NASA Contractor Report 178047

OPTIMAL AIRFRAME SYNTHESIS

FOR GUST LOADS

Prabhat Hajela

NASA-CR-178047

19860010915

" , I

UNIVERSITY OF FLORIDA

Gainesville, Florida

"., : j .t ';'

Grant NAGl-579

February 1986

NI\S/\

National Aeronautics and

Space Administration

Langley Research Center

Hampton,Virginia 23665

.I-I,/';S,Li:\' '-",,,,,,._,; (;;<;'1 {l::~

L:nR,'\/{Y, N/\~;/\

!i/IJViPTON. VIHGINIA

..

Introductory Remarks

The application of mathematical nonlinear programming algorithms has enjoyed

considerable success in the automated structural synthesis environment. A

sizeable majority of research pertaining to optimum structural design has

primarily focussed on statically loaded structures. The addition of dynamic loading in the form of harmonic excitation (Ref. 1) or random loads (Ref. 2) to

the structure introduces significant new problems. Since all aerospace vehicles

operate in a dynamic loads environment, it is imperative that efficient

automated structural sizing procedures be developed that adequately account for

these complexities. Furthermore, an increasing focus on multidisciplinary

design and optimization dictates a realistic representation of each

participating discipline.

The optimum sizing of airframe structures is performed in a complex analysis environment where structural stability must be carefully monitored in addition

to elastic deformation under static and dynamic loads. Hence an analysis tool

that accounts for the interaction of structural deformations and unsteady airloads, is a necessary ingredient to the development of any synthesis

capability. The present report documents the framework of an optimization

system, developed around the ISAC computer program (Ref. 3), with SPAR (Ref. 4)

and CONMIN (Ref. 5) as the structural analysis and optimization programs,

respectively. The NOS control language feature on the CDC Cyber computer is

used to direct the flow between various segments of the system. In its present form, the system retains a degree of modularity, permitting substitutions of the

analysis packages.

The thrust of the present work was directed towards establishing an optimization capability for sizing airframe structures that are subjected to a combination of

deterministic and random fliQht loads. The random vibration environment

introduces the need for selecting a statistical process that best describes the

random loads and permits computation of the dynamic response parameters of

interest. Furthermore, it requires a formulation of design constraints that

would minimize the conservativeness in the design and retain computational

viability. In the present work, the random loads are treated as a stationary, homogeneous process with a Gaussian probability distribution. A frequency domain analysis is selected for the solution of the dynamic response problem.

This permits a power spectral density input for the gust velocities, a

representation that is typically available from experimental observations. The

ISAC system of programs has the feature to incorporate aribitrary gust velocity

input spectra.

Subsequent sections of this report discuss the formulation of the analysis problem, the structure of the optimization programming system and a

representative numerical example. An appendix with procedure files and FORTRAN

pre- and post-processor listings is included for completeness•
Dynamic Response Analysis

In a frequency domain analysis, the system equations of motion can be written as

( -w

2[M] + [K] - [A]) {W} ={G} (1)

where [M] and [K] are the mass and stiffness matrices, respectively; {W} is the

displacement vector; [A] is the matrix of loads due to oscillation at frequency

00, and {G} is the force coefficient array per unit gust velocity. As is typical

of large structural configurations, a modal approach is adopted wherein a finite

number of elastic modes are used to model the structural deformations. The

displacement {W} can be represented approximately by the superposition of the

characteristic modes

..

(2)

where [,J is the matrix of 1m' normalized eigenmodes and {~l is an m-dimensional

vector of generalized coordinates. SUbstituting equation (~) into equation (1)

and then transforming the resulting equation from the frequency domain into the

Laplace domain yields the equations of motion in the following form

(3)

where M~~ is the generalized mass matrix; A~~ and [ are the generalized

aerodynamic force matrices due to motion and gust respectively; g is the

structural damping coefficient and oo~ is the natural frequency associated with

the ~-th generalized coordinate. Equation 3 is a system of linear,

nonhomogenous equations that are solved for the vector of generalized

coordinates. A similar approach can be adopted to include a control surface,

and the option to do so exists in the ISAC system.

Typical response parameters for which design constraints can be formulated

include stresses, nodal displacements, and accelerations at specified locations. The focus of the present work was in implementing structural

reliability constraints for which element stresses are the primary response quantities of interest. In the modal displacement approach, the stress at a

location j is computed as

(4 )

where cij is the stress coefficient at location Ij' due to a unit displacement

in the i-th generalized coordinate ;i. For a random gust input, these quantities are obtained as root mean square (rms) values which are then used in the

constraint formulation. •

Structural Reliability Constraints

For a structure subjected to random gust loads, failure can be caused by a

single overstress or as a result of cumulative damage in fatigue. These failure

conditions are termed by Johnson (Ref. 6) as single excursion and fatigue,

2
respectively. Constraints must be formulated for both these failures modes.

For a stress response S(t) that is stationary and has a Gaussian probability distribution, an assumption that large values of S(t) arrive independently, leads to a Poisson probability function for the number of times Inl that a large

magnitude S is exceeded in time It l• If the occurrence of this large stress

magnitude is not permitted in time T , the single excursion constraint, gs E'

can be written as s e

(5)

Fatigue damage can be estimated on the basis of the Palmgren-Miner theory and

results in a fatigue constraint, 9f' of the following form

aeL f b 2 b 1 b+2

gF:: : c (2 )-y- as - r (-2-) -. 1 0 (6 )

e

where, L

f is the specified fatigue life; r is the gamma function; as and as

are the rms values of the stress and stress rates and band c are constants

obtained from empirical relations for different materials.

Failure constraints derived from a fracture mechanics standpoint have also been

proposed (Ref. 7) where the constraints expressed in equations (5) and (6) are

essentially unified into a single constraint. The initiation and propagation of

cracks in a material results in both a reduced allowable stress and can also be

viewed as accumulated damage in the structure. In the present work constraint

equations (5) and (6) were implemented in the design.

Optimization System

This section of this report gives a brief description of the optimization system

and its component programs. The optimization systern combines a finite element

program SPAR, a general-purpose, nonlinear programming-based optimization

program CONMIN, and a system of aeroelastic response analysis programs ISAC.

The flow between these programs is controlled in a manner similar to the PROSSS

system for optimum design (Ref. 8). The role of each of these programs is

discussed next. The reader is referred to Appendix A for a listing of the

various routines described in this section.

SPAR

The program is a system of independent processors which communicate with each

other through a data base which consists of libraries of named data sets. The

structural model geometry definition, material specification and element connectivity are defined in a SPAR input runstream NREPT, and the data set library is

stored as NRLA. This is the non-repeatable part of the structural analysis program and does not have to be re-executed as the program iterates in the optimi- zation mode. The SPAR program is used to generate for the ISAC system, quantities such as mode-shapes, eigenvalues, generalized masses and stress coefficients defined in equation (4). It is also used to generate finite-difference

3
gradients for the eigenmodes and frequencies. A FORTRAN program GRAD generates

an input runstream corresponding to the set of new design variables. This input

runstream» SECPROP» is executed before the repeatable segment REPT is called to

obtain the new response parameters. A FORTRAN program EIGSTR employs the SPAR

data handling utilities (Ref. 9) to extract the desired information from the

data set libraries and store the information for post processing.

ISAC

The ISAC system of routines is employed to compute the aeroelastic response of

the flight vehicle. The structural node deflections corresponding to the vibration modes obtained in SPAR are related to the deflections and slopes on aerodynamic boxes by a 2-D» spline interpolation technique in OLIN. These aerodynamic slopes and deflections are used by a doublet lattice program DLAT» in the computation of the generalized aerodynamic forces for a range of reduced

frequencies. The generalized mass» stiffness and aerodynamic matrices are

passed to the routine DYNARES where a gust spectrum is selected and the aeroelastic response parameters are obtained. For a random gust input, the rms

responses can be computed by numerical integration of the response spectra within this routine. In the present organization, however» DYNARES writes a

state space representation of the system equations and passes the system matrices to another group of programs PADLOCS (Ref. 10), where the rms responses

are computed. Additionally, this program provides correlation coefficients

between various response components which are required in the formulation of

stress constraints in the event of a combined stress failure criterion

(Ref. 11). The input files required for ISAC execution are listed in

Appendix A. For a detailed description of the input parameters, the reader is

referred to Reference 3.

CONMIN

CONMIN is a general purpose optimization subroutine for solving constrained and

unconstrained» linear or nonlinear» continuous problems. It is based on the

method of feasible-usable search directions (Ref. 5) and was adapted in the

present framework in a piecewise linear mode of operation. The general optimi- zation problem for CONMIN can be posed as follows

Minimize a function

•

Subject to the inequality constraints

gj ( d1 , d2»···dn) 0

and the side constraints on the design variables di

1 u d. d. d 1 1 I

j = 1,2, .••m

i = 1,2, .•• n

(7)

(8 )

(9)

In general» both the objective function and constraints can be nonlinearly dependent on the design variables. In a piecewise linear mode of operation, the

objective function and design constraints are regarded to be linear functions of

the design variables» eliminating the need to compute function derivatives at

4
every iteration for a general nonlinear problem. A linear approximation to a

general nonlinear problem requires that constraints be imposed on design variable change for a given cycle of optimization. An appropriate choice of design variables (reciprocal variables) will often enhance the linearity in the design

space.

Program Organization

A flow chart depicting the implementation of the optimization system is shown in

Figure 1. The corresponding procedure file PRLOOP is listed in Appendix A. The

structural model is initialized for the starting design and the eigenmodes,

natural frequencies and response coefficients and their sensitivity to perturbations in design variables are computed. This information is then used to compute the response constraints sensitivity in a finite difference operation. The

two sensitivity computations were separated on purpose. If the eigenvalue and

eigenvector sensitivities are assumed constant, the outer gradient loop can be

executed once in the optimization sequence. The inner gradient loop for constraint sensitivities is the only required operation for subsequent cycles of

optimization. By the same token, if the eigenvalue/eigenmode sensitivities are

known to be more nearly constant over a wider variation in design variables, the

outer loop can be executed a lesser number of times in the optimization

sequence. The objective function, constraints and their gradients are passed to

an optimization program where the design variables are altered within the limits

imposed by the side constraints. This sequence is repeated until convergence.

Numerical Examples

A built up finite element model of a wing structure was developed as a test

problem for the program implementation described in the preceeding sections.

