NASA Technical Memorandum 4796

........ ,:::/::.::_.......... :iiiii:z _: ::::":'::"

.... / •.............. /

Finite-Element Analysis of a

Mach-8 Flight Test Article

Using Nonlinear Contact

lements ...............................

W. Lance Richards

June 1997

NASA Technical Memorandum 4796

Finite-Element Analysis of a

Mach-8 Flight Test Article

Using Nonlinear Contact

Elements

W. Lance Richards

Dryden Flight Research Center

Edwards, California

• ,, '? •

National Aeronautics and

Space Administration

Office of Management

Scientific and Technical

Information Program

1997

ABSTRACT

A flight test article, called a glove, is required for a Mach-8 boundary-layer experiment to be conducted on a

flight mission of the air-launched Pegasus ® space booster. The glove is required to provide a smooth, threedimensional, structurally stable, aerodynamic surface and includes instrumentation to determine when and where

boundary-layer transition occurs during the hypersonic flight trajectory. A restraint mechanism has been invented to

attach the glove to the wing of the space booster. The restraint mechanism securely attaches the glove to the wing in

directions normal to the wing/glove interface surface, but allows the glove to thermally expand and contract to

alleviate stresses in directions parallel to the interface surface. A finite-element analysis has been performed using

nonlinear contact elements to model the complex behavior of the sliding restraint mechanism. This paper provides

an overview of the glove design and presents details of the analysis that were essential to demonstrate the flight

worthiness of the wing-glove test article. Results show that all glove components are well within the allowable

stress and deformation requirements to satisfy the objectives of the flight research experiment.

INTRODUCTION

Preparations are currently underway for a flight experiment that will acquire data necessary to validate

boundary-layer transition prediction methods for hypersonic flight conditions. Success of the flight experiment

depends on the design and development of a flight test fixture, called a glove, which can provide a smooth, threedimensional, structurally stable, aerodynamic surface from which detailed information regarding the atmospheric

flight environment to a maximum of Mach 8 could be obtained.

A flight test article has been designed, analyzed, manufactured, and installed on the wing of the air-launched

Pegasus ® (Orbital Sciences Corporation, Fairfax, Virginia) space booster. Figure l shows the geometry of the

booster and the location of the glove for the boundary-layer experiment. The Pegasus ®is a multistaged, air-launched

rocket designed to place small payloads into low Earth orbit. The booster follows a predetermined trajectory

designed for a particular payload requirement. For a typical mission, the booster separates from the carrier aircraft

at Mach 0.8 and an altitude of approximately 13,000 m. The booster descends for 5 sec before the first stage ignites.

After approximately 70 sec, the vehicle has accelerated to Mach 8 and an altitude of approximately 61,000 m. The

glove experiment concludes as the first stage burns out and is jettisoned and second-stage ignition occurs.

6.7 m

First stage _15.2 m

Third Second

stage stage

m

45 °

Figure 1: Plan view of Pegasus ® space booster with glove.

Payload

bay

970034
J

i :

ii_i:i_

Figure 2 shows a photograph of the Pegasus ® space booster mounted under the wing of the NASA

B-52 airplane, which was the original carrier aircraft. The booster has recently been air-launched from a modified

L-1011 aircraft. Details of previous research experiments conducted on the Pegasus ® booster have previously been

provided. 2,3 Plans for future studies have also been previously presented. 4

A comprehensive structural test and analysis program has been successfully completed to validate the integrity

of the complex glove design. 5,6 Complexity of the design stemmed from the use of a nonlinear restraint mechanism

that attaches the glove to the wing of the space booster. The restraint mechanism securely attaches the glove to the

wing in directions normal to the wing/glove interface surface, but allows the glove to thermally expand and contract

to alleviate stresses in directions parallel to the interface surface. This design allows the glove to maintain a

geometrically stable shape, reduces the thermal stress in the glove to acceptable levels, and results in safe and

efficient structural performance.

A finite-element analysis was performed using nonlinear contact elements to model the complex behavior of

the sliding restraint mechanism. This paper provides an overview of the glove design and presents details of the

finite-element analysis, which included the use of nonlinear contact elements to accurately predict the structural

response of the test article prior to flight. Results from the analysis show that all glove components are well within

the allowable stress and deformation requirements to satisfy experiment objectives.

