7438E+01 O.O 0.0

0.3996E*01 0.0

0.4419E+00

$ GENERALIZED DRMPING

O.O000OO00E+O00.OOOOOO00E+GO O.OOOOOO00E+O00.O0000000E+O0

O.OOOOOO00E*OO O.OOOOOOOOE+OO O.OOO00OOOE+OO O.OOOOOOOOE+OO

O.OOOOOOOOE+OO O.OOOOOOOOE+OO O.OOOOOOOOE+O00.O00000OOE+OO

O.OO000OOOE+O0

$ Natural Frequencies (radians)

O.O 0.0 O.O .63715276E+02

.?SZ2400SE+02 .92261642E÷02 .18064940E÷03 .18729576E+03

.20387943E*03 .22453529E÷03 .32130318E+03 O.O

0.0

$ PHI,THETA, PSI, US, US, WS, PS, QS, RS, PHID, THAD, PSID, HOOF

O.O, O.O, 0.0, 871.27, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, O.O, -3

$ SENSOR DATA

O

300.00 O.O SO.O

O.O 0.0 0.0 I.O O.O O.O

300.00 O.O SO.O

0.0 O.O 0.0 O.O 0.0 1.0

STARS-ASE-PADI_ analysis results:

The state-space matrices generated in this module by the Version I data file are used for the flutter

solution. Table 32 shows the results. Results derived through use of Version II data are used for

subsequent ASE frequency-response and damping analyses in the next section.

Table 32. Aircraft test model: An aeroelastic antisymmetric analysis using a direct interpolation for

AEROS paneling.

Solution

k p-k ASE

Instability Velocity, Frequency, Velocity, Frequency, Velocity, Frequency

Mode number KEAS rad/sec KEAS rad/sec KEAS rad/sec

Fuselage first FI 443.3 77.4

bending

Vertical fin F2 861.3 147.3

first bending

Fin first D1 647.7 0.0

bending

Fin first D2 728.7 0.0

torsion

441.7 77.4 474.1 77.3

863.4 147.1 728.9 136.2

651.9 0.0

728.9 0.0

Analysis notes:

1) F: Flutter point

2) D: Divergence point

3) Mach = 0.90

4) Altitude = Sea level

189
7.6 Aircraft Test Model: Aeroservoelastic Analysis (STARS-ASE-CONTROL)

The input data presented here pertain to the frequency-response analysis of the aircraft test model at

Mach 0.9 and an altitude of 40,000 ft. Thus, phase and gain margins as well as damping and frequency

values are generated from this module. Figure 60 shows the block diagram for the aircraft test model

lateral-mode analog control system.

V3 _ 0.1s+511

V4 Gain 8 + Gain 10

-T

Filter

o.1 IL 112+ 1111+ 10 I_

Aileron actuator

J._ 20 11

e+20 I

_1 20 12

Rudder actuator

I O.le IL

11+0.1 J_

Filter

Roll-rllte aenllor

1372 5

II2 + 19311+ 1372

t

V1 _ P = roll rate

Is, _ pl_

V2 r =yaw rate

11372] S2 + 193S + 1372 6

Yaw rate aenllor

970350

Figure 60. Aircraft test model lateral mode analog control system.

STARS-ASE-CONTROL input data (atm_ase_controlo.dat), open-loop case:

$ ATM ANTI-SYMMETRIC 3 RIGID, O ELASTIC, AND 2 CONTROL MODES- OPEN LOOP CASE

C LOOP OPEN BETWEEN BLOCKS 3 AND 9 RS WELL AS BETWEEN 4 AND I0

58, O.O, 0.0, 3, 3

1O 4 2 I 1

48, 12, 4, 4,

I0 4 tO 6

2 I 1 2

$ BLOCK COHHECTIUITY

1 3 0 0 0 0 0

2 10 O 0 0 0 0

3 7 O 0 0 0 0

4 6 O 0 0 0 0

5 O 0 0 t 0 0

6 0 O 0 2 0 0

7 0 0 0 3 0 0

B 0 0 0 4 0 0

9 5 0 O O 0 0

10 8 0 0 O 0 0

$ TRANSFER FUNCTION DESCRIPTIONS

1 I 2 0

2 1 2 0

3 2 2 0

4 2 2 0

5 2 I I

6 1 3 0

7 1 I 0

8 1 I 0

9 2 I I

10 I I 0

$ LISTING OF POLYNOMIRL COEFFICIENTS

1 .2000E*02.0000E+OO .O000E+OO

0 .20ODE+02 .IO00E+OI ,OOOOE+OO

2 ,2000E÷02.000OE+OO ,OOOOE-OO

0 ,2000E÷02 ,lOOOE+Ot .OOOOE+OO

3 .5000E+01 ,lODGE+GO .0000E+OO

O .0000E+00 ,IOOOE+OI .OO00E+OO

190
4.0000E+O0 ,IO00E+01 .O000E+O0

0 ,IO00E+O0 .1000E+01 .O000E+O0

6 .1877E+05.0000E+O0.0000E+O0

0 .1877E+05 .1930E+03 .IO00E+OI

7 ,IO00E+OI .O000E*O0.0000E+O0

0 .1000E÷01 .O000E+O0.0000E+O0

8 ,1000E+01 .O000E+O0.0000E+O0

0 .1000E+01 .O000E+O0,0000E+O0

10 ,IO00E+OI .O000E+O0.0000E+O0

0 .IOOOE+O$ .O000E+O0.0000E*O0

$ Listing of state space matrices of control block

5 2 I 1

,000 1,000 0.0

-18770.000 -193.000 18770.

1,000 O, O.

9 2 I 1

.000 1.000 .000

-10.000 -I1,000 .100

1,000 .000 .000

$ GAIN INPUTS FOR EACH BLOCK

1 ,IO00E+OI 2 ,IO00E+OI

6 .IO00E+01 7 .1000E+01

3 .IO00E+OI 4 .IOOOE+O0 5 .IO00E÷01

O ,IO00E+O1 9 ,IOOOE+OI I0 .IO00E+O1

$ SPECIFICATION FOR SYSTEM OUTPUTS

? 8 0 0 0 0 0 0

0 0 0 0 0 0

$ SPECIFICATION FOR SYSTEM INPUTS

7 8 0 0 0 0 0 0

$ CONNECTION DETAILS FROM PLANT TO BLOCKS

2 2 0

? 1

8 2

t 1

2 2

$ FREQUENCY RANGE SPECIFICATIONS

0,1 .9 200

1.0 9. 200

I0. 90. 200

I00. 500. 100

$ LOOP DEFINITIONS - out block

I 0

4 8 I I

9 ? 1 I

0 0 O 0

Inp block outblock row

0 0 0 0

input block rol

STARS-ASE-CONTROL input data (atm_ase_controlc.dat), closed-loop case:

$ ATM ANTI-SYMMETRIC 3 RIGID, 8 ELASTIC, fiND 2 CONTROL MODES- CLOSED-LOOP CASE

C LOOP CLOSED BETWEEN BLOCKS 3 AND 9 RS WELL RS BETWEEN 4 AND 10

48, 12, 4, 4, 58, 0.0, 0.0, 3, 3

10 4 10 6 I0 4 2 1 1

2 1 1 2

$ BLOCK CONNECTIVITY

I 3 O 0 0 0 0

9 0 0 O 0 5 3

3 7 0 0 0 0 0

5 0 0 0 1 0 0

6 0 0 0 2 0 0

7 O 0 0 3 0 0

8 0 0 0 4 0 O

2 10 0 0 0 0 0

4 0 0 0 0 6 I0

I0 8 0 0 O 0 0

$ TRANSFER FUNCTION OESCRIPTIOMS

1 l 2 0

2 1 2 0

3 2 2 O

4 2 2 0

5 2 1 I

6 I 3 0

7 I 1 O

8 I 1 0

g 2 I 1

I0 1 I 0

$ LISTING OF POLYNOMIAL COEFFICIENTS

I .2000E+02.0000E+O0,0000E+O0

0 .2000E+02 ,IO00E÷01 ,O000E+O0

2 .2000E+02.0000E+O0.0000E+O0

0 .2000E+02 .1000E+01 .O000E+O0

3 ,5000E+01 ,IO00E+O0,0000E+O0

0.0000E+O0 ,I000E+01 .O000E +00

191
4.0000E*O0 .IO00E+01.0000E+O0

0 ,IO00E+O0 ,IO00E*O1 .O000E+O0

6 .187?E+05,0000E+O0.0000E+O0

0 .1877E*05 .1930E+03 .tO00E+01

7 .1000E+01 .O000E+O0.0000E+O0

0 .IO00E+01 .O000E*O0,0000E+O0

8 .IO00E*Ot .O000E+O0,0000E+O0

0 .IO00E+Ot .O000E+O0.0000E*O0

10 .IO00E+01 .O000E*O0.0000E+O0

0 .IO00E+01 .O000E+O0.0000E+O0

$ Lteting of state opaco matrices of control block

5 2 1 I

.000 1.000 0.0

-18770.000 -193,000 18??0,

1,000 O, O.

9 2 1 1

.000 1.000 .000

-I0.000 -11.000 .100

1.000 .000 ,000

$ GRIN INPUTS FOR EACH BLOCK

1 .1000E+01 2 ,tO00E+01

6 .IO00E+OI 7 .IO00E+01

3 ,1000E+01 4 .IO00E*O0 5 .1000E+01

8 .1000E+01 9 .1000E+01 10 ,1000E+01

$ SPECIFICATION FOR SYSTEM OUTPUTS

? 8 0 0 0 0 0 0 0

0 0 0 0 0 0

$ SPECIFICRTION FOR SYSTEM INPUTS

? 8 0 0 0 0 0 0

$ CONNECTION DETAILS FROM PLANT TO BLOCKS

2 2 0

7 I

B 2

1 I

2 2

$ FREQUENCY RRNGE SPECIFICRTIONS

0.1 .9 200

1.0 9. 200

10. 90, 20O

100. SO0, tO0

$ LOOP DEFIMITtOMS - out block inp block outblock row

0 0

999 8 B 1

999 T 7 1

0 0 0 0 0 0 0

input block row

STARS-ASE-PADt_ analysis results:

Figures 61 and 62 show the lateral-loop gains for the roll and yaw modes, respectively. The gain

margins are tabulated in table 33.

Table 33. Aircraft test model gain and phase

margins.

Phase crossover, Gain margin,

Mode rad dB

Roll 20.20 78.26

Yaw 2.90 -0.80

192
50 --

0

B50 --

-150 --

- 200 --

- 250

.1

Gain, _ 100

dB

11 l[tlll [ II IIIIII I II IIIIII t II tlllll

1 10 100 1000

Frequency, red/aec

970351

(a) Gain.

Phase

angle,

deg

200 --

100--

0

-100 --

- 200

.1

II

1 10

Frequency, rad/sec

\

II IIIIII

100

(b) Phase.

Figure 61. Aircraft test model lateral loop gains, roll mode.

I II ILIIII

1000

970352

193
2O

0

- 20

Gain, - 40

dB

- 60

-80

-100

-120

.1

I II IIIIII I II IIIIII I II IIIIII I II

1 10 100

Frequency, racl/sec

(a) Gain.

It1111

1000

970353

200

IO0

Phase

angle, 0

deg

-100

I I I IIIIII I

I

_=00 I IIIIII I II IIIIII I II IIIIII

.I 10 100 1000

Frequency, rsd/aec

970354

(b) Phase.

Figure 62. Aircraft test model lateral loop gains, yaw mode.

Figure 63 shows the closed-loop damping and frequency plots. These results were obtained

by running the output of STARS-ASE-CONTROL through STARS-ASE-FRESP. Approximately

20 altitudes, represented by pairs RHOR and VEL data in STARS-ASE-PADI_, were required to track

194
the modes,startingat analtitudeof 80,000ft, whereaerodynamicforcesarenegligible andfrequencies

approximate the structural frequencies,and descendingto sealevel. Most of the analyseswere

performed betweenaltitudes of 10,000and 30,000 ft, and the remainder were performed at each

10,000-ft increment. Root locus plots (either of real against imaginary frequency or frequency

magnitudeagainstgain)canbemadeto helpin thetrackingprocess.Frequencycoalescenceof the first

two modesoccursat approximately77.42rad/secandanequivalentvelocity of 263 knots; aroundthis

point, mode2 goesunstable(dampinggoesnegative),andtheaircraftflutters.

Damping,

g

1.0

.8

.6

.4

.2

0

_,2

140

120

Frequency,

rad/sec 100

D

m

o

0 Mode 1

I-I Mode 2

o o

0 [] []

I I I ] I I

D Frequency

coalescence --__

8o _ _ /VD []

oo jo t I I I I

60 0 1O0 200 300 400 500 600

Equivalent velocity, kn 970355

Figure 63. Aircraft test model closed-loop damping, v-g, and frequencies, v-f.

7.7 Aircraft Test Model: Run-Stream Details

This section provides details for analyzing the aircraft test model. Most of these details are

applicable to any analysis to be performed with these modules. All aircraft test model analyses were

performed using double-precision (RL) arithmetic. Any file name can be chosen by the user for the input

and output, although a large number of FORTRAN tapes (for example, fort.20, in Unix notation)

are used by the module and should be avoided. Table 34 shows the file names used for the aircraft

test model.

In each analysis, the user is requested to give an output file name. The standard STARS procedure is

to use filename.out. The modules automatically append the ". 1" (and in the case of STARS-SOLIDS,

".2") to the ".out" file extension and should not be added by the user.

195
Table34.Input files forlinearaeroelasticandaeroservoelasticanalysis.

DATA INPUT FILES (atm_*.dat)

ASEanalysis(frequency

Aeroelasticanalysis(flutter anddivergence) responseanddamping)

k method p-k method State-spacemethod State-spacemethod

solids(SRUN)

genmass(ARUN)

aero_k(ARUN)

solids

genmass

aero_pk(ARUN)

Note:Run-streamtypeindicatedatthe

first appearenceof theanalysismode

(appendixC).

solids

genmass

aero_ase(ARUN)

aero_convert(ASERUN)

aero_pade(ASERUN)

solids

genmass

aero_ase

ase_convert(ASERUN)

ase_pade(ASERUN)

ase_controlo(ASERUN)

ase_controlc(ASERUN)

STARS-SOLIDS(SRUN):

The solids analysisis performedwith MAINIB (matrix assembly)andEIGLAN (eigensolver)but

without RESPONSE(staticor dynamicresponse).The input file is atm_solids.dat,andtheoutputfiles

areatm_solids.out.1andatm_solids.out.2.

STARS-AEROS-GENMASS(ARUN):

The generalizedmassis calculatedusing atm_genmass.datas the input file. The output file is

atm_genmass.out. 1.

STARS-AEROS-AEROL (ARUN):

The k flutter solution is achieved using atm_aero_k.datas the input file. The output file is

atm_aero_k.out.1.An input file, atm_aero_pk.dat,is usedto obtainthe p-k flutter solution.Theoutput

file is atm_aero_pk.out.1.The ASEflutter solutionis obtainedby usingatm_aero_ase.datastheinput

file; theoutputfile is atm_aero_ase.out. 1.

In both k andp-k methods,for a particular combinationof Mach numbersand altitudes(density

ratios),analysesareperformedfor anumberof reducedvelocities(V/bt.o).In thek method,any change

in sign of damping value betweentwo reducedvelocities indicates the occurenceof flutter. In the

p-k method,results areobtained for each modecorrespondingto a specifiednumber of equivalent

velocities,and a flutter occurenceis indicatedby a sign changein damping.In the ASE method,the

state-spacematricesare computedfor a numberof equivalentvelocities, and the onsetof flutter is

detectedsimilarly.

Thek flutter solutionis determinedby trackingmodes.Theheading"FLUTTER SOLUTIONS"can

beusedto find the tracking datain the file. In the caseof the aircraft testmodel,the rigid-body and

control modes were included in the STARS-SOLIDS input file and not eliminatedin the STARSAEROS-GENMASSrun,soremovalof thesemodeswasrequiredwithin theSTARS-AEROS-AEROL

196
run.Removalof thesemodesin this way is evidencedby two (or more)modal-eliminationcyclesleft in

the outputfile: the first cycle occurswithout modalelimination,andthe subsequentcyclesoccurwith

the specifiednodeseliminated.Thesesubsequentcyclesarethe onesrequiredfor modaltracking, and

thekeyword"ELIM" canbeusedto find eachcycle.In this procedure,solutionsareachievedfor each

reducedvelocity involving all input modes.

Thek flutter solutiontakesthefollowing form:

1 FLUTTER SOLUTIONS

MRCH NO = .900 RNO/RHO(SL) = 1.0000 UDO - 2.?500

C.P.S. U,EOUIU. DAMPING RRO/SEC UTRUE

9.4611 313.8998 -.009525 59.4460 313.8990

12.3253 408.9283 -.001258 77,4424 408.9283

13.7619 456.589? -,241010 86,4685 456,5897

20.8653 692.2663 -.859586 131,1006 692.2663

23.5406 781.0279 -.096159 147,9102 781.0279

29.6637 984.1816 -.001318 186.3832 984.1816

31,0034 1028.6278 -.208656 194.8004 1028.6270

50.6504 1680,7400 -,004821 318.2968 1680,7400

ALL ROOTS CHECK AND ARE UNIQUE

FLUTTER SOLUTIONS

MRCH NO - .900 RHO/RHO(SL) " I.O000 UDO - 3.1500

C.P.S, U,EQUIU. DAMPING RRDISEC UTRUE

9.1079 349.1747 -,687537 57,7293 349.1747

12,3159 468.0528 ,000904 77.3835 460.0528

13.7629 523.0422 -.250741 86.4750 523.0422

17_9128 680,7542 -.812183 112.5496 680.7542

23,4177 889.9632 .034412 147,1303 889.9632

29.6160 1125.5208 -.001017 186,0833 1125,5208

31.5363 1198.4995 -.240497 198,1489 1198,4995

50.5501 1921,4016 -,005552 317,6668 1921,4016

Divergence occurs when the frequency becomes 0 with nonzero velocity. In this case, divergence is

assumed to occur when the frequency comes close to zero:

I FLUTTER SOLUTIONS

MRCH NO = .900 RHO/RNO(SL) • 1.0000 UBO - 1200.0000

C,P,S, U,EQUIU. DAMPING RRD/SEC UTRUE

,0447 647.6351 -.004645 .2011 647.6351

,0503 720.6937 -.002378 .3162 729.6937

.3510 5092.5231 .000631 2.2101 5092.5231

.6277 9087.7691 .000319 3.9440 9087.7691

1,0180 14730,4153 -.001101 6.3964 14730,4153

,0000 .0000 .O000OO .OOOO .O00O

.0000 .0000 .000000 .OOOO .0000

.O00O ,0000 .000000 ,OOOO .0000

The p-k flutter solution takes the following form:

VELOCITY, DAMPING, fiND FREQUENCY VARIATIONS

...........................................

UELOCITY, KNOTS DAMPING

MODE NO EQUIUALEHT TRUE RRTIO

FREQUENCY

CYC/SEC RRDISEC

1 200.0000 200,0000 -.402503E+DO 10.3220

2 208.0000 200.0000 -.503228E+00 10.3706

3 216.0000 216.0000 -.524200E+00 10,4226

4 224.0000 224.0000 -,545422E+00 10.4782

5 232.0000 232.0000 -.566906E+00 10,5378

6 240.0000 240.0000 -.506644E*00 IO.6Ol?