The cross-section and planform of this stringer-membrane, cantilever structure

is shown in Figures 2 and 3. The model element sizes were preprocessed by a

fully-stresssed design cycle for 1-g cruise loads. These member sizes were

established as the lower bounds for the gust design. A Dryden spectrum with a

gust intensity of 2.54 m/sec (typical of storm conditions) was specified in the

input. The first six elastic modes were chosen to represent the structural

deformation and were considered adequate for such a cantilever structure. In

more realistic designs for gust loads, rigid body modes in plunge and pitch

should also be included. The addition of these in the present system constitutes no added complexity. The design variables selected for this minimum

weight design were the cross-sectional areas of the bar elements. An allowable

stress of 1761.4 kg/cm2 was used in the computation of the first excursion

failure constraints. First excursion and fatigue failure lives of 2 years were

specified in the design process. The design converged in 13 piecewise linear

cycles to the values shown in Table 1. The first cantilever mode in bending

dominates the stress distribution in the structure, as is evidenced by a concentration of material at the root section. The first excursion constraint is

active at the optimum.

Concluding Remarks

This report documents the development and implementation of an optimization

system around ISAC for the structural design of airframe structures with aeroelastic constraints. The programming system is regarded as the necessary first

5
step for further studies in the systematic design of aircraft structures,

operating in a random gust load environment. Although developed primarily for

the design of structures under random gust loads, the program in its present form is suitable for inclusion of static stress, displacement and frequency constraints. An s-plane formulation of the flutter constraint can also be added

with minor modifications. These features coupled to a built-in control analysis capability, make this programming system an extremely powerful tool for multidisciplinary analysis and design. Furthermore, the programming system provides

a natural test-bed for multilevel optimization studies. The computational efficiency of the system can be significantly enhanced with the inclusion of an

analytical gradient capability.

References

(1) Cassis, J. H.: Optimum Design of Structures Subjected to Dynamic Loads.

UCLA-ENG-7451, UCLA, School of Engineering and Applied Science, June 1974.

(2) Hajela, P.: Comments on Gust Response Constrained Optimization. NASA CP

2327, April 1984.

(3) Peele, E. L., and Adams, W. M., Jr.: A Digital Program for Calculating the

Interaction Between Flexible Structures, Unsteady Aerodynamics and Active

Controls. NASA TM 80040, January 1979.

(4) Whetstone, W. D.: SPAR Structural Analysis Sytem Reference Manual - System Level 13A, Volume 1 Program Execution. NASA CR 158970-1, 1978.

(5) Vanderplaats, G. N., and Moses, F.: Structural Optimization by Methods of

Feasible Directions. Computers and Structures, Vol. 3, 1973, pp. 739-755.

(6) Johnson, E. H.: Optimization of Structures Undergoing Harmonic or

Stochastic Excitation. SUDAAR No. 501, Stanford University, August 1976.

(7) Hajela, P., and Lamb, A.: Optimum Structural Design Under Stochastic

Loading Conditions. Proceedings of the Tenth Canadian Applied Mechanics

Congress, June 2-7, 1985, pp. D-7, 8.

(8) Rogers, J. L., Jr., Sobieski, J. E., and Bhat, R. B.: An Implementation of

the Programming Structural Synthesis System (PROSSS). NASA TM 83180,

December 1981.

(9) Giles, G. L., and Haftka, R. T.: SPAR Data Handling Utilities. NASA TM

78701, September 1978.

(10) Newsom, J. R., et al: Active Controls: A Look at Analytical Methods and

Associated Tools. NASA TM 86269, July 1984.

(11) Gross, D. W., and Sobieski, J. E.: Application to Aircraft Design of

Nonlinear Optimization Methods Which Include Probabilistic Constriants.

Presented at the 18th AIAA Aerospace Sciences Meeting, San Diego, CA,

January 1980, AIAA Preprint No. 80-0153.

6
•

ISTART I

INITIALIZE STRUCTURE

Fully stressed design

,

SPAR (NREPT)

non-repeatable part

,

ITER=O

IT=O

t

GRAD - create spar input

IT=IT+ 1

t yes

IT>NDV+ 1;

too

SPAR (SECPROP)

new section properties

t

SPAR (REPT)

repeatable part

yes , ---- EIGSTR

store response Quantities

t

no EXTPlT

ew Structural l1near extrapolat1on to create

An8)ysis inform8tion needed in ISt\C

,

1SAC

OLIN

DLAT

DYNARES

,

PADlOCS

rms responses and covariances

t

OBJFUN

objective, constraints & gradients

t

/ITER=ITER+ 1

,

CONT

piecewise linear optimization

1 yes

converge ')

~STOP \

no

no yes

/ ITER>ITMAX /'

Figure 1. Flowchart depicting the organization of the optimization system

7
00

• :"1

membrane elements

(size fixed)

rod elements

(design variables)

Figure 2. Cross section of wing structural box

"
6,5

7,4

8,3

1,2

__----rod elements

2,21

membrane elements

57,58

73,74

Figure 3. Finite element model of Wing Structural Box. Node numbers nl, n2 represent lower and upper surface co-ordinates, respectively. Panel elements were

sized by a fully-stressed design approach.
.. Design Element Connectivity Init i a1 Desi gn ~1i nimum Gage Fi na1 Design

Variable (cm2) (cm2) (cm2)

1 1-9,9-17,8-16,16-24 10.3226 10.1096 17.9516

7-15,15-23,6-14,14-22

2 17-25,25-33,24-32,32-40 10.3226 4.6297 9.4458

22-30,30-38,23-31,31-39

3 33-41,41-49,40-48,48-56 10.3226 0.6452 2.5239

39-47,47-55,38-46,46-54

4 2-10,10-18,3-11 ,11-19 10.3226 10.1096 17.9574

4-12,12-20,5-13,13-21

5 18,26,26-34,19-27,27-35 10.3226 4.6309 9.5703

20-28,28-36,21-29,29-37

6 34-42,42-50,35-43,43-51 4.516 0.6452 2.5298

36-44,44-52,37-45,45-53

7 54-62,62-70,70-78 4.516 0.6452 1.1761

55-63,63-71,71-79

56-64,64-72,72-80

49-57,57-65,65-73

8 53-61,61-69,69-77 4.516 0.6452 0.9661

52-60,60-68,68-76

51-59,59-67,67-75

50-58,58-66,66-74

Objecti ve Function Weight 286.33 Kg 195.56 270.41 Kg

Table 1. Numerical results for the cantilevered wing structural box

10
Appendix A

LIST,FN=SUBFIL

PHLOOP,T6000.

USER, 358625C,PATHA.

CHARGE,102632,LRC.

DELIVER. 1229 PH PROC TEST CASE ..

.. THIS FILE IS PRLOOP

*

MAP,OFF.

BEGIN,PRLOOP.

COPYSBF,INPUT,OUTPUT.

DAYFILE,L=DAYPRLP.

REPLACE,DAYPRLP.

EXIT.

COPYSBF,INPUT,OUTPUT.

DAYFILE,L=DAYPRLP.

REPLACE,DAYPRLP.

EOI ENCOUNTERED.

/

Above procedure file is used to initiate a batch run for optimization.

A-I
PROCFIL is a listing of all procedure files used in the present

optimization system. .

LIST,FN=PROCFIL

.PROC,DYNA.

GET,DCM=DCMV2A/UN=887010N.

GET,DYNARES=DYNAV3A/UN=887010N.

REVERT •

• PROC,CONT.

GET,CONMINB/UN=753437N.

GET,CONB.

COPYBR,CONB,PRAT.

COPYBF,CONMINB,PRAT.

GET,DESIGN,OLDOBJ,CONMDT,CONPAR.

REWIND,*.

PRAT.

REWIND,TAPE6.

APPEND,CONOUT,TAPE6.

REPLACE,OLDOBJ.

REPLACE,DESIGN.

REVERT .

. PROC,OBFUN.

RETURN,*.

GET,OBJFUB,DECIS,ITER,DESIGN,CVD1,OBDJ.

PACK,CVD1.

OBJFUB.

REPLACE,CONMDT.

RETURN,*.

F:EVERT .

• PROC,DYNDES.

GET,TAP2G.

BEGIN,DYNA.

BEGIN,PRDES.

BEGIN,DYNA.

BEGIN,PRDES.

BEGIN,DYNA.

BEGIN,PRDES.

BEGIN,DYNA.

BEGIN,PRDES.

BEGIN,DYNA.

BEGIN,PRDES.

BEGIN,DYNA.

BEGIN,PRDES.

BEGIN,DYNA.

BEGIN,PRDES.

BEGIN.DYNA.

BEGIN,PRDES.

BEGIN,DYNA.

BEGIN ,PRDES. I

REVERT •

. PF:OC , PRGUST •

GET,TAPE5=POUT.

A-2
JI

BEGIN, DCr·l.

DCM"",DCMIN1.

RETURN,DCM~TAPE5.

REWIND,TAPE9.

REPLACE,TAPE9=PHT9.

BEGIN,DLIN.

GET,TAPE1=W2POS1,TAPE3=TAPE31,TAPE5.

DLIN.

REt<JI NO,*.

RETURN,TAPE1,TAPE3.

GET,TAPE1=W2POS2,TAPE3=TAPE32.

OLIN.

REWIND,*.

RETURN,TAPE1,TAPE3.

GET,TAPE1=W2POS3,TAPE3=TAPE33.

OLIN.

REWIND,*.

REPLACE,TAPE9=PHT9.

RETURN,*.

REVERT.

• DATA,DCMIN1.

BATCH

STORE

GMASS -11 3241

F

GENERALIZED MASSES

STORE

FREQ -1

1 181

F

FREQUENCIES IN HZ

STORE

LOADS -11 12961

F

STRESS COEFFICIENTS

STORE

DAMPINGS -11 181

F

DAMPING COEFFICIENTS

STORE

Gt"1ASS -12 3241

F

GENERALIZED MASSES

STORE

FREQ -12 181

F

FREQUENCIES IN HZ

STORE

LOADS -12 12961

F

STRESS COEFFICIENTS

STORE

DAMPINGS -12 181

F

DAMPING CONSTANTS

STOF:E

A-3
GMASS -1 3 324 1

F

GENERALIZED MASSES

STORE

FRED -1 3 18 1

F

FREQUENCIES IN HZ

STORE

LOADS -1 3 1296 1

F

STRESS COEFFICIENTS

STOF:E

DAMPINGS -1 3 18 1

F

DAMPING CONSTANTS

END

.PROC,PRDES.

GET,TAPE9=PHT9.

COPYBR,TAP2G,TAPE2.

REWIND,TAPE2.

DYNARES. ----- --

REPLACE,TAPE1=TAPE7.

