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APPLICATION OF INTERFACE TECHNOLOGY IN NONLINEAR ANALYSIS OF ASTITCHED/RFI COMPOSITE WING STUB BOX

John T. Wang* and Jonathan B. Ransom*

NASA Langley Research Center, Hampton, VA

Abstract

A recently developed interface technology wassuccessfully employed in the geometrically nonlinearanalysis of a full-scale stitched/RFI composite wing boxloaded in bending. The technology allows mismatchedfinite element models to be joined in a variationallyconsistent manner and reduces the modeling complexityby eliminating transition meshing. In the analysis, localfinite element models of nonlinearly deformed wide baysof the wing box are refined without the need fortransition meshing to the surrounding coarse mesh. TheCOMET-AR finite element code, which has the interfacetechnology capability, was used to perform the analyses.The COMET-AR analysis is compared to both aNASTRAN analysis and to experimental data. Theinterface technology solution is shown to be in goodagreement with both. The viability of interfacetechnology for coupled global/local analysis of largescale aircraft structures is demonstrated.

Introduction

The wing stub box, see Figures 1 and 2, represents theinboard portion of a high-aspect-ratio wing box for afuture civil-transport-aircraft. It was designed andmanufactured by the McDonnell Douglas AerospaceCompany under the NASA Advanced CompositesTechnology Program. The fabrication employs aninnovative stitched/RFI manufacturing process whichhas the potential for reducing manufacturing costs andproducing damage-tolerant composite primary aircraftstructures. Test results for the wing stub box1 reveal thatlarge nonlinear deformations exist in the wide baysoutboard of the upper-cover access door when the testarticle is subjected to upbending. Investigations2

following the test show that mesh refinement of theinitial (pretest) finite element model in the wide bays ofthe stub box is required to accurately account fornonlinear deformations. To connect the refined mesh_______________________________________

* Aerospace Engineer, CSB/SD, Member AIAA

Copyright ©1997 by the American Institute of Aeronautics andAstronautics, Inc. No copyright is asserted in the United Statesunder title 17, U.S. Code. The U.S. Government has a royalty-freelicense to exercise all rights under the copyright claimed herein forgovernment purposes. All rights are reserved by the copyrightowner.

the stub box is required to accurately account fornonlinear deformations. To connect the refined meshregion to the surrounding coarse mesh region,conventional transition meshing can be used. However,transition meshing usually creates triangular and/or badlydistorted quadrilateral elements which cause modelingcomplexity and deteriorate solution accuracy. Instead ofusing a transition mesh, the interface technology3,4 can beused to connect the refined mesh region directly to thecoarse region without remeshing the common boundariesof the two regions. Using this technology (see theAppendix for a brief description of the formulation), thematching of nodes at the common boundary of therefined and coarse mesh regions is not needed.Considering a design process in which critical (local)regions may need remeshing many times due to variousdesign changes, the elimination of transition meshingbetween the critical (local) regions and the noncritical(global) regions can significantly improve modelingefficiency and hence shorten the design time.

Application of the interface technology to linearstructural analyses has been investigated and itsadvantages over conventional transition meshing havebeen documented.3,4,6,7 However, the use of thistechnology on complex structures undergoing largenonlinear behavior has not been investigated. Theobjective of this paper is to apply the interfacetechnology in a geometrically nonlinear analysis of theMcDonnell Douglas wing-stub-box test article using aprocedure recently developed by Ransom.5 Finiteelement analysis results from the interface technologymodel are compared herein with NASTRAN results2 andwith experimental data.8

Wing-Stub-Box Test Article

The wing-stub-box test article consists of an inboardmetallic load-transition structure at the wing root, thecomposite wing stub box, and an outboard metallicextension structure from the composite wing stub boxout to the wing tip. A photograph of the test article inthe NASA Langley Research Center StructuralMechanics Test Laboratory is shown in Figure 1. Asshown in Figure 2, the composite wing stub box isapproximately twelve feet long and eight feet wide. Themaximum box depth at the root of the composite wingstub box is approximately 2.3 feet. The load-transition

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structure is located inboard of the composite wing stubbox (between the composite wing stub box and thevertical reaction structure at the wing-stub-box root).The wing-tip extension structure is located outboard ofthe composite wing stub box. The load-transitionstructure is mounted to a steel and concrete verticalreaction structure resulting in a near-clamped endcondition.