7 248,0000 248.0000 -.610640E+OO 10.6701

64.8549

65,1604

65,4070

65.8366

66.2111

66.6124

67,0427

197
89

10

11

12

13

14

15

16

17

18

19

2O

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

7O

71

72

73

74

75

76

77

78

79

00

81

82

83

84

85

06

87

88

09

9O

256.0000

261,0000

272.0000

280.0000

288.0000

296.0000

304.0000

312.0000

320.0000

328.0000

336.0000

344,0000

352.0000

360.0000

368.0000

376.0000

384.0000

392.0000

400.0000

408.0000

416.0000

424.0000

432.0000

440,0000

441,6702

448.0000

456.0000

464.0000

472.0000

480.0000

488.0000

496.0000

504.0000

512.0000

520.0000

528.0000

536.0000

544.0000

552.0000

560.0000

568.0000

576.0000

584.0000

592.0000

600,0000

608.0000

616.0000

624.0000

632.0000

640.0000

648.0000

656.0000

664.0000

6?2.0000

680.0000

680.0000

696.0000

704.0000

712.0000

720_0000

728.0000

736.0000

744.0000

752,0000

760,0000

768.0000

776.0000

784.0000

792.0000

800.0000

808.0000

816.0000

824.0000

832.0000

840.0000

840.0000

856.0000

863.3683

864.0000

872.0000

880.0000

888.0000

896_0000

256.0000

264.0000

272.0000

280,0000

288.0000

296,0000

304.0000

312.0000

320.0000

328.0000

336,0000

344.0000

352.0000

360.0000

368.0000

376,0000

384.0000

392.0000

400.0000

408.0000

416.0000

424.0000

432.0000

440.0000

441.6702

448.0000

456.0000

464.0000

472.0000

480.0000

488.0000

496,0000

504.0000

512.0000

520.0000

528,0000

536.0000

544.0000

552.0000

560.0000

568.0000

576.0000

584.0000

592.0000

600.0000

608.0000

616.0000

624.0000

632.0000

640.0000

648.0000

656.0000

664.0000

672,0000

680,0000

688,0000

696.0000

704,0000

712.0000

720.0000

728,0000

736.0000

744.0000

752.0000

760,0000

768,0000

776,0000

784.0000

792.0000

800.0000

808.0000

816.0000

624.0000

832,0000

840.0000

840,0000

856,0000

863.3683

864.0000

872.0000

880.0000

888,0000

896,0000

-.632889E÷00

-.656156E+00

-.680545E+00

-.705171E+00

-.729992E+00

-.754972E+00

-.780058E+00

-.805191E+00

-.830310E÷00

-,855324E+00

-.880149E+00

-,904681E+00

-.928800E+00

-.952380E+00

-.975270E+00

-.997305E+00

-.101830E+0t

-.103806E+01

-.105635E+01

-.107294E+01

-.I08758E*01

-.I09998E+01

-. I0985E+01

-. 11685E÷01

-, tl792E+01

-. 12063E+01

-. 12078E+01

-, 11676E+01

110791E+01

-.109325E+01

-.107116E+01

-,103952E+01

-,988966E+00

-.872770E*00

-.740957E+00

-.650212E+00

-.597452E+00

-.540848E+00

-.508324E+00

-,473635E+00

-,443306E+00

-.415878E+00

-.391273E+00

-.369042E+00

-.348601E+00

-.3295?3E÷00

-.311710E÷00

-.294838E+00

-.278031E+00

-.263592E+00

-,249045E+00

-.235127E+00

-.22178?E÷00

-.208978E+00

-,196662E+00

-.104804E+00

-.173373E+00

-.162341E+00

-.151684E+00

-,141379E+00

-.131407E*00

-.121748E+00

-.112385E+00

-.I03305E+00

-.944923E-01

-.859339E-01

-.776179E-01

-.695336E-01

-.616707E-01

-.540198E-Ot

-.465723E-01

-.393199E-01

-.322551E-01

-.253710E-01

-,186608E-01

-,121184E-01

-.573800E-02

.190619E-06

.485787E-03

,655809E-02

.124896E-01

.182745E-01

.239220E-01

10.7436

10.8196

10.8989

10.9855

11.0800

11.1831

11.2955

11.4179

11,5513

11.6967

11.8550

12.0275

12.2153

12.4199

12.6427

12.6854

13.1498

13.4377

13.7514

14.0931

14.4654

14.8712

15.3134

15.7956

t5.9017

16.3216

16,8958

I?.5233

18.2101

18.9636

19,7932

20,7511

22.0363

23.4992

23.9871

24.0359

23,9970

23,9279

23,8488

23.7701

23,6974

23.6303

23.5740

23,5291

23,4930

23,4635

23,4390

23.4183

23.4004

23.3849

23.3714

23.3594

23.3489

23.3397

23.3317

23.3248

23.3191

23.3143

23.3106

23.3078

23.3060

23,3051

23,3052

23.3062

23.3080

23,3107

23,3143

23,3108

23.3241

23.3302

23.3372

23.3450

23.3535

23.3629

23.3731

23.3840

23,3958

23.4072

23.4082

23.4215

23,4355

23,4502

23.4657

67.5044

67.9820

68.4800

69.0240

69.6179

70.2655

70.9716

71.7410

72.5794

73.4927

74.4875

75.5710

76.7514

?8.0368

79.4368

80.9617

82.6227

84.4319

86.4027

88.5499

90,8893

93.4385

96.2174

99.2471

99.9135

102.5521

106.1598

110.1023

114,4175

119,1522

124,3645

130.3832

138.4584

147.6503

150.7160

151.0224

150,7777

150.3436

149.8466

149,3525

140.8955

140,4737

148.1200

147.8379

147.6111

147.4260

147,2720

147.1417

147.0296

146.9322

146.8469

146,7718

146,7058

146.6480

146.5978

146.5547

146.5183

146.4885

146.4650

146.4477

146.4363

146,4309

146,4312

146,4373

146.4489

146.4661

146.4887

146.5167

146,5500

146,5805

146,6322

146,6011

146,7350

146,7939

146.8578

146,9265

147.0002

147.0723

147.0786

147.1618

147.2499

147.3425

_47,4398

198
91 904.0000 go4.0000 ,294363E-01 23,4819 147,5416

92 912.0000 912.0000 .348190E-01 23.4989 147.6482

93 920.0000 920.0000 .400?74E-01 23.5166 147,7592

94 928.0000 928.0000 .452131E-01 23.5349 147.8747

95 936.0000 936.0000 .129788E-01 12.2056 ?6.6904

96 944.0000 944.0000 .131716E-01 12.2022 76.6690

97 952.0000 952.0000 .133626E-01 12.1988 76.6473

98 960.0000 960.0000 .135516E-01 12.1953 76.6252

In the above table, flutter mode 2 is tracked first, and zero damping can be noted corresponding to an

equivalent velocity of 863.3 KEAS. The first flutter is listed in the next table in the file, and so forth.

Divergence cannot be found with the p-k technique. Elimination cycles are also permitted with the

p-k method, similar to the k method, and the information applicable to the k method also applies to the

p-k method.

The ASE flutter solution does not use modal-elimination cycles, so the rigid-body and control modes

are included in the run. The results in the file atm_aero_ase.out. 1 are not useful to examine because the

run is an intermediate step toward the solution.

STARS-ASE-CONVERT (ASERUN):

This module converts the results from the STARS-AEROS-AEROL ASE flutter solution into

a form that can be used with the Pad6 curve-fitting module, STARS-ASE-PADt_. Modes can also

be eliminated.

The input file for flutter solution is atm_aero_convert.dat, and the output file is

atm_aero_convert.out. 1. This solution method eliminates all rigid-body and control modes.

The input file for response analysis is atm_ase_convert.dat, and the output file is

atm_ase_convert.out. 1. Because control and perfect rigid-body modes are desired for this analysis, they

are not eliminated.

STARS-ASE-PADI_ (ASERUN):

For flutter solution, the input file is atm_aero_pade.dat, and the output file is atm_aero_pade.out. 1. A

file to store the A, B, C, and D matrices is requested for flutter solution. These matrices are not stored

after the solution, so this file can be anything the user desires because it will be empty.

The first flutter is shown below, wherein flutter has not occured at an equivalent velocity of

414.8 KEAS but has occured by 474.1 KEAS. The column labeled "1" is the damping, and the column

labeled "2" is the frequency (rad/sec). The modes are ordered by velocity (knots).

DENSITY RATIO : I.O00000000OOOO0000

UELOCITY (FPS): 700.000000000000000

UELOCITY EOUIU, TRUE (KTS): 414.614814814814781 414.814814814814781

DYNAMIC PRESSURE (PSF): 582.609986886382103

ROOT

I 2

I -.2831E+00 .3205E+03

2 -.2831E+DO -.3205E+03

3 -,5420E+02 .2141E+03

4 -.5420E+02 -.2141E*03

5 -.3040E+02 .2057E*03

199
6 -,3040E+02 -.2057E+03

7 -,2144E*00 ,1870E+03

8 -.2144E+00 -.1870E+03

9 -.1544E+02 .1789E*03

10 -.1544E÷02 -.1789E+03

11 -,7873E÷01 .8676E+02

12 -.7873E+01 -.8676E+02

13 -.3130E-0! .7737E+02

14 -,3130E-01 -,7737E+02

15 -.4080E+02 ,7863E÷02

16 -.4080E+02 -,7863E+02

17 -.I007E*03 .3933E+01

18 -.I007E+03 -.3933E+01

19 -,2821E+02 ,2302E+02

20 -.2821E+02 -.2382E+02

21 -,3657E+02 ,2775E+02

22 -.3657E+02 -.2775E+02

23 -.9187E+02 .O000E*O0

24 -.3723E÷02 .O000E+O0

25 -.8742E÷02 .O000E+O0

26 -.8750E+02 ,O000E+O0

27 -.8751E+02 .O000E+O0

28 -.4186E+02 ,O000E÷O0

29 -.4313E÷02 .O000E+O0

30 -.4380E+02 .O000E+O0

31 -.4375E+02 .4767E-02

32 -,4375E+02 -.4767E-02

OENSITY RATIO : 1.00000000000000000

UELOCITY (FPS): 800.000000000000000

UELOCITY EOUIU, TRUE (KTS): 474.074074074074019 474.074074074074019

OYHAMIC PRESSURE (PSF): 760,95998287200927?

ROOT

5

6

7

8

9

10

1t

12

13

4

5

5

7

8

9

20

2t

22

23

24

25

26

27

28

29

30

31

32

I 2

1 -.3242E*00 .3204E+03

2 -.3242Eo00 -.3204E+03

3 -,7224E+02 ,2091E+03

4 -,7224E+02 -.2091E+03

-,4511E*02 .2045E+03

-,4511E*02 -.2045E+03

-.2121E+00 ,1869E+03

-.2121E*00 -.1860E+03

-.1690E+02 .1812E+03

-.1690E+02 -.1812E+03

-.4300E+02 .9909E+02

-.4300E+02 -.9909E+02

-.7930E÷01 .8671E+02

-.7930E+01 -.8671E+02

.7707E-01 .7730E+02

,7707E-01 -,7730E+02

-.1162E÷03 .5194E+01

-,1162E+03 -,5194E+01

-,2408E+02 .2008E+02

-.2488E+02 -.2008E÷02

-,3325E+02 .3279E+02

-.3325E+02 -,3279E+02

-,1061E+03 .O000E+OO

-.4139E+02 .O000E+O0

-,9990E+02 .O000E+O0

-.9999E+02 .O000E*O0

-.IO00E+03 ,O000E+O0

-.4737E+02 .O000E+O0

-.4911E+02 .O000E+O0

-,5006E+02 .O000E+O0

-.5000E÷02 ,7061E-02

-.5000E+02 -,7061E-02

The keyword "DENSITY" can be used to find each mode.

For response analysis, the input file is atm_ase_pade.dat, and the output file is atm_ase_pade.out. 1.

The file to store the A, B, C, and D matrices is abcd.dat.

2O0
STARS-ASE-CONTROL(ASERUN):

Open-andclosed-loopanalysesareperformedwith this module.Open-loopanalysesneedto berun

throughthemoduleSTARS-ASE-FRESP,asdescribedlater.

For closed-loopanalysis,theinput file is atm_ase_controlc.dat. The file containingthe A, B, C, and

D input matricesis abcd.dat.Theloop conditionmustbesetto closed;the closed-loopeigensolutionis

set to root40k.datfor the40,000-ft altitudecasepresentedin the manual.The closed-loopoutput file

nameis setto atm_ase_controlc.out. 1

The closed-loopeigensolutionof the state-spaceA matrix containsfive columnsof data:the mode

number;columnsfor thereal,imaginary,andmagnitudeof thefrequency(rad/sec);andthedamping.

THE CLOSED LOOP EIGENURLUE SOLUTIONS

MOOE • REEL IMAG DAMP FRO (Pod)

I -.104187E+00 ,321131E+03 ,321131E+03

2 -,104187E+00 -,321131E+03

3 -.212778E+02 .220098E+03

4 -+212778E+02 -.220098E+03

5 -,I00747E+02 .203305E+03

6 -.IOD747E+02 -.203305E+03

7 -.157889E+00 ,187182E*03

8 -,157889E+O0 -.187182E+03

9 -,710996E+01 .178727E+03

IO -,710996E+01 -.I?D72?E+03

11 -.965000E+02 .972510E+02

12 -.96500DE+02 -.g?2510E+02

13 -.963736E+02 .972677E+02

14 -.963736E+02 -.972677E+02

15 -.253805E+DI .909924E+02

16 -.253DOSE+Of -,909924E+02

17 -,I09440E+00 .777426E*02

18 -,109440E÷00 -.777426E+02

19 -,866177E+01 .642722E+02

20 -,866177E+01 -,642722E+02

21 -,711187E*02 .186862E+02

22 -.711187E+02 -.186862E+02

23 -,685767E+02 ,160566E+02

24 -.685767E+02 -,160566E+02

25 -,I14222E+03 .608432E+00

26 -,114222E+03 -.608432E+0D

27 -,212286E+02 .O000OOE+O0

28 -.199939E+02 ,OOO000E+O0

29 -,110663E+03 ,O00000E+O0

30 -.I00750E+02 .O00000E+O0

31 .384948E-01 .289516E+01

32 .384948E-01 -.289516E+01

33 -,192633E+01 .896479E*00

34 -,192633E+01 -,896479E+00

35 .991211E+00 .O00000E+O0

36 -.501516E+02 ,O00000E+O0

37 ,357147E-03 .O00000E*O0

38 -,233887E-03 .O00000E*O0

39 -.802861E-02 .O00000E+O0

40 -.I08601E+03 .873500E-01

41 -.I08601E+03 -.873500E-01

42 -,996977E-01 .O00000E+O0

43 -.539246E+02 .160797E+00

44 -.539246E+02 -.160797E+00

45 -.547465E+02 ,O00000E+O0

46 -,544839E+02 .O00000E+OO

47 -,108890E+03 .O0000OE+OO

48 -,I08903E+03 ,465731E°02

49 -,I08903E+03 -.465731E-02

50 -,544333E+02 ,O00000E+O0

51 -.544496E+02 ,O00000E*O0

52 -.544520E+02 ,OOO000E+O0

53 -,108900E+03 .OOOO00E+O0

54 -.544500E+02 .OOOO00E+O0

55 -,544500E+02 .OOOOOOE÷O0

56 -_10890DE+03 .O0000OE+O0

57 -.108900E+03 .O00000E+O0

58 -.544500E+02 .OOOOOOE+OO

DAMP 1

,640879E-03

.321t31E+03 ,640879E-03

.221124E+03 ,191557E+00

,221124E+03 ,191557E+00

,203554E+03 .988669E-01

.203554E+03 .988669E-01

.187182E+03 ,168700E-02

.187182E+03 ,168700E-02

.178869E+03 ,794364E-01

.178869E+03 ,794364E-01

.137004E+03 ,999970E+00

,137004E+03 ,999970E+00

.136927E+03 .999957E*00

.136927E+03 .999957E+00

,910278E+02 .557426E-01

,910278E+02 .557426E-01

,777427E+02 .281544E-02

,777427E+02 ,281544E-02

.648533E+02 ,264726E+00

.648533E+02 .264726E+00

.735327E÷02 .491559E+00

.735327E+02 ,491559E+00

.704314E+02 .443943E*00

.704314E+02 ,443943E+00

.114224E+03 ,I06532E-01

.114224E+03 .I06532E-01

.212286E+02 ,O00000E+DO

,199939E+02 ,OOOOOOE*O0

,I10663E+03 .OOOO00E°O0

,I00750E+02 .O00000E÷O0

,289541E+01 -.265879E-01

,289541E°01 -.265879E-01

,212472E+01 .765065E*00

,212472E+01 .765065E+00

,991211E+00 .OOOO00E+O0

.501516E°02 .O00000E+O0

.357147E-03 .O00000E+O0

.233887E-03 .O00000E+O0

,802861E-02 .O00000E*O0

,10860IE+03 .160864E-02

.I08601E*03 ,160864E-02

.996977E-01 .OOOOOOE+O0

.539249E+02 ,596371E-02

.539249E+02 ,596371E-02

.547465E+02 ,O00OOOE+O0

.544839E*02 .OOO000E+O0

,108890E+03 ,O00000E+OD

,108903E+03 .855313E-04

,108903E+03 ,855313E-04

.544333E+02 ,O00000E+O0

,544496E+02 .O00000E+O0

,544520E+02 .O00000E+O0

.I08900E*03 .O00000E*O0

.544500E+02 .O00000E+O0

.544500E*02 .O00000E+O0

,I08900E+03 .O00000E+O0

,I08900E+03 ,O00000E+OO

.544500E+02 ,OO0000E+O0

201
As with thek flutter solution,modesmustbetracked.This trackingis accomplishedby startingwith

an altitude with a low-density ratio (for example,analtitude of 80,000ft), and working down to sea

level. The requireddatafor the STARS-ASE-PADI_input file (densityratio and truevelocity) canbe

obtainedfrom a referencesuchas U. S. Standard Atmosphere.* True velocity is defined as VTRUE = Cs

x M, where Cs is the speed of sound at altitude and M is the Mach number. Figure 63 shows the

damping and frequency for the first two elastic structural modes plotted as a function of the equivalent

velocity, where equivalent velocity is defined as VE = VTRUE × the square root of the density ratio

at altitude.

For this altitude, flutter mode 1 corresponds to modes 19 and 20 in the above table; flutter mode 2

corresponds to modes 17 and 18.

For open-loop analysis, the input file is atm_ase_controlo.dat, and the file containing the A, B, C,

and D input matrices is abcd.dat. The loop condition must be set to open. The file containing the

augmented A, B, C, and D matrices is abcd.aug. The STARS-ASE-FRESP input file created by this

module is atm_ase_frespo.dat, and the open-loop output file name is set to atm_ase_controlo.out. 1.

STARS-ASE-FRESP (ASERUN):

Open-loop analyses must be run with this module. The STARS-ASE-FRESP parameter file is the

one created in STARS-ASE-CONTROL, atm_ase_frespo.dat. The file containing the augmented A, B,

C, and D matrices is abcd.aug, and the output file is atm_ase_frespo.out. 1. The response is contained in

files named RESP*.DAT, where the * are numbers ranging from 001 through 999, based on the number

of loop definitions in the STARS-ASE-CONTROL input file. The first twenty lines of the first-loop

definition response are shown below:

.1000 -.415401E÷02 -.782232E+02

.1040 -.411397E+02 °.785038E,02

.1080 -,407553E+02 -.787834E*02

.1120 -,403056E+02 -.790614E+02

.1160 -.400298E+02 -.793375E+02

.1200 -.396868E+02 -.796112E+02

.1240 -.393560E*02 -.798821E+02

.1280 -.390365E*02 -.801500E÷02

.1320 -.387277E+02 -.804144E*02

.1360 -,384289E+02 -.806753E+02

.1400 -,381395E+02 -,809324E+02

.1440 -.378590E+02 -.811856E+02

.1480 -.375869E*02 -.814348E+02

.1520 -.373227E+02 -.816800E+02

1560 -.370660E+02 -.019210E*02

1600 -.360164E+02 -.821579E+02

1640 -.365736E÷02 -.823906E÷02

1680 -.363371E+02 -,826192E+02

1720 -.361067E+02 -.828436E+02

1760 -.358820E+02 -.830640E+02

The columns show the frequency (rad/sec), gain (dB), and phase angle (deg) for the response.

*National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration, United States Air

Force, U.S. Standard Atmosphere, 1976, Washington, D.C., 1976.

202
8. STARS-CFDASE MODULE DESCRIPTION: COMPUTATIONAL

FLUID DYNAMICS, NONLINEAR AEROELASTICITY, AND

AEROSERVOELASTICITY

A number of consistent disciplines and innovative algorithms must be incorporated into an integrated

system that is required to simulate nonlinear performance characteristics of advanced engineering

systems such as aerospace vehicles. Because the finite-element technique can be commonly used to

discretize relevant solids and fluids continua, its employment ensures accurate interaction of various

disciplines. Figure 1 shows a number of disciplines that are involved in the multidisciplinary modeling

simulation of such systems. Some relevant details of finite-element formulations, adopted for

computational fluid dynamics (CFD) and nonlinear-stability analysis, are presented next.

8.1 Finite-Element Computational Fluid Dynamics

The CFD analysis requires two major fundamental solution capabilities, effective generation of

unstructured and solution adaptive fluids domain meshes and finite-element analysis of the relevant flow

problem; and effective development of related numerical tools that are vital to the efficient solution of

complex practical problems. These two solution capabilities have been appropriately incorporated in the

STARS program.

8.1.1 Mesh Generation

An advancing front technique, developed for automated generation of unstructured meshes, has been

found suitable for discretization of complex domains. This procedure has the advantages of flexibility

with regard to the specification of arbitrary shapes and varying grid density throughout the domain and

facility in adaptive mesh generation in accordance with the solution trend.

Such an algorithm was initially developed 21 for arbitrary, multiconnected, planar domains in which

the interior nodes are generated first, then suitably linked to yield the best possible triangulation. During

this process, the generation front is continually updated each time a new element is constructed. Further

improvement and extension of this technique in three dimensions have previously been described. 22 The

nodes and triangles here are formed simultaneously for all boundary surfaces. This formation is followed

by the generation of tetrahedra by the advancing front approach to fill the entire solution domain.

Suitable background grids are used to specify important mesh parameters defining node spacing,

stretching parameters, and directions.

The three-dimensional, automated, unstructured mesh generation scheme, as above, has been

versatile for modeling the practical CFD solution domain around complex structural forms such as an

aircraft. However, because the advancing front technique involves an extensive search for nodes and

faces on the front, the grid generation time tends to be large for such complex configurations. A simple

modification of the procedure, implemented during the current effort, has proven to be efficient

and economical. In this method, the usual technique is first used to generate a grid whose cells have

linear dimensions approximately twice the desired size, and then each cell is reduced locally to its

desired size. 23

203
8.1.2 Finite-Element Computational Fluid Dynamics Analysis

The dynamic equation for a viscous, heat-conducting, compressible fluid obeying the conservation of

mass, momentum, and energy can be expressed by a set of partial differential equations,

_V _F i

--+--=fb, i= 1,2,3 (76)

3t Ox i

where the solution, flux, and body-forces column vectors and the viscous stress tensor are defined as

F i = {PUi

v_-{o

k_T'_

Puiuj + PSij + _ij ui(PE + p) + Ui_li + o3xi j

fb={ 0 fbj Ulfbl}

2 _Uk¢, (OU i OUj/

)

follows:

(77)

(78)

(79)

(8O)

in which p, p, and E are the density, average pressure intensity, and total energy, respectively; _ij is the

Kronecker delta; uj is the velocity component in the direction xj of a Cartesian coordinate system; B is

the viscosity; k is the thermal conductivity; and fb is the body forces. The above equations are

supplemented with state equations

 uiui] (81)

and

T:[E_I. 2 u_uxIcy (82)

for a complete solution, in which _, is the ratio of specific heats and Cv is the specific heat at constant

volume. Such a formulation is valid for a perfect gas.