RETURN,*,TAP2G.

GET,DESDAT,TAPE7,DESIGN=DEZIGN.

DESIGN,DESDAT.

REWIND,CVDATA.

GET,REDUB.

REDUS.

APPEND,CVD1,CVDATA.

RETURN,*,TAP2G.

REVERT .

• PROC,PREXT.

GET,EXTPLB,DECIS,DESIGN,CoNDAT,ITER,NoDAL.

REWIND,*.

EXTPLB.

REWIND,*.

REPLACE,WPOS=W2POS1,WPOS1=W2POS2,WPOS2=W2POS3.

REPLACE, POUT.

REVERT •

. PROC,STORE.

GET,EIGSTRB,ITER,GRDATA,L001=RRLA.

REL>J IND,*.

EIGSTRB.

REPLACE,GRDATA.

REVERT .

• PROC,PRLOOP.

SET <R2=10)

SET (R3=O)

1OPT, CT Il'1E •

SET(Rl=(l)

t-1AP, OFF.

WHILE,Rl.LT.R2,FIN1.

SET(Rl=Rl+1)

DISPLAY (FU)

GET,GRADB,ITER,DECIS,GRDATA,OBDJ.

GRADB.

A-4

..
PRLOOP is the procedure file

to execute the various segments of the optimization sequence.

REPLACE,ITER,CONDAT,OBDJ.

RETURN,GRDATA.

IFE,Rl.LT.R2,JMP1.

BEGIN,PRRSPAR.

BEGIN, STORE.

RETURN,*.

ENDt>J, FIN!.

ENDIF ,JMP1.

BEGIN,PREXT.

BEGIN,PRGUST.

GET ,TAPE5=TAPE5T ,TAPE9=PHT9.

BEGIN,DLAT.

ALPHA.

REPLACE,TAPE9=PHT9.

RETURN,*.

BEGIN,DYNDES.

BEGIN,OBFUN.

GET,CVD1=CV.

REPLACE,CVD1.

SET(R3=R3+1)

BEGIN,CONT.

GET,DECIS,DESIGN,ITER,POSB.

POSB.

REPLACE,DECIS.

IFE,R3.LT.9,JMP2.

IFE,FILECIFLG,.NOT.AS),JMP3.

RETURN,*.

GOTO,10PT.

ENDIF,JMP2.

ENDIF,JMP3.

REVERT . ....-------------.1

.PROC,PRCSTR,XXX=W2ZPOS.

*

* EXECUTE THIS PROCEDURE AS FOLLOWS:

* -DLNPROC,DLNPROC.

*

RETURN,LGO.

GET,DLNLIB.

*PUT HERE A GET TO YOUR TAPE5 - INPUT FILE

*NEXT MAkE AVAILABLE A SPAR FILE WHICH TO EXTRACT DATA FROM GET,L001=RR~A.

GET,X=EIGSTR.

GET,GRDATA,ITER.

REWIND,X,ITER,GRDATA.

FTN,I=X,L=O,OPT=O,STATIC.

GTR,LGO,LL.REL/EIGSTR

GTR,DLNLIB,LL.REL/BLKDAT.

RENAME,LGO=LL.

LDSET(LIB=DLNLIB,MAP=SBEX/OUT)

LOAD,LGO.

NOGO(EIGSTRB).

HEVERT .

• F'ROC,PRRSPAR .

.*

.* REPEATABLE SPAR

.*

A-5
GET,SPAR=SPAR14I,DCU=DCU141/UN=750756N.

GET,SPARLA=NRLA.,

REWIND,SECPROP.

SPAR,SECPROP,SPOUT.

RETURN,SPOUT.

REWIND,*.

GET,REPT.

SPAR,REPT,SPOUT.

REL<J I ND , SPARLA.

REPLACE,SPARLA=RRLA.

RETURN,*.

REVERT •

• PROC,PRNSPAR•

.*

.* NONREPEATABLE SPAR

.*

GET,SPAR=SPAR141,DCU=DCU141/UN=750756N.

GET,NREPT. '

SPAR,NREPT,SPOUT.

REPLACE,SPARLA=NRLA.

RETURN,*.

REVERT •

• PROC,DLIN.

GET, DCM=DCMV2A/UN=887010N.

GET,OLIN=DLINV3A/UN=887010N.

REVERT •

• PROC,OLAT.

GET,DCM=DCMV2A/UN=887010N.

GET,ALPHA=DLATV5A/UN=887010N.

REVERT •

. PROC, DCt"!.

GET,DCM=DCMV2A/UN=887010N.

REVERT •

. PROC,PLOT.

REL<J I ND , SAVPLT •

PLOT.TEKPOST,TE(AUTOCO».

NOTE.I:G507>

REVERT. WHAT A CRUMMY PLOT! !

• PF:OC ,PLTRVAX.

REL'J I NO , SAVPLT .

.PLOT.TEKPOST,TE(AUTO(O) .RVAX).

NDTE./:G507>

REVERT.

EDI ENCOUNTERED.

I

A-6
LIST,FN=CONT

PROGRAM CONOPT(CONPAR,OLDOBJ,DESIGN,CONMDT,IFLG,

*TAPE56=CONPAR,TAPE12=OLDOBJ,

*TAPE31=DESIGN,TAPE22=CONMDT,TAPE14=IFLG,OUTPUT,

*TAPE6)

C

C ***************************************************************

C

C THIS IS THE OPTIMIZER WITH PIECEWISE LINEAR APPROXIMATION

C

C PRABHAT HAJELA JUNE 1985

C

C ***************************************************************

C

COMMON/CNMNI/DELFUN,DABFUN,FDCH,FDCHM,CT,CTMIN,CTL,CTLMIN,

*ALPHAX,ABOBJ1,THETA,OBJ,NDV,NCON,NSIDE,IPRINT,NFDG,NSCAL,LINOBJ,

*ITMAX, ITRM,ICNDIR,IGOTO,NAC, INFO, INFOG, ITER

COMMON/CNMN2/RDUM(50),IDUMC50)

COMMON/CONSAV/REAL(50),INT(25)

DIMENSION X(50),VLB(50),VUBC50),GC200),SCAL(50),

*DF(50),A(50,200),S(50),Gl(200),G2(200),B(200,200),

*C(200),ISC(200),IC(200),MS1(400)

DIMENSION VLBTMP(50),VUBTMP(50),XINIT(50),GI(200),

*GRDG(50,200),GRDOBJ(50)

DATA NDV/8/,NCON/1441

C

C

C COMPUTE CONMIN DIMENSIONS

C

NLIMl=NDV+l

Nl=NDV+2

N2=NCON+2*NDV

N3=N2+5

N4=MAXOCN3,NDV)

N5=2*N4

C

C

C READ CONMIN PARAMETERS

C

READ(56,*)NITER,IPRINT,NSIDE,NFDG,LINOBJ,ITMAX,ICNDIR,NSCAL,

*ITRM,IGOTO,NDV,NCON,FDCH,FDCHM,CT,CTMIN,CTL,CTLMIN,THETA,PHI,

*DELFUN,DABFUN,ALPHAX,ABOBJI

C

C READ OLD OBJECTIVE FUNCTION VALUES

C

READ(12,*)OBJl,OBJ2,OBJ3,TOL

C

DO 5 I=l,NCON

5 ISC(I)=O

C

C PRESCRIBE BOUNDS ON DESIGN VARIABLES FOR OVERALL OPTIMIZATION

C

A-7
VLBTMP(1)=1.567

VLBTl'lP (2) =0. 7176

VLBTMP(3)=0.1

VLBTMP(4)=1.567

VLBTMP(5)=0.7178 .

VLBTMP(6)=0.1

VLBTMP(7) =.0. 1

VLBTMP(8)=0.1

DO 6 I=1,NDV

VUBTl"lP (I) =5.°

6 CONTINUE

C

C READ INITIAL DESIGN VARIABLES

C

READ (31 , *) (X I NIT ( I) , 1=1 , NDV)

C

C PRESCRIBE BOUNDS FOR LOCAL OPTIMIZATION CYCLE

C

DO 12 I=l,NDV

VUB(I)=1.4*XINIT(I)

VLB(I)=O.6*XINIT(I)

X(l)=XINIT(I)

IF(VUB(I).GT.VUBTMP(I»VUB(I)=VUBTMP(I)

IF(VLB(I).LT.VLBTMP(I»VLB(I)=VLBTMP(I)

12 CONTINUE

C

C READ INITIAL FUNCTION AND GRADIENT INFORMATION

C

READ(22,*) (GI(I),I=1,NCON),OBJl

*,«GRDG(I,J),I=l,NDV),J=l,NCON),

*(GRDOBJ(I),I=l,NDV)

OBJ=OBJI

100 CONTINUE

C

C CALL TO CONMIN OPTIMIZER

C

CALL CONMIN(X,VLB,VUB,G,SCAL,DF,A,S,Gl,G2,B,C,

*ISC,IC,MS1,Nl,N2,N3,N4,N5)

C

IF(IGOTO.EQ.O)GO TO 555

IF(INFO.EQ.2)GO TO 24

C

C FUNCTION AND CONSTRAINT VALUES

C

SUl'l=OBJ 1

DO 23 I=l,NDV

DX=X(I)-XINIT(I)

SUM=SUM+GRDOBJ(I)*DX

23 CONTINUE

OBJ=SUt'l

DO 22 J=1,NCON

SUt'l=G I (J)

DO 21 1=1, NDV

DX=X(1) - XINIT(l)

21 SUM=SUM+GRDG(I,J)*DX*(XINIT(I)/XCI»

GCJ) =SUt1

22 CONTINUE

GO TO 100

24 CONTINUE

A-8
C

C GRADIENT INFORMATION

C

DO 25 I=l,NDV

25 DF(I)=GRDOBJ(I)

NAC=O

DO 26 J=l,NCON

IF(G(J).LT.CT)GO TO 26

NAC=NAC+l

IC(NAC)=J

26 CONTINUE

DO 27 I=1,NDV

DO 28 J=l,NAC

J1=IC(J)

A(I,J)=GRDG(I,J1)

28 CONTINUE

27 CONTINUE

C

GO TO 100

C

C TERMINATE OPTIMIZATION LOOP

C

555 CONTINUE

REl.JIND 31

WRITE(31 ,*) (X (1),1=1 ,NOV)

C

C TEST FOR CONVERGENCE OVER THREE CYCLES

C

OBJ3=OBJ2

OBJ2=OBJ1

OBJ1=OBJ

REL-JIND 12

WRITE(12,*)OBJ1,OBJ2,OBJ3,TOL

IF(ABS(OBJ2).LE.O.0001)GO TO 666

DA=ABS«OBJ3-0BJ2)/OBJ2)

DB=ABS«OBJ2-0BJ1)/OBJ2)

C

C TERMINATE PROGRAM

C

IF(DA.GT.TOL.OR.DB.GT.TOL)GOTO 666

WR I TE ( 14 ,*)NCON

666 CONTINUE

STOP

END

EOr ENCOUNTERED.