The composite wing stub box was fabricated byusing an innovative RFI process.9 AS4/3501-6 andIM7/3501-6 graphite-epoxy materials (Hercules, Inc.)were stitched together using Kevlar thread (E. I. DuPontde Nemours, Inc.). IM7 graphite fibers were used onlyfor the 0-degree fibers in the lower cover panel skin. Asshown in Figures 3 and 4, the composite wing stub boxconsists of ribs, spars, and upper and lower cover panels.The stringers and intercostals were stitched to the coverpanels. The stub box was subjected to a series of tests atthe NASA Langley Research Center’s StructuralMechanics Test Laboratory. In the final test, the wingstub box was loaded to failure after the infliction of a100 ft-lb impact damage at a critical location. The finalfailure load was 154 kips.

Finite Element Models and Analysis Codes

Analytical results presented in this paper wereobtained from two finite element models, the NASTRANmodel and the COMET-AR interface technology model.These models are refined versions of the initial finiteelement model shown in Figure 5. The NASTRANmodel and the interface technology model are shown inFigures 6 and 8, respectively. The primary differencesbetween the NASTRAN model and the initial model arethat; (a) the mesh density of the wide bays of the upper-cover-panel skin outboard of the access door areincreased, and (b) the blade stringers are modeled asplate elements in place of the beam elements used in theinitial model (see Figures 6 and 7). Note that the refinedregion in Figure 6 is connected to the outside coarsemesh region using a transition mesh. The process oftransition meshing, in which the skin, stiffeners and ribsneed to be remeshed, is complex (see Figures 6 and 7).In addition, many elements in the resulting transitionmesh are distorted (hence, accuracy may becompromised.) The transition mesh is eliminated in theinterface technology model shown in Figure 8. Therefined region is directly connected to the coarse regionusing interface elements4,5 as discussed in the Appendix.

Solution sequence 106 of the MSC/NASTRAN10

finite element code, Version 68, was used to perform thegeometrically nonlinear analysis with the NASTRANmodel. The COMET-AR11 code was used to perform thenonlinear analysis with the interface technology model

(see Appendix for nonlinear analysis with interfacetechnology). Quadrilateral AQ4 shell elements12 withdrilling degrees of freedom, triangular MIN3 elements13,and two-noded beam E210 elements14 were used in theCOMET-AR analysis. MSC/PATRAN15 was used tocreate the models and to postprocess the analyticalresults.

Analysis Results

Analytical results from the interface technologymodel are compared with the NASTRAN results and theexperimental data. Correlation plots of displacement andstrains are presented.

Correlation of displacements

The predicted deformed shapes of the compositestub box from the NASTRAN model and the interfacetechnology model are shown in Figures 9 and 10 for thecase of failure loading (154 kips). The relatively largeout-of-plane deformation in the upper cover paneloutboard from the access door shown in both figures iscaused by the lack of longitudinal support in this region.Analytical predictions and experimental results for thevertical displacements, measured by Direct CurrentDifferential Transformers (DCDT’s), at six locations onthe bottom surface of the stub box and at the wing tip areshown in Figures 11-13. These figures show thevariation of vertical displacements with the applied loadat the wing tip. Rigid body motions of the load-transition structure relative to the vertical reactionstructure were removed from the measured data to obtainthe results presented in these figures. Tip and bottomsurface displacement results from the NASTRANanalysis and the COMET-AR interface technologyanalysis were found to be within 1% of each other. Atthe wing tip, the difference between the experimentaland the analytical results is approximately 6 %, as shownin Figure 11. Measurements at three locations along therear spar are shown in Figure 12, and measurements atthree locations along the front spar are shown in Figure13. The correlation between the analytical results andthe experimental results at these six locations isconsidered to be good for such a large, complex testarticle.