GLOVE DESIGN

Figure 3 shows a top view of the glove, the rigid attachment at the inboard leading edge, and a cross-sectional

view of the glove. The test surface has a plan view area of approximately 1 m 2. Ceramic tile and ablative-coated

aerodynamic fairings 5 were used to blend the metallic portion of the glove to the existing Pegasus ®wing. Details of

2

Figure 2: Pegasus ® space booster mounted under the wing of the B-52 aircraft.
1.3 m

See fig. 3(b)

Fixed at inboard

leading edge

3(c)

(a) Plan view.

970035

- Leading-edge fitting

\ _--Inboard leading edge

_ \ of test skin

I_ i-- Fixed

\. / attachment

Pegasus ®_,.__

wing ---/

960004

(b) Glove leading-edge detail.

Steel skin

steel

leading edge

(c) Glove internal assembly.

Figure 3: Glove assembly.

960005

the design process, which consisted of aerodynamic heating analysis, thermal analysis, structural analysis, and

small-scale laboratory testing, have been published. 5 This process resulted in a glove design with a relatively thin

metallic outer skin and a large leading-edge heat sink (fig. 3(c)) to accommodate the extreme stagnation-point

heating rates during flight.

3
Preliminaryanalysisshowedthatif theglovewasrigidlyconstrainedduringthehypersonicflightexperiment,

thenthethermalstressesproducedby aerodynamicheatingwouldcausethethin skinsto buckle,or therigid

attachmentstoyield,orboth.Thermalexpansionandcontractioncapabilitywas,therefore,acriticalrequirementin

theglovedesign.Thisrequirementwassatisfiedbytwomeans:thethickleadingedgewasrigidlyfixedatasingle

pointonly(fig.3(b)),andthethinmetallicskinwasallowedtofreelyexpandoverabalsawoodsupportfoundation

duringheating.Thepreliminarydesignconstrainedthemovementof theglovein thedirectionnormalto the

Pegasus®wingleadingedge;however,movementinthedirectionparallelto thePegasus®wingleadingedgewas

allowedbyaseriesof slidingattachments. Therigidattachment oftheglove(fig.3(b))forcedallthermalexpansion

of thegloveaftandspanwiseparallelto theleadingedge.Thedesignensuredglovedimensional stabilityatthe

leadingedgewhereboundary-layer transitionisthemostsensitivetomoldlineshape.

Figure3(c)showsadetailedcross-sectional viewof thegloveattachedto thePegasus®wingattheleading

edge.Themetallictestskinwasattachedtoa balsawoodsupportsurfacethatwaspreshapedandbondedto the

Pegasus®wing(fig. 3(c)).Thedesignprocessusedto definetheaerodynamicshapeof theglovehaspreviously

beendescribed. 7Thethinskinwasattachedto thecontouredbalsawoodsurfaceusingaseriesof spring-loaded

swivelstudsspacedapproximately6.35cmapart.Thesestudsweredesignedtoholdtheskinsecurelytothesurface

whileallowingtheskinto expandthermallywithonlyasmallresistancecausedbyslidingfriction.Eachstudis

bondedtotheinnersurfaceof thegloveskinwithhigh-temperature epoxy.Aninitialpreloadisappliedthroughthe

springto reactagainstaerodynamicforcesexpectedduringtheflightexperiment.

FINITE-ELEMENT ANALYSIS

Figure 4 shows the top, outboard, forward, and isometric views of the three-dimensional glove model, which

was generated using MSC/NASTRAN (Version 68). 8 The fixed attachment point is located at the inboard end of the

leading-edge mass (fig. 3(b)). This section describes the elements, analysis cases, loads, boundary conditions, and

the solution strategy employed in the nonlinear analysis.

Description of Elements

The model consists of 3777 hexahedron elements, 187 pentahedron elements, and 1194 nonlinear contactfriction elements, resulting in a total of 7500 degrees of freedom. This section describes the types of elements used

in the non- linear analysis.