Solution of the nonviscous form of equation (76) is achieved by first obtaining a Taylor series

expansion of V in the time domain. The spatial domain, f2, is next discretized by unstructured meshes

consisting, of three-dimensional tetrahedron elements. Using linear finite-element approximations

V = aV, V being nodal variable values, and employing a Galerkin weighted residual procedure, a timedependent form of the governing equations can be obtained as follows:

(83)

r

204
in whichR includesartificial viscosityeffectsessentialfor capturingshocks.Solutionof equation(83)is

effectedby advancingthis time-dependentform until steadyconditionsareobtained.An explicit timesteppingiterative scheme22andanalternativequasi-implicit solutionschemehasbeenimplementedin

the STARS program to that effect. An acceleratedEuler solution procedure basedon the Aitken

accelerationtechniquethat effects considerableimprovementin the solution convergencerate has

recentlybeenimplemented.24

8.2 Nonlinear, Computational Fluid Dynamics-Based Aeroelastic and

Aeroservoelastic Analysis (CFDASE)

This process starts with the finite-element structural modeling and subsequently computes the natural

frequencies, to, and modes, 0, that consist of rigid-body, elastic, and control-surface motions, by solving

Mfi + Ku = 0 (84)

in which M and K are the inertial and stiffness matrices, respectively, and u is the displacement vector.

This solution is achieved by an efficient block Lanczos procedure that fully exploits matrix sparsity. 7,25

Next, a steady-state Euler solution is effected in which optimum solution convergence is achieved

through an explicit or alternative quasi-implicit, local time-stepping solution procedure that also

employs a residual smoothing strategy. The resulting vehicle equation of motion is then cast into the

frequency domain as follows:

l_Iq + Cq + I_q + ia(t) + iI (t) = 0 (85)

in which the generalized matrices and vectors are as follows:

q

A

fa(t)

fi(t)

= inertia matrix (= oTMo)

= stiffness (= oTKo) and damping (= oTco) matrices

= displacement vector (= oTu)

= aerodynamic (CFD) load vector (=OTpA), where p is the Euler pressure, A is the

appropriate surface area, and • a is the modal vector pertaining to the aerodynamic

grid points interpolated from relevant structural nodes

= impulse force vector (=oTfi)

and where fI is the user input that contains a number of modes of interest. Equation (85) can next be

formulated in the state-space matrix equation form as

X = AX + ba(t) + b I (t) (86)

where

205
andatime-responsesolutionof equation(86)in anintervalA t (= tn+ 1 - t n ) is obtained as

Xn+l = eAAtXn + A -1 [eA'St - I] [ba(tn) +bI(tn)] (87)

Data consisting of q and ti vectors are then stored for later processing. The structural deformations, u,

and velocities, ti, are then computed from q and q, respectively, and the aerodynamic mesh is updated

only if large motions are encountered. The u and li values are fed into the CFD code to change velocity

boundary conditions at the solid boundary, which is then followed by a one-step Euler solution using a

global time-stepping scheme. 25 The entire solution process is repeated for the required number of

time steps.

The response data can be resolved into modal components using a fast Fourier transform as follows:

p

X = ZeC:nt(amCOS _m t + bmsin _m t) (88)

m=l

which yields the damping, 4, and frequency, co, values. This process is repeated for a number of dynamic

pressure values,

= lpv2

and the _ and co values plotted against _ or Mach number. A plot depicting stability characteristics of

the vehicle enables the prediction of the onset of flutter or divergence occurring within the entire flight

regime. Figure 64 shows a flowchart of the nonlinear flutter analysis methodology adopted in the

STARS program. Alternatively, the generalized modal velocity values are also plotted as a function of

time, and an onset of flutter can also be predicted from their pattern of convergence. A similar solution is

also effected by a root tracking procedure that identifies the coalescence of the roots.

In ASE analysis, assuming that a control law has been designed based on the linear characteristics of

the control derivatives, the control law can be interfaced with the CFD analysis procedure. Thus, the

input to the control law will consist of angle of attack, ct, and also q, q, q, and the control hinge

moment, Mc. Based on such input, the flight control derives the necessary control-surface deflections to

alleviate the aircraft response.

For a more realistic case, where the control derivatives are not known beforehand because the nonlinear

CFD analysis has been used, an autoregression procedure can be used to reconstruct a model based on

the past history of the aircraft input and output information. Thus, for a small incremental motion of a

control surface, the vehicle body forces and moments are first computed from the surface pressure

distribution. This computation is followed by an estimation of parameters such as angle of attack (t_),

206
angleof side slip (_l), control-surfacedeflectionsand hingemoments,and roll, pitch, and yaw rates

employing q and (i values computed from appropriate equations of motion. These calculations are

performed for a large number of time steps that represent the entire range of control-surface motion, and

the resulting data are then employed to obtain static and dynamic stability derivatives for the vehicle

simulation analysis.

I Input aerostructural data [ [ Modal analysis I

I I

Steady-state

Euler/Navier-Stokes solution

(local time stepping)

I

lmpulse load for"_

t = ts thru to /

I

fl:(l) t[fl] I

Solve for q, ¢! I

u = ([_q I

If u is large, regrid

aerodynamic mesh

I solid Changeboundary velocity B.C. at feed u, t_

Perform Euler/Navier-StokeSsolution [

(one-step global time stepping)

_'_ Save q, ¢1

970356

Figure 64. Nonlinear flutter analysis methodology.

207
9. DATA INPUT PROCEDURE

(STARS-CFDASE)

Figure 65 shows the analysis flow chart for nonlinear aeroelastic and ASE analyses. This module is

activated by typing the command "cfdaserun." Thus, a steady-state solution of the flow is first

implemented that requires input data 26 for two-dimensional surface and three-dimensional volume

generation involving triangular and tetrahedral elements, respectively. For surface and volume grid

generation, two input files having background (job.bac) and surface (job.sur) definitions are generated;

plots of these surfaces are achieved by the XPLT program. The input data file, 26 job.bco, is used to set

up boundary conditions, and the file job.cons is the required input file for steady-state flow analysis. An

alternative procedure for only steady-state flow analysis can also be performed in double precision by

using the STEADYDP solution module (fig. 65).

The data files needed for subsequent CFD-based aeroelastic analysis relate to structural vibration

analysis. The data files solids.dat (the term "solids" is a generic identifier that can be set to any name)

and genmass.dat need to be prepared in accordance with the input procedures detailed in sections 3 and

6, respectively. These data inputs are to be followed by data related to structural damping (damp.dat).

For subsequent unsteady flow analysis, related input data 26 are represented by the file job.scalars.

The control file data, job.conu, contains parameters that dictate the pattern of solution convergence. In

all such data sets, the term "job" is generic and signifies the problem under consideration.

Detailed, color graphic plots of solution results are conveniently obtained by using the POSTPLOTF

submodule of the STARS program. The unsteady generalized displacements can also be plotted by

employing the QUICKPLOT program (activated by typing "qp"), and black-and-white contour plots of

solution results are achieved by the XPLT 26 program, which is part of POSTPLOTF.

9.1 Input Data for Background Grid (job.bac)

9.1.1 $ Title for Background Grid File

Format (FREE)

1. Description: Title card for the background grid file.

2. Note:

A maximum of 80 characters on one line of data.

9.1.2 NPBG, NEBG, NPS, NLS, NTS

Format (FREE)

1. Description: Basic data parameters.

208
job.bac job.aur

Surface

jobacI _J

I Vo,um.I

JOi 'CO lJ°b'gi job.fro

I ,s_S"°' I

l job.cons

_ _'_(job.unk)

Steady ] i

job.geo

job.pit

job.unl

J SOLIDS

genmass.dat

I GENMASS

1

W

W

I

i J°b'ic° I

job.grl job.fro

I s_""°l I

_ solids.dat

I

t solids,out;2

.','rim"'.°'"' job.fro

damp.dat

Damping J I job.phia / t,o, .,ro

Arrays I

job.pit

t t j°b'uni*

POSTPLOTF

0ohunk, t '°b''''" t I job.scalars

job.geo job.conu

[_ I _ _ '°b'fr°

II Unataady I

(job.unk) I xn.dat

L QUICKPLOT I

I I-_--_job.fro

I sT-oYoPI (

staadydp.out I /

Job.geodpl I *J °b.fr°

I POSTPLOTF I

Legend

User data

input

t Results output

job.bac

job.sur

job.fro

lob.plt

job.cons

iob.bco

(job.unk)

B/W screen

display

* i : 1, 2..... at selected time steps

J-- restart option

( ) renamed file

970357

Figure 65. Flowchart for CFD-based aeroelastic analysis.

209
2. Notes:

9.1.3

9.1.4

1. Description:

2. Notes:

NPBG

NEPG

NPS

NLS

NTS

= number of points in the background grid

= number of tetrahedral elements in the background grid

= number of point sources

= number of line sources

= number of triangular plane sources

9.1.5

JP, XP, YP, ZP

Format (FREE)

(DBG(I, 1), DBG(I, 2), DBG(I, 3), DBG(I, 4)), I-1, 3)

Format (FREE)

NPBG sets of background grid nodal data.

JP =

XP =

YP =

ZP =

DBG(I, 1) =

DBG(I, 2) =

DBG(I, 3) =

DBG(I, 4) =

index defining the point number

X coordinate of the point

Y coordinate of the point

Z coordinate of the point

x local-global coordinate

y local-global coordinate

z local-global coordinate

scale factor; a unit length along this axis is subdivided into approximately

1.0/DBG(I,4) divisions, with finer divisions being made near point I.

(JE, KEL(I), I=1, 4)

Format (FREE)

1. Description: NEBG sets of background grid element data.

210
2. Notes:

9.1.6

9.1.6.1

9.1.6.2

JE = index defining the element number

KEL(I) = node defining a vertex of the tetrahedral element

The background grid is required to completely enclose the computational domain as defined

in the surface data file. The fineness of the generated grid is controlled mainly by the

parameter DBG(I,4). The smaller this value is, the larger the number of elements there are.

$ Point Sources Data

Format (FREE)

$ Text

Format (FREE)

X, Y, Z, S, R, D

Format (FREE)

1. Description:

2. Notes:

9.1.7

9.1.7.1

9.1.7.2

9.1.7.3

1. Description:

Localized background weighting caused by point sources.

X,Y,Z

S

R

D

= Cartesian coordinates at the point sources

= weight at the point source

= radius of the sphere with a constant weight, S

= distance from the source at which the spacing is 2 x S

Data for sections 9.1.6.1 and 9.1.6.2 are repeated NPS times.

$ Line Sources Data

Format (FREE)

$ Text

Format (FREE)

X1, Y1, Z1, $1, R1, D1

Format (FREE)

X2, Y2, Z2, $2, R2, D2

Format (FREE)

Localized background weighting caused by line sources.

211
2. Note:

9.1.8

Data for sections 9.1.7.1 through 9.1.7.3 are repeated NLS times; definition as above pertains

to two points defining the line source.

$ Plane Triangular Sources Data

Format (FREE)

9.1.8.1 $ Text

Format

9.1.8.2 X1, Y1,

Format

9.1.8.3 X2, Y2,

Format

9.1.8.4 X3, Y3,

Format

1. Description:

2. Note:

9.2.1

1. Description:

2. Note:

9.2.1.1

1. Description:

2. Notes:

(FREE)

Z1, S1, R1, D1

(FREE)

Z2, $2, R2, D2

(FREE)

Z3, $3, R3, D3

(FREE)

Localized background weighting caused by triangular surface sources.

Data for sections 9.1.8.1 through 9.1.8.4 are repeated NTS times; definition as above pertains

to three points defining the triangular plane source.

9.2 Input Data for Surface Grid (job.sur)

$ Title for Surface Definition File

Format (FREE)

Title card for the surface definition file.

A maximum of 80 characters on one line of data.

NIS, NSF

Format (FREE)

Basic data parameters.

NIS = number of boundary edges for defining normals

212

v
9.2.2

9.2.2.1

9.2.2.2

9.2.2.3

1. Description:

2. Notes:

9.2.3

9.2.3.1

9.2.3.2

9.2.3.3

NSF = number of support surfaces defining normals

Multiple surfaces can be defined in each support surface region.

$ Boundary-Edge Definitions

Format (FREE)

JS, ITIS

Format (FREE)

NIP

Format (FREE)

((CIP(I, J), J=l, 3), 1=1, NIP)

Format (FREE)

NIS sets of boundary-edge definition data.

JS

ITIS

NIP

CIP(I, 1)

CIP(I, 2)

CIP(I, 3)

= index defining the boundary edge

= index defining the type of boundary edge

= 1, normal generation (Ferguson)

= number of points on the boundary edge

= X coordinate of a point defining the boundary edge

= Y coordinate of a point defining the boundary edge

= Z coordinate of a point defining the boundary edge

$ Support-Surface Definitions and Orientation

Format (FREE)

ISS, ITSF,

Format (FREE)

NU, NV

Format (FREE)

((CSP(I, J), J=l, 3), I=1, NU*NV)

Format (FREE)

1. Description: NSF sets of support-surface definition data.

213
2. Notes:

9.2.4

ISS

ITSF

NU

NV

csP(I, 1)

CSP(I, 2)

CSP(I, 3)

= index defining the support surface

= index defining support-surface type

-- 1, composite surfaces, curved (Ferguson)

= number of points in the U parametric direction

= number of points in the V parametric direction

= X coordinate of a point defining the support surface

= Y coordinate of a point defining the support surface

= Z coordinate of a point defining the support surface

For NV > 1, the first set of NU is read, then the second, and so forth. The normal for a plane

determined by these points should point into the computational domain. For a composite

surface, the u axis is along the first input line, and the v axis is along the line connecting the

first node on each line.

$ Curved-Edge Definition

Format (FREE)

9.2.4.1 NSG, NRG

Format (FREE)

.

2.

Description: Number of surface-region data sets.

Notes:

NSG = number of curved segments

NRG = number of surfaces regions

These data define the regions of interest on each support surface; see section 9.2.1.1.

9.2.4.2 $ Text

Format (FREE)

9.2.4.3 ISG IDCV ITSG

Format (FREE)

1. Description: NSG sets of curved-segment data.

214
2. Notes:

9.2.5

9.2.5.1

9.2.5.2

ISG = index defining the curved segment

IDCV = index defining the boundary edge from section 9.2.1.1

ITSG = index defining the generation type

= 1

$ Support-Region Definition by Boundary Edges

Format (FREE)

IRG, IDSF, ITRG

Format (FREE)

NN

Format (FREE)

(ISBS(I), I=l, NN )

Format (FREE)

1. Description: NRG sets of surface-region data.

2. Notes:

IRG

IDSF

ITRG

NN

ISBS(I)

= index defining the surface number

= index defining the support-surface from section 9.2.1.1

= index defining the generation type

= 1

= number of curved segments

= indices of curved segments along the mesh region

The edges should be listed in such a manner that the direction of the normal points into the

computational domain, and the edges are traversed in the opposite sense of their above

definition when given a negative sign.

3. Additional notes:

This data file contains the geometrical definition of the boundary of the computational

domain. The general data are the number of boundary edges and the number of support

surfaces. First, each support surface is defined as a plane, composite, or degenerate surface.

Second, each support surface is defined by traveling about it, along the boundary edges, so

that the direction normal to the surface points into the computational domain for all of the

215
9.3.1

surfaces (using the right-hand rule). The normals in sections 9.2.3.1 and 9.2.5.1 should be

consistent. If one is traveling along a boundary edge in the opposite sense of its original

definition, its index is given a negative value.

9.3 Input Data for Boundary Conditions (job.bco)

$ Title for Boundary-Condition File

Format (FREE)

1. Description:

2. Note:

9.3.2

1. Description:

2. Notes:

Description:

Notes:

IRG

IBCO

9.3.3

9.3.4

.

2.

Title card for the boundary-condition file.

A maximum of 80 characters on one line of data.

NRG, NSG

Format (FREE)

Number of data sets.

NRG = number ofboundary surfaces

NSG = number ofboundary segments

These numbers should match those in section 9.2.4.1.

$ Surface-Region Boundary-Condition Definitions

Format (FREE)

IRG, IBCO

Format (FREE)

NRG sets of surface-region boundary-condition data.

index defining the surface number

= index defining the surface boundary condition

= 1, wall

= 2, symmetry

= 3 and 4, far field

= 5 and 6, engine inlet

= 7 and 8, engine outlet

216
9.3.5

9.3.6

.

2.

.

2.

$ Curve-Segment Boundary-Condition Definitions

Format (FREE)

JS, ICBCO

Format (FREE)

Description: NSG sets of curved-segment boundary-condition data.

Notes:

JS = index defining the curved segment

IBCO = index defining the curved-segments boundary-condition

= 0, no singularity

= 1, all are singular

= 2, singular point at first and last

= 3, singular point at first only

= 4, singular point at last only

9.4 Input Data of Control File for Steady-State Computational Fluid Dynamics

(Euler) Solution (job.cons)

Description: Parameters for a name list control file used in the steady-state Euler solution.

Notes:

Each name parameter must begin with "&control" and end with "/". These parameters are on

their own lines with no other data appearing on the lines. Each parameter must be separated

with a comma, even if each appears on a separate line. Parameters not included by the user

will be automatically set to their default values, listed in parentheses after each definition.

&control

nstep

nstou

nstage

cfl

diss 1

diss2

relax

mach

alpha

beta

restart

= total number of solution time steps (1)

= number of time substeps for writing the unknowns file job.unl (ncycl

substeps for each time step) (5)

writing also occurs after each solution time step

if nstou > ncycl, writing occurs once every solution time step

= number of stages in the Runge-Kutta time integration, to a maximum of 5 (5)

= value of the CFL (Courant-Friederich-Lax) number (2.8)

= first dissipation constant (1.0)

= second dissipation constant (1.0)

= boundary-condition relaxation factor (1.0)

= free stream Mach number (0.6)

= free-stream angle of attack (0.0)

= free-stream angle of sideslip (0.0)

= index defining restart option (.false.)

= .true., restart run

217
nlimit =

lg =

nite0 =

nite1 =

nite2 =

ncycl =

ncyci =

tlr =

debug =

meshc =

meshf =

.false.,initial run

limiter functiontype(1)

1,minmod

2,Thomas

multigridcycle(1)

presmoothingiterations(1)

smoothingiterations(1)

postsmoothingiterations(1)

numberof substepsfor eachtimestep(1000)

ncycl(1000)

stoppingtolerance(0.0)

debuggingoption(.false.)

.true.,debug

.false.,donotdebug

coarsestmesh(mmeshfromthefile *.geo)

startingmesh(1)

cbt(1),cbt(2),cbt(3),cbt(4),

cbt(5) = beta1,beta2,beta3,beta4,beta5(1.0,0.5,0.0,0.0,0.0)

bulkvis = indexfor computingbulk viscosity(.false.)

= .true.,computebulk viscosity

= .false.,donotcomputebulk viscosity

for Mach> 2.5,setbulkvis = .true.

disx,xc1,xc2,

XC3, XC4 =

nsmth =

smofc =

low =

trans =

gamma --

epslm =

/ =

parameters defining the bulk viscosity (6.0, -1.2, -0.2, 0.014, 0.0714)

number of residual smoothing iterations (0)

residual smoothing coefficient (0.25)

order of solution (.false.)

.true., low-order solution

.false., high-order solution

index for defining transient analysis (.false.)

.true., transient analysis

.false., no transient analysis

for steady flow, set to .false.

ratio of specific heats (1.4)

harten fix constant, (0.05)

end file

9.5 STARS-SOLIDS Vibration Analysis Data (solids.dat)

See section 3 for details regarding the STARS-SOLIDS input format.

9.6 STARS-AEROS-GENMASS Data (genmass.dat)

See section 6.1 for details regarding the STARS-AEROS--GENMASS input format.

218
9.7.1

9.7.2

1. Description:

2. Note:

9.7.3

9.7.4

1. Description:

2. Note:

9.7.5

9.7.6

1. Description:

2. Note:

9.7.7

9.7.8

1. Description:

9.7 Input Data for Damping (damp.dat)

$ Number of Roots

Format (FREE)

NR

Format (FREE)

Number of roots for the damping solution.

NR = number of roots

$ Scaling Factor from Solid.Out.1

Format (FREE)

SCF

Format (FREE)

Scaling factor listed in the STARS-SOLIDS output file.

SCF = shift factor from the solids analysis out. 1 file

$ Generalized Stiffness Matrix

Format (FREE)

(GK(I, J), J=l, NR), I=1, NR)

Format (FREE)

Components of the generalized stiffness matrix.

GK(I, J) = generalized stiffness matrix components

$ Generalized Mass Matrix

Format (FREE)

(GM(I, J), J=l, NR), I=1, NR)

Format (FREE)

Components of the generalized mass matrix.

219
2. Note:

9.7.9

9.7.10

GM(I, J) = generalized mass matrix components

$ Frequency

Format (FREE)

FREQ(1)

Format (FREE)

1. Description:

2. Note:

9.8.1

Frequency of each root used in the damping solution.

1. Description:

2. Note:

9.8.2

9.8.3

1. Description:

2. Notes:

NR

IBC

FREQ = structural frequency, Hz

9.8 Input Data for Unsteady Flow (job.scalars)

$ Title for Scalars File

Format (FREE)

Title card for the scalars file.