Correlation of strains

Analytical and experimental axial strains for straingages 17, 20, and 84 are plotted in Figures 14-16. Theaxial direction is parallel to the rear spar of the wing stubbox. These strain gages are located sufficiently far fromthe access-door cutout and the nonlinearly deformedregion to be considered as far field results. In Figures14-16 and 19-22, the hatched region in the sketch of thewing stub box is the mesh refinement region. The

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correlation plots in Figures 14-16 indicate that the farfield strains predicted by the analysis are reasonablyaccurate.

Circumferential strain results on the external surfaceof the upper-cover-panel skin at the edge of the access-door cutout, measured by strain gages 78 and 79, areshown in Figures 17 and 18. Analytical andexperimental results for these external strain gagesindicate approximately linear behavior. Results from theinterface technology model are in good agreement withNASTRAN predictions and experimental data.

Predicted and measured axial strain results for thefirst and second bays outboard of the access-door cutoutof the upper cover panel are shown in Figures 19-21.The first and second bays are 18 inches wide, and hadnonlinear deformations due to the lack of longitudinalstiffeners. Results for; (a) strain gages 67 and 68 on theupper-cover-panel skin in the first bay, immediatelyoutboard from the access door are shown in Figure 19,(b) strain gages 63 and 64 on the upper-cover-panel skinin the second bay outboard of the access door are shownin Figure 20, and (c) strain gages 22-24 at the edge ofthis bay are shown in Figure 21. In general, goodcorrelation was obtained between experimental andanalytical results in the skin and on the stiffeners for thefirst and second bays outboard of the access door, asshown in Figures 19-21. This indicates the interfacetechnology model and the NASTRAN model canreliably predict strains in these two nonlinearly deformedbays. Predicted and measured strain results for straingages 49 and 50, located at the center of the third baybays outboard of the access-door cutout on adiscontinuous stiffener (see Figure 3), are also shown inFigure 22. The correlation between experimental andanalytical strain results shown is acceptable.

Concluding Remarks

Interface technology is successfully employed in thegeometrically nonlinear analysis of a full-scalestitched/RFI composite wing stub box loaded in bending.In the interface technology model, local nonlinearlydeformed wide bays are refined and interface elementsare used in connecting the refined region to thesurrounding coarse mesh region. The interfacetechnology model is analyzed using the COMET-ARfinite element code. Results from the interfacetechnology model are compared with results from aNASTRAN model and experimental data. The interfacetechnology model results are in good agreement withboth the NASTRAN results and the experimental data.The advantages of using interface technology inconnecting a refined local region to a unrefined globalregion are evident when comparing the interfacetechnology model with the NASTRAN model.

Transition meshing as used in the NASTRAN model andthe possible errors arising from the distorted elementsused in the transition meshing region are eliminated.This paper clearly demonstrates that the use of interfacetechnology can substantially reduce the modeling effortrequired to couple local refined finite element models tocoarse global models in the analysis of large scaleaircraft structures.

Acknowledgement

The authors wish to acknowledge the PATRANmodeling and COMET-AR support provided by BrianMason and Christine Lotts of Analytical Services andMaterials, Inc.

References

1. Hinrichs, S. C., Jegley, D. C., and Wang, J. T.,“Structural Analysis and Test of a StitchedComposite Wing Box,” Presented in the 6thNASA/DoD Advanced Composite TechnologyConference, Anaheim, CA, August 7-11, 1995.

2. Wang, J. T., Jegley, D. C., Bush, H. G., and Hinrichs,S. C., Correlation of Structural Analysis and TestResults for the McDonnell Douglas Stitched/RFIAll-Composite Wing Stub Box, NASA TM-110267,July 1996.

3. Aminpour, M. A., Ransom, J. B., and McCleary, S.L., “Coupled Analysis of Independently ModeledFinite Element Subdomains,” 33rd AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics, and Materials Conference, AIAA-92-2235-CP, 1992.

4. Ransom, J. B., McCleary S. L., and Aminpour, M.A., “A New Interface Element for ConnectingIndependently modeled Substructures,” 34thAIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics, and Materials Conference , AIAA-93-1503-CP, 1993.

5. Ransom, J. B., “Interface Technology forGeometrically Nonlinear Analysis of MultipleConnected Subdomains,” to be published as AIAA-97-1298-CP, 1997.