Solid Elements

The massive leading-edge heat sink was modeled with solid, linear, is®parametric elements to incorporate the

severe, spatially varying temperature distributions in all three dimensions: radially (through the thickness of the

leading edge), circumferentially (around the leading-edge radius), and in the spanwise direction (parallel to the

leading edge). Figure 5 shows the reference system. The radial and circumferential temperature variations at the

leading edge were produced by severe stagnation-point heating during hypersonic flight. Several layers of

is®parametric elements were needed in these directions to adequately define the nonlinear temperature distribution

produced by the aerodynamic heating at the leading edge.

Severe temperature gradients also occurred in the spanwise direction because the structurally stiffened

attachment points, referred to as bosses (fig. 5), were located at several locations behind the leading edge to secure

the glove to the Pegasus ® wing. These bosses produced large discontinuities in thermal capacitance that resulted in

the temperature variations in the spanwise direction.
F A

A = Inboard leading edge

B = Outboard leading edge

C = Inboard trailing edge

D = Outboard trailing edge

D

c\

A

_--C

(a) Top view

_-C /,---D

L,

(c) Forward view

(b) Isometric view

B

(d) Outboard view

Figure 4: Finite-element model.

970036

Radial

tt

Circumferential

-Typical

boss locations

Figure 5: Model detail showing boss locations.

970037
Solid elements were also required in the analysis because of their ability to model the irregular surface topology

existing behind the leading edge at the boss locations. To ensure element compatibility, particularly at the interface

boundary between the thick and thin regions of the structure, the entire thin skin was also modeled with solid

elements. Hexahedron brick-type elements were used wherever possible, and pentahedron wedge-type elements

were judiciously used in areas of especially irregular surface geometry.

Although solid elements were selected to model both the thick and thin regions of the structure, it was

recognized that solid elements, which are better suited for plane-strain type problems, were not the ideal choice for

modeling the thin skin. Therefore, preliminary studies were performed to quantify the reduced computational

accuracy in using solid elements to model plane-stress and buckling-critical areas on the glove. In these studies,

fiat-plate models were constructed with four-noded plate elements and eight-noded solid elements. These models

were subjected to large compressive in-plane forces at the panel boundaries, and the critical buckling values were

determined for successive refinements in the element mesh. The critical eigenvalues computed from finite-element

analysis were compared to analytical solutions based on Timoshenko plate theory. 9 The results showed that the use

of solid elements produced a 2.5-percent increase in stiffness compared with similar models constructed with plate

elements. When the final glove models were constructed and the fully three-dimensional thermal loads were applied

to the glove, the membrane forces produced in the thin skin were determined to be well below critical values.

Therefore, the additional stiffness provided by the solid elements was not an issue. The choice of the solid elements

to model the glove was the best compromise between the many competing modeling requirements.

Nonlinear Contact Elements With Friction

The element used to model the contact surface between the metallic thin skin and the balsa wood is called an

"adaptive gap" element in MSC/NASTRAN. 1° The gap element simulated point-to-point frictional contact and

used an adaptive solution procedure based on the penalty method, l° Initial penalty values were defined prior to the

analysis run and were automatically updated during the solution process based on the penetration of the contacting

surfaces. The initial penalty value was increased by one order of magnitude if the surface penetration was greater

than the user-specified amount. Conversely, the penalty value was automatically decreased by an order of

magnitude if the penetration was less than a user-specified amount. The lower and upper bounds of the penalty

values were also limited during the analysis. Both static and kinetic friction were considered in the formulation of

the element.

The contact surfaces were meshed to ensure that a node was located at each of the 270 swivel-stud assemblies

in the balsa wood support system. Each assembly was represented by a gap element that was defined by a pair of

noncoincident nodes (similar in geometry to a rod element). Figure 6 shows a schematic of the noncoincident gap

element with three possible conditions. The noncoincident gap elements allowed the specification of 1) a closed

stiffness, kw, for the condition when the two surfaces were in contact and resisted by static friction, _ts; 2) a frictional

stiffness that represented the slip forces produced when the surfaces were in contact and resisted by kinetic friction, _tk; and 3) an open stiffness, ks, when the surfaces exceeded an initial preload and had separated. In addition to

the noncoincident gap, the element can also be defined, similar to a zero-length element, by a pair of coincident

nodes. All parameters described above, except k s, can be specified for the so-called "coincident" gap elements.