I

A-9
************************************************************

THIS PROGRAM READS AND STORES THE DATA REQUIRED FOR

THE EIGENANALYSIS AND STRESS COEFFICIENT GRADIENTS

PRABHAT HAJELA JUNE 1985

LIST,FN=EIGSTR

PROGRAM EIGSTR(GRDATA,ITER,TAPE2=ITER,TAPE32=GRDATA,

*OUTPUT)

C

C ************************************************************

C

C

C

C

C

C

C

C

DIMENSION Gl(100)~G2(13000),G3(10000),G4(10),X(10) ,Y(10)

DIMENSION AMODE(3,80),FREQ(25) ,STRS(72,6,1),STRl(10000)

DATA NLIB/l/,NMODE/6/,ND41/10/,NSTR/72/,PI/3.14159/

*,NNODE/SO/,NELT/72/,NDOF/240/

C

C READ FREQUENCY

C

CALL DAL(NLIB,11,FREQ,O,O,KADL,IERR,NW,NE,LB,IT,

*4HVIBR,4HEVAL,4HMASK,4HMASK)

C

C STRESS COEFFICIENTS

C

CALL DAL (NLIB,ll,STRl(l),O,O,KADL,IERR,NW,NE~LB,lr,

1 4HSTRS,4HE23 ,1,1)

CALL DAL (NLIB,11,STR1(433),O,O,KADL,IERR,NW,NE,LB,IT,

1 4HSTRS,4HE23 ,1,2)

CALL DAL (NLIB,11,STR1(865) ,O,O,KADL,IERR,NW,NE,LB,IT,

1 4HSTRS,4HE23 ,1,3)

CALL DAL (NLIB,11,STR1(1297) ,O,O,KADL,IERR,NW,NE,LB,IT,

1 4HSTRS,4HE23 ,1,4)

CALL DAL (NLIB,11,STR1(1729),O,O,KADL,IERR,NW,NE,LB,IT,

1 4HSTRS,4HE23 ,1,5)

CALL DAL (NLIB,11,STR1(2161),O,O,KADL,IERR,NW,NE,LB,IT,

1 4HSTRS,4HE23 ,1,6)

C

C OBJECTIVE

C

CALL DAL(NLIB,11,OBJP,O,O,KADL,IERR,NW,NE,LB,IT,

*4HOBJF,4HAUS ,4HMASK,4HMASK)

C

C EIGENMODES

C

CALL DAL (NLIB,10,AMODE,O,O,KADR,IERR,NWDS,NE,LB,IT,

1 4HVIBR,4HMODE,4HMASK,4HMASK)

C

C

READ(2,*)ITER.NDV

NCOEF=NELT*NMODE

NLIM1=NDV+l

NLIM2=NMODE*NLIMl

NLIM3=NCOEF*NLIMl

NLIM4=NDOF*NLIM1*NMODE

A-IO
...

C

C IF ITER.EQ.O CREATE GRDATA

C

IF(ITER.GT.O)Go TO 2000

DO 1000 1=1,NLIM2

1000 G1(1)=0.0

DO 1001 I=1,NLIM4

1001 G2(I)=0.0

DO 1002 1=1,NLIM3

1002 G3(1)=0.0

DO 1003 I=1,NLIMl

G4(I)=0.0

1003 CONTINUE

WR I TE (32 , *) (G1 ( I) , 1=1 , NL 1M2) ,

* (G2 (I) ,1=1 ,NLIM4) ,

*(G3(I),1=1,NLIM3),

*(G4(1) ,I=1,NLIM1)

2000 CONTINUE

C

REL>JIND 32

C IF ITER.GT.O READ DATA FROM OLD GRDATA FILE

C

READ (32, *) (81 (I) ,1=1, NLIM2) ,

*(82 ( I) , 1=1 , NL I M4) ,

*<G3(I),I=1,NLIM3),

*(84(1) ,I=1,NLIM1)

REtlJIND 32

C

C STORE DATA

C

C OBJECTIVE

C

G4(ITER+1)=oBJP

C

C FREQUENCY

C

DO 2 1=1,NMODE

FREQCY=SQRT(FREQ(I»/(2.*PI)

K=(ITER*NMODE)+I

Gl(K)=FREQCY

2 CONTINUE

C

C EIGENMoDES

C

ID=ITER*NDOF*NMoDE

DO 4 I=1,Nt1oDE

KS=KADR + (I-l)*NSECTS(LB)

CALL RIO(NLIB,2,2,KS,AMoDE,LB)

DO 6 J=1,NNODE

DO 7 K=1,3

ID=ID+1

G2(ID)=AMoDE(K,J)

7 CONTINUE

6 CONTINUE

4 CONTINUE

C

C STRESS COEFFICIENTS

C

A-ll
ID=ITER*NCOEF

JC=O

DO 8 I=l,NMODE

ID1=(I-l)*NELT*6

DO 9 J=l,NELT

ID2=(J-l)*6 + 5 + 101

IOI<=ID2+1

IO=ID+l

G3(ID)=STR1(IDK)

9 CONTINUE

8 CONTINUE

C

C WRITE OBJECTIVE,EIGEN-INFO AND STRESS COEFFICIENTS

C

WR I TE (32, *) <G1 (1) , 1=1 , NL I M2) ,

*<G2(I),I=1,NLIM4),

* (G3 ( I ) , 1=1 , NL I M3) ,

*<G4(I),I=1,NLIM1)

REllJIND 32

STOP

END

EOI ENCOUNTERED.

I

A-12

..

..
*******************************************************

THIS PROGRAM PROVIDES A NEW SET OF EXTRAPOLATED MODES

EIGENFREQUENCIES AND RESPONSE COEFFICIENTS TO ANALYSIS

PRABHAT HAJELA JUNE 1985

LIST,FN=EXTPLT

PROGRAM EXTPLT(DECIS,DESIGN,CONDAT,POUT,NODAL,ITER,

*WPOS,WPOSl,WPOS2,

*TAPE33=DESIGN,TAPE22=CONDAT,TAPE7=POUT,TAPEl=NODAL,

*TAPE4=WPOSl,TAPE8=WPOS2,

*TAPE31=DECIS,TAPE9=ITER,TAPE3=WPOS,INPUT,OUTPUT)

C

C *******************************************************

C

C

C

C

C

C

C

C

..

DIMENSION 81(100),G2(1500) ,83(1100),G4(10),DD(60)

DIMENSION GRD8(S,1500) ,GRDG1(8,1100),GRDG2(8,10),

*GRDOBJ ( 10)

DIMENSION NODE(80),X(10),Y(10),XX(10),AMODE(6,3,80)

DIMENSION G(1000),FREQ(10),DELT(10),VECN(1500)

DIMENSION GMAS(54,54) ,51(100) ,52(10000) ,STRS(72,54,1)

DATA NMODE/6/,NDOF/240/,NELT/72/,NE41/10/,

*NSNODE/40/,NNODE/801

OPEN(UNIT=7,FILE='POUT')

OPEN(UNIT=l,FILE='NODAL')

OPEN(UNIT=33,FILE='DESIGN')

OPEN(UNIT=22,FILE='CONDAT')

OPEN(UNIT=31,FILE='DECIS')

OPEN(UNIT=9,FILE='ITER')

OPEN(UNIT=3,FILE='WPOS')

OPEN(UNIT=4,FILE='WPOSl')

OPEN(UNIT=8,FILE='WPOS2')

READ(9,*)ITER,NDV

NCOEF=NELT*NMODE

N1=NDOF*NMODE

NLIMl=ND\l+l

NLIM2=NMODE*NLIM1

NLIM3=NCOEF*NLIMI

NLIM4=NDOF*NLIM1

NSTR=NELT

DO 40 1=1,18

DO 41 J=I, 18

GMi%S ( I , J ) =0. 0

IF(I.EQ.J)GMAS(I,J)=1.0

41 CONTINUE

40 CONTINUE

READ (31, *) (X (!) ,1=1, NDV) , (Y (1) ,1=1, NE41> , FDCH

READ ( 1 , *') (NODE ( I) , 1=1 ,NSNODE)

READ (22, *) (G 1 ( I ) , I:::: 1 , NMODE) , (G2 ( I ) , 1=1 , N1 ) ,

*' (G3 ( I ) , 1= 1 , NCOEF) , G4 ( 1 ) ,

*(GRDOBJ(I) ,I=I,NDV), *' ((GRDG ( I , J) , 1:::: 1 ,NDV) ,J=1 , N1) ,

* ((GRDG2 ( 1 ,J) , I:::: 1 , NDV) ,J= 1 ,Nt-lODE) ,

* «GRDGI (I ,J) ,1=1 ,NOV) ,J=l ,NCOEF)

A-13
DO 30 INN=I,NLIMI

READ (33, *) (X.X (I) ,1=1, NDV)

REWIND 33

IF q.N.N.• ~G! •.}.}§g J.9 _ 1_ _ _ .o. ••

XX(INN-l)=XX(INN-l)*(I.+FDCH)

31 CONTINUE

C

C UPDATE STRESS COEFFICIENTS

C

DO 2 I=1,NCOEF

STR=G3 (I)

DO 4 J=1,NDV

DELT(J)=XX(J)-X(J)

STR=STR + GRDGl(J,I)*DELT(J)

4 CONTINUE

G(I) =STR

2 CONTINUE

C

C FREQUENCIES

C

DO 6 I=l,NMOOE

EIG=Gl <I)

DO 8 J=I,NOV

DELT(J)=XX(J)-X(J)

EIG=EIG+GRDG2(J,I)*DELT(J)

8 CONTINUE

FREQ <I) =EIG

6 CONTINUE

C

C EIGENMODES

C

DO 10 I=1,N1

VEC=G2 (I)

DO 12 J=1, NDV

DELT(J)=XX(J)-X(J)

VEC=VEC+GRDG(J,I)*OELT(J)

12 CONTINUE

VECN ( I ) =VEC

10 CONTINUE

10=0

DO 14 I=1,NMODE

DO 16 J=l,NNODE

DO 17 1<=1,3

1D=ID+1

AMODE(I,K,J)=VECN(ID)