6. Aminpour, M. A., Krishnamurthy T., McClearly S.L., and Baddourah, M. A., “Application of NewInterface Element to the Global/Local Analysis of aBoeing Composite Crown Panel,” Proceedings ofthe Fourth NASA/DoD Advanced CompositesTechnology Conference , NASA CP 3229, pp. 773-788, 1993.

7. Housner, J. M., Aminpour, M. A., Davila, C. G.,Schiermeier, J. E., Stroud, W. J., Ransom, J. B.,Gillian, R. E., “An Interface Element for

4

Global/Local and Substructuring Analysis,”Presented at MSC World Users’ Conference, LosAngles, CA, May 8-12, 1995.

8. Jegley, D. C. and Bush, H. G., Test Documentationand Results of the Structural Tests on the All-Composite McDonnell Douglas Wing Stub Box,NASA TM 110204, April 1996.

9. Markus, A. M., Thrash, P., and Grossheim, B. G.,“Manufacturing Development and Requirements forStitched/RTM Wing Structure,” Proceedings of theFourth NASA/DoD Advanced CompositesTechnology Conference , NASA CP 3229, pp. 503-523, 1993.

10. MSC/NASTRAN Quick Reference Guide, Version68, edited by Reymond, M. and Miller M., TheMacNeal-Schwendler Corporation, February 1994.

11. Stanley, G. M., Hurbut, B., Levit, I., Stehlin, B.,Loden, W., and Swenson, L., COMET-AR AdaptiveRefinement Manual, LMSC Report #F318482, 1991

12. Aminpour, M. A., “An Assumed-Stress Hybrid 4-Node Shell Element with Drilling Degrees ofFreedom,’ International Journal for NumericalMethods in Engineering, Vol. 33, pp. 19-38, 1992.

13. Tessler, A., “A Co-anisoparametric three-nodeshallow shell element,” Computer Methods inApplied Mechanics and Engineering, Vol. 78, pp.89-103, 1990.

14. Nour-Omid, S., Brogan F. A., Stanley, G. M., TheComputational Structural Mechanics TestbedStructural Element Processor ES6: STAGS BeamElement, NASA CR-4359, May 1991.

15. Anon., MSC/PATRAN V5.0 Release Notes, TheMacNeal-Schwendler Corporation Publication No.903057, March 1996.

16. Rankin, C. C., and Brogan, F. A.: “An Element-Independent Corotational Procedure for theTreatment of Large Rotations.” In Collapse Analysisof Structures, edited by , L. H. Sobel and K.Thomas, ASME, New York, pp. 85-100, 1984.

17. Riks, E., “On the Numerical Solution of SnappingProblems in the Theory of Stability,” August 1970,Stanford University, SUDAAR Report No. 401.Also available as AFOSR Report No. 70-2258TR.

18. Wempner, G. A., “Discrete Approximations Relatedto Nonlinear Theories of Solids,” InternationalJournal of Solids and Structures, Vol. 7, pp. 1581-1589, 1971.

19. Crisfield, M. A., Non-linear Finite Element Analysisof Solids and Structures, Vol. 1, John Wiley &Sons, ISBN 0 471 92956 5(v.1), 1991.

Appendix - Interface Technology

Recently, a method for connecting finite elementmodels without the use of transition modeling has beendeveloped3.4. This method, called interface technology, isan improved technique for connecting multiple dissimilarmeshed subdomains or substructures to form a singlefinite element model. It is based on employing interfaceelements that make use of a hybrid variationalformulation to provide for compatibility betweenindependently modeled subdomains.

The interface element for linear and nonlinearanalyses was developed in detail in references 4 and 5,respectively. The formulation for nonlinear analysis andthe associated nonlinear solution strategy are brieflydescribed, herein. It allows the independent modeling ofdifferent substructures or components without concernfor one-to-one nodal coincidence between the finiteelement models. Moreover, it acts as “mathematicalglue” between independent finite element models withdifferent mesh densities and nodal layouts. It is based onan analytical variational procedure and avoids the use oftransition meshes.

Interface Element Formulation

ΓI1 Γ I3Γ I2

ΓI

Interface elementand pseudo-nodes

Ω3

Finite elementnodes

Ω2

Ω1

qsv

Figure A-1. Typical Interface Element Definition.