Initially, only noncoincident gaps elements, which represented the swivel-stud assemblies, were used in the

analysis to avoid the excessive computational expense associated with these nonlinear elements. Further studies

showed, however, that coincident gap elements were also required to provide stiffness on the contact surface and

prevent unrealistic penetration of the thin skin into the balsa wood substructure. Coincident gap elements were

added on the contact surface at all other degrees of freedom where swivel-stud assemblies were not present.

Preliminary studies showed that without the coincident contact elements, the buckling resistance of the thin skin

was not realistically modeled, causing spurious mode shapes to develop because of buckling.

6
' i _,

Prelosd force Prelosd force

GSp status: Gap status:

losed slipped

Gap status:

open

Figure 6: Nonlinear gap elements.

970038

Analysis Cases

In a preliminary analysis, a single time in the trajectory was initially analyzed near the end of the boundarylayer experiment to provide what was assumed as a "worst-case" design condition. Because the first stage of the

Pegasus ® booster begins to burn out at approximately 69 sec after launch, this time was initially selected for the

preliminary analysis. A more rigorous and quantitative analysis later showed, however, that the worst-case

condition in the glove will not occur at a single time in the trajectory and that multiple analysis cases were necessary

to capture this condition.

Figure 7 shows predicted temperature time histories at the thick leading edge and the thin skin approximately

10 cm in the direction normal to the leading edge of the glove. This figure shows how radically the temperature

250 -- --

2O0

150

°C 100

5O

- 50

Leading edge /- Thin

- - - Thin skin /_... skin

_ _--Leading _ /

¢ _

-- I II

-- ¢ I"

90 sec

75 sec

/A f____ 500 L

AT I

r. - - - ---I 400

--4 300

-_ 200

-_ 100

-_ 0

I I I I I

20 40 60 80

Time, sec 970039

Figure 7: Analysis cases for structural analysis.

oF
differences (and consequently the thermal stresses) can vary over the glove during the course of the trajectory.

Approximately 10 analysis cases between 25 and 90 sec were analyzed to ensure that a truly worst-case design in

the transient profile was considered. Results from these cases confirmed that maximum thermal stresses in the glove

occurred at a flight profile time between 45 and 90 sec. Accordingly, analysis cases discussed in this paper are

focused at four critical times in the trajectory: 45, 69, 75, and 90 sec. Times of 45 and 75 sec correspond to the

points at which the thermal gradient between the thick and thin regions was the most extreme (fig. 7). As mentioned

earlier, a profile time of 69 sec is when first-stage burnout initiates and is the time that was originally chosen for

preliminary analyses. At 90 sec, second-stage ignition has occurred and reflects a condition well beyond the

conclusion of experiment.

Load and Boundary Conditions

During the flight experiment, the glove will experience a combination of loads from external and internal

sources. The external loads chiefly pertain to the aerodynamic loads imparted to the glove (in the form of pressures)

as the rocket, to which the glove is mounted, traverses through the atmosphere at increasing hypersonic speeds. To

counteract these aerodynamic loads, the thin skin areas of the glove are preloaded mechanically to secure the glove

to the Pegasus ®wing. These preloads are referred to as "mechanical loads."

In addition, the glove will experience significant thermal loading (in the form of increased temperatures) caused

by aerodynamic heating, which increases with the square of the speed. These thermal loads are highly nonuniform,

especially near the stagnation region of the glove. Large thermal stresses develop at the boundary restraints between

the glove and the Pegasus ® wing as the glove attempts to expand and contract with the increased variation in

temperature. This section describes how the mechanical, thermal, and aerodynamic loads, as well as the boundary

conditions, were modeled in the finite-element analysis.

Mechanical Loads

Mechanical loads were applied in directions normal to the exterior surface of the glove at each of the

210 noncoincident gap element locations (fig. 6). The mechanical loads represented a 110-N initial preload to

which each of the swivel-stud mechanisms were subjected when the glove was assembled and attached to the

Pegasus ® wing. These preload forces were designed to resist against the aerodynamic forces predicted to occur

during the experiment.