17 CONTINUE

16 CONTINUE

14 CONTINUE

DO 21 1<=1, NMODE

DO 20 I=1,NSNODE

IFCINN.LE.3)THEN

WRITEC3,1000) (AMODE(K,J,NODE(I»,J=1,3)

1000 FORMATC3E15.8)

A-14
GO TO 19

ENDIF

IF(INN.LE.6)THEN

WRITE (4,1000) (AMODE (K,J ,NODE (I» ,J=1 ,3)

GO TO 19

ENDIF

IF(INN.LE.9)THEN

WR I TE (8, 1000) (AMODE O( , J , NODE ( I ) ) , J = 1 ,3)

ENDIF

19 CONTINUE

20 CONTINUE

21 CONTINUE

IJ= (INN-l) *NMODE

DO 50 II<=1,NMODE

IJK=IJ+IK

50 S1(IJK)=FREQ(IK)

IL= (INN-l) *NCOEF

DO 51 IM=1,NCOEF

I Ll'l= I L+ I M

51 S2(ILM)=G(IM)

30 CONTINUE

JP=O

DO 52 J=1,NLIM2

DO 53 I=l,NELT

DO 54 K=l,l

JP=JP+l

STRS(I,J,K)=S2(JP)

54 CONTINUE

53 CONTINUE

52 CONTINUE

IC=NLIM2/18

DO 61 IZ=1,54

61 DD(IZ)=O.01

DO 60 1=1, IC

WR I TE (7, *) ( (Gi1AS ( I I ,J) ,J=1 , 18) , I 1=1 , 18)

KP= ( 1-1 )*18

WR I TE (7, *) (S 1 (J<P+ I I ) , I I = 1 , 18)

DO 55 IEL=1,NELT

DO 56 1<=1,1

llJR I TE (7, *) (STRS ( I EL , I Y , 10 , I Y=KP+ 1 ; l<P+ 18)

56 CONTINUE

55 CONTINUE

WRITE(7,*) (DD(IZ) ,IZ=! ,18)

60 CONTINUE

STOP

END

EOI ENCOUNTERED.

I

A-15
PRABHAT HAJELA, JUNE 19S5

*******************************************************

THIS PROGRAM IS A PREPROCESSOR TO A GRADIENT COMPUTING

SEGMENT - GRADIENTS OF EIGENVALUES, EIGENVECTORS AND

STRESS COEFFICIENTS ARE COMPUTED

LIST , FN=GRAD

PROGRAM GRAD(DECIS,ITER,GRDATA,CONDAT,SECPROP,FLAG,OBDJ,

*TAPE31=DECIS,TAPE30=ITER,TAPE32=GRDATA,TAPE22=CONDAT,

*TAPE7=SECPROP,TAPE14=FLAG,TAPE2=OBDJ)

C

C *******************************************************

C

C

C

C

C

C

C

C

C

DIMENSION GRDG(B,1500) ,6RDOBJ(10),X(10),Gl(100)

* , 62 ( 13000) ,63 ( 10000) , G4 ( 10) , Y( 10)

*,GRDG1(S,1100),GRDG2(S,10)

NMODE=6

ND41=10

NSTR=72

NDOF=240

NCOEF=NSTR*NMODE

OPEN(UNIT=30,FILE='ITER')

OPEN(UNIT=31,FILE='DECIS')

OPEN(UNIT=7,FILE='SECPROP')

OPEN(UNIT=22,FILE='CONDAT')

READ(30,*)ITER,NDV

REWIND 30

c

C READ DESIGN VARIABLES AND FINITE DIFFERENCE STEP SIZE

C

READ (31 , *) (X ( I ) , 1=1 , NDV) , (Y ( I) , 1=1 , ND41 ) , FDCH

ITER=ITER+l

C

C

C IF ITER.EQ.NDV+1 THEN ALL DV'S PERTURBED

C

IF(ITER.EQ.NDV+l)GO TO 100

IF(ITER.GE.1)X(ITER)=X(ITER)*(1.+FDCH)

C

C WRITE SPAR INPUT RUNSTREAM

C

98

1

99

REl'JIND 7

WRITE(/,98)

FORMAT ( , [XQT TAB', / , . BC' )

DO 1 I=l,NDV

WRITE(7,*)I,X(I)

CONTINUE

ltJRITE (7,99)

FORMAT ( 'SA' )

DO 2 I=1,ND41

WRITE(7,*)I,Y(I)

A-16
c

1010

100 CC

•

2 CONTINUE

lIJRITE (7,1010)

FoRMAT('[XQT EXIT')

REWIND7

WRITE(30,*>ITER,NDV

GoTa 110

CONTINUE

COMPUTE GRADIENTS

ITER=-l

WRITE(30,*)ITER,NDV

NLIM1=NDV+l

NLIM2=NMODE*NLIMl

NLIM3=NCOEF*NLIMl

NLIM4=NDOF*NLIM1*NMODE

OPEN(UNIT=32,FILE='GRDATA')

READ (32,*) (G1 (I) ,1=1 ,NLIM2),

*(G2 (I) ,1=1 ,NLIM4),

* (G3 (I) 1=1 ,NLIM3),

*(G4( I) , 1=1 ,NL11"11)

CC OBJECTIVE C

DO 10 1=1, NDV

Jl=l+l

GRDOBJ(I)=(G4(J1)-G4(1»/(FDCH*X(I»

10 CONTINUE CC FREQUENCY C

DO 25 J=1,NDV

I I =Nt10DE*J

DO 20 I=1,NMODE

111=11+1

GRDG2 (J , I )= (G 1 ( I I 1 ) -G 1 ( I) ) / (FDCH*X(J ) )

20 CONTINUE

25 CONTINUE cC STRESS COEFFICIENTS C

DO 27 J=1,NDV

II=NCOEF*J

DO 22 I=1,NCOEF

111=11+1

GRDG1(J,I)=(G3(IIl)-G3(I»/(FDCH*X(J»

22 CONTINUE

27 CONTINUE CC EIGENMODES C

Nl=NDOF*NMODE

DO 29 J=l, NDt.;

II=Nl-1i-J

DO 24 I=l,Nl

111=11+1

GRDG(J,I)=(G2(IIl)-G2(I»/(FDCH*X(J»

24 CONTINUE

29 CmHI~JUE c

A-I?
C WRITE GRAD INFO

C

WR I TE (22 , *) (G 1 ( I) , 1=1 , NMODE) ,

* (G2 ( I) , 1=1 ,N1) ,

* (G3 ( I ) , 1=1 , NCOEF ), G4 ( 1) ,

*(GRDOBJ(I),I=l,NDV),

*«GRDG(I,J),I=1,NDV),J=1,N1),

*«GRDG2(I,J) ,I=l,NDV) ,J=1,NMODE),

* «GRDGl (I ,J) ,1=1 ,NDV) ,J=1 ,NCOEF)

C

REWIND 22

OPEN (UNIT=2.~ FILE=' qBpJ.' )

WR I TE (2, * ) G4 ( 1) , (GRDOBJ ( I) , I::: 1 , NDV )

C

C EXIT FROM GRADIENT LOOP BY DECLARING TAPE14 AS LOCAL

C

OPEN(UNIT=14,FILE='FLAG')

WRITE (14,*) ITER

110 CONTINUE

STOP

END

EOI ENCOUNTERED.

/

A-I8
•

LIST,FN==OBJFUN

PROGRAM OBJFUN(DECIS,ITER,DESIGN,CVD1,CONMDT,OBDJ,

*TAPEB==CVD1,TAPEI0==DESIGN,TAPE16==CONMDT,

*TAPE4=DECIS,TAPE7==ITER,TAPE2==OBDJ)

C

C****************************************************

C

C THIS PROGRAM COMPUTES AND WRITES THE SENSITIVITY

C INFORMATION AS REQUIRED BY THE OPTIMIZATION

C PROGRAM, CONOPT.

C

C PRABHAT HAJELA JULY 1985

C

CC **************************************************

C

DIMENSION A(12000),STR(1000),STRR(1000)

DH1ENSION Y(10) , X(10) , XX (10) , TEM (1000)

DIMENSION GSE(1000),GFF(1000),GRDOBJ(10) ,GRDG(10,200)

DATA NSTR/72/,SIGAL/25000./,TSE/6. 15168E+7/,PI/3. 14159/,

*TFF/6.15168E+7/,GAM5/24./,CEE/l.E+41/,ND41/10/

OPEN(UNIT=8,FILE='CVD1')

OPEN(UNIT=10,FILE=='DESIGN')

OPENCUNIT==16,FILE='CONMDT')

OPEN(UNIT=4,FILE='DECIS')

OPENCUNIT=7,FILE=='ITER')

OPEN(UNIT=2,FILE='OBDJ')

READC7,*)ITER,NDV

READ(2,*>OBJ1,(GRDOBJ(I),I=1,NDV)

READ ( 10, * > (X ( I) , 1=1 , NOV)

READ (4, *) (X X( I) , 1==1 , NDV) , (Y ( I ) , 1==1 , ND41 ) , FDCH

NLII"11=NDV+l

NLIM2=NLIM1*NSTR

NSTR1=1 + 2*NSTR

NSTRSQ=NSTR1**2

NDIM=(NSTRSQ+NSTR1)/2

READ(B,*>N1

DO 2 IJ=l,NLIMl

READ (B, *) N1 , (A CI) , 1=1 , ND 1M)

IN= (IJ-l) *NSTR

JCK==l

DO 4 I==1,NSTR1-1

TEM(I)=SQRTCACJCK»

JCK==JCK+NSTR1-(I-l)

4 CONTINUE

DO 6 I=l,NSTR

K=NSTR+I

STR(I+IN)=TEM(I)

6 STRR(I+IN)=TEMCK)

2 CmHINUE

C

C CONSTRAINT - SINGLE EXCURSION FAILURE

C

A-19
DO 10 I=1,NLIM2

STR(I)=STR(I)*100.

STRR(I)=STRRCI)*100.