A maximum of 80 characters on one line of data.

$ Basic Parameters

Format (FREE)

NR, IBC, RBCX

Format (FREE)

Basic data parameters.

RBCX

number of mode shapes used in the unsteady analysis

= index defining the debug switch

= 0, displacement is calculated from the response

= 1, displacement is set to the RBCX value

= 2, displacement is set to the velocity vectors

= 3, displacement is set to RBCX plus velocity

mode-shape multiplication factor

220
9.8.4 NNR, (NS(I), I=1, NNR)

Format (FREE)

1. Description:

2. Notes:

9.8.5

9.8.6

1. Description:

2. Notes:

9.8.7

9.8.8

Boundary-condition modification data.

o

2.

NNR = number of surfaces upon which the boundary condition needs to be modified

NS = index defining the surface number

$ I/O Parameters

Format (FREE)

IRFORM, IPFORM

Format (FREE)

Indices to set data input and output formats.

IRFORM

IPRINT

= index defining the input read format

= 1, free format, ASCII file

= 2, binary file

= index defining the output print format

= 0, no print out

= 2, print out k, m, and c generalized matrices

$ Dimensional Parameters

Format (FREE)

MACHI, RHOI, AI, GAMMA, PINF

Format (FREE)

Description: Dimensional parameters at infinity.

Notes:

MACHI = Mach number at infinity

RHOI = density at infinity

AI = speed of sound at infinity

GAMMA = gamma constant, Cv/Cp

PINF = air pressure at infinity

221
9.8.9

9.8.10

$ Shift Factor and Gravitational Constant

Format (FREE)

SCF, GR

Format (FREE)

1. Description:

2. Notes:

9.8.11

9.8.12

1. Description:

2. Notes:

9.8.13

9.8.14

1. Description:

2. Notes:

ICFA

222

Basic constants.

SCF = scaling factor, as defined in section 9.7.4

GR = gravity constant, as defined in section 6.1.2

$ Impulse-Force Data

Format (FREE)

IFLAG, FFI, NS/XS, NE/XE

Format (FREE)

Data for specifying the impulse force.

IFLAG = index defining the generalized impulse-force input mode

= 1, applied from times XS to XE (real time)

= 2, applied from steps NS to NE step

FFI = magnitude of the generalized impulse force

NS/XS = starting step or time

NE/XE - ending step or time

$ Force Activation Parameters

Format (FREE)

ICFA, ICFI

Format (FREE)

Parameters to activate aerodynamic and applied generalized forces.

= index defining the activation of aerodynamic force

= 0, do not activate

= l, activate
ICFI = indexdefiningtheactivationof appliedgeneralizedforce

= 0, donot activate

= 1,activate

9.8.15 $ Transition Matrix Parameters

Format (FREE)

9.8.16 NTERMS, NSTEPS

Format (FREE)

1. Description: Parameters used in calculating the transition matrix, eAAt.

2. Notes:

NTERMS = number of terms used in the calculation of c A"at

NSTEPS = option to calculate the transition matrix e AAt at specified intervals

9.9 Input Data of Control File for Unsteady Computational Fluid Dynamics

(Euler) Solution (job.conu)

1. Description: Parameters for a name list control file used in the unsteady Euler solution.

2. Notes:

The data below are to be augmented with the data in section 9.4; nstou from section 9.4 is

replaced by nout. See section 9.4 for other details regarding using the name list.

&control

nout

restart

freq

nstpe

x0, y0 ,z0

WUX, wuy,

wyz

phase

amplitude

pistonn_sol

= number of time steps for writing the unknowns file job.uni (1)

= index defining the restart option (1)

= 0, start from a far-field boundary condition

= 1, start from the steady-state solution unknowns

= 2, restart from the last unsteady solution

= size adjustment of the time step for a transient analysis (0.0)

= size adjustment of the time step of the transient analysis ( 1 )

= center of rotation (0.0, 0.0, 0.0)

= axis of rotation (0.0, 0.0, 0.0)

= angle, phi, used to switch an input signal from a sine to a cosine wave,

A x sin(c0t+ phi), in the pitching problem (0.0)

= magnitude, A, of the input signal (0.0)

= index for solution type (0)

= 0, use the CFD unsteady Euler solver

= 1, use the alternative piston and modified Newtonian impact theory

= 2, use the perturbation method

= end file

223
9.10.1

1. Description:

2. Note:

9.10.1.1

1. Description:

2. Note:

9.10.2

1. Note:

9.10.2.1

1. Description:

2. Note:

9.10.3

9.10 Input Data of Control File for STEADYDP (job.consdp)

NLINES

Format (FREE)

Specifies the number of the following comment lines.

NLINES = number of comment lines to follow

$ Comment Lines

Format (FREE)

NLINES sets of comment lines.

A maximum of 80 characters for each line of comments.

$ Problem Dimension

Format (FREE)

9.10.3.1

1. Description:

Comment line. Not included in NLINES.

NDIM

Format (FREE)

Problem dimension size.

NDIM = number of dimensions in the problem

=3

$ Problem Size Parameters

Format (FREE)

NELEM, NPOIN, NBOUN

Format (FREE)

Basic data parameters.

224
2. Notes:

NELEM = numberof tetrahedralelements

NPOIN = numberof points

NBOUN = numberof boundaryelements

9.10.4 $ Solution Acceleration Parameters

Format (FREE)

9.10.4.1 KACCEL, NACCEL

Format (FREE)

1. Description: Parameters to accelerate the solution.

2. Notes:

KACCEL = number of iterations between acceleration

NACCEL = index defining the starting acceleration time step

If no acceleration is desired, set NACCEL to significantly exceed the expected value of

NTIME+ITIN, as defined in sections 9.10.10.1 and 9.10.18.1, respectively.

9.10.5 $ General Parameters

Format (FREE)

9.10.5.1 GAMMA, C1, IDIFF, EPS, IVISC, WBR

Format (FREE)

1. Description: Basic fluid data parameters.

2. Notes:

GAMMA = gas constant

= 1.4, for air

C1 = pressure switch coefficient

= 0.3, recommended for completely subsonic

= 0.5-0.8, recommended for transonic

= 1.0, recommended for transonic to hypersonic

IDIFF = index defining the smoothing type for artificial dissipation

= 0, metric weighted, acting on the sides

= 1, area weighted, acting on the sides (old code)

= 2, area weighted, acting at the element level (new code)

= 3, new diffusion scheme with side eigenvalues

225
EPS = pressureswitchtolerance;it mustbesetto a smallnumberor 0.0

= 0.1,normally

If EPS= 0.0, apressureswitchof thetype (Mc-ML)p/(Mc-ML) is evaluated;otherwise, the

presstire switch is evaluated as psw = Y_ (Pi-Pj)/_ (I Pi-Pj I), and EPS is used to avoid

division by zero. Because of the way that the division by zero has been avoided, if EPS = 1,

the pressure switch is evaluated as Y. (Pi-Pj)/PMEAN, where PMEAN is the mean value in

the surrounding elements.

IVISC = viscous flow indicator

= 0, for Euler

WBR = wall boundary relaxation parameter, to be used when strong boundary

conditions are applied (pointwise velocity projection at wall)

WBR normalizes wall boundary conditions at each step to avoid big jumps. At each step, 0.2

would normalize by 20 percent. Even 1.0 will normally work. Hypersonically, problems may

exist. For unsteady flow, set WBR to 1.0 to be time accurate.

9.10.6 $ Far-Field Boundary Condition Parameter

Format (FREE)

9.10.6.1 NFFBC

Format (FREE)

1. Description: Number of far-field boundary conditions.

2. Note:

NFFBC = number of far-field boundary conditions

9.10.7 $ Far-Field Boundary Condition Data

Format (FREE)

9.10.7.1 ROINF, UXINF, UYINF, UZINF, PINF, MACHINF

Format (FREE)

1. Description: NFFBC sets of far-field boundary-condition data.

2. Notes:

ROINF = density at infinity

UXINF = velocity in X at infinity

UYINF = velocity in Y at infinity

226
9.10.8

9.10.8.1

°

2.

9.10.9

UZINF = velocity in Z at infinity

PINF = pressure at infinity

= ROINF/(GAMMA*MACHINF** 2)

MACHINF = Mach number at infinity

$ Engine Intake/Outlet Boundary-Condition Parameter

Format (FREE)

NENBC

Format (FREE)

Description: Number of engine inlet/exit boundary conditions.

Note:

9.10.9.1

.

2.

Description:

9.10.10

Notes:

NENBC = number of engine inlet/exit boundary conditions

$ Engine Boundary-Condition Data

Format (FREE)

ROENG, UXENG, UYENG, UZENG, PENG, MACHENG

Format (FREE)

NENBC sets of far-field boundary-condition data.

ROENG = specified density

UXENG = velocity in X

UYENG = velocity in Y

UZENG = velocity in Z

PENG = specified pressure

MACHENG = specified Mach number

$ Iteration Parameters

Format (FREE)

(Required if NENBC ;_ 0)

(Required if NENBC ;e 0)

227
9.10.10.1 NTIME, NITER, ILOT

Format (FREE)

1. Description: Parameters to set the number of solution time steps.

2. Notes:

NTIME = maximum number of iterations

NITER = number of mass-consistent iterations

= 1, mass-lumped solution used (steady state)

= 2, mass-consistent solution used (transient)

ILOTS = time-stepping indicator

= 0, global time stepping (steady or transient)

= 1, local time stepping (steady, faster than 0)

9.10.11 $ General Convergence Parameters

Format (FREE)

9.10.11.1 CSAFE, IFCT, NQUAN, (IDO(1), I = 1, NQUAN), CLIMAX

Format (FREE)

1. Description: Data to specify solution convergence.

2. Notes:

CSAFE = Taylor-Galerkin safety factor; usually, 0.0 < CSAFE < 1.0

= 0.7, a reasonable value

IFCT = FCT routine switch

= 0, no FCT

= 1, FCT

= -1, low order only (not generally used)

NQUAN = number of FCT quantities to limit; set to 1, 2, or 3

DO(I) = variable to be limited for FCT

= 1, density

= 2, energy

= 3, pressure

CLIMAX = maximum limiter allowed; usually 0.00 to 0.95

The FCT should decrease "smearing" near a strong shock but does not always work and

increases the solution time. Normally, this option would not be used.

228
9.10.12 $ File Formats and I/O Direction

Format (FREE)

9.10.12.1 INFOG, INFOU, OUFO, NIOUT

Format (FREE)

1. Description: Indices to specify input and output.

2. Notes:

INFOG = index defining the geometry file format specification

= 0, input file is formatted in ASCII

= -1, input file is unformatted

INFOU = index defining the restart initial values file format specification

= 0, input file is formatted in ASCII

= -1, input file is unformatted

= -2, input file is not required, initial values are generated from

specifications

far-field

OUFO = index defining the output file specification

= 3, unformatted output on channel 15 (graphics)

= 2, formatted output to channel 4; five unknowns at each point in mesh

= 1, unformatted output to the front end (VAX)

= 0, formatted output to the front end

= -1, formatted output to a Cray computer with the name FILE3 and overwriting

= -2, no output file written

= -3, unformatted output to a Cray computer with the name FILE3 and

overwriting

= -4, formatted output to a Cray computer with a new file generated every

NIOUT iteration with the name FILE3iter

= -5, unformatted output to a Cray computer with a new file generated every

NIOUT iteration with the name FILE3iter

NIOUT = number of iterations between outputs

= 0, output written only at the end of the job

WARNING: If OUFO = 0 or 1, (for example, a result file sent to the front end), an

unformatted copy of the file (named FILE3) is also sent to the Cray computer.

Note: For INFOU set to 0 or-1, use the previous output file for FILE4 in section 9.10.19.1

for the initial values. Remember to update ITIN in section 9.10.18.1 as well.

9.10.13 $ Residuals Smoothing Parameters

Format (FREE)

229
9.10.13.1 CSMOO, NSMOO

Format (FREE)

1. Description: Data for defining residuals smoothing.

2. Notes:

CSMOO = residual smoothing coefficient

= 0.25 for Jamesons's method

NSMOO = number of smoothing iterations

= 2 for Jamesons's method

9.10.14 $ Enthalpy Damping Coefficient

Format (FREE)

9.10.14.1 ALPHA

Format (FREE)

1. Description:

2. Notes:

Enthalpy damping coefficient.

ALPHA = enthalpy damping coefficient to enforce constant enthalpy; does not always

work

= 1.0, normally

9.10.15 $ Residuals and Lift Parameters

Format (FREE)

9.10.15.1 IRPR, IRLOG, ILPR, ILLOG, AXIS(I, I = 1, 3), RCHORD

Format (FREE)

1. Description:

2. Notes:

Data for residuals and lift.

IRPR = number of iterations between evaluations of diffusive fluxes for a

Taylor-Galerkin scheme

IRLOG = type of logging for residuals

= 0, print to log file only

= 1, print to RESID, and print to log file

= 2, print to RESID

ILPR = number of iterations between outputs of lift, drag, and moment coefficients;

uses the centroids of the elements with a boundary condition of 2

= 0, no output for lift

230
ILLOG = typeof loggingfor lift

= 0, print to log file

= 1, print to Lwr, and print to log file

= 2, print to LIFT

AXIS(I) = end points of a position vector, in x, y, and z, parallel to which the lift acts

RCHORD = reference chord for use in lift and moment calculations

9.10.16 $ Residual Smoothing Iteration Parameters

Format (FREE)

9.10.16.1 IRFR, IRFS

Format (FREE)

1. Description: Data for defining residuals smoothing iterations.

2. Notes:

IRFR = number of iterations between smoothing residuals, starting from iteration N;

this parameter is a tradeoff with the CSAFE parameter

= 1, if CSAFE = 1.2

= 3, if CSAFE -- 0.9

IRFS = number of initial iterations before an altemate evaluation of diffusive fluxes

For Taylor-Galerkin schemes, irrespective of IRFR, the diffusive fluxes are evaluated at

every time step for the first IRFS iterations. This option is not presently used.

9.10.17 $ Boundary-Condition Types and Geometry Checking

Format (FREE)

9.10.17.1 ISTRON, ICHECK

Format (FREE)

1. Description: Specifies boundary-condition types.

2. Notes:

ISTRON = boundary-condition type

= 0, weak boundary conditions; flux is corrected on the outer bounds

= 1, strong boundary conditions with velocity projection at the sides included

into the right-side boundary integral

= 2, strong boundary conditions with full boundary integral evaluation

ICHECK = geometry consistency-checking parameter

= 0, no checking

= 1, checking done

231
9.10.18

9.10.18.1

.

2.

$ Initial Time and Iterations

Format (FREE)

TIMEIN, ITIN

Format (FREE)

Description:

Notes:

TIMEIN

ITIN

3. Additional notes:

9.10.19

9.10.19.1

Parameters to control starting times.

= initial time (only for transient)

= initial iteration number; the iteration counter starts at (ITIN+ 1)

This code does not check itself for convergence and stop automatically. Convergence is

generally said to have occurred when a drop of 4 to 5 orders of magnitude has occurred in the

average of the residuals. The lower the Mach number is, the slower the convergence is.

$ File Names

Format (FREE)

FILE3, FILE2, FILE4

Format (FREE)

1. Description:

2. Notes:

Listing of files for input and output control.

FILE3 = output file for the results

FILE2 = input geometry file

FILEA = restart the input file with initial values

Each file name can have a maximum of 16 characters. Only the prefix is required.

$ CPU Parameters

Format (FREE)

NCPU

Format (FREE)

9.10.20

Number of central processing units (CPUs) to be used in the solution.

9.10.20.1

1. Description:

2. Notes:

NCPU = Number of CPUs requested

Set to 0 or 1 for a nonmultitasked version.

232

v
10. NUMERICAL EXAMPLE (STARS-CFDASE)

A large number of CFD-based aeroelastic analyses has been performed in support of NASA projects

such as Pegasus ®, the SR-71 airplane, SR-71/Hypersonic Launch Vehicle, High Speed Civil Transport

(HSCT), National Aerospace Plane (NASP), and generic hypersonic vehicle projects, among others.

Some analysis results have been correlated with those obtained from flight testing. In the area of

aeroelasticity, the associated solution module has been checked out by comparing results with those

obtained from tests as well as other analysis methods. A typical example problem of a detailed, CFDbased, aeroelastic analysis is presented next.

10.1 Cantilever Wing Nonlinear Aeroelastic Analysis

Figure 66 shows a cantilever plate with a NACA 0012 airfoil and solution domain. The figure also

shows the edges and surfaces, marked appropriately. Figure 67 shows the background mesh.

20 In.

Z

of

symmetry

11

[] Top of airfoil

[] Bottom of airfoil

[] End cap of airfoil

Note: all dimensions in S.I.

970358

Figure 66. Cantilever wing with aeroelastic solution domain.

Important data parameters are as follows:

Wing span = 2.0178

Wing chord length = 1.0089

Mach number = 0.5

Angle of attack = 0 °

Speed of sound at infinity = 340.29

Structural data

Young's modulus = 6.8947E+10

Poisson's ratio = 0.3

Density = 2764.925

233
8

2

7

970359

Figure 67. Background domain for aeroelastic analysis.

Data pertaining to the finite-element CFD models are as follows:

Number of fluid nodes = 54,759

Number of fluid elements = 297,700

Number of structural nodes = 861

Number of structural elements = 1,610

Detailed data input in this connection is given next.

10.1.1 Input Data

Data for the surface file, wing.sur, are given first.

STARS-CFDASE input data:

his nsf ..... quasi-2D nacaOOl2

22 tO

=egments

t I

41

0.10089E+01 0.0 O.O0000E+O0

0.10069E*01 0.0 -0.28900E-03

0.10013E*0! 0.0 -0.10810E-02

0,99239E+00 0.0 -0.23220E-02

0.98043E+00 0.0 -0.39740E-02

0.96555E+00 0.0 -0.59930E-02

0.94792E*00 0.0 -0.83390E-02

0.92771E*00 0.0 -O.10971E-O1

0.90508E+00 0.0 -0.13843E-01

0.88019E*00 0.0 -0,16915E-01

0.85323E+00 0.0 -0.20146E-01

O,B2436E+O0 0.0 -0,23494E-01

0.79375E+00 0.0 -0,26920E-01

0.76160E*00 0,0 -0.30386E-01

O.72BOBE+O0 0,0 -0.33853E-01

0,69336E+00 O.O -0,37281E-01

234
2

41

3

41

0.65765E+00

0.621t1E+00

0.58394E+00

0.54633E+00

0,50846E+00

0.47053E+00

0,43273E+00

O.39526E+O0

0.35831E+00

0.32208E+00

0.28677E+00

0.252S9E÷00

0.219?3E+00

0.18841E÷00

0.15882E÷00

0.13117E+00

0,10564E+00

0,82428E-01

0.61717E-01

0.43684E-OI

0.28501E-01

O.IG337E-OI

0.73750E-02

0.18480E-02

O.O0000E÷O0 I

O.O000OE+O0

0,18480E-02

0.73750E-02

0,16338E-01

0,28501E-01

0,43684E-01

0.61716E-01

0.82428E-01

0,I0564E*00

0.13117E°00

0.15882E*00

0.18841E+00

0.21973E*00

0.2525gE*00

0.28677E+00

0,32208E+00

0,35831E+00

0,39526E+00

0.43273E+00

0,47054E+00

0.50846E+00

0.54633E+00

0.58394E+00

0.62111E+00

0.65765E÷00

0.69336E÷00

0.72808E*00

0,76160E+00

0.79375E+00

0.82436E÷00

0,85323E÷00

0.88019E*00

0.90508E*00

0,92771E+00

0.94792E÷00

O,96SSSE*O0

0,98043E*00

0,9923gE+00

0.10013E*01

0.10069E÷01

0.10089E+01 I

0,10089E+01

O.to06gE+O1

0,10013E+01

0.9923gE+00

0,98043E+00

0,9655SE*00

O.94792E+O0

O,g2771E*O0

O,gOSO8E+O0

0.88019E*00

0.85323E*00

0,82436E+00

0,79375E+00

0,0

0.0

0.0

0.0

O,O

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0,0

0.0

0.0

0,0

0.0

0.0

0,0

0,0

0,0

0.0

0,0

0.0

0.0

0.0

0,0

0.0

0,0

0.0

0,0

0,0

0,0

0,0

0,0

0,0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0,0

0.0

0.0

0.0

0.0

0.0

0,0

0,0

0.0

0,0

0,0

0.0

2.0178

2,0178

2.0178

2.0178

2.0178

2,0178

2.0178

2,0178

2.0178

2,0178

2.0178

2.0178

2.0178

-0.40632E-01

-0.43863E-01

-0,46931E-01

-0,49791E-01

-0.52398E-01

-0.54701E-01

-0,56653E-OI

-0,58203E-01

-0.59303E-01

-0.59908E-01

-O.59g?SE-Ot

-0.5947SE-01

-0.58374E-01

-0.$66SSE-01

-0.54310E-01

-0,51339E-01

-0.47753E-01

-0.43572E-01

-0,38825E-01

-0.33541E-01

-0.277S2E-01

-0.21479E-01

-0,14730E-01

-0,75170E-02

O,O0000E*O0

O,O0000E*O0

0.75170E-02

0,14730E-01

0.21479E-01

0.277S2E-01

0,33S41E-01

0,38825E-01

0.43572E-01

0.47753E-01

0.51339E-01

0.54310E-01

0.56656E-01

0.58374E-01

0.59476E-01

0.$9978E-01

D.SggOgE-DI

0.59304E-01

0.$8203E-01

0.56653E-01

0,54702E-01

0,$2398E-01

0,49792E-01

O,46931E-01

0,43863E-01

0,40632E-01

0,37282E-01

0.338S3E-01

0.30387E-01

0.26920E-01

0.23494E-01

0,20146E-01

0.16915E-01

0.13843E-01

0.10971E-01

0.83390E-02

0.59930E-02

0.3g?40E-02

0.23220E-02

0.10810E-02

0.28900E-03

O.O0000E+O0

O.O0000E*O0

-0,28900E-03

-0.I0810E-02

-0.23220E-02

-0,39740E-02

-O,5gg30E-02

-0,83390E-02

-O.IOg?IE-OI

-0,13843E-01

-O,16gISE-01

-0.20146E-01

-0.23494E-01

-O,26920E-01

235
41

0.70160[+00

0.72808E+00

0.69336E+00

0.65765E+00

0.62111E+00

0.58394E+00

0.54633E+00

0.50846E+00

0.47053E+00

0.43273E*00

0.39526E+00

0.35831E+00

0.32208E+00

0.28677E*00

0.25259E+00

0.21973E+00

0.18841E+00

0.15882E+00

0.13117E+00

0.10564E+00

0,82428E-01

0.61717E-01

0.43684E-01

0.28501E-01

0.16337E-01

0.73750E-02

0.18480E-02

O.O0000E+O0 4 1

O.O0000E+O0

0,18480E-02

0.73750E-02

0.16338E-01

0.28S01E-01

0.43684E-01

0.61?16E-01

0.82428E-01

0.10564E+00

0.13117E+00

0,15882E+00

0.18841E+00

0,21973E+00

0.25259E+00

0.28077E+00

0,32208E+00

0.35831E+00

0.39526E÷00

0.43273E+00

0.47054E*00

0.50846E+00

0.54633E+00

0.58394E+00

0.62111E+00

0.6S765E+00

0.69336E+00

0.72808E+00

0.76160E+00

0.79375E+00

0.82436E+00

0.85323E+00

0.88019E+00

0.90508E+00

0.92771E+00

0.94792E+00

0.96SSSE+O0

0,98043E+00

0.99239E+00

0.10013E+01

0,I0069E+01

0.10089E+01 I 2

O.