Thermal Loads

The transient temperature distributions on the glove were determined by the aerodynamic heating and thermal

analysis discussed in a previous publication. 6 The temperature distributions at a given trajectory time were mapped

onto the structures model so that a unique temperature value was assigned to every node in the model. The code

determined the thermal strain at each node by multiplying the coefficient of thermal expansion of the material by

the difference between the prescribed nodal temperature and the initial reference temperature. Temperature

dependency of the glove material properties were considered in the analysis. The calculated temperature

distribution varied considerably over the glove, depending on the time in the trajectory being analyzed. For

example, the temperature distribution at 69 sec varied from approximately 400 °C at the inboard end of the leading

edge to approximately 65 °C near the trailing edge of the thin skin.

Aerodynamic Loads

In a separate analysis, aerodynamic loads on the glove were determined to only be significant early in the

trajectory (achieving a peak at approximately 16 sec after launch and decreasing to zero by approximately 20 sec).
5

Figure 7 shows that the thermal gradients in the glove are not significant until after approximately 25 sec. The

aerodynamic loads were therefore sufficiently decoupled from the thermal structural loads, because they occur at

mutually exclusive times in the trajectory. The aerodynamic loads were analyzed separately and will not be

addressed in this paper.

Boundary Conditions

The fixed boss at the top inboard area is the only location on the glove rigidly attached to the wing (fig. 3(b)).

The degrees of freedom at this location were therefore constrained in the analysis. Initially, the preliminary analysis

at 69 sec described above predicted that the attachment of the glove to the leading edge of the wing was well within

design allowances. However, the additional analysis cases revealed that the original attachment scheme exceeded

design limits at the other times in the flight profile. This problem forced modifications to the design at the inboard

restraint and sliding attachments at the leading edge. Originally, the leading edge was prevented from moving in the

direction normal to the 45 ° sweep angle of the wing. This constraint was removed to allow thermal expansion and

contraction to occur freely in a direction normal to the leading edge. These design changes allowed greater thermal

distortion of the glove outer moldline than previously observed but were essential to reduce thermal stresses in the

glove throughout the heating profile.

Nonlinear Solution Procedure

A computationally intensive, nonlinear solution process 9 was used to determine thermal stress and

displacements of the glove at each of the analysis cases previously described. Optimization and fine-tuning of the

solution strategy were key requirements because of the large number of nonlinear contact elements necessary in the

analysis and because friction was considered, which is path dependent. Preliminary studies were performed to

define an acceptable compromise between computational efficiency and solution accuracy. This section describes

the salient features of the solution process.

User Interface

Prior to the analysis run, important "control" parameters were required as input to define and adjust the

algorithm during the solution process. Parameters for the nonlinear process defined advancing schemes, iteration

frequency, convergence criteria, load increment and bisection control, and stiffness update strategy. 9 The maximum

number of bisections allowed during a load step, stiffness update frequency, divergence and convergence

contingencies, and output frequency were also specified. The code permitted some of these parameters to be

automatically updated during the solution process to efficiently respond to the nonlinear environment. These

parameters were also important because they helped to circumvent numerical difficulties encountered with the

contact elements.

Analysis Case Control

The critical loading cases described in an earlier section were divided into separate subcases. The mechanical

forces that represented the initial preload on the gap elements were applied separately in the first subcase, and then

concurrently applied with thermal load distributions at 45, 69, 75, and 90 sec for the subsequent subcases.

Load Increment and Iteration Strategy

The solution sequence invokes a subincremental algorithm for load application control and stiffness updates.

The load application process begins by the calculation of the incremental load to be applied during a given subcase.
Anyresultingloadfromaprevioussubcaseissubtractedfromthetotalloadtobeappliedduringthenextsubcase.

Forexample,if thethermalloadsat45secwereappliedinthepreviousubcase,andthethermalloadsat69secare

tobeappliedinthenextsubcase, thentheresultingloadsat45secaresubtractedfromtheloadsat69sec(ateach

degreeof freedom)to determinethe"deltaload"to beappliedduringthenextsubcase.Thisdeltaload,which

includesboththermalandmechanical loads,isthenfurtherdividedbyauser-specifiedvaluesothatonlya small

incrementof thedeltaloadisattemptedatatimeduringthesubcase.