Consider the three independently discretizedsubstructures shown in Figure A-1. The interfaceelement is discretized with a mesh of evenly-spacedpseudo-nodes (open circles in the figure) which need notbe coincident with any of the interface nodes (filledcircles in the figure) of any of the substructures. Thehybrid variational formulation3,4 employs an integralform for the compatibility between the interface lineelement and the finite element substructures. The dis-placement vector, v, of the interface element is assumedto be independent of the displacement vectors, u, of thesubstructures to which it is attached. The weak form ofthe principle of virtual work leads to a modified virtualwork expression which may be written as

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δ δ δW W Wk

k

N

ci

Nss

i

I

= + == =∑ ∑

1 10

(1)

where Nss is the total number of substructures and NI isthe total number of interface elements.

For the kth substructure,

δ δ δWk q K q q fkT

T k k kT

k= ( ) − (2)

and

f N F N Sk kT

k k kT

k kSkk

= + ( )( )∫∫ d dΩ

Ωφ σ

σ

(3)

where (KT)k is the tangent stiffness matrix, Nk are thefinite element shape functions, δqk are the variations ofgeneralized displacements, qk , Fk are the external appliedforces, and φk are the applied tractions on the subdomain

boundary, Skσ( ) .

The compatibility between interface element i andits connecting substructures is enforced through the useof the constraint integral

δ

δλ

δ λ δ λW

v u

uijT

ij ij viT

ij ijij

c

ijT

ij

i ij ij

ij

j

n i

i

ss

=

−( ) −

+ ∫∫

∫∑=

ΓΓ

Γ ΓΓΓ

d

d d1

( )

(4)

where nss (i) is the number of substructures connected tothe interface element i, uij are the displacements at theboundary of substructure j connected to interfaceelement i, and vi are the displacements of the interfaceelement i, and λij are the Lagrange multipliers.

The independent approximations for the finiteelement displacements, interface displacements, andinterface tractions are, respectively

u N q

v T q

R

ij ij ij

i i s

ij ij ij

i

==

=

λ α

(5)

where qij and qsiare the nodal degrees of freedom

corresponding to uij and vi, and α ij are the unknown

coefficients of the Lagrange multipliers, λij. The matrixNij is the matrix of finite element shape functions onsubstructure j along interface i, Ti is formed as a resultof passing a cubic spline through the evenly-spacedpseudo-nodes, Rij is formed as a result of using constantfunctions for linear finite elements and linear functionsfor quadratic finite elements.

The interface matrices may be defined as

M N R G T Rij ijT

ij ij ij iT

ij ij

ij ij

= − =∫ ∫ d and dΓ ΓΓ Γ

(6)

Thus, for arbitrary qk on Ωk, arbitrary qsi on ΓI and

arbitrary α ij on ΓI, the interface element system ofequations is given as

K M

G

M G

q

q

fT I

I

IT

IT

s

00 0

000

=

α

(7)

where KT , q and f are the assembled tangent stiffnessmatrix, displacement vector and force vector for theentire structure, and MI, GI, qs and α are the assembledMij, Gij, qsi

, and αij for all interface elements.

Nonlinear Solution Strategy

The nonlinear solution procedure employed herein isbased on an automatic load incremental control and theNewton/Raphson iteration method. The so-calledmodified Newton/Raphson method, which forms andfactors the tangent stiffness matrix periodically ratherthan at every nonlinear iteration, has been used in thenonlinear analysis of the wing stub box. A corotationalformulation16 which identifies the reference state as thecurrent deformed configuration is used to describe themotion. This formulation separates the rigid bodymotion from the strain-producing motion thus allowingfor either linear or nonlinear strain-displacementrelations at the finite element level. Strain-producingdeformations are computed based on the originalconfiguration within the local corotated frame. An arc-length control strategy17,18,19 is used for automatic loadincremental control to obtain the load-deflectionresponse and to handle limit points. This nonlinearsolution strategy has been adapted to incorporate theinterface element5 and was implemented within ageneral-purpose, finite element code COMET/AR.11

Wing-root load transitionstructure

Hydraulicjack

Compositewing stub box

Vertical reactionstructure

Figure 1. Wing-stub-box test article attached to the vertical reaction structure.