O.

1

2

1,0089

1.0089

I

2

-15.

O,

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2,0178

2.0178

2.01?8

2.0178

2,0178

2,0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2,0178

2.0178

2.0178

2,0178

2.0178

2.0178

2.0178

2.0178

2.0t78

2,0178

2.01?8

2.0178

2.0178

2.0178

2,0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2,0t78

2,0178

2.0178

2.0178

2.0178

2,0178

2,0178

2.0178

2,0178

2.0178

2.0178

2.0178

2,0178

2.0178

2,0178

2.0178

O.

2.0178 0

2,0178

O.

O.

-0.30386E-01

-0.33853E-01

-0,37281E-01

-0.40632E-01

-0.43863E-01

-0.46931E-01

-0.49791E-01

-0.52398E-01

-0,54701E-01

-0.56653E-01

-0.58203E-01

-0.59303E-01

-0.59908E-01

-0.59978E-01

-0.59475E-01

-0.58374E-01

-0.5665SE-01

-0.54310E-01

-0.51339E-01

-0.47753E-01

-0.43572E-01

-0.38825E-01

-0,33541E-01

-0,27752E-01

-0,21479E-01

-0.14730E-01

-0,75170E-02

O.O0000E+O0

O,O0000E+O0

0.75170E-02

0.14730E-01

0.21479E-01

0.27752E-01

0.33541E-01

0.38825E-01

0.43572E-01

0.47753E-01

0,51339E-01

0.54310E-01

0.56656E-01

0,58374E-01

0,59476E-01

0,59978E-01

0.59909E-01

0.59304E-01

0.58203E-01

0.56653E-01

0_54702E-01

0,52398E-01

0.49792E-01

0,46931E-01

0.43863E-01

0.40632E-01

0.37282E-01

0,33853E-01

0,30387E-01

0,26920E-01

0.23494E-01

0.20146E-01

0.16915E-01

0.13843E-01

0,I0971E-01

0.83390E-02

0,59930E-02

0.39740E-02

0.23220E-02

0,10810E-02

0.28900E-03

O.O0000E+O0

O,

O.

O.

O,

O.

O,

kv

236
I0

11

2

1.0089 O. O.

15, O. O.

2

-15. O. O.

-15. O, I0.

2

15. O. O,

15. O, 10,

2

-15. O, -10.

-15. O, O.

12

2

13

2

14

2

15I

2

15, O, -10,

15. O, O,

-15. O. -10.

15. O, -I0.

-15. O, 10.

15. O, fO.

-15. 10. I0.

15. 10. I0.

16I

2

-15.

15,

17I

2

-15.

-15,

18I

2

-15,

-15,

19I

2

-15,

-15,

20I

2

15,

15,

21I

2

15,

15,

22I

2

15,

15,

$ support surfaces 1 I

412

O, 10089E+01

O, 10069E÷01

0.I0013E+01

O, -10,

10 -10. 0 10

10 10

10, 10

10. -I0

0, -tO

I0, -10

0.0 0,00000Eo00

0.0 -0.28900E-03

0.0 -O,IOB10E-02

0.99239E+00 0,0 -0,23220E-02

0,98043E+00 0.0 -0,39740E-02

0.96555E+00 0.0 -0,Sgg30E-02

0,94792E÷00 0.0 -0,83390E-02

0.92771E+00 0.0 -O.10g?1E-01

0,90508E.00 0.0 -0,13843E-01

0,88019E_00 0,0 -0,16915E-01

0.85323E*00 0,0 -0.20146E-01

0,8243GE+00 0.0 -0.23494E-01

0.79375E÷00 0.0 -0,26920E-01

0.76160E÷00 0.0 -0.30386E-01

0.72808E+00 0.0 -0.33853E-01

0.69336E+00 0.0 -0.37281E-01

0.65765E+00 0,0 -0.40632E-01

0.62111E÷00 0,0 -0.43863E-01

O,$B394E÷00 O,O -0,46931E-01

0,54633E÷00 0,0 -O.49791E-Ol

237
2

41

0.50846E*00

0.47053E+00

0,43273E+00

0,39526E+00

0.35831E+00

0.32208E+00

0.28677E+O0

0.25259E+00

0,21973E_00

0,18841E+00

0.15882E+00

0.13117E+00

0,10564E+00

0.82428E-01

0.61717E-01

0.43684E-01

0.28501E-01

0.16337E-01

0,73750E-02

0.18480E-02

O.O0000E*O0

0.I0089E+01

0,I0069E+01

0.10013E+01

0.99239E+00

0.98043E+00

0.96555E÷00

0,94792E+00

0.92771E+00

0.90508E+00

0,88019E+00

0,85323E+00

0.82436E+00

0.79375E+00

0,76160E+00

0,72808E+00

0.69336E÷00

0,65765E+00

0.62111E+00

0.58394E+00

0.54633E+00

0.50846E÷00

0.47053E+00

0.43273E+00

0.39526E÷00

0_3583tE÷00

0.32208E+00

0.28677E+00

0.25259E+00

0,21973E+00

0,18841E+00

0,15882E+00

0,13117E+00

0,I0564E÷00

0,82428E-01

0.61717E-01

0,43684E-01

0,28501E-01

0.16337E-01

0.73750E-02

0.18480E-02

O,O0000E+O0

1

2

O,O0000E+O0

0,t8480E-02

0.73750E-02

0,16338E-01

0,28501E-01

0,43684E-01

0.61716E-01

0,82428E-01

0,10564E÷00

0,13117E+00

0.15882E+00

0.18841E+00

0.21973E+00

0.25259E÷00

0.28677E+00

0.32208E+00

0.35831E+00

0.39526E+00

0.43273E+00

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0,0

0,0

0,0

0.0

0,0

2.0178

2.0178

2.0178

2.0178

2.0178

2.0t78

2,0178

2,0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2,0178

2.0178

2.0178

2,0178

2.0178

2.0178

2,0178

2.0t78

2,0178

2,0t78

2.0178

2,0178

2.0178

2 _0178

2.0178

2,0178

2,0178

2,0178

2.0178

2.0178

2,0178

2.0178

2,0178

2,0178

0,0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0,0

0_0

0.0

0,0

-0.52398E-01

-0.54701E-01

-0,56653E-01

-0.58203E-01

-0.59303E-01

-0.59908E-01

-0,59978E-01

-0,59475E-01

-0.58374E-01

-0.56655E-01

-0.54310E-01

-0.51339E-01

-0.47753E-01

-0.43572£-01

-0,38825E-01

-0.33541E-01

-0.27752E-01

-0,2147gE-01

-0.14730E-01

-0,75170E-02

O,O0000E+O0

O.O0000E+O0

-0.28900E-03

-0.10810E-02

-0.23220E-02

-0.39740E-02

-0.59930E-02

-0.83390E-02

-0.10971E-01

-0.13843E-01

-0.16915E-01

-0.20146E-01

-0.23494E-01

-0.26920E-01

-0.30386E-01

-0.33853E-01

-0.37281E-01

-0.40632E-01

-0.43863E-01

-0.46931E-01

-0,49791E-01

-0.52398E-01

-0.54701E-01

-O,56GS3E-OI

-0.58203E-01

-0.59303E-01

-0,59908E-01

-0,59978E-01

-0,5947SE-01

-0,$8374E-01

-0,5668SE-01

-0,54310E-01

-0,51339E-01

-0.47753E-01

-0,43572E-01

-0,38825E-01

-0.33541E-01

-0.27752E-01

-0.21479E-01

-0,14730E-01

-0,75170E-02

O.O0000E+OD

O,O0000E+O0

0.75170E-02

0,14730E-0t

0.21479E-01

0.27752E-01

0.33541E-01

0.38825E-01

0,43572E-01

0,47753E-01

0.51339E-01

0.54310E-01

0.56656E-01

0.$8374E-01

0.59476E-01

0.$9978E-01

0.$9909E-01

0.59304E-01

0.$8203E-01

0.56653E-01

238
0.47054E+00

0.50846E+00

0.54633E+00

0.58394E÷00

0,62111E÷00

0,65765E+00

0,69336E+00

0.72808E+00

0.76160E+00

0.79375Ee00

0.82436E+00

0.85323E+00

0,88019E+00

0.90508E+00

0,92771E+00

0.94?92E+00

0_96555E÷00

O.g8043E+O0

0.99239E+00

0.10013E+01

0.10069E+01

0.10089E_01

O.O0000E*O0

0.18480E-02

0.73750E-02

0.16338E-01

0.28501E-01

0,43684E-01

0,61716E-01

0,82428E-01

0.10564E+00

0.13117E+00

0,15882E+00

0,18841E+00

0.21973E+00

0,25259E+00

0.28677E+00

0.32208E+00

0,3S831E*00

0,39526E*00

0,43273E+00

0,47054E+00 0 50846E*00

0,54633E+00

0.58394E*00

0,62111E*00

0.65765E*00

0,69336E÷O0

0,72808E*00

0,76160E+00

0.79375E*00

0,82436E+00

0.85323E+00

0.88019E+00

O.gOSOSE+O0

O,g2771E+O0

0,94792E+00

0,96555E+00

0,98043E÷00

o,gg23gE+O0

0,I0013E+0_

0,I0069E*01

0,I0089E÷01 I

41

O.O0000E+O0

O.O0000E+O0

0.18480E-02

0,18480E-02

0,73750E-02

0,737SOE-02

0,16338E-01

0.16338E-01

0.28501E-01

0.28S01E-01

0.43684E-01

0,43684E-01

0,61716E-01

0,61716E-01

0,82428E-01

0,82428E°01

0,I0564E+00

0,10564E+00

0.0

0.0

0.0

0,0

0.0

0,0

0.0

0.0

0.0

0,0

0.0

0.0

0.0

0,0

0.0

0.0

0.0

0,0

0.0

0.0

0.0

0.0

2,0178

2.0170

2.0170

2.0170

2,0178

2.0178

2.0170

2,0178

2.0170

2.0170

2,0178

2.0178

2.0178

2.0178

2.0170

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2,0178

2,0178

2,0178

2,0178

2,0178

2,0178

2,0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2,0178

2.0178

2.0178

2.0178

2,0178

2.0178

2.0178

2.0178

2.0178

2.0170

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

0.54702E-01

O.52398E-01

O.49792E-OI

0,46931E-01

0,43863E-01

0.40632E-01

0.37282E-01

0.338S3E-01

0,30387E-01

0.26920E-01

0_23494E-01

0_20146E-01

0.16915E-01

0.13843E-01

0,10971E-01

0,83390E-02

0.59930E-02

0.39740E-02

0.23220E-02

0,10810E-02

0,28900E-03

O.O0000E+O0

O.O0000E*O0

0.75170E-02

0,14730E-01

0.2147gE-01

0.27752E-01

0.33541E-01

0.38825E-01

0.43572E-01

0,477S3E-01

0,51339E-01

0.54310E-01

0.56656E-01

0.58374E-01

0.$9476E-01

0,59978E-01

0.5990gE-01

0,59304E-01

0,58203E-01

0,56653E-01

0,54702E-01

0,52398E-01

0,49792E-01

0,46931E-01

0,43863E-01

0.40632E-01

0,37282E-01

0.33853E-01

0,30387E-01

0,26920E-01

0,23494E-01

0,20146E-01

0.16gISE-OI

0,13843E-01

0,I0971E-01

0.83390E-02

0.59930E-02

0,39?40E-02

0.23220E-02

0,I0810E-02

0.28gOOE-03

O.O0000E*O0

O,O0000E+O0

O,O0000E+O0

-0,75170E-02

0,75170E-02

-0,14730E°0I

0,14730E-01

-0,21479E-01

0,2147gE-01

-0,27752E-01

0,27752E-01

-0,33S41E-01

0,3354tE-01

-0.38825E-01

0,38825E-01

-0,43572E-01

0,43572E-01

-0.47753E-01

0.47753E-01

239
0.13117E+00

0.13117E+00

0,15882E+00

0.15882E+00

0.18041E+00

0.10841E+00

0.21973E+00

0.21973E+00

0.25259E+00

0.25259E+00

0.20677E*00

0.28677E+00

0.32208E÷00

0.32208E*00

0.35831E+00

0.35831E+00

0.39526E+00

0.39526E*00

0.43273E+00

0.43273E+00

0.47054E_00

0.47054E+00

0.50846E+00

0.50846E+00

0,54633E+00

0.54633E+00

0.58394E÷00

0.58394E+00

0.62111E+00

0.62111E+00

0.65765E+00

0.65765E+00

0.69336E+00

0.69336E+00

0.72808E÷00

0.72008E+00

0,76160E÷00

0.76160E+00

0.79375E+00

0.7937SE+00

0.82436E+00

0,82436E+00

0 85323E+00

0.85323E*00

0,80019E+00

0.88019E+00

0.90508E÷00

0.90508E+00

0,92771E+00

0.92771E+00

O.g4792E+O0

0,94792E+00

0.96555E+00

0.96SSSE+O0

0.98043E+00

0.98043E+00

0.gg239E+O0

0.99239E+00

0.I0013E+01

0.I0013E+01

0.10069E+01

0.10069E+01

0.10089E+01

0.10089£+01

I

2

-15.

15,

-15,

15,

I

2

-15.

15,

-15.

15,

I

2

-15.

15.

-15.

15.

I

2.0178

2.0178

2.0178

2,0170

2.0170

2.0178

2.0178

2.0178

2.0178

2,0178

2,0178

2.0178

2.0178

2.0178

2.0178

2,0178

2,0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2,0170

2.0178

2.0178

2.0178

2.0178

2,0170

2,0178

2,0178

2,0178

2.0178

2.0178

2.0170

2.0170

2,0178

2.0178

2.0178

2.0178

2.0178

2,0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2.0178

2,0178

2.0178

2.0178

2,0178

2.0178

2.0170

2.0178

2.0178

2.0178

10.

10,

O.

O.

10.

10,

10.

10.

O.

O.

I0.

I0.

-0.51339E-01

0.St339E-Ol

-0.54310E-01

0.54310E-01

-0.56656E-01

0.566S6E-01

-0.$8374E-01

0_$8374E-01

-0.59476E-01

0.$9476E-01

-0.59978E-01

0.59970E-01

-0.59909E-01

0.$9909E-01

-0.$9304E-01

0.59304E-01

-0.$8203E-01

0.58203E-01

-0.56653E-01

0.56653E-01

-0.54702E-01

0.$4702E-01

-0.52398E-01

0.52398E-01

-0,49792E-01

0.49792E-01

-0.46931E-01

0.46931E-01

-0.43863E-01

0.43863E-01

-0.40632E-01

0,40632E-01

-0.37282E-01

0,37282E-01

-0.33853E-01

0.33853E-01

-0,30387E-01

0.30387E-01

-0.26920E-01

0_26920E-01

-0.23494E-01

0.23494E-01

-0.20146E-01

0.20146E-01

-0.16915E-01

0.16915E-01

-0.13843E-01

0.13843E-01

-0.10971E-01

0,10971E-01

-0.83390E-02

0.03390E-02

-0,59930E-02

0,59930E-02

-0.39740E-02

0,39740E-02

-0.23220E-02

0.23220E-02

-0.I0810E-02

0.I0810E-02

-0.28900E-03

0.20900E-03

O.O0000E+O0

O.O0000E÷O0

10.

10.

10,

10,

-10,

-10,

10.

10.

-10.

-10.

-10.

-I0,

240
2

2

-15.

-15.

-15,

-15,

8I

22

15,

15.

15,

15.

9I

22

-15.

15.

-15.

15.

10I

22

-15

15.

-15.

15.

$ mesh generat ion

22 10

$

II

22

33

44

55

66

77

88

99

10 10

11 11

12 12

13 13

14 14

15 15

16 16

17 17

18 18

Ig 19

20 20

21 21

22 22

$ regions

111 4

5 -3 -61

221 43 3 2

00

O.

O,

6 -4 -5

O. -I0.

10. -10,

0, 10,

I0. 10.

O. I0,

10. 10.

O. -10.

I0. -10,

I0.

I0.

O,

O,

O.

O.

-10.

-10.

44

4

-20 -14 17 15

55

4

18 16 -21 -15

66

4

13 22 -16 -19

77

5

-18 -17 -9 -II 19

881 5

20 21 -22 12 10

991

6

14 -10 -8 -2 -79

10 10I

6

7 -I8 -12 -13 11

241
Data for the background grid file, wing.bac, are given below.

STARS-CFDASE input data:

4

5

6

* points

" I inas

* background mash ... quasi-2D NACRO012

8 6042

I .IO000E+06 -.I0000E+06 -,I0000E+06

1.00 .00 .00 3.000

.00 |.00 .00 3,000

,00 .OO 1.00 3.000

2 .IO000E+06 .IO00OE+06 -.10000E+06

I_00 ,00 .00 3.000

.00 I.O0 .00 3,000

.00 .00 1.00 3.000

3 -.10000E+06 ,I0000E+06 -.I0000E+06

1.go .00 ,00 3.000

.00 1.00 .00 3.000

.00 .00 1.00 3.000

4 -.10000E+06 -,10000E+06 -.IO000E+06

1.00 .00 .00 3.000

.00 1.00 .00 3.000

.00 ,00 1.00 3.000

S .I0000E+06 -.10000e+06 .IOOOOE+O6

1,00 .00 .00 3.000

.00 1.00 .00 3.000

,00 .00 1.00 3.000

6 .10000E+06 ,10000E*06 ,10000E+06

1,00 .00 .00 3.000

,00 1.00 .00 3.000

.00 .00 1.00 3.000

? -.10000E+06 .I0000E+06 ,10000E+06

1.00 .00 .00 3.000

.00 1.00 .00 3.000

.00 .00 l.O0 3.000

8 -.I0000E*06 -.I0000E+06 .I0000E+06

1.00 .00 .00 3.000

.00 1.00 .00 3.000

.00 .00 1.00 3,000

I I 2 4 8

2 I 2 8 6

3 I 6 8 5

2 3 4 7

2 7 4 8

2 7 8 6

I.- leading edge

-.O0000E+O0 .O0000E+O0 .O000OE+O0 .040 ,100

-,O0000E+O0 .21000E+01 .O000E+OI .040 ,I00

2.- leading edge

-,O00OOE+O0 .O0000E+O0 .O0000E+O0 .015 .050

-,O0000E*O0 .21000E*01 ,O0000E+OI ,015 .050

3.- tralting edge

.1007E+01 .O0000E*O0 .O0000E+O0 .040 ,100

.1007E+01 .21000E+0t .O0000E+O0 ,040 ,100

4.- trailing edge

.1007E+01 .O0000E+O0 .O0000E+O0 ,025 ,050

.I007E+01 .21000E+01 ,OOO00E+O0 .025 ,OSO

* triangles

I.- wing

-.IO000E*O0 .O00000E+O0 ,O0000E*O0 .04 .160

-.IO000E+O0 .210000E+0_ .O0000E+O0 .04 ,160

,101E+01 .210000E+OI .O0000E÷O0 .04 .160

2,- wing

.I01E+01 .21000E*01 .OOOOOE÷O0 .04 .160

.I01E+01 .O00OOE+O0 .O0000E+O0 .04 .160

-_IO000E+O0 .O0000E+O0 .O0000E+O0 .04 ,160

la,- wing

-.IO000E+O0 ,000000E+00 .O00OOE+O0 .055 .090

-.IO000E+O0 .210000E+01 .O0000E+O0 .055 .090

.101E+01 .210000E+01 ,O0000E+O0 .055 ,090

2a.- wing

.101E+01 .21000E+01 .O0000E*O0 .055 .090

,101E+01 ,O000OE+O0 .O0000E÷O0 .055 .090

-.IO000E+O0 .O0000E+O0 .O0000E+O0 .055 ,ogo

.308

,308

.089

.089

.377

.377

.179

.179

,500

,500

.500

,500

,500

50

1.500

1,500

1,500

.500

.500

1,500

242
Datafortheboundary-conditionfile, wing.bco,aregivenbelow.

STARS-CFDASEinput data:

Boundary Condition Flogs

10, 22

$ Surface Regions

I I

2 I

3 I

4 I

5 I

6 I

? 3

8 3

9 2

10 2

$ Curved Segments

I 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

10 0

11 0

12 0

13 0

14 0

15 0

16 0

I? 0

18 0

19 0

20 0

21 0

22 0

Data for the steady CFD solution control file, wing.cons, are given below.