An initial loadincrementof 10percentwasselectedfor eachsubcasein theanalysis.TheNewton-Raphson

iterationmethodwasusedtoachievequilibriumbetweentheloadincrementappliedandtheinternalnodalforces

producedin theresidualstructure.Duringtheapplicationof anincremental load,if thecodefailedto converge

efficientlyafterseveraliterations,theloadincrementwasautomaticallybisectedandtheiterationprocedurewas

resumedfromthelastconvergedloadcondition.Thisprocesswasrepeateduntilconvergencewasachievedateach

incrementalloadappliedduringthesubcase. Aftertheentiredeltaloadto beappliedduringthesubcasewas

completed,thealgorithmadvancedto thenextsubcase, andtheprocesswasrepeateduntilall theloadfor all the

subcaseswasapplied.

Convergence Criterion

The convergence criterion used in the iteration process was based on the work performed by the incremental

load during an iteration, normalized by the total work performed throughout the analysis run. Although

displacement and load criteria were also available options, a work criterion option set at l x 10-7 (the default value)

produced an acceptable balance between solution performance and numerical accuracy.

Adaptive Penalty Values

In addition to checking for convergence during the iteration process, the program also checked to see if any gap

elements had changed configuration (for example, from closed to open, or stick to slip) or if unacceptable

penetration had occurred at the contact points. If any gap elements changed status, the stiffness matrix was updated

to reflect these changes. If unacceptable penetration at the contact points had occurred, then the penalty values for

the gap element were automatically adjusted and the iteration process was repeated.

RESULTS AND DISCUSSION

Thermal stresses and displacements of the glove were calculated for multiple analysis cases along the transientheating profile. This section highlights some of the significant results from the finite-element analysis.

Stress Results

Table 1 shows a summary of the stress results and factors of safety of the most critical components for four of

the analysis cases studied. As these results show, all critical glove components are well below the allowable stress

with an acceptable margin of safety. The maximum stress result during the trajectory, which is highlighted, was

used to determine the component safety factor. As table 1 shows, the maximum stress in various glove components

is predicted to occur at different times during the experiment. This result underscores the need for transient

analyses; conventional analyses techniques that use static, linear assumptions to simplify the problem would

produce erroneous predictions and nonconservative design results.

Figure 8 shows typical output of the program in which the maximum shear stress at 69 sec is mapped on the

upper surface of the finite-element model. This figure shows that the area of highest stress at this time occurs at the

10
Table1.Stressresults.

Experimentdesigncase Allowable Factorof

Glovecomponent Time,sec stress safety

45 69 75 90

Upperskin

_ 55 241 2.9 Max.shearstress,MPa 82 80 _

Lowerskin

Max.shearstress,MPa 113 _!_:::::_,_!_I_ 117 89 241 2.0

Upperjoint

Max.skinshearstress,MPa 90 Iiiii_iiii_l 82 62 241 2.5

Lowerjoint

Max.skinshearstress,MPa 134 129 97 241 1.8

Leadingedge

Max.shearstress,MPa i!.... ii_iii i 104 112 118 241 2.0

Bossbearingstress,MPa 48 49 63 i_iii! 241 3.7

leadingedgein theregionsexperiencingthehighestthermalgradients. Thethinskinis relativelystress-freeaway

fromtheleadingedge,especiallyneartheaftendof theglove.Figure9 showsthemaximumshearstress,alsoat

69sec,onthelowersurfaceof themodel.Theresultsfromthisfigureshowthatthethinskinisagainrelatively

stress-freeawayfromtheleadingedgebecauseoftheuseof nonlinearcontactelements.

Deformation Results

The contact elements were critical in the modeling of the expansion and contraction of the thin skin during the

severe temperature environment expected during flight. Figure 10 shows the thermal expansion of the glove at

69 sec. (Displacements are magnified by 100 times to show detail.) This figure shows how the gaps have slipped

during the trajectory to significantly reduce the thermal stress in the thin skin. For comparison purposes, the same

model was also used in a linear finite-element solution to determine the effect of not updating the contact elements

during the application of the thermal load. Results from the linear solution showed that thermal expansion was not

permitted to this degree, and von Mises stress approaching twice the yield stress of the thin skin material

was predicted.