FUN=(SIGAL**2)/(2.*STR(I)*STR(I»

FUN=-FUN

IF(FUN.LE.-675.0)FUN=-675.0

IF(FUN.GE.741.0)FUN=741.0

10 GSE(I)=(TSE/PI)*(STRR(I)/STR(I»*EXPCFUN) - 1.

C

C CONSTRAINT - FATIGUE FAILURE

C

DO 12 I=1,NLIM2

FUN=(TFF/(PI*CEE»*8.*GAM5

12 GFFCI)=(FUN*STRR(I)*(STR(I)**7» - 1.

C

C CONSTRAINT DERIVATIVES

C

DO 14 I=1,NDV

I(=I*NSTR

DO 16 J=1,NSTR

GRDG(I,J)=(GSE(K+J)-GSE(J»/(FDCH*X(I»

16 CONTINUE

14 CONTINUE

DO 18 I=l,NDV

I<=I*NSTR

DO 20 J=NSTR+1,2*NSTR

GRDG(I,J)=(GFF(K+J-NSTR)-GFF(J-NSTR»/(FDCH*X(I»'

20 CONTINUE

18 CONTINUE

C

C WRITE OBJECTIVE, CONSTRAINTS AND THEIR DERIVATIVES

C

(.1JR I TE ( 16, *) (GSE (I) , 1=1 , NSTR) , *<GFF(I),I=1,NSTR),OBJ1,

*«GRDG(I,J),I=1,NDV),J=1,2*NSTR),

*(GRDOBJ(I),I=1,NDV)

C

STOP

END

EOI ENCOUNTERED.

/

A-20

..
THIS PROGRAM REDUCES THE SIZE OF THE COVARIANCE MATRIX

DIMENSION CV(145,145) .

OPEN(UNIT=3,FILE='CVDATA')

READ(3,*)Nl

READ ( 3 • "*) ( (CV ( I , J) , J =1 • N 1 ) , 1=1 ,. N 1 )

REWIND 3

L'JR I TE ;; 3, *) N 1

DO 2 I=l,Nl

l1JRITE(3,*) (CV(I,J) ,J=I.Nl>

2 CONTINUE

CLOSE (UNIT=3)

STOP

END

EOI ENCOUNTERED.

LIST,FN=POST

PROGRAM POST(DESIGN,DECIS,ITER,TAPE2=ITER,

*TAPE7=DECIS,TAPE8=DESIGN)

C

C ***********************************************************

C

C THIS PROGRAM UPDATES THE DECIS FILE AND CAN ALSO BE USED

C TO DETERMINE IF MODES NEED TO BE RECOMPUTED IN PROBLEM

C

C PRABHAT HAJELA JULY 1985

C

C ***********************************************************

C

DIMENSION X(10),Y(10),XX(10)

DATA ND41/10/

OPEN(UNIT=2,FILE='lTER')

OPEN(UNIT=7,FILE='DECIS')

OPEN(UNIT=8,FILE='DESIGN')

READ(2,*)ITER,NDV

READ (7 , *) (X X( I) , 1=1 , NDV) , (Y ( I ) , 1=1 ,ND41) , FDCH

READ (8 *) (X ( I ) , 1= 1 , NDV)

DO 2 I=l,NDV

2 XX(l)=X(l)

RELoJIND 8

F:EWIND 7

WR I TE (7, 100) (X X ( 1) , 1=1 , NDV) , (Y ( I ) , 1=1 , ND41) , FDCH

100 FORMAT(FI0.4)

STOP

END

EOl ENCOUNTERED.

/

LIST,FN=REDUC PROGRAM REDUC(CVDATA,TAPE3=CVDATA,OUTPUT)

C

***********************************************

C *************.

C

C

C

CC

C PRABHAT HAJELA JULY 1985

C . .****************************************** C ******************

C

/

A-21
LIST,FN=NREPT non-repeatable part of SPAR

[XQT TAB

START 80,4

5

6

MATC 1 10.5+6

<

.'-' • 1

2 10.5+6

<

• .j . 1

JLOC1 0.00 -67.50 3.78 2 0.00 -67.50 7.02 .... < 0.00 -37.50 10.80 4 0.00 -7.50 10.80 5 0.00 22.50 7.02 6 0.00 22.50 3.78 7 0.00 -7.50 0.00 8 0.00 -37.50 0.00 9 40.00 -81.57 3.89

10 40.00 -81.57 6.91

11 40.00 -53.61 10.43

12 40.00 -25.64 10.43

13 40.00 2.32 6.91

14 40.00 ,., ooz'") Jl...~4 3.89

15 40.00 -25.64 0.37

16 40.00 -53.61 0.37

17 80.00 -95.64 4.00

18 80.00 -95.64 6.80

19 80.00 -69.71 10.07

20 80.00 -43.79 10.07

21 80.00 -17.86 6.80

22 80.00 -17.86 4.00

23 80.00 -43.79 0.73

24 80.00 -69.71 0.73

25 120.00 -109.71 4.11

26 120.00 -109.71 6.69

27 120.00 -85.82 9.70

28 120.00 -61. 93 9.70

29 120.00 -38.04 6.69

30 120.00 -38.04· 4.11

31 120.00 -61.93 1.10 "'Z",

_I':" 120.00 -85.82 1.10 "':!""':!" 160.00 -123.78 4.22' --"')

34 160.00 -123.78 6.58 71::"

..;•..J 160.00 --101.92 9.33

36 160.00 -80.07 9.33

37 160.00 -58.22 6.58

38 160.00 -58.22

4 .~~'"??

39 160.00 -80.07 1.47

40 160.00 -1

f

)1.92 1.41

• 41 200.00 -,137.84 4.33

42 200.00 -,137.84 6.47

43 200.00 --118.03 8.97

44 200.00 -98.22 8.97

45 200. ')0 -78.40 6.47

46 200.00 -78.40 4.33

A-22
47 200.00 -98.22 1. 83

48 200.00 -118.03 1.83

49 240.00 -151.91 4.44

50 240.00 -151. 91 6.36

51 240.00 -134.14 8.60

52 240.00 -116.36 8.60

53 24(,. ()()

_ roro C'ro

- I- '7';

• -70

• ..JO o. ~10

54 240.00 -98.58 4.44

55 240.00 -116.36 2.20

56 240.00 -134.14 2.20

57 280.00 -165.98 4.55

58 280.00 -165.98 6.25

59 280.00 -150.24 8.23

60 280.00 -134.50 8.23

61 280.00 -118.76 6.25

62 280.00 -118.76 4.55

63 280.00 -134.50 2.57

64 280.00 -150.24 2.57

65 320.00 -180.05 4.66

66 320.00 -180.05 6.14

67 320.00 -166.35 7.87

68 320.00 -152.64 7.87

69 320.00 -138.94 6.14

70 320.00 -138.94 4.66

71 320.00 -152.64 2.93

72 320.00 -166.35 2.93

73 360.00 -194.12 4.77

74 360.00 -194.12 6.03

75 360.00 -182.45 7.50

76 360.00 -170.79 7.50

77 360.00 -159.12 6.03

78 360.00 -159.12 4.77

79 360.00 -170.79 3.30

80 360.00 -182.45 3.30

CON

1

ZERO 1,2,3;1,

8

BC

1 1.567 2 .7176 3 O. 1 4 1.567 C'

..J ;7178 6 • 1 7 · 1 8 • 1

SA1 .05 2 · ()52

--' .05 4 .05 5 .05 .. 6 • (j52 7 .05

A-23
8

• ()5

9 .05

10 .0675

[XQT ELD

E41

NSECT=1

•

'"' 4 10 11

3

1

2

<

~.

NSECT=2

18 26 27 19

1

2

3

NSECT=3

34 42 43 35

12 oJ<

NSECT=4

50 58 59 51

1

<

< '-' ,J

NSECT=5 1 9 16 8 1 '"'

....

8 16 15

7

1

2

2

NSECT=6

17 25 32 24

1

2

24 ..,. ...... 31 ...... ..,.. .j":" .L-~•

1

2

2

I ;\lSECT=7

33 41 48 40

12

40 48 47 39

1 ....

2

NSECT=8

49 57 64 56

13

56 64 63 55

1

< ':> 'J 4

NMAT=2

NSECT=

9

9 16 11 10

16 15 12 11

15 14 13 I'"' .... 17 24 19 18

24 23 20 19 '-:'l~ '?""J 4'J .... L 21 20

25 ..,. ...... '';''4 27 26

32 31 28 27

31 30 29 28 "":!"~

'-"J 40 35 34

40 39 36 ""'1::" ....;.-J

39 38 37 36

41 48 43 42

48 47 44 43

47 46 45 44

49 56 51 50 ~lb

=, ==...J..J 52 51 I::"t="

..J....J 54 1::""'" ..J"':' 52

57 64 59 58

64 L<

'-'~. 60 59

63 62 61 60

• 65 72 67 66

72 71 68 67 .. 7i 70 69 68

73 80 75 74

80 79 76 ~I::"

/....J

A-24
79 78 77 76

NSECT=10

1 9 10 2. 1 9

6 14 13 5 1 9

E23

Nt1AT=1

NSECT= 1 • 1 9 1 ..,

.... 2 7

6 14 1 2 2 1

NSECT=2

22 30 1 2 2 1

17 25 1 2 2 7

NSECT=3

38 46 1 .., .., .... .... 1

33 41 1 2 2 7

NSECT=4

2 10 1 2 4 1

NSECT=5

18 26 1 2 4 1

NSECT=6

34 42 -I

... 2 4 1

NSECT=7

54 62 1 3 2 1

49 57 1 .....

< 2 7

NSECT=8

50 58 1 <0") 4 1

[XQT EXIT

EOr ENCOUNTERED.

I

•

A-25
LIST ,FN=REPT repeatable part of SPAR

[XQT E

RESET G=386.

[XQT TOPO

[XQT EKS

[XQT K

[XQT INV

[XQT EIG

RESET INIT=8,NREQ=6,HIST=O

[XQT DCU

PRINT 1 VIBR EVAL

[XQT VPRT

PRINT VIER MODE

[XQT AUS

SYSVEC; UI'·J I T VEC

I=l;J=l,BO; 1.0

DEFINE UN=UNIT VEC

DEFINE DM=DEM DIAG

OBJF=XTY <UN ,DM)

DEFINE Vl=VIBR MODE 1 1 1,6

XDIS=UNION (VI)

[XQT GSF

SOURCE=XDIS AUS

[XQT DCU

TOC 1

[XQT EXIT

EOI ENCOUNTERED.

/

LIST,FN=SECPROP

[XQT TAB

Be

1 1.0923

new section properties file created in GRAD

.324

"< .-..J

"<

·-'

.,.-

·

...;,

"< .-..J

"<

·-'

·3

·05

.05

·05

.05

·

05

·05 11-

• (l5

6

7

8 .05

9 .05

10 .065

[XQT EXIT

EOI ENCOUNTERED.