STARS-CFDASE input data:

&control

nstep = 270,

nstou " 10,

nstage = 4,

cfl - 1.0,

dissl - 1.0,

dies2 = 1,0,

relax = 1,0,

mach = 0.5,

alDha = 0,0,

beta • 0,0,

restart ,false._

nlimlt • 2,

Ig = I,

nlteO = I_

nitel - I,

nlte2 = 0,

ncycl = 25,

ncyci - 25,

tlr = 0.0001,

debug = .false.,

leehc = I_

meohf - I,

cbt(l) = 1.0,

cbt(2) • 0,5,

cbt(3) = 0,0,

cbt(4) - 0.0,

trans = ,false,,

I

243
Datafor thesolidsfile, wing.dat,aregivenbelow.

STARS-SOLIDSinput data:

manual solids metric unlt_ - solids medel fer vlbratien

861, 1610,

O, O,

I, 1,

2, O,

I, 8,

$ NODAL DATA

I .OOOO

21 .0089

22 .OOOO

42 .0089

43 .0000

63 .0089

64 .0000

84 ,0089

85 ,OOOO

105 .0089

106 ,0000

126 ,0009

127 .OOOO

147 .O08g

148 .0000

168 .0089

169 .0000

189 .0089

190 .0000

210 .0089

211 .0000

231 _0089

232 .0000

252 1,0089

253 .0000

273 1.0089

274 ,0000

294 1.0089

295 ,0000

315 !,0089

316 ,0000

336 1.0089

337 .0000

357 1.0009

358 .0000

378 1.0089

379 .0000

399 I_0089

400 .O00O

420 1,0089

421 .0000

441 1.0089

442 .0000

462 .0089

463 .0000

483 .0089

484 .0000

504 .0089

505 ,0000

525 .OOBg

526 .DO00

546 .0089

547 .0000

567 ,0089

568 ,0000

588 ,0089

589 .0000

609 .0089

610 .0000

630 1.0089

631 .0000

651 1.0089

652 .DO00

672 1.0089

673 .0000

693 l,OOOg

694 ,0000

714 1,0089

715 .0000

I, 4, I, I, O, O, O,

O, O, O, O, O, O, 0

O, O, 0, O, O, 0

2, O, I, O, O, O, O,

O, 6.0000E+04, .O00OE+O0, .OO00E+O0

analysis - 20x40

0

,0000 .OOO0 I I I I I I 0 0 O

.O00O .O00O I I I I I I 0 0 I

.0504 .0000 O 0 0 O 0 0 0 0 O

•0504 .0000 0 0 0 O 0 0 0 0

.lOOg .0000 0 0 0 O 0 0 0 0

.1009 .DO00 0 0 0 O 0 0 O 0

.1513 .0000 0 0 0 0 0 0 0 0

.1513 .0000 0 0 0 0 0 0 0 0

.2018 .0000 0 0 0 0 0 0 0 0 0

,2018 ,ODD0 0 0 0 0 0 0 0 0

.2522 ,0000 0 0 0 0 O 0 0 0 0

.2522 ,0000 0 0 0 0 O 0 0 0

,3027 ,0000 0 0 0 0 O 0 0 0 0

.3027 .0000 0 0 0 0 0 0 0 0

,3531 .0000 0 0 0 0 0 0 0 0 0

,3531 ,0000 0 0 0 0 0 0 0 0

.4036 .0000 0 0 0 0 0 O 0 0 0

.4036 ,0000 0 0 0 0 0 0 0 0

.4540 ,DO00 0 0 0 0 0 0 0 0 0

.4540 ,DO00 0 0 0 0 0 0 0 0

.5045 .0000 0 0 0 0 0 0 0 0

.5045 ,0000 0 0 0 0 0 0 0 0

.5549 .0000 0 0 0 0 0 0 0 0

.5549 .0000 0 0 0 0 0 0 0 0

.6053 .0000 0 0 0 0 0 O 0 0

.6053 .0000 0 0 0 0 0 0 0 0

,6558 .0000 0 0 0 0 0 0 0 0 0

.6550 .0000 0 0 0 0 0 0 0 0

.7062 .0000 0 0 0 0 0 0 0 0 0

.7062 .0000 0 0 0 0 0 0 0 0

.7567 .0000 0 0 0 0 0 0 0 0 0

.7567 .0000 0 0 0 0 0 0 0 0

.8071 .0000 0 0 0 0 0 0 0 0 0

.8071 .0000 0 0 0 0 0 0 0 0

.0576 .0000 0 0 0 0 0 0 0 0 0

.8576 .0000 O 0 0 0 0 0 0 0

.9080 .0000 0 0 0 0 0 0 0 0 0

.9080 .0000 0 0 0 0 0 0 0 0

.9585 ,0000 0 O 0 0 0 0 0 0 0

.g585 ,0000 0 0 0 0 0 0 0 0

1.0009 .0000 0 0 0 0 0 0 0 0 0

1.0089 .0000 0 0 0 0 0 O 0 0

1.0593 .0000 0 0 0 O 0 0 0 0 0

1.0593 .0000 0 0 0 0 0 0 0 0

1.1098 .0000 0 0 0 0 0 0 0 0 0

1.t098 ,0000 0 0 0 0 0 0 0 O

1.1602 .0000 0 0 0 0 0 0 0 0

1.1602 .0000 0 0 0 0 0 0 0 0

1,2107 ,OOOO 0 0 0 0 0 0 0 0 0

1.2t07 .0000 0 0 0 0 0 0 0 0

1.2611 .0000 0 0 0 0 0 0 0 0 0

1.2611 .0000 0 0 0 0 0 0 0 0

1.3116 .0000 0 0 0 0 0 0 0 0 0

1.3116 .0000 0 0 0 0 0 0 0 0

1.3620 .0000 0 0 0 0 0 0 0 0 0

1.3620 .DO00 0 0 0 0 0 0 0 0

1.4125 ,0000 0 0 0 0 0 0 0 0 0

1.4125 .0000 0 0 0 0 0 0 0 0

1.4629 .0000 0 0 0 O 0 0 0 0 0

1.4629 .0000 0 0 0 0 0 0 0 0

1.5134 .0000 0 0 0 0 0 0 0 0 0

1,5134 .0000 0 0 0 0 0 0 0 0

1.5638 .0000 0 0 0 0 0 0 0 0

1.5638 .O00O 0 0 0 0 0 0 0 0

1.6142 .0000 0 0 0 0 0 0 0 0

1.6142 .0000 0 0 0 0 0 0 0 0

1.6647 .0000 0 0 0 0 0 0 0 0

1.6647 .0000 0 0 0 0 0 0 0 0

1.7151 .0000 0 0 0 0 0 0 0 0

244
735

736

756

757

7?7

778

798

"/99

819

820

840

861

1.0089 1.7151

.0000 ,7656

1.0089 .7656

.0000 .8160

1.0089 .8160

.0000 .8665

1.0089 ,8665

.0000 .9169

1.0089 .9169

.0000 .9674

1.0089 .96?4

.0000 !.0178

1,0089 2,0178

.000000000000

.0000000000000

.000000000000

.0000000000000

.000000000000

.0000000000000

.000000000000

,0000000000000

.000000000000

.0000000000000

.000000000000

.0000000000000

.000000000000

$ ELEMENT CONNECTIUITY CONDITIOMS 3 1 1 2 23 0

0000

3 20 20 21 4200000

3 21 23 22100000

3 40 42 41 2000000

3 41 22 23 4400000

3 60 41 42 6300000

3 61 44 43 2200000

3 80 63 62 4100000

3 81 43 44 6500000

3 I00 62 63 8400000

3 I01 65 64 4300000

3 120 84 83 6200000

3 121 64 65 8600000

3 140 83 84 10500000

3 141 86 85 6400000

3 160 105 104 8300000

3 161 8S 86 10700000

3 180 104 I05 12600000

3 181 107 106 8500000

3 200 126 125 10400000

3 201 106 I07 12800000

3 220 125 126 14700000

3 221 128 127 10600000

3 240 147 146 12500000

3 241 127 128 14900000

3 260 146 147 16800000

3 261 149 148 12700000

3 280 168 167 14600000

3 281 148 149 17000000

3 300 167 168 18900000

3 301 170 169 14800000

3 320 189 188 16700000

3 321 169 t?O 19100000

3 340 188 189 21000000

3 341 191 190 16900000

3 360 210 209 18800000

3 361 190 191 21200000

3 380 209 210 23100000

3 381 212 211 19000000

3 400 231 230 20900000

3 401 211 212 23300000

3 420 230 231 25200000

3 421 233 232 21100000

3 440 252 251 23000000

3 441 232 233 25400000

3 460 251 252 27300000

3 461 254 253 23200000

3 480 273 272 25100000

3 481 253 254 27500000

3 SO0 272 273 29400000

3 501 275 274 25300000

3 520 294 293 2?200000

3 521 274 275 29600000

3 540 293 294 31500000

3 541 296 295 27400000

3 560 315 314 29300000

3 561 295 296 317O0000

3 580 314 315 33600000

3 581 317 316 29500000

3 600 336 335 31400000

3 601 316 317 33800000

3 620 335 336 3S?00000

3 621 338 337 31600000

3 640 357 356 33500000

3 641 337 338 35900000

3 660 356 357 37800000

3 661 359 358 33700000

3 680 378 377 35600000

3 681 358 359 38000000

000

000

0000

000

0000

000

0000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

245
3 700 377 378 399 3 701 380 379 358 3 720 399 398 3?7 3 721 379 380 401 3 740 396 399 420 3 741 401 400 379 3 760 420 419 398 3 761 400 401 422 3 780 419 420 441 3 781 422 421 400 3 600 441 440 419 3 601 421 422 443 3 620 440 441 462 3 621 443 442 421 3 840 462 461 440 3 841 442 443 464 3 660 461 462 483 3 861 464 463 442 3 880 483 482 461 3 881 463 464 485 3 900 462 463 504 3 901 485 464 463 3 920 504 503 482 3 921 484 485 506 3 940 503 504 525 3 941 506 505 464 3 960 525 524 503 3 961 505 506 527 3 980 524 525 546 3 981 52? 526 SOS 3 1000 546 545 524 3 1001 526 527 548 3 1020 545 546 567 3 1021 548 547 526 3 1040 567 566 545 3 1041 547 548 569 3 1060 566 567 568 3 1061 569 568 547 3 1080 588 587 566 3 1081 568 569 590 3 100 587 588 609 3 I01 590 589 568 3 120 609 608 587 3 121 589 590 611 3 140 608 609 630 3 141 611 610 589 3 160 630 629 608 3 161 610 611 632 3 160 629 630 651 3 181 632 631 610 3 1200 651 650 629 3 1201 631 632 653 3 1220 650 651 672 3 1221 653 652 631 3 1240 672 671 650 3 1241 652 653 674 3 1260 671 672 693 3 1261 674 673 652 3 1280 693 692 671 3 1281 673 674 695 3 1300 692 693 714 3 1301 695 694 673 3 1320 714 713 692 3 1321 694 695 716 3 1340 713 714 735 3 1341 716 715 694 3 1360 735 734 713 3 1361 715 716 737 3 1380 734 735 756 3 1361 737 736 715 3 1400 756 755 ?34 3 1401 736 737 758 3 1420 755 756 777 3 1421 758 757 736 3 1440 777 776 755 3 1441 757 758 779 3 1460 ?76 ?77 798 3 1461 779 778 757 3 1480 798 797 ?76 3 1481 778 779 800 3 1500 797 798 819 3 1501 800 799 778 3 1520 819 818 797

246

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

o00

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000
3 1521 799 800 821 0 0 O O 0

3 1540 818 819 840 0 0 0 O 0

3 1541 821 820 799 0 0 0 O 0

3 1560 840 839 818 0 0 0 O 0

3 1561 820 821 842 0 0 0 0 0

3 1580 839 840 861 0 0 0 0 0

3 1581 842 841 820 0 0 0 0 0

3 1600 861 860 839 0 0 0 0 0

I 1601 6 90 11 0 0 0 0 0

I 1610 762 846 11 0 0 0 0 0

$ line element properties

1 6,4516e-46,93719e-83.46859e-83,46859e-8

$ element thlckneee

I 0,0127

$ material properties

I I

6.8947e+10 0.3 0.0 2764,925

0 0 0

O 0 0 I

O 0 0

0 0 0 I

O 0 0

O 0 0 1

0 0 0

0 O 0 I

84

Data for the generalized mass file, genmass.dat, are given below.

STARS-AEROS-GENMASS input data:

$ Genease input panel for flat plate

I O I_0

$ Lateral ly moving nodes

Data for the damping file, damp.dat, are given below.

STARS-CFDASE input data:

$ nr

8

$ scaling factor from eollds,out.l

,349360438E+02

$ COMPLETE GENERALIZED STIFFNESS MATRIX

.806021E+04 ,418052E-06 ,379135E-06 -,425624E-08 ,223142E-06 -.399296E-07

.233825E-06 ,477367E-07

,49311?E-06 ,130742E+05 ,988797E-07 -.314734E-07 ,I18463E-06 -,775960E-07

,147543E-07 .237048E-07

,249164E-06 .121627E-06 .351742E+05 .728556E-08 .348321E-07 ,854473E-08

,407196E-07 °,500201E-07

-.244357E-G? -,522126E-07 .116631E-07 .817425E*05 ,209431E-08 .137403E-07

-.120515E-07 .646512E-07

.198223E-06 .140394E-06 .128440E-07 -_480750E-08 _827184E+05 ,289550E-07

.408151E-08 .225324E-07

-.581061E-07 -.710594E-07 .403392E-08 ,192696E-07 .319938E-07 ,650692E+05

-_168824E-07 ,246665E-07

,256499E-06 ,I04723E-07 .438142E-07 -,134610E-07 .319909E-09 -.239153E-07

,135508E+06 -.197322E-07

,509064E-07 .317361E-07 -.482843E-07 .693115E-07 ,199359E-07 .240971E-07

-.308757E-07 ,175971E+06

$ COMPLETE GENERALIZED MASS MATRIX

.643225E+03 -.938282E-12 -.141859E-II .849467E-12 -,775268E-12 .256675E-12

,276248E-12 -.186761E-12

-,821309E-12 .867958E+02 -.I05381E-12 -,268356E-II ,187751E-II -,657684E-11

,141576E-I0 .786985E-II

-,161409E-11 -.943559E-13 ,I05094E+03 ,164435E-12 .378709E-13 ,881064E-13

,188706E-12 -.277491E-13

.850017E-12 -,265596E-11 _121782E-12 .527647E*02 ,176344E-13 -.419275E-12

-.252774E-12 ,433612E-12

-_769083E°12 ,187845E-11 -.562751E-13 .433663E-13 .320364E+02 .249026E-12

-,113669E-12 -,310070E-12

,261829E-12 -.657559E-11 .824586E-13 -,438865E-12 .246023E-12 .116968E+02

,149394E-11 ,225071E-11

,277?67E-12 ,I41633E-10 .179429E-12 -,241234E-12 -,I08202E-12 .149770E-11

,235345E+02 -,124289E-11

-.183677E-12 .787373E-11 -.364222E-13 .431543E-12 -,301428E-1Z ,226022E-II

-,123894E-11 .180567E+02

$ frequency

2.747612098619857

11.39123359704445

17,10682426130278

36,97839054058097

47.76388409022645

70.13811875845710

71.35699307350842

92.84741756506145

247
Datafor theaeroelasticscalarsfile, wing.scalars,aregivenbelow.

STARS-CFDASEinput data:

$ aeroelaetic scalre data file, supmrcritlcal, fp=O.gSxsl

$ nr, ibc ( O-full modes, 1=q(1) = 0.01, 2=q(nr+l)=O.Ol )

2, O, 0.001

6, I, 2, 3, 4, 5, 6

$ iread, Iprint

2, I

$ dimensional parameters; mach-inf, rho-lnf(kglmSm3), a-lnf(m/eec), gamma,

0.5 1.16375 340.29 1.4

$ shift factor and gravity constant

.349360438E*02 , 1.0

$ flag, ffi, he, ne

2, 10., 3, 5

$ era, eli

I, I

$ ntarms, nsteps

20, 2

plnf

0

Data for the unsteady CFD solution control file, wing.conu, are given below.

STARS-CFDASE input data:

&control

nstep = 230,

nout = 50,

netags = 3,

cfl - 1.0,

math • .5,

alpha = 0.0,

beta • 0,0,

restart • I,

ncycl = 40,

ncyci • 40,

tlr = 0.01,

debug = .false.,

meshc = I,

meshf = 1,

cbt(1) = I,,

cbt(2) • 0,5_

cbt(3) • 0.,

cbt(4) = 0.,

nsath = 2,

sIOfC = 0.2,

low = .false.,

tranm - .true.

freq = 0.0125,

nstpe = 500,

xO = 0.0,

yO - 0.0,

zO = 0.0,

aux = 0.0,

mug = 0.0,

muz • 1,0,

phase = 0.0,

amplitude = .I,

/

Data for the alternate steady CFD solution control file, wing.consdp, are given below.

STARS-CFDASE input data:

4 (lines of title)

$ VERSION USING FILES FROM SURFACE, VOLUME, AND 'CFDRSERUN' ROUTINE, JUNE 1990

$ cantilever wing

$ moch=0.5 alpha=O

$

$ PROBLEM DIMENSION

3

$ NELEM, NPOIN, NBOUN

297700, 54759_ 12594

$ KRCCEL, NACCEL

I00, 25000

$ GAMMA, C1, IDIFF, EPS, IUISC, UBR

1.4, 1.0, 2, 0.1, 0, 0.2

$ NFFBC

I

$ ROINF, UXINF, UYINF, UZINF, PINF, MRCHINF

1.0, 1,0, 0.0, 0.0, 2,8571428, 0,5

248
$ NEN§C

0

$ NTIME, NITER, ILOT

2000, 1, 1

$ CSRFE, IFCT, NOURN, 100(1), ID0(2), CLIMAX

0.7, O, 2, 3, 1, 0.90

$ INFOG, IHFOU, OUFO, N;OUT

-I, -2, 3, 500

$ CSMO0, NSMO0

.2, 0

$ ENTHALPY DAMPING COEFFICIENT

1.0

$ IAPR, IRLOG, ILPR, ILLOG, AN(1), AN(2), RX(3), RCHORD

I, I, I, I, 1.0, 0.0, 0.0, 2.5

$ IAFR, IRFS

3, 5500

$ ISTRON, ICHECK

2 1

$ TIMEIN, ITIM

0.0, 0

$ FILE3, FILE2, FILE4 ( Output film noge - gmo film name - Input film name )

fort.15_dp

manual.geodp

IN

$ NCPU

I

10.1.2 Analysis Results

Figure 68 shows the aerodynamic surface grid on the wing and the solution domain. Figure 69 shows

the Mach and pressure distribution on the wing for the steady-state solution. Figure 70 shows the first

few structural modes. For stability analysis, the damping values are calculated from the generalized

displacements, and figure 71 shows some typical plots in this connection. Figure 72 shows analysis

results from when the flutter parameter (density ratio) is calculated to be 0.934, pertaining to a zero

damping value.

970360

Figure 68. Aerodynamic surface grid of wing and solution domain.

249
I

(a) Mach distribution.

970361

(b) Pressure distribution.

Figure 69. Cantilever wing steady-state Mach and pressure distributions.

970362

250
Mode 1, first bending

2.748 Hz

Mode 2, first torsion

11.39 Hz

_- Mode 3, second bending

17.11 Hz

Mode 4, second torsion

36.98 Hz

_-- Mode 5, third bending

70.14 Hz

Mode 6, third torsion

71.36 Hz

Figure 70. Structural modes of cantilever wing.

970363

251
ql

-.2

w .3

0 x 100

--.1

I I

q2

- .05

- .10

.05 x 100

0

! I I

li 1

-2

-4

4 x 100

2

0

I I J

X1

_12

-1

-2

2 x 10 0

1

0

I t

0 .S 1.0

Time

970364

Figure 71. Typical wing generalized displacement plots for flutter parameter (fp) = 0.95.

X3

X4

.2

Damping, .1

z

0--

-.1- I I I

.80 .85 .90 .95 1.00 1.05 1.10 1.15

Flutter parameter

970365

Figure 72. Aeroelastic stability plot for cantilever wing.

252
11. COUPLED HEAT TRANSFER AND STRUCTURAL ANALYSIS

In this section, the input data and relevant outputs of several typical test cases involving heat-transfer

analysis results, interpolating to structural model as thermal loading, are provided in detail. The input

data are prepared in accordance with the procedures described in section 3 and are defined in consistent

unit form.