Figure 11 graphically shows the leading-edge distortion at the four critical times analyzed in the heating

profiles. This figure also shows why a transient structural analysis was required. The 69-sec deflection, initially

assumed as the worst-case condition for the preliminary design, appears the most benign of the four cases studied.

The center leading edge thermally distorts inward (toward the Pegasus ® wing) at 45 sec in the profile. This

phenomenon is consistent with figure 7, which shows the thick leading edge much lower in temperature than the

thin skin. At 69 sec, the stagnation heating at the leading edge has forced the leading-edge deflection through its

initial undeformed shape. At 75 sec, the thermal gradient between the leading edge and thin skin has caused a

displacement nearly equal in magnitude and opposite in sign to the displacement at 45 sec. At 90 sec, the

displacement has reached its maximum of 0.30 mm.

11
Shear stress,

MPa

120.

100.1

'_:_'_:'_"_:_;_÷_:_:i_%_!_:'_'_ SO.

40" !

20.

o.U

97004O

Figure 8: Maximum shear stress at 69 sec.

Shear stress,

MPa

120

100.

80.

i:ii.i:i• ii _o.

40.

20._

: :

oj_j

970041

Figure 9: Maximum shear stress on inner surface of lower glove skin at 69 sec.

sUpper thin skin

....... _.._--__--__ -----_._',_ £i _i_._._ _ -.._,,t,_ Leading edge

_---G ernents ___'_

Lower thin skin

970042

Figure 10: Nonlinear gap element displacements at 69 sec (magnified 100 times).

12
Leading-edge center

deflection = 0.20 mm

Undeflected

shape;

time - 0 sec _

g-edge center

deflection = 0.08 mm

Undeflected

shape;

time = 0 sec

970043

(a) Leading-edge deflection

at 45 sec.

970044

(b) Leading-edge deflection

at 69 sec.

Leading-edge center

deflection = 0.20 mm

e

center deflection

0.30 mm

Indeflected

shape; shape;

time=Osec \ time= \

\ \\0 sec \

\ \

970045 970046

(c) Leading-edge deflection (d) Leading-edge deflection

at 75 sec. • at90 sec.

Figure 11: Leading-edge thermal displacement of wing and glove.

13

CONCLUDING REMARKS

A nonlinear finite-element analysis has been performed to validate a test article design for an in-flight Mach-8

aerodynamic research experiment. A nonlinear analysis was required to represent several complex design features.

Complexity of the design was caused in large part by the use of a nonlinear restraint mechanism that attaches the

glove to the wing of the space booster. The restraint mechanism was designed to securely attach the glove to the

wing in directions normal to the wing/glove interface surface, but allow the glove to thermally expand and contract

to alleviate stresses in directions parallel to the interface surface. This design allows the glove to maintain a

geometrically stable shape, reduces the thermal stress in the glove to acceptable levels, and results in a safe and

efficient structural design. The finite-element analysis used nonlinear contact elements to model the complex

behavior of the sliding restraint mechanism. The contact elements were shown to be critical in modeling the thermal

expansion and contraction of the glove during the severe temperature environment expected in the experiment.

These elements allowed the thin skin on the glove to remain nearly stress-free away from the leading edge. Results

show that all glove components are well within the allowable stress and deformation requirements to satisfy the

objectives of the boundary-layer experiment.

REFERENCES

I Bertelrud, Arild, Kolodziej, Paul, Noffz, Greg K., and Godil, Afzal. "Plans for In-Flight Measurement of

Hypersonic Crossflow Transition on the Pegasus ® Launch Vehicle," AIAA-92-4104, Aug. 1992.

2 Noffz, Gregory K., Curry, Robert E., Haering, Edward A., Jr., and Kolodziej, Paul. Aerothermal Test Results

From the First Flight of the Pegasus Air-Launched Space Booster, NASA TM-4330, Oct. 1991.

3 Noffz, Gregory K., Moes, Timothy R., Haering, Edward A., Jr., and Kolodziej, Paul. Aerothermal Test Results

From the Second Flight of the Pegasus Booster, NASA TM-4391, Oct. 1992.

4 Curly, Robert E., Meyer, Robert R., Jr., and Budd, Gerald D. "Pegasus Hypersonic Flight Research,"

SAE Technical Paper Series 921995, Oct. 1992.