/

c

..J

4

2

1

2

8

7

5

6

4

3

SA

A-26
•

•

LIST,FN=TAP2G

-2

PHWING ONESIX

$INPUT NM=18, NR=O, NC=O, NK=7, ISPLANE=3, C=69.58,

NLOAD=72, IDCM=1, IAPLT=O, ISTABLE=l,IGUST=l,

BN=.30,.65, NCOEF=5, NCOL=O,6*1, NKK=7*7,

ICONSYS=O, NS=O, ISELECT=1, ICSACT=l, IBLOCK=2, KVAR=3,

GL=30000., ISPECT=2, IPRINT=1,ISOUT=O,

VO=8876.6,RHOO=O., DV=1.873E-9, NV=O,NG=l,

NINT=5,RFLOW=O.,RFCUT=1.0,UU=8876.56,NVEL=1,RHO=5.716E-8,

IFLPLT=O,IFRFPLT=1$

ALL 1 0

END

$ACTINP $

$SELECT NMODES=6 , NCNEW=O, NOC=1,2,3,4,5,6$

$PLTSEL $

°

-2

MODES SEVEN TWELVE

$INPUT NM=18, NR=O, NC=O, NK=7, ISPLANE=3, C=69.58,

NLOAD=72, IDCM=1, IAPLT=O, ISTABLE=l,IGUST=l,

BN=.30,.65, NCOEF=5, NCOL=O,6*1, NKK=7*7,

ICONSYS=O, NS=O, ISELECT=1, ICSACT=l, IBLOCK=2, KVAR=3,

GL=30000., ISPECT=2, IPRINT=l,ISOUT=O,

VO=8876.6,RHOO=O., DV=1.873E-9, NV=O,NG=1,

NINT=5,RFLOW=O.,RFCUT=1.0,UU=8876.56,NVEL=1,RHO=5.716E-8,

IFLPLT=O,IFRFPLT=l$

ALL 1°

END

$ACTINP $

$SELECT NMODES=6,NCNEW=O,NOC=7,8,9,10,11,12$

$PLTSEL $

o

-2

MODES THIRTEEN EIGHTEEN

$INPUT NM=18, NR=O, NC=O, NK=7, ISPLANE=3, C=69.58,

NLOAD=72, IDCM=!, IAPLT=O, ISTABLE=1,IGUST=1,

BN=.30,.65, NCOEF=5, NCOL=O,6*1, NKK=7*7,

ICONSYS=O, NS=O, ISELECT=l, ICSACT=l, IBLOCK=2, KVAR=3,

GL=30000., ISPECT=2, IPRINT=l,ISOUT=O,

VO=8876.6,RHOO=O., DV=1.873E-9, NV=O,NG=l,

NINT=5,RFLOW=O.,RFCUT=1.0,UU=8876.56,NVEL=1,RHO=5.716E-8,

IFLPLT=O,IFRFPLT=l$

ALL 1°

END

$ACTINP $

$SELECT NMODES=6,NCNEW=O,NOC=13,14,15,16,17,18$

$PLTSEL $

o

-2

MODES NINETEEN TWENTYFOUR

$INPUT NM=18, NR=O, NC=O, NK=7, ISPLANE=3, C=69.58,

NLOAD=72, IDCM=1, IAPLT=O, ISTABLE=1,IGUST=1,

BN=.30,.65, NCOEF=5, NCOL=O,6*1, NKK=7*7,

ICONSYS=O, NS=O, ISELECT=l, ICSACT=l, IBLOCK=2, KVAR=3,

GL=30000., ISPECT=2, IPRINT=1,ISOUT=O,

VO=8876.6,RHOO=O., DV=1.873E-9, NV=O.NG=1.

A-27
. . NINT=5,RFLOW=O.,RFCUT=1.0,UU=8876.56,NVEL=1,RHO=5.716E-8,

IFLPLT=O,IFRFPLT=l$

ALL 2°

END

$ACTINP $

$SELECT NMODES=6,NCNEW=O,NOC=1,2,3,4,5,6$

$PLTSEL $

o

-2

MODES TWENTYFIVE THIRTY

$INPUT NM=18, NR=O, NC=O, NK=7, ISPLANE=3, C=69.58,

NLOAD=72, IDCM=1, IAPLT=O, ISTABLE=1,IGUST=1,

BN=.30,.65, NCOEF=5. NCOL=O,6*1, NKK=7*7,

ICONSYS=O, NS=O, ISELECT=1, ICSACT=1, IBLOCK=2, KVAR=3,

GL=30000., ISPECT=2, IPRINT=l,ISOUT=O,

VO=8876.6,RHOO=O., DV=1.873E-9, NV=O,NG=l,

NINT=5,RFLOW=O.,RFCUT=1.0,UU=8876.56,NVEL=1,RHO=5.716E-8,

IFLPLT=O,IFRFPLT=l$

ALL 2 0

END

$ACTINP $

$SELECT NMODES=6,NCNEW=O,NOC=7,8,9,10,11,12$

$PLTSEL $

°

-2

MODES THIRTYONE THIRTYSIX

$INPUT NM=18, NR=O, NC=O, NK=7, ISPLANE=3, C=69.58,

NLOAD=72, IDCM=1, IAPLT=O, ISTABLE=1,IGUST=1,

BN=.30,.65, NCOEF=5, NCOL=O,6*1, NKK=7*7,

ICONSYS=O, NS=O, ISELECT=l, ICSACT=l, IBLOCK=2, KVAR=3,

GL=30000., ISPECT=2, IPRINT=l,ISOUT=O,

VO=8876.6,RHOO=O., DV=1.873E-9, NV=O,NG=l,

NINT=5,RFLOW=O.,RFCUT=1.0,UU=8876.56,NVEL=1,RHO=5.716E-8,

IFLPLT=O,IFRFPLT=l$

ALL 2°

END

$ACTINP $

$SELECT NMODES=6,NCNEW=O,NOC=13,14,15,16,17,lS$

$PLTSEL $

°

-2

MODES THIRTYSEVEN FORTYTWO

$INPUT NM=18, NR=O, NC=O, NK=7, ISPLANE=3, C=69.58,

NLOAD=72, IDCM=1, IAPLT=O, ISTABLE=l,IGUST=l,

BN=.30,.65, NCOEF=5, NCOL=O,6*1, NKK=7*7,

ICONSYS=O, NS=O, ISELECT=l, ICSACT=l, IBLOCK=2, KVAR=3,

GL=30000., ISPECT=2, IPRINT=1,ISOUT=O,

VO=8876.6,RHOO=O., DV=1.873E-9, NV=O,NG=l,

NINT=5,RFLOW=O.,RFCUT=1.0,UU=8876.56,NVEL=1,RHO=5.716E-8,

IFLPLT=O,IFRFPLT=l$

ALL 3°

END

$ACTINP $

$SELECT NMODES=6,NCNEW=O,NOC=1,2,3,4,5,6$

$PLTSEL $

A-28

•

•

•
•

°

-2

MODES FORTYTHREE FORTYEIGHT

$INPUT NM=18, NR=O, NC=O, NK=7, ISPLANE=3, C=69.58,

NLOAD=72, IDCM=1, IAPLT=O, ISTABLE=l,IGUST=l,

BN=.30,.65, NCOEF=5, NCOL=O,6*1, NKK=7*7,

ICONSYS=O, NS=O, ISELECT=l, ICSACT=l, IBLOCK=2, KVAR=3,

GL=30000., ISPECT=2, IPRINT=l,ISOUT=O,

VO=8876.6,RHOO=O., DV=1.87~~-9, NV=O,NG=l,

NINT=5,RFLOW=O.,RFCuT=1.0,UU=8876.56,NVEL=1,RHO=5.716E-8,

IFLPLT=O,IFRFPLT=1S

ALL 3 0

E~

SACTINP $

$S~LECT NMODES=6,NCNEW=O,NOC=7,8,9,10,11,12$

$PLTSEL $

°

-2

MODES FORTYNINE FIFTYFOUR

$INPUT NM=18, NR=O, NC=O, NK=7, rSPLANE=3, C=69.58,

NLOAD=72, IDCM=1, IAPLT=O, ISTABLE=l;IGUST=l,

BN=.30,.65, NCOEF=5, NCOL=O,6*1, NKK=7*7,

ICONSYS=O, NS=O, ISELECT=1, ICSACT=l, IBLOCK=2, KVAR=3,

GL=30000., ISPECT=2, IPRINT=1,ISOUT=O,

VO=8876.6,RHOO=O., DV=1.873E-9, NV=O,NG=l,

NINT=5,RFLOW=O.,RFCUT=1.0,UU=8876.56,NVEL=1,RHO=5.716E-8,

IFLPLT=O,IFRFPLT=l$

ALL 3°

END

$ACTINP $

$SELECT NMODES=6,NCNEW=O,NOC=13,14,15,16,17,lB$

$PLTSEL $

°

12

Eor ENCOUNTERED.

/

A-29
•

•

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4-

4

4

4

4

4

4

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-,5

-5

-5

-5

-5

-5

-5

-5

-5

-5

-5

3

3

'<"-'

3

'<"-'

3

3

3

'<"-'

3

3

-""-'

-""-'

'<"-'

'<,-'

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

'"

....

-"

...'

3

4

1

5

2

·3

32

36

33

22

23

24

34

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

26

27

28

29

30

31

37

38

39

40

1 O. O. 1.

1

67.5000 0.0000

37.5000 0.0000

7.5000 0.0000

-22.5000 0.0000

81.5700 40.0000

53.6100 40.0000

25.6400 40.0000

-2.3200 40.0000

95.6400 80.0000

69.7100 80.0000

43.7900 80.0000

17.8600 80.0000

109.7100 120.0000

85.8200 120.0000

61.9300 120.0000

38.0400 120.0000

123.7800 160.0000

101.9200 160.0000

80.0700 160.0000

58.2200 160.0000

137.8400 200.0000

118.0300 200.0000

98.2200 200.0000

78.4000 200.0000

151.9100 240.0000

134.1400 240.0000

116.3600 240.0000

98.5800 240.0000

165.9800 280.0000

150.2400 280.0000

134.5000 280.0000

118.7600 280.0000

180.0500 320.0000

166.3500 320.0000

152.6400 320.0000

138.9400 320.0000

194.1200 360.0000

182.4500 360.0000

170.7900 360.0000

159.1200 360.0000

Eor ENCOUNTERED.