11.1 Clamped-Clamped Beam: Thermal Loading

A beam with both ends fixed (fig. 73) has been subjected to varying temperatures. Results of

vibration, static, and buckling analysis with thermal loading, derived from heat-transfer analysis, are

presented as follows:

Y

*.,, x

L_-60

970366

(a) Heat-transfer mesh.

Y

I..., L=60

_. --------.!_ X

970367

(b) Structural mesh.

Figure 73. Finite-element model of a beam.

Important data parameters:

Heat-transfer analysis:

Coefficient of conductivity, k

Length, L

Area, A

Perimeter, P

Wall temperature, T

wl

Tw 9

Structural analysis:

Young's modulus, E

Cross-sectional area, A

Moment of inertia:

About the y axis

About the z axis

Length, L

Mass density, p

Coefficients of thermal expansion, ot

= 132.0

= 60

= 0.001365

= 0.13091

= 10.0

= 0.0

= 30 x 106

= 1.0

= 1/12

= 1/24

= 60

= 0.1666

= 6.6 x 10 --6

253
STARS-SOLIDSthermalinput datafor heat-transferanalysis:

HEAT TRANSFER - LINE

10, B, I, 11,1,0,O,O,O,O

O,O,O, 1,2,O,O,O,O

lO.O,O, 1,O,O,O,O

2,0,1,O,O,O,O,l,0,0

$ NODAL DATA

I O.O O.O

2 7.500 O.O

3 15.000 0.0

4 22.500 O.O

5 30.000 O.O

6 37.500 0.0

? 45.000 0.0

8 52.500 O.O

9 60.000 O.O

10 O.O IOO.O

$ ELEMENT CONNECTIVITY

1 1 1 2 I0

I 2 2 3 IO

t 3 3 4 I0

I 4 4 5 IO

1 5 5 6 IO

I 6 6 7 I0

1 7 7 8 I0

I 6 O 9 I0

O,O O 1

O.O D I

O.O O I

O.O 0 I

O.O 0 1

O.O 0 I

O.O 0 t

O.O O 1

O,O 0 I

O.O I 1

0 0 0 0 0

O O 0 0 0

0 O 0 0 O

O O O 0 O

O 0 0 0 0

0 0 0 0 - O

O O 0 0 0

0 O O 0 0

$ LINE ELEMENT BASIC PROPERTIES

1 0,001365 0.13091

$ ELEMENT MATERIAL PROPERTIES

I 6

13.2E01 0.0 O O.O O0.O

O,O O.O 0 O.O

$ DISPLACEMENT/TEMPERATURE BOUNDARY CONDITION DATA

I I 1 1 1O.

9 1 9 t 0.

O.O 0.0

STARS-SOLIDS coupled heat-transfer/structures input data:

BEAM WITH BOTH END5 FINED - 10 ELEMENT IDEALIZATION

12, IO, 1, 4, 1, O, O, O, O, O

-I, O, O, O, O, O. O, O, O

I, I, O, 0, 0, O, 0,0

2, O, 2, 0, 1, O, 0, 0, 0, I

I, 6, O, 500.0, O.O, O.O

$ NODAL DATA

I O,O 0.0 O,O I I 1 I

2 6.0 0.0 O,O O O O O

3 12.0 0.0 O,O D O O O

4 18.0 O.O O,O O 0 O O

5 24.0 0.0 O_O 0 0 0 O

6 30,0 O.O O.O O O O O

? 36.0 O.O O.O O 0 0 O

8 42.0 0,0 O,O 0 O 0 O

9 48.0 O,O O.O 0 0 O 0

IO 54.0 0.0 0.0 O 0 O 0

11 60.0 0.O O,O I I 1 1

12 25.0 15,0 O,O I 1 1 1

$ ELEMENT CONNECTIVITY

1 1 I 2 12 0 0 O O O 1

1 IO IO II 12 O 0 O O 0 1

$ LINE ELEMENT BASIC PROPERTIES

I l,O 0.125000.083333330.04166667

$ ELEMENT MATERIAL PROPERTIES

I

30.0E+06 0.30 6.6E-6 0.166666

0 O I 0

0 O I I

STARS-SOLIDS output summary: tables 35(a), (b) and (c) show the output summary of vibration,

static, and buckling analysis, respectively.

--._j

254
Mode

Table 35(a).Thermallyprestressedvibrationanalysisresults.

Naturalfrequencies(co),rad/sec

Without temperature

With temperatureinput With temperatureinput

from heat-transfermesh from datafile

1 17.019 16.416 16.416

2 24.067 23.645 23.645

3 46.916 46.105 46.105

4 66.331 65.761 65.761

5 92.013 91.128 91.128

6 130.051 129.428 129.428

Table35(b).Nodaldeformationfor

staticanalysis.

Node X displacement

1 0.0

2 0.1733E-03

3 0.2970E-03

4 0.3960E-03

5 0.4703E-03

6 0.49590E-03

7 0.4703E-03

8 0.3960E-03

9 0.2970E-03

10 0.1733E-03

11 0.0

Table 35(c). Buckling load factor

for buckling analysis.

Buckling load

Mode parameter

1 13.849

Resultsshownin tables35(b)and35(c)havealsobeenverifiedby directtemperaturedatainput.

255
11.2 Cantilever Plate: Thermal Loading

A cantilever plate model, described in section 4.1.4, has been used for vibration and static analysis,

and the same plate with two opposite edges fixed has been chosen for buckling analysis. Figure 74

shows a different finite-element mesh for heat-transfer analysis; relevant input data and analysis results

are given as follows:

I_ L

/////

/ ///

/////

/////

/////

/////

/////

/////

T1

>;

///

///

///

///

///

///

//¢//

970368

(a) Heat-transfer mesh.

T 81

L v

// _'//,///

(b) Structural mesh.

Figure 74. Finite-element model of a plate.

7-

970369

256
Importantdataparameters:

Heat-transferanalysis:

Coefficientof conductivity,k = 1.0

Length,L = 10

Thickness,t = 0.1

Nodaltemperature,T1 = 10.0

T81 = 0.0

Structuralanalysis:

Young'smodulus,E = 10x 106

Thickness,t = 0.1

Poisson'sratio,la = 0.3

Length,L = 10

Massdensity,p = 0.259× 10-3

Coefficientsof thermalexpansion,cx = 3.5× 10-6

STARS-SOLIDSthermalinput datafor heat-transferanalysis:

PLATE 8XB MESH - HEAT TRRHSFER ANALYSIS

81, 12B, 1, 44, 0, 0, 0,

0, 0, 0, I, 4, 0, D,

10, 0, 0, 1, 0, 0, 0,

2, O, 2, O, I, O, O,

$ NODAL DATA

I .0000 .0000 .0000 0

9 .0000 10.0000 .0000 0

10 1.2500 0,0000 ,0000 0

18 1,2500 10,0000 .0000 0

19 2.5000 .0000 .0000 0

27 2.5000 I0.0000 .0000 0

28 3.7500 0.0000 .0000 0

36 3.7500 10.0000 .0000 0

37 5.0000 .0000 .0000 0

45 5.0000 I0.0000 ,0000 0

46 6.2500 .0000 ,0000 0

54 6,2500 10,0000 .0000 0

55 7,5000 .0000 .0000 0

63 7.5000 10.0000 .0000 0

64 8.7500 .0000 .0000 0

72 8,7500 I0.0000 ,0000 0

73 10,0000 ,0000 .0000 O

81 10.0000 I0.0000 .0000 0

$ ELEMENT COHHECTIUITY CONDITIONS

7 I 1 2 11 0 0

? 8 8 9 18 0 0

7 g 11 10 1 0 0

7 16 18 17 8 0 0

7 17 I0 11 20 0 0

7 24 17 18 27 0 0

7 25 20 lg 10 0 0

7 32 27 26 17 0 0

7 33 Ig 20 29 0 0

? 40 26 27 36 0 0

7 41 29 28 19 0 0

7 48 36 35 26 0 0

7 4g 28 29 38 O 0

7 56 35 36 45 0 0

7 57 38 37 28 0 0

7 64 45 44 35 0 0

I, I,

O, 0

0

O, O,

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0 0 0

0 0 I

0 0 0

0 0 1

0 0 0

0 0 t

0 0 0

0 0 1

0 0 0

0 0 1

0 0 0

0 0 1

0 0 0

0 0 I

0 0 0

0 0 I

0 0 0

0 0 1

0 0 0 0 0

0 0 0 0 I

0 0 0 0 0

0 0 0 0 I

0 0 0 0 0

0 0 0 0 I

0 0 0 0 0

0 0 0 0 I

0 0 0 0 0

0 0 O 0 I

0 0 0 0 0

O 0 0 0 I

0 0 0 0 0

0 O 0 0 I

0 0 0 0 0

0 0 0 0 I

257
? 55 37

? 72 44

? "/3 4"/

"/ on 54

? 01 46

./ 80 53

7 09 56

? 96 63

7 9./ 55

? 104 62

? 105 65

7 112 ./2

./ 113 64

? 120 ./I

"/ 121 "/4

"/ 128 81

$ COMPOSITE SHELL

I 1 I

I ,IO00E+O0

38 47 0 0

45 54 0 0

46 37 0 0

53 44 0 0

4? 56 0 O

54 63 0 0

55 46 0 0

62 53 0 0

56 65 0 0

63 72 0 0

64 55 0 0

71 62 0 0

65 74 0 0

72 81 0 0

73 64 0 0

80 71 0 0

ELEMENT STACK DESCRIPTION

1 0 0 0 0

1

$ SPECIFICATION FOR MATERIAL AXIS ORIENTATION

I 2 0

0.0

$ ELEMENT MRTERIRL PROPERTIES

I O

I, O, I, 1. O. 0

O, O. O, O. O. 0

O. O. O. O_ O. 0

O, O, O. O. O. 0

O, O, O. O, O, 0

O. O, 0. O. O. 0

O. O,

$ TEMPERATURE OOUNDRRY CONOIT IONS DATA

1 I 1 1 10,

1 2 1 2 10.

81 1 81 I O,

81 2 81 2 O,

0 0 0 0

0 0 0 0

O O 0 0 0

0 0 0 0

0 0 0 0 0

0 0 0 0

0 0 0 0 0

0 0 0 0

0 0 0 0 0

0 0 0 0

0 0 0 0 0

0 0 0 0

0 0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

'RTR

O,

O,

O.

O.

O.

O.

STARS-SOLIDS coupled heat-transfeffstmctures input data:

CRHTILEUER SQUARE 4 OV 4 PLATE

25, t6, 1, 4, O, 1, O, O, O, 0

-I, O, O, I, O, O, O, O, 0

I, 1, O, I, O, O, O, 0

2, O, 2, O, I, O, O, I, 0, 0

I, 6, O, 6000.0, 0.0, O, 0.0

$ NODAL DATA

1 0.0 0.0

5 I0.0 0.0

6 0.0 2.5

10 10.0 2.5

II 0.0 S.O

15 10.0 5.0

16 0.0 ?,S

20 10.0 7,5

21 0.0 10,0

25 10.0 10.0

$ ELEMENT COHNECTIUITY

2 I I 2 7 6

2 4 4 5 10 9

2 5 6 7 12 II

2 8 9 10 15 14

2 9 II 12 17 16

2 12 14 15 20 19

2 13 16 I"/ 22 21

2 16 19 20 25 24

TEMPERATURE LOADING

0.0 1 1 1

0.0 1 I I

0,0 0 0 0

0.0 0 0 0

0.0 0 0 0

0.0 0 0 0

0.0 0 0 0

0.0 0 0 0

0.0 0 0 0

0_0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

$ SHELL ELEMENT THICKNESSES

t 0,1

$ ELEMENT MATERIAL PROPERTIES

I I

I .OE+O? 0.30 0.35E-5 0.259E-3

1 I

I I

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

I 0

I 0

I 0

1 0

I 0

1 0

1 0

1 0

0 0 0

0 0 1

0 0 0

0 0 I

0 0 0

0 0 I

0 0 0

0 0 I

0 0 0

0 0 I

0 0

0 0 I

0 0

0 0 I

0 0

0 0 I

0 0

0 0 I

STARS-SOLIDS output summary: tables 36(a), (b), and (c) show the output summary of vibration,

static, and buckling analysis, respectively.

258
Table36(a).Thermally prestressedvibrationanalysisresultsfor acantileverplatewith

varyingtemperaturedistribution.

Naturalfrequencies(co),rad/sec

With temperatureinput With temperatureinput

Mode Withouttemperature from heat-transfermesh from datafile

1 214.02 213.92 213.92

2 506.62 507.58 507.58

3 1248.40 1249.69 1249.69

4 1538.29 1537.72 1537.72

5 1765.53 1766.13 1766.13

6 2889.11 2888.35 2888.35

Table36(b).Nodaldeformationfor staticanalysis.

Node X displacement Y displacement

6 -0.809997E-04 0.631047E-04

7 -0.242790E-04 0.734264E-04

8 0.719179E-05 0.650178E-04

9 0.346446E-04 0.580581E-04

10 0.735603E-04 0.354295E-04

11 --0.771033E-04 0.125418E-03

12 -0.299133E-04 0.120472E-03

13 0.154035E-04 0.113178E-03

14 0.555337E-04 0.993192E-04

15 0.919275E-04 0.842963E-04

16 -0.615285E-04 0.177819E-03

17 -0.163020E-04 0.164476E-03

18 0.276178E-04 0.151509E-03

19 0.669176E-04 0.136094E-03

20 0.959403E-04 0.124534E-03

21 -0.435429E-04 0.222953E-03

22 0.108579E-05 0.206311E-03

23 0.452413E-04 0.188285E-03

24 0.834809E-04 0.164283E-03

25 0.104933E-03 0.146110E-03

Table 36(c). Buckling load parameterfor

thermalloadbucklinganalysis.

Bucklingloadparameter

Mode

1 19.048

Resultsshownin tables36(b)and36(c)havealsobeenverifiedby directtemperaturedatainput.

259
12. COUPLED COMPUTATIONAL FLUID DYNAMICS AND

STRUCTURAL LOAD TRANSFER PROBLEMS

In this section, an example problem illustrating the transfer of CFD pressure data on structural mesh is

presented. The input data are prepared in accordance with the procedures described in section 3 and are

defined in consistent unit form.

12.1 Cantilever Wing: Coupled Computational Fluid Dynamics

and Structural Analysis

The cantilever wing described in section 10.1 has been chosen for static and vibration analysis.

Figure 75 shows the finite-element mesh for structural analysis. Pressures are converted from CFD

steady-state analysis; relevant input data and analysis results are as follow:

970370

Figure 75. Cantilever wing with structural mesh.

v _

Important data parameters:

Young's modulus, E

Poisson's ratio, Ix

Wing span, A

Wing chord length, B

Shell thickness, t

Mass density, p

= 6.8947 × 106

= 0.3

= 2.0178

= 1.0089

= 0.0254

= 2765.0

STARS-SOLIDS input data

CimdCI'ILEk_ WII_ PI_SSt,I_S _ON - l:t_aSt.l_ _Ilxl_

462,980, i, 6, O, 1,0, O, O, 0

0,-I,0,1,0,0, O, 0,0, 4805

1,0,0,0,0,0,0,0

2,0,2,0,I,0,0,i,i,0

1,10,0,600.0,0.0,0.0

N3_L _k_1_

i 0.0000 .0000 .0000 i 1

2 .0000 .i000 .0000 0 0

21 0.O(X)O 2.0178 .0000 0 0

1 1 1 1 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 1

260
22 .0074

23 .0074

42 0.0074

43 .C_85

44 .CQ_5

63 0.0285

64 0.1056

(5 .1066

8¢ 0.1056

85 0.2197

86 .2197

105 0.2197

106 0.3583

107 .3583

126 0.3583

127 0.5085

128 .5085

147 0.5085

148 O. 6576

149 .6576

168 O. 6576

i_ 0.7937

179 .7937

IS9 O. 7937

190 0. 9051

191 .9(51

210 O. 9051

211 0.9804

212 .9804

231 0.9804

232 1.0089

233 i. 0089

9q> i. 0089

253 .0074

254 .0074

273 O. 0074

274 .(P.85

275 .CG85

294 0.0285

295 0.1056

296 .1056

3/5 O. 1056

316 0.2197

317 .2197

336 0.2197

337 0.3583

138 .3583

3S7 0. 3583

358 0. 5085

359 .5085

378 O. 5085

379 O. 6576

380 .6576

389 0. 6576

G30 0. 7937

401 .7937

4_3 O. 7937

421 0. 9051

422 .9051

441 0.9051

442 0. 9804

443 .9804

462 0.9804

.0147111111000

.0147000000000

.0147000000001

.0277111111000

.0277000000000

.0277000000001

•0478111111000

.0478000000000

•0478000000001

.0584111111000

.0584000000000

.0584000000001

.0593111111000

•05930000

.05930000

.05241111

.05240000

.05240000

.04061111

.04060000

00000

00001

11000

00000

00001

11000

00000

.0406000000001

.0269111111000

.0269000000000

.C_69000000001

•0138111111000

•0138000000000

•0138000000001

.0040111111000

.OO4O000000000

.0O4O000000001

.0000111111000

.0000000000000

,0000000000001

-.0147111111000

-. 0147000000000

-. 0147000000001

-.0277111111000

-. 0277000000000

-. 0277000000001

-. 0478111111000

-.0478000000000

-. 0478000000001

-. 0584111111000

-. 0584000000000

-.0584000000001

-. 0593111111000

-. 0593000000000

-.0593000000001

0.0000

.1000

2.0178

0.0000

.1000

2.0178

.0000

.1000

2.0178

.0000

.1000

2. 0178

.(XX)O

.1000

2.0178

.0000

.1000

2. 0178

.000(3

.1000

2.0178

.0000

.i000

2.0178

.0000

.i000

2.0178

.0000 .i000

2. 0178

.0000

.10(30

2. 0178

0.0000

.I000

2. 0178

0.0030 •I000

2• 0178

.0000 .i000

2. 0178

.0000

.i000

2.0178

.0000 •1(300

2. 0178

.0000 -.0524111111000

•i000 -. 0524000000000

2. 0178 -. 0524000000001

.0000 -.0406111111000

.i000 -.0406000000000

2.0178 -.0406000000001

.0000 -.0269111111000

.i000 -. 0269000000000

2. 0178 -. 0269000000001

.0000 -.0138111111000

.i000 -.0138000000000

2. 0178 -. 0138000000001

.00O0 -.0040iii1i1000

.1000 -.0040000000000

2. 0178 -. 0040000000001

_ CONDITIONS

31I2 2300000ii0000

3 30 20 21 4200000i1000i

3 21 23 22100000i10000

3 40 42 41 2000000ii000i

3 41 22 23 4400000II0000

3 6D 41 42 6300000ii000i

3 61 44 43 22000001i0000

3 80 63 62 4100000ii000I

3 81 43 44 _500000i10000

3 100 62 63 8400000ii0001

3 iQ1 65 64 4300000Ii0000

0110001

3 120 84 83 62000.0

3 121 64 _5 8600000i10000

3 140 83 84 10500000ii000i

3 141 86 _5 6400000110000

3 160 1C5 104 8300000110001

3 161 _5 86 10700000iI0000

3 180 104 105 12600000ii000i

3 IS1 107 106 8500000ii0000

261
3 200 126 125

_0000011000I

3 201 106 107 12800000110000

3 220 125 126 14700000110001

3 221 128 127 10600000110000

3 _0 147 146 12500000110001

3 241 127 128 14900000110000

3 280 146 147 16800000110001

3 261 149 148 12700000110000

3 280 168 167 14600000110001

3 281 148 149 17000000110000

3 300 167 168 18800000110001

3 301 1";0 168 14800000110000

3 320 189 188 1670000

3 321 189 170 1910000

3 340 iBB 188 2100000

3 341 191 190 1690000

3 38D 210 209 1880000

3 361 190 191 2120000

3 380 209 210 2310000

3 381 212 211 1900000

3 400 231 230 2090000

01I0001

0i10000

0110001

0ii0000

01i0001

0ii0000

0110001

0110000

0110001

3 401 211 212 23300000110000

3 420 230 231 25200000110001

3 421 233 232 21100000110000

3 440 2_ 251 23000000110001

3 44121 25300000ii0000

3 460 21 20 2720000011000i

3 461 253 254200000110000

3 480 272 273 2100000110001

3 481 254 253 27400000110000

3 500 273 272 29300000110001

3 501 274 275 25400000110000

3 5_9 293 294 27300000110001

3 521 275 274 29500000110000

3 540 294 293 31400000110001

3 541 295 296 2750000

3 560 314 115 2940000

3 561 296 295 3160000

3 580 315 314 3350000

3 581 316 317 296 3 600 335 336 315 3 601 317 316 337 3 620 336 335 366 3 621 337 338 317 3 640 356 3.57 336 3 641 338 337 358 3 660 357 356 377 3 661 358 359 338 3 680 377 378 _-7

0110000

0110O01

0110000

0110001

00000110000

00000110001

00000110000

00000110001

00000110000

00000110001

00000110000

00000110001

00000110000

00000110001

3 681 359 268 37900000110000

3 700 378 377 39800000110001

3 7_L 379 380_00000110000

3 720 398 399 37800000110001

3 721 380 379 40000000110000

3 740 399 388 41900000110001

3 741 400 401 38000000110000

3 760 419 420 39900000110001

3 761 4_ 400 4,2100000110000

3 780 420 419 44000000110001

3 781 421 422 40100000iI0000

3 830 440 441 42000000110001

3 801 422 421 44200000110000

3 82D 441 440 46100000110

3 821 442 443 42200000110

3 840 461 462 4410000

3 841 443 442 2320000

3 860 462 461 2510000

3 861 232 233 4430000

3 880 251 2_ 4620000

3 881 21 42 2730000

3 882 42 63 2730000

3 883 294 273 630000

3 884 63 84 315 3 885 315 294 63 3 886 84, IB5 215 3 887 336 315 105 3 888 1(25 126 357 3 889 357 336 105 3 880 126 147 _7 3 891 378 3.5-/ 147