5Richards, W. Lance and Monaghan, R. C. "Analytical and Experimental Verification of a Flight Article for a

Mach-8 Boundary-Layer Experiment" Computational Methods and Testing for Engineering lntegrit3',

Computational Mechanics Publications, Southampton, United Kingdom, 1996, pp. 115-130.

6 Gong, Leslie, Richards, W. Lance, Monaghan, Richard C., and Quinn, Robert D. Preliminary Analysis for a

Mach 8 Crossflow Transition Experiment on the Pegasus ® Space Booster, NASA TM-104272, Nov. 1993.

7Godil, A. and Bertelrud, A. "Design of a Wing Shape for Study of Hypersonic Crossflow Transition in Flight,"

Computing Systems in Engineering, vol. 3, no. 1-4, Pergamon Press Ltd, Great Britain, 1992, pp. 115-130.

8 Lahey, Robert S., Miller, Mark P., and Reymond, Michael (ed). MSC/NASTRAN Reference Manual,

Version 68, vol. 1, The MacNeal-Schwendler Corporation, USA, 1994.

9 Timoshenko, Stephen P. and Gere, James M. Theory of Elastic Stability, second edition, McGraw Hill Book

Company Inc., New York, 1961.

10Lee, Sang H. (ed). MSC/NASTRAN Handbook for Nonlinear Analysis, Version 67, The MacNeal-Schwendler

Corporation, USA, 1992.

14
L

ii__

I Form Approved REPORT DOCUMENTATION PAGE OMBNo0_04-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and

maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this cotlection of information,

including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington,

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1, AGENCY USE ONLY (Leave blank) 2, REPORT DATE 3. REPORT'FYPE AND DATES COVERED

June 1997 Technical Memorandum

,4.TITLE AND SUBTITLE 5. FUNDING NUMBERS

Finite-Element Analysis of a Mach-8 Flight Test Article Using Nonlinear

Contact Elements

6. AUTHOR(S)

W. Lance Richards

7.PERFORMINGORGANIZATIONNAME(S)ANDADDRESS(ES)

NASA Dryden Flight Research Center

P.O. Box 273

Edwards, California 93523-0273

9.SPONSORING/MONITORINGAENCYNAME(S)ANDADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

WU 529-60-24

8. PERFORMING ORGANIZATION

REPORT NUMBER

H-2169

10, SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM-4796

11,SUPPLEMENTARY NOTES

Presented at the Contact Mechanics 1997 Conference, Madrid, Spain, July 1-3, 1997.

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified--Unlimited

Subject Category 39

12b.DISTRIBUTION CODE

'13. ABSTRACT (Maximum 200 words)

A flight test article, called a glove, is required for a Mach-8 boundary-layer experiment to be conducted on a

flight mission of the air-launched Pegasus ® space booster. The glove is required to provide a smooth, threedimensional, structurally stable, aerodynamic surface and includes instrumentation to determine when and

where boundary-layer transition occurs during the hypersonic flight trajectory. A restraint mechanism has

been invented to attach the glove to the wing of the space booster. The restraint mechanism securely attaches

the glove to the wing in directions normal to the wing/glove interface surface, but allows the glove to

thermally expand and contract to alleviate stresses in directions parallel to the interface surface. A finiteelement analysis has been performed using nonlinear contact elements to model the complex behavior of the

sliding restraint mechanism. This paper provides an overview of the glove design and presents details of the

analysis that were essential to demonstrate the flight worthiness of the wing-glove test article. Results show

that all glove components are well within the allowable stress and deformation requirements to satisfy the

objectives of the flight research experiment.

14. SUBJECTTERMS

Computational methods, Finite element analysis, Hypersonic flight research,

Nonlinear analysis, Structural design

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION

OF REPORT OFTHIS PAGE OF ABSTRACT

Unclassified Unclassified Unclassified

NSN 7540-01-280-5500 Available from the NASA Center for AeroSpace Information, 800 Elkridge Landing Road,

Linthicum Heights, MD 21090; (301)621-0390

15, NUMBER OF PAGES

18

16. PRICE CODE

A03

20. LIMITATION OF ABSTRACT

Unlimited

Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102