Wing-tip extension structure

Failure line

Impact site

Metallic load transition structure

Composite wingstub box Metallic wing-tip

extension structure

8 ft

12 ft

12 ft

8 ft

Outboard

Aft

Up

Front spar

Rear spar

Figure 2. Dimensions of the wing-stub box test article.

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20 22,23,24

79

78

63,64 49,50

Access door cutout

67,68

1784

Figure 3. Upper cover and strain gage locations (gage numbers are shown on the figure).

Figure 4. Interior of the composite stub box.

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Figure 5. Finite element mesh of the initial model.

Mesh refinement region

Figure 6. Finite element mesh of the the NASTRAN model.

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Coupling refined element region with coarse element region using interface technology

Figure 8. Finite element mesh of the interface element model.

Figure 7. Mesh refinement for the skin, blade stiffeners, and intercoastals in the NASTRAN model.

Stringer webs connnect to skin

30 in

Ribs

Skin

Stringer webs andintercostal webs

Intercostalsconnnect to ribs

Transit ion Mesh

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Figure 10. Deformed shape of the interface element model at a load of 154 kips.

Figure 9. Deformed shape of the NASTRAN model at a load of 154 kips.

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Vertical displacement, in.

TipLoad,

kips

Figure 12. Vertical displacements for DCDTs 1 to 3.

Vertical displacement, in.Figure 11. Stub box test article tip displacement.

NASTRANInterface Technology

Test

xx

x

Tip load

1Rear spar 3

2

DCDT 1DCDT 2DCDT 3

5.04.03.02.01.00.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

x

Tip load

TipLoad,

kips

20.018.016.014.012.010.08.06.04.02.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0


Test

0.0

11

Tip load

Frontspar

6 54

xx

x

Figure 13. Vertical displacements for DCDTs 4 to 6.

Figure 14. Correlation of far field strains for strain gage 17 on the top surface of the upper cover panel.

Gage 17

X

1000.00.0-1000.0-2000.0-3000.0-4000.0-5000.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

Interface TechnologyNASTRANTest

Strain, microinches/inch

Load,

kips17

Vertical displacement, in.

TipLoad,

kips

DCDT 6DCDT 5DCDT 4

5.04.03.02.01.00.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0


Test

12


Gage 20

X



1000.00.0-1000.0-2000.0-3000.0-4000.0-5000.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0



Load,

kips

84 X

Gage 84

1000.00.0-1000.0-2000.0-3000.0-4000.0-5000.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0


Load,

kips20

13

Figure 17. Correlation of strains for strain gage 78.

2000.00-2000.0-4000.0-6000.0-8000.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

Interface Technology

TestNASTRAN


Load,kips

x

Gage 78

2000.00.0-2000.0-4000.0-6000.0-8000.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0


Strain, microstrains/inch

Load,kips

Gage 79

x

Figure 18. Correlation of strains for Gages 79.

14

X

Gages 67/68

1000.00.0-1000.0-2000.0-3000.0-4000.0-5000.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0



Load,kips

67

68

Gage 67 Gage 68

Figure 19. Correlation of strains for strain gages 67 and 68.

Figure 20. Correlation of strains for strain gages 63 and 64 on the upper cover panel skin.

X

Gages 63/64

2000.00.0-2000.0-4000.0-6000.0-8000.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

200.0


TestNASTRAN

Load,

kips

64

63

15


Figure 22. Correlation of strains for strain gages 49 and 50 on the runout stringer.

50

X

Gages 49/50

1000.00.0-1000.0-2000.0-3000.0-4000.0-5000.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0


NASTRANTest


Load,kips

49

Gage 50 Gage 49

Gages 22/23-24

X

22

2324

6000.04000.02000.00.0-2000.0-4000.0-6000.00.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0



Load,kips

Gage 22Gage 23 - Open symbolsGage 24 - Solid symbols

Figure 21. Correlation of strains for strain gages 22 , 23, and 24 at the aft edge of the highly nonlinearly deformed region.

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