0000

0000

0000

0000

0000

0000

0000

0000

3 8S2 147 168 3890000

3 883 399 378 1470000

0110

0110

0110

0110

0110

011

011

011

011

011

011

011

011

011

011

011

011

011

3 894 168 _8 3890000011

001

000

001

000

001

000

001

262
3 895 42D 389 I_8 3 886 189 210 441 3 897 441 4_0 I_9 3 898 210 231 441 3 899 462 441 231 3 900 231 2_ 4_ 3 901 17 38 _9 3 9_ 38 5) 269 3 903 290 _6B S@ 3 904 _19 83 311 3 905 311 290 B9 3 906 8{) 101 311 3 90/ 13;2 311 1DI 3 90B 101 122 353 3 909 353 332 101 3 910 122 143 353 3 911 374 353 143 3 9"12 143 164 385 3 913 395 374 143 3 914 164 185 385 3 915 416 395 185 3 916 iS5 206 437 3 917 437 416 _5 3 91B 206 _7 437 3 919 458 437 _7 3 9_0 _7 248 458 3 _ 13 34 _5 3 9_ 34 _ 2_ 3 _3 286 265 3 99A 55 76 3O7 3 925 307 286 3 9_6 76 97 307 3 g27 328 307 97 3 928 97 118 349 3 929 349 328 97 3 930 LIB 139 349 3 931 370 349 139 3 9_ 139 160 391 3 933 391 370 139 3 934 1.60 IBl 391 3 935 412 391 181 3 936 181 202 433 3 937 433 412 181 3 938 _C_ 223 433 3 939 454 433 223 3 940 223 244 454 3 941 9 30 261 3 942 30 51 261 3 943 282 261 51 3 944 51 72 ]38 3 945 303 282 %-I 3 946 72 93 303 3 947 324 303 93 3 948 93 i14 345 3 949 345 3Z4 93 3 950 114 135 345 3 951 366 345 135 3 952 135 156 387 3 953 387 366 135 3 954 156 177 387 3 9_5 408 387 177 3 956 177 198 429 3 957 429 408 177 3 858 198 219 429 3 959 450 429 219 3 960 219 240 450 3 961 5 26 257 3 9_ 26 47 _$7 3 963 278 _ 47 3 964 47 68 299 3 9(5 299 278 47 3 966 6B 89 299 3 967 32O 299 3 968 89 LID 341 3 9(B 341 320 89 3 970 110 131 341 3 971 362 341 131 3 972 131 152 383 3 973 383 362 131 3 974 152 173 383 3 975 404 383 173 3 976 173 194 425 3 977 425 404 173

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

001i

00II

00ii

00i1

0011

00ii

00i1

0011

0011

0011

0011

0011

00ii

0011

0011

0011

00ii

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

00Ii

0011

0011

0011

00ii

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

00l1

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

0011

263
3 978 194 215 4_5 0 0 0 0 0 1 1

3 979 446 425 215 0 0 0 0 0 1 1

3 980 215 236 446 0 0 0 0 0 ! 1

$ _-_:.L I_ _'IIC_

1 .2540_-01 .254G_-01 .254GE--01

$ N_IAL l'aO_

1 1

.6895E+II .3_ ._ .2765E+04 .0000E+00 .0(X)0E+00

STARS-SOLIDS output summary: tables 37(a) and (b) show the results of static and vibration analysis,

respectively.

Table 37(a). Maximum deflection in the Z direction for static analysis (free-edge

deformation).

Node Z displacement (10E-04) Node Z displacement (10E-04)

252 -0.392772 230 -0.372728

231 -0.391481 251 -0.372621

462 -0.391467 209 -0.371897

210 -0.387958 377 -0.371267

441 --0.387896 461 -0.370395

420 -0.383524 357 -0.370059

189 -0.383506 126 -0.369516

399 -0.378819 335 -0.368904

168 -0.378722 336 -0.366274

378 -0.374320 398 -0.366066

147 -0.373934 105 -0.365630

356 -0.373760

Table 37(b). Natural frequencies from vibration analysis.

Natural frequencies (co), rad/sec

Mode Free vibration Prestressed vibration

1 162.497 162.491

2 623.103 623.114

3 762.972 762.959

4 1041.57 1041.59

5 1467.85 1467.86

6 1911.79 1911.77

264
APPENDIX A

PREPROCESSOR MANUAL

The preprocessor routine PREPROCS is an integral part of the set of routines that form the STARS

program. This routine has been developed to automate the generation of finite-element models and

corresponding data files. Instead of defining a complete structure by independently describing each node

and element, the preprocessor allows the automatic formation of such data. The preprocessor minimizes

data input and eliminates data editing, thereby enhancing the efficiency of the STARS program.

To run the preprocessor, the user types the command PREPROCS; the program will prompt a list of

different terminals. The user then chooses the type of terminal to be used (for example, IBM, Tektronix,

and various compatible terminals). Next, the user is prompted with menu options in a progressive fashion.

At any level of the menu, the user can exit by entering Control-C.

A brief description of the primary menu is given here; because of the interactive nature of the program,

the user is automatically exposed to more extensive details.

PREPROC MENU

MENU OPTIONS:

0 STOP

Stop the program.

COMPUTER-AIDED DESIGN

Generate graphics objects.

PROPERTIES AND ANALYSIS SPECIFICATION

Specify STARS data.

3 READ

Read the STARS data file.

4 WRITE

Write the STARS data file.

5 DELETE

Delete the current structure.

1 COMPUTER-AIDED DESIGN

DESIGN OPTIONS:

0 QUIT

Quit this menu.

1 LINES

Generate line segments.

2 SURFACES

Generate surface segments.

265
3 SOLIDS

Generatesolid segments.

4 SYNTHESIS

Generatesurfacesfrom existinglinesegments.

5 REPRODUCE

Generatenewsegmentsusingexistingones.

6 DRAW

Plotthecurrentstructure.

7 EDITOR

Modify existingdata.

AUTOMESH

Generatethesurface/solidautomatically.

1.1 LINES

o Quit

Quit this menu.

4

STRAIGHT LINE

Generate a straight line segment.

PARABOLIC CURVE

Generate a parabolic line segment.

CIRCULAR CURVE

Generate a circular line segment.

ELLIPTIC CURVE

Generate an elliptical line segment.

1.2 SURFACES

o QUIT

Quit this menu.

1 SIMPLE SURFACE

Generate a four-node surface segment.

2 COMPLEX SURFACE

Generate a nine-node surface segment.

3 ELLIPTICAL SURFACE

Generate an elliptical surface segment.

1.3 SOLIDS

o Qurr

Quit this menu.

266
_d

1.4

1.5

1.6

1.7

1 8-POINT SOLID

Generate an eight-node segment.

2 ELLIlrrlCAL SOLID

Generate a solid cylinder.

3 4-POINT SOLID

Generate a four-node segment.

4 6-POINT SOLID (PRISM)

Generate a six-node segment.

SYNTHESlS

0 QUIT

Quit this menu.

ARC: LINE SEGMENT _ SURFACE

Generate surface segments by moving a line segment along a curve.

GLIDE: 2-LINE SEGMENT _ SURFACE

Generate surface segments using two line segments.

REPRODUCE

0 Qurr

1 COPY

Quit this menu.

Reproduce by directly copying.

2 MIRROR

Produce a mirror image.

ROTATE

Reproduce by rotating the original about an axis.

DRAW

The preprocessor will draw the generated structure on a standard terminal with multiple options.

EDITOR

0 QUIT

Quit this menu.

2

3

STRUCTURE STATUS

Display the structure status.

LOCATION

Display nodes at the nearest location.

ADDNODE

Add nodes to the current structure.

267
4 ADDELEM

Addelementstothecurrentstructure.

5 MOVENODE

Movenodesto anotherlocation.

6 MOVE SEGMENT

Movesegmentsto anotherlocation.

7 DELETENODES

Deletenodesfrom thecurrentstructure.

8 DELETEELEMS

Deleteelementsfromthecurrentstructure.

9 DELETESEGMENT

Deletesegments.

10 ELEMENT SPECIFICATION

Defineelementproperties.

1.8 AUTOMESH

0 QUIT

Quit this menu.

1 SURFACE

Automatically generate two-dimensional surfaces.

2 VOLUME

Automatically generate a three-dimensional solid with tetrahedron elements.

3 XPLT

Plot the mesh generated from automesh in black-and-white (not available on the PC

version).

2 PROPERTIES AND ANALYSIS

This option enables the automatic generation of a complete STARS data set in which the user is

prompted for the appropriate input.

268
APPENDIX B

POSTPROCESSOR MANUAL

The POSTPLOTS, POSTPLOTA, and POSTPLOTF routines are designed to provide graphic

depiction of analysis results pertaining to the major SOLIDS, AEROS, ASE, and FLUIDS (CFDASE,

including CFD) modules. This graphic depiction is effected by the POSTPLOTS, POSTPLOTA, and

POSTPLOTF commands. The program runs on a variety of terminals, such as IBM, Tektronix, and other

PLOT 10/PHIGS-compatible machines.

POSTPLOTS is menu-driven and has the following features:

1.0

1.1

BASIC MENU

1.1 On/off switches

1.2 Load database

1.3 Delete database

1.4 Miscellaneous

1.5 Edit color

1.6 Exit

ON/OFF SWITCHES

1.1.1 Original structure

1.1.2 Deformed structure

1.1.3 Dynamic response

1 1.4 Displacement as a function of time

1 1.5 Stress as a function of time

1 1.6 Node number

1 1.7 Element number

1 1.8 Element group

1 1.9 Depth clipping

1 1.10 Hardcopy

1 1.11 Save plot

LOAD DATA BASE

1.2.1 Deformed or mode shape

1.2

269
1.2.2

1.2.3

1.2.4

1.2.5

1.2.6

1.2.7

1.2.8

1.2.9

1.2.10

Renderingdeformedormodeshape

Dynamicresponse

Renderingstress

Renderingdeformation

Displacementasafunctionof time

Stressasafunctionof time

Nodenumbers

Elementnumbers

CFDdensity,Mach,andpressureplots(analternativeto somePOSTPLOTFoptions)

1.3 DELETE DATA BASE

Essentially any one of the loaded data bases, given above.

1.4 MISCELLANEOUS

A host of additional options.

1.5 EDIT COLOR

1.5.1 Index location (left, center, right)

1.5.2 Color octave

1.5.3 Number of colors (9, 10, 14)

The POSTPLOTA is also menu-driven and has the following features:

2.1 Aerodynamic paneling plots

2.2 Interpolated mode shape for aerodynamic load calculation

2.3 Aerodynamic pressure distribution

2.4 Frequency-damping-velocity plots, k, p-k, and ASE solutions

2.5 Phase and gain plots as a function of frequency for analog and digital systems

2.6 ASE damping and frequency plots as a function of velocity

The POSTPLOTF program is graphical user interface-based (GUI-based) and is self-explanatory.

270

_J
APPENDIX C

SYSTEMS DESCRIPTION

The STARS computer program is set up using a main directory and many subdirectories. The setup

described in this section uses the directory names employed on various computer systems at NASA

Dryden. Figure C-1 shows the top-level directories;/trial is the main directory that contains the six major

subdirectories named as commands, sources, objects, executions, test cases, and utilities. The commands

subdirectory contains the command files that are used to guide the user in running the STARS program

system. The sources subdirectory contains the source elements for the program. This subdirectory is

further subdivided into the solids, aerodynamics (linear), ASE (linear), CFDASE (nonlinear), utilities and

associated graphics subdirectories. The latter subdirectory includes the preprocessor, which performs the

automatic generation of finite-element meshes and subsequent STARS analysis data, and the

postprocessor, which performs the depiction of solution results. The objects subdirectory contains the

object elements required for creating the execution elements. The object elements have been combined into

various object libraries to ease the linking process. The executions subdirectory contains the execution

elements used to run the program. The test cases subdirectory contains representative example problems

that facilitate the learning and debugging of the program. Additional data manipulation capabilities are

facilitated by the use of the routines in the utilities subdirectory.

271
i

slOmalmlp.a

bit_cLo

mllnH_J

e_olcm.i

oldJ

gelglanM.a

_rlJ

-I _+,o-- I

r

•i m I

I +o.*,m.. I

ii+_. I

II "_' I

p-tl.ota. I

I lu cei I

II v_ume., I

I I Nm.nd+., I

II m,m.mm..I

I ,,_dp., I

I un,_.. I

I remuh.a I

i .,._T. ]

I ndlll I

2,

r

"t _m_ I

r+.

7 .ro,r,. I

['] _daa.e

ii,,_

lurlICI.I

volume.o

letl_ndl .e

utbnd2+o

itaady.e

/interlace

ItalKlydp.e

Jnlltaldy.ll

mmllh.e

XPLT.I

)Ollplott.o

- -;_Tda-I

__'r"nLj

"_ _oii,m.comI

!

____o._)j

'7 nManl.com

L _mui.com I

cf(Ime_h.com I

lUtill.COm I

_" T_--I

(_run)_ I

---_--I

(uorun)_. j

-_ .+.©o,. I

postplotlLcom ]

- _.'- I

(c<mmrun) l

__t-_da..°o.I

* See ulllitl_ and NSTARS (convemlo_ of NASTRAN

inpul data Into STARS format) mlnUllll.

070371

Figure C-1. STARS systems description.

V

272
REFERENCES

1Gupta, K. K., STARS mA General-Purpose Finite Element Computer Program for Analysis of

Engineering Structures, NASA RP-1129, Oct. 1984.

2Collins, R. J., "Bandwidth Reduction by Automatic Renumbering," International Journal for

Numerical Methods in Engineering, vol. 6, no. 3, 1973, pp. 345-356.

3Gupta, K. K., "Development of a Unified Numerical Procedure for Free Vibration Analysis

of Structures," International Journal for Numerical Methods in Engineering, vol. 17, Feb. 1981,

pp. 187-198.

4Gupta, K. K., "On a Finite Dynamic Element Method for Free Vibration Analysis of Structures,"

Computer Methods in Applied Mechanics and Engineering, vol. 9, Sept. 1976, pp. 105-120.

5przemieniecki, J. S., Theory of Matrix Structural Analysis, Dover Publications, Inc., New York,

1985.

6Gupta, K. K., "Formulation of Numerical Procedures for Dynamic Analysis of Spinning Structures,"

International Journal for Numerical Methods in Engineering, vol. 23, Dec. 1986, pp. 2347-2357.

7Gupta, K. K., and C. L. Lawson, "Development of a Block Lanczos Algorithm for Free Vibration

Analysis of Spinning Structures," International Journal for Numerical Methods in Engineering, vol. 26,

May 1988, pp. 1029-1037.

8Zienkiewicz, O. C., and Taylor, R. L., The Finite Element Method, Fourth edition, McGraw Hill

Book Company, London, 1994.

9Huebner, Kenneth H. and Thornton, Earl A., The Finite Element Method for Engineers, Second

edition, John Wiley and Sons, New York, 1982.

l°The NASTRAN Theoretical Manual, NASA SP-221(06), Jan. 1981.

11Meriam, James L., Statics, Second edition, John Wiley and Sons, New York, 1971.

12Ross, C. T. F., Computer Methods in Engineering, Elis Howard Publishers, United Kingdom,

1982.

13Timoshenko, S., Strength of Materials, Van Nostrand, New York, 1982.

14Rutkowski, M. J., The Vibration Characteristics of a Coupled Helicopter Rotor-Fuselage by a Finite

Element Analysis, NASA TP-2118, Jan. 1983.

15Gupta, K. K., Brenner, M. J., and Voelker, L. S., "Integrated Aeroservoelastic Analysis Capability

with X-29A Comparisons," Journal of Aircraft, vol. 26, no. 1, Jan. 1989, pp. 84-90.

273
16Abel,I., An Analytical Technique for Predicting the Characteristics of a Flexible Wing Equipped

With an Active Flutter-Suppression System and Comparison With Wind-Tunnel Data, NASA TP-1367,

Feb. 1979.

17Appa, K., "Constant Pressure Panel Method for Supersonic Unsteady Airload Analysis,"

Journal of Aircraft, vol. 24, no. 10, Oct. 1987, pp. 696-702.

18Taylor, R. F., Miller, K. L., and Brockman, R. A., A Procedure for Flutter Analysis of FASTOP-3

Compatible Mathematical Models, Vol. 1 --Theory and Application, AFWAL-TR-81-3063, June 1981.

19Geising, J. P., Kalman, T. P., and Rodden, W. P., Subsonic Unsteady Aerodynamics for General

Configurations, vols. 1 and 2, AFFDL-TR-71-5, Nov. 1971.

2°Gupta, K. K., Brenner, M. J., and Voelker, L. S., Development of an Integrated Aeroservoelastic

Analysis Program and Correlation with Test Data, NASA TP-3120, May 1991.

2 ILo ' S. H., "A New Mesh Generation Scheme for Arbitrary Planar Domains," International Journal

for Numerical Methods in Engineering, vol. 21, Aug. 1985, pp. 1403-1426.

22peraire, Jaime, Peir6, Joaquin, Formaggia, Luca, Morgan, Ken, and Zienkiewicz, Olgierd C.,

"Finite Element Euler Computations in Three Dimensions, International Journal for Numerical Methods in

Engineering, vol. 26, Oct. 1988, pp 2135-2159.

23Gupta, K. K., Petersen, K. L., and Lawson, C. L., "Multidisciplinary Modeling and Simulation of

a Generic Hypersonic Vehicle," AIAA-91-5015, Dec. 1991.

24Gupta, K. K., Petersen, K. L., and Lawson, C. L., "On Some Recent Advances in Multidisciplinary Analysis of Hypersonic Vehicles," AIAA-92-5026, Dec. 1992.

25paraire, J., Peir6, J., and Morgan, K., "A 3-D Finite Element Multigrid Solver for the Euler

Equations," AIAA-92-0449, Jan. 1992.

26peir6, J., Paraire, J., and Morgan, K., FELISA System Reference Manual: Part 2--User Manual,

Dec. 3, 1993.

274

REPORT DOCUMENTATION PAGE FormApproved

OMB No. 0704-0188

Public reporting burden for this collection of informetion is estimated to everege I hour per response, including the time for reviewing instructions, searching existing date sources, gathering and

meintaining the data needed, end completing and revmwing the collection of information. Send comments regarding this burden estimete or any other aspect ot this collection of information,

including suggestions for reducing this burden, to Washington Hae0cluartars Services, Directorate for Information Operations end Rq ;)orts, 1215 Jefferson Davis Highway, Suite 1204, Arlington,

VA 22202-4302. end to the Office ot Management and Budget, Paperwork Reduction Proisot (0704-0188), Washington, DC 20503,

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORTTYPE AND DATES COVERED

May 1997 Technical Memorandum

4.TITLE AND SUBTITLE 5. FUNDING NUMBERS

STARS--An Integrated, Multidisciplinary, Finite-Element, Structural,

Fluids, Aeroelastic, and Aeroservoelastic Analysis Computer Program

6. AUTHOR(S)

K. K. Gupta

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Dryden Flight Research Center

P.O. Box 273

Edwards, California 93523-0273

9. SPONSORING/MONrrORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

WU-953-3600-00

8. PERFORMING ORGANIZATION

REPORT NUMBER

H-2151

:10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM-4795

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified--Unlimited

Subject Category 39

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

A multidisciplinary, finite element-based, highly graphics-oriented, linear and nonlinear analysis capability

that includes such disciplines as structures, heat transfer, linear aerodynamics, computational fluid dynamics,

and controls engineering has been achieved by integrating several new modules in the original STARS

(STructural Analysis RoutineS) computer program. Each individual analysis module is general-purpose in nature

and is effectively integrated to yield aeroelastic and aeroservoelastic solution of complex engineering problems.

Examples of advanced NASA Dryden Flight Research Center projects analyzed by the code in recent years

include the X-29A, F-18 High Alpha Research Vehicle/Thrust Vectoring Control System, B-52/Pegasus ®,

Generic Hypersonics, National AeroSpace Plane (NASP), SR-71/Hypersonic Launch Vehicle, and High Speed

Civil Transport (HSCT) projects. Extensive graphics capabilities exist for convenient model development and

postprocessing of analysis results. The program is written in modular form in standard FORTRAN language to

run on a variety of computers, such as the IBM RISC/6000, SGI, DEC, Cray, and personal computer; associated

graphics codes use OpenGL and IBM/graPHIGS language for color depiction. This program is available from

COSMIC, the NASA agency for distribution of computer programs.

14. SUBJECTTERMS

Aeroelasticity, Aeroservoelasticity, Computational fluid dynamics, Finite elements,

Graphics, Nonlinear aeroelasticity, Structural analysis

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIRCATION

OF REPORT OF THIS PAGE OF ABSTRACT

Unclassified Unclassified Unclassified

NSN 7540-01-280-5500 Availab/e from fhe NASA Center for AeroSpace Information, 800 Elkndge Landing Road,

Linthicum Heights, MD 21090; (301)621-0390

lS. NUMBER OF PAGES

285

16. PRICE CODE

A13

20. LIMITATION OF ABSTRACT

Unlimited

Standard Form 298 (Rev. 2-89)

Preemdbed by ANSI Std. 739-18

298-1_