/

LIST,FN=TAPE31

PHWING TEST MODEL

ANYTHING

(3E15.8)

$DLINPT NSECTNS=1,NSECTNA=1,NDF=3,NNODES=40,NNODET=40,

IDLAT=1,NELAST=18,IPLTMS=O,

IPRINT=O,ISYM=+l,

NPMX=40,IPLTBOX=0,IPLTNOD=0,SCX=30.,SCY=30.,IDCM=1,ITOC=1$

DISP -1 1

MODES 1 1

HHD 1 1

SPLINE 1 1

END

1 40

1 48

A-3D
1 3 -5 4

2 3 -5 4

3 " -5 4 -'

4 -:0" ...;, -5 4

5 3 -5 4

6 "

..... -5 4

7 " -5 4 -'

8 3 -5 4

9 7' -' -5 4

10 3 -5 4

11 " -5 4 -'

12 3 -5 4

13 3 -5 4

14 3 -5 4

15 " -5 4 -'

16 "..... -5 4

17 " -5 4 -'

18 3 -5 4

19 3 -5 4

20 "

v -5 4

21 -y-' -5 4

22 "

v -5 4

23 "-' -5 4

24 3 -5 4

25 ".j -5 4

26 "-' -5 4

27 '" -5 4 -'

23 "

v -5 4

29 "":!

.... -5 4

30 "":!.... -5 4

31 3 -5 4 -=:"":1 "":! v"'- ._' -5 4 ""?"~ "":! -5 4 o_l_. -'

34 "":! -' -5 4 7C" "":! .':'..J -' -5 4

36 '"-' -5 4

37 '"

•...J -5 4

38 3 -..J= 4

39 -:0"

-..) -5 4

40 3 -5 4

A-31

/

LIST,FN=TAPE32

PHWING TEST MODEL

ANYTHING

(3E15.8)

$DLINPT NSECTNS=1,NSECTNA=1,NDF=3,NNODES=40,NNODET=40,

IDLAT=1,NELAST=6,IPLTMS=0,

IPRINT=0,ISYM=+1,

NPMX=40,IPLTBOX=O,IPLTNOD=0,SCX=30.,SCY=30.,IDCM=1,ITOC=1$

DISP -1 2

MODES 2 2

HHD 2 2

SPLINE 2 2

END

1 40 1 O. O. 1.

1 48 1

67.5000 0.0000

37.5000 0.0000

7.5000 0.0000

-22.5000 0.0000

81.5700 40.0000

53.6100 40.0000

25.6400 40.0000

-2.3200 40.0000

95.6400 80.0000

69.7100 80.0000

43.7900 80.0000

17.8600 80.0000

109.7100 120.0000

85.8200 120.0000

61.9300 120.0000

38.0400 120.0000

123.7800 160.0000

101.9200 160.0000

80.0700 160.0000

58.2200 160.0000

137.8400 200.0000

118.0300 200.0000

98.2200 200.0000

78.4000 200.0000

151.9100 240.0000

134.1400 240.0000

116.3600 240.0000

98.5800 240.0000

165.9800 280.0000

150.2400 280.0000

134.5000 280.0000

118.7600 280.0000

180.0500 320.0000

166.3500 320.0000

152.6400 320.0000

138.9400 320.0000

194.1200 360.0000

182.4500 360.0000

170.7900 360.0000

159.1200 360.0000

EOI ENCOUNTERED.

•
LIST,FN=TAPE33

PHl<JING TEST MODEL

ANYTHING

(3E15.8)

$DLINPT NSECTNS=1,NSECTNA=1,NDF=3,NNODES=40,NNODET=40,

IDLAT=1,NELAST=6,IPLTMS=0,

IPRINT=0,ISYM=+1,

NPMX=40,IPLTBOX=O,IPLTNOD=0,SCX=30.,SCY=30.,IDCM=1,ITOC=1$

DISP -1 3

MODES <

~, ~,

HHD - 3

SPLINE 3 3

END

1 40 1 O. O. 1.

1 48 1

67.5000 0.0000 1 ...;. -5 4

37.5000 0.0000 2 <.... -5 4

7.5000 0.0000 <

~, 3 -5 4

-22.5000 0.0000 4 v -5 4

81. 5700 40~0000 5 .,..

.;:.. -5 4

53.6100 40.0000 6 oJ -5 4

25.6400 40.0000 7 3 -5 4

-2.3200 40.0000 8 ..,..

....;. -5 4

95.6400 80.0000 9 <..... -5 4

69.7100 80.0000 10 < -5 4 '"" 43.7900 80.0000 11 <..... -5 4

17.8600 80.0000 12 ..,..

-..) -5 4

109.7100 120.0000 1< 3 -5 4 ~,

85.8200 120.0000 14 3 -5 4

61.9300 120.0000 15 -.:> -5 4

38.0400 120.0000 16 <

~, -5 4

123.7800 160.0000 17 3 -5 4

101.9200 160.0000 18 3 -5 4

80.0700 160.0000 19 3 -5 4

58.2200 160.0000 20 3 -5 4

137.8400 200.0000 21 3 -5 4

118.0300 200.0000 22 3 -5 4

98.2200 200.0000 ,.,~ < "'-' ~, -5 4

78.4000 200.0000 24 3 -5 4

151.9100 240.0000 25 <

~, -5 4

134.1400 240.0000 26 3 -5 4

116.3600 240.0000 27 3 -5 4

98.5800 240.0000 28 3 -5 4

165.9800 280.0000 29 <

'-' -5 4

150.2400 280~OOOO 30 <

"-' -5 4

134.5000 280.0000 31 3 -5 4

118.7600 280.0000 "":!,..., < _'.a:.., -5 4 ,) .....

180.0500 320.0000 -- 7 .~I.,::.l ...:. -5 4

166.3500 320.0000 34 "< -5 4 -'

152.6400 320.0000 71::" "< t::" .';'.J '-' -.J 4

138.9400 320.0000 36 < I::" -l ·oJ -.J

194.1200 360.0000 37 3 -5 4

182.4500 360.0000 38 7

'._' -5 4

170.7900 360.0000 39 < l::" 4 -' -.J

159.1200 360.0000 40 .,..

..:. -5 4

ED! ENCDutJTEF:ED.

/

A-32
)

LIST,FN=TAPE5T

PHWING TEST MODEL

$DLATINP ACAP=22500.0,REFCHD=69.44,

FMACH=.700,

NDELT=1,NP=1,NB=O,NRF=7,RFREQ=0.O,0.05,0.15,0.30,0.5,0.75,1.05,

NSTRIP=12,NSV=0,NBV=0,NMODES=18,NDATA=0,

NELAST=18,REFSPN=1.0,NBOX=48,NSNC=65,

XZERO=-22.5,NR=0,

NC=0,IDCM=1,ITOC=1 $

HHD 1 0

AERO 1 1

AlC 0 1

END

-22.5 67.5 159.12 194.12 0.0 360.0

7.02 69.51 13 5 1.0

0.0 0.25 0.5 0.75 1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.666 0.732 0.798 0.864 0.93 1.0

1 4 5 8 9 12 13 16 17 20 21 24

25 28 29 32 33 36 37 40 41 44 45 48

SECOND CASE

$DLATINP ACAP=22500.0,REFCHD=69.44,

FMACH=.700,

NDELT=1,NP=1,NB=0,NRF=7,RFREQ=0.0,0.05,0.15,0.30,0.5,0.75,1.05,

NSTRIP=12,NSV=0,NBV=0,NMODES=18,NDATA=0,

NELAST=18,REFSPN=1.0,NBOX=48,NSNC=65,

XZERO=-22.5,NR=0,

NC=0,IDCM=1,lTOC=2 $

HHD 2 0

AERO 2 2

Arc 1 0

END

-22.5 67.5 159.12 194.12 0.0 360.0

7.02 69.51 13 5 1.0

0.0 0.25 0.5 0.75 1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.666 0.732 0.798 0.864 0.93 1.0

1 4 5 8 9 12 13 16 17 20 21 24

25 28 29 32 33 36 37 40 41 44 45 48

THIRD CASE

$DLATINP ACAP=22500.0,REFCHD=69.44,

FMACH=.700,

NDELT=1,NP=1,NB=O,NRF=7,RFREQ=0.O,O.05,0.15,0.30,O.5,0.75,1.05,

NSTRIP=12,NSV=O,NBV=0,NMODES=18,NDATA=0,

NELAST=18,REFSPN=1.0,NBOX=48,NSNC=65,

XZERO=-22.5,NR=0,

NC=0,IDCM=1,lTOC=3 $

HHD 3 0

AERO 3 3

AlC 1 0

END

-22.5 67.5 159.12 194.12 0.0 360.0

7.02 69.51 13 5 1.0

0.0 0.25 0.5 0.75 1.0

0.0 0.10.2 0.3 0.4 0.5 0.6 0.666 0.732 0.798 0.864 0.93 1.0

1 4 5 8 9 12 13 16 17 20 21 24

25 28 29 32 33 36 37 40 41 44 45 48

EOI ENCOUNTERED.

/

A-33
1. Report No.

NASA CR-178047

12. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle

OPTIMAL AIRFRAME SYNTHESIS FOR GUST LOADS

5. Reoort Da te

February 1986

6. Performing Organization Code

"

7. Author(s) 8. Performing Organization Report No.

Prabhat Hajela I---------------------------~ 10. Work Unit No.

9. Performing Organization Name and Address

Department of Engineering Sciences

University of Florida

Gainesville, FL 32611

11. Contract or Grant No.

NAGl-579

1----------------------------1 13. Type of Report and Period Covered

12. Sponsoring Agency Namll and Address

National Aeronautics and Space Administration

Washington, DC 20546

Contractor Report

14. Sponsoring Agency Code

505-63-21-04

15. Su pplementary Notes

Langley Technical Monitor: Boyd Perry III

Final Report

16. Abstract

The present work is a first step towards establishing an optimization capability

for sizing airframe structures that are subjected to a combination of deterministic and random flight loads. The random vibration environment introduces the

need for selecting a statistical process that best describes the random loads

and permits computation of the dynamic response parameters of interest.

Furthermore, it requires a formulation of design constraints that would minimize

the conservativeness in the design and retain computational viability. In the

present work, the random loads are treated as a stationary, homogeneous process

with a Gaussian probability distribution. This report discusses the formulation

of the analysis problem, the structure of the optimization programming system

and a representative numerical example.

17. Key Words (Suggested by Author(s)) 18. Distribution Statement

Optimal airframe synthesis

Gust loads

Deterministic and random loads

Unclassified-Unlimited

Star Categories 05, 65

19. Security Classif. (of this report) 20. Security Classif. (of this pagel 21. No. of Pages 22. Price

Unclassified Uncl assifi ed 44 A03

H-305 For sale by the National Technical Information Service, Springfield, Virginia 22161
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3 1176 00190 5257

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