Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc.

A97-31305 AIAA-97-1507

UTILIZING A GENERAL PURPOSE FINITE ELEMENT CODE FOR AEROELASTICANALYSIS OF A RAM-AIR INFLATED FABRIC WING

Vipul B. PatelUnited Technologies Corporation / USBI

Kennedy Space Center, Florida

ABSTRACT

To this point finite element analysis techniques havenot been widely utilized for the structural analysis offabric wings. Although special codes like CANO andCANO3 are available for such analysis, they aremostly limited to round parachutes. Currently, nospecial code exists that can be successfully utilizedfor the aeroelastic structural analysis of gliding para-chutes. Therefore, an attempt is made here to uti-lize a general purpose finite element code in con-junction with an aerodynamic code to predict thebehavior of a ram-air inflated fabric wing under asteady aerodynamic loading. The interaction be-tween both the aerodynamic and structural problemshas been solved using a vortex-lattice simulation ofthe steady potential flow and the shape representedby a finite element model of the wing. The proce-dure is iterative in nature. The aerodynamic code isutilized first to generate the required pressure load-ing on the undeformed wing. A nonlinear finite ele-ment analysis is then performed and the resultingdeformed shape of the wing is utilized to revise theoriginal pressure loading. The wing is then reana-lyzed using the revised pressures and the resultingdeflected shape is once again utilized to generate anew pressure loading. This iterative procedure iscontinued until no appreciable change in the result-ing pressure loading is realized. A Liquid RocketBooster Recovery Wing is analyzed using this pro-cedure and the result is presented.

INTRODUCTION

Aeroelastic analysis of ram-air inflated wings hasbecome an interesting subject among engineers andresearchers involved in design and analysis of glid-ing parachutes. This is due to the fact that theaeroelastic analysis of ram-air inflated wings involveseveral basic nonlinearities in the structural side ofthe problem. One obvious nonlinearity is due to the

Copyright © 1997 by USBI Co. Published bythe American Institute of Aeronautics andAstronautics, Inc. with permission.

fact that these wings are basically fabric membranespossessing little or no bending stiffness. Therefore,any pressure load applied normal to the surface hasto be resisted by in-plane tensile forces producedin the membranes. Also, fabric membranes do notsupport any in-plane compressive forces. Anothernonlinearity is introduced due to the large displace-ments produced by the higher flexibility present inthe fabric structure. The stretch in the membranescause stress stiffening, yet another source ofnonlinearity. Finally, the analyst may be forced todeal with nonlinearities based on material proper-ties of the fabric.

The interaction between the nonlinear structuralproblem and the linear aerodynamic problem hasto be solved to predict the behavior of the wing un-der aerodynamic loading. In the past, methods andtheories have been presented to solve theaeroelastic problem, sometimes without taking theelasticity of the wing into consideration.Chatzikonstantinou1 developed a theory of elasticflexible wings providing the theoretical basis for acombined finite element/integral-equation method,making it possible to solve the integrodifferentialequation descriptive of three dimensional flow pasta flexible elastic membrane wing. In this methodChatzikonstantinou used a three-dimensional mem-brane element and solved the nonlinear structuralproblem for every linear aerodynamic problem.

Elements similar to the one used byChatzikonstantinou are readily available in manypublic domain general purpose finite element codes.A few of these codes additionally offer large deflec-tions, tension only, and stress stiffening options veryimportant for the nonlinear analysis. Moreover, theyprovide the proof of verification for the elements andnumerical solvers used in the analysis. If an appro-priate aerodynamic routine can be used in conjunc-tion with one of these finite element codes, then theaeroelastic problem can be solved without goinginto extensive formulation and verification of theproblem. The only precaution then required is tomake sure that the data between the two are trans-

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ferred back and forth in a systematic and error-freemanner.

As shown in Figure 1, the procedure presented tiesa well-known finite element code to a text book styleaerodynamic routine with the aid of several userwritten data management routines. An example ispresented where both problems, the aerodynamicas well as the structural, were solved in a loop fash-ion leading to a converged solution.

The problem takes into consideration the directionalnature of the fabric, multiple fabrics, pretension, andmetallic components like tubes and struts.

ANALYSIS PROCEDURE

Since the method uses a general purpose finite ele-ment code and a user developed or readily avail-able aerodynamic routine, a means of exchangingdata between these two is required. Also, the ex-change of data is required to occur with no errors orloss of information and in a format which is mutuallycompatible. This could be easily accomplished bygenerating a set of small FORTRAN routines capableof translating data in specific formats with the abilityto perform the required computations. The routinesare executed in a step by step fashion back and forthbetween the finite element structural problem andthe linear aerodynamic problem. For a large flex-ible wing requiring many load iterations for conver-gence, this could become a very cumbersome pro-cess. However, the procedure offers considerablebookkeeping and traceability very essential for suchtime consuming and costly analysis. Also, themethod provides an ability to examine the deflec-tions and the resulting changes in the pressure atevery load iteration. This can avoid any skepticismregarding the validity of the process which wouldotherwise exist had the transfer and manipulation ofdata been kept transparent to the analyst.

The typical problem flow is shown in Figure 2. Thefigure depicts a block diagram which starts with thefinite element model of the undeflected orundeformed shape and ends with final convergedstresses and deflections. The blocks representingthe intermediate deformed shapes are a result ofthe combined finite element nonlinear and the linearaerodynamic analysis. The aerodynamic code gen-erates the initial pressures and the revised pressureswith the aid of the user written FORTRAN routines.

EXAMPLE

The above procedure was applied in the preliminaryaeroelastic analysis of a ram-air inflated fabric wing.The work was carried out as part of a grant awardedby Marshall Space Flight Center (MSFC) of NationalAeronautics and Space Foundation (NASA) in Hunts-ville, Alabama.

Background

USBI was contracted by NASA to conduct a studyon the recovery of the proposed Space Shuttle Liq-uid Rocket Boosters (LRBs). Each LRB would havea deployable wing packaged alongside the boosterbody. Once deployed, the wing would begin to liftand rotate up to a gliding angle of attack The wingedLRB would thus be allowed to free glide to reach itsdesired landing destination.

Description of the Wing

The deployable wing, as shown in Figure 3, con-sists of a double surface fabric sail totally enclosingan internal rigid structure. The sail is made up ofupper and lower surface membrane joined to eachother around the perimeter. Vertical fabric ribs trans-verse between upper and lower surfaces on the in-terior. These ribs are cut to an airfoil shape to givethe wing section it's lifting profile. A ram-air inflationopening is located at the nose stagnation point whichprovides internal sail pressure upon forward veloc-ity. The rigid frame consists of two tubular leadingedge structures, two tubular cross tube or spreaderstructures, and a tubular keel structure. The crosstubes are pivotably mounted to the leading edge atone end and a keel slider sleeve at the other. De-ployment is accomplished when the drogue para-chute force is transferred to this keel slider whichforces rearward movement, thus swinging the lead-ing edges outward. Based on the wind tunnel re-sults, critical dimensions of the wing were chosenas follows:

Span = 235 feetKeel length = 79.5 feetArea =11,714 square feetSwept angle = 37.5 degreesMaximum foil thickness = 9.3 feetDihedral angle = 5 degrees

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Materials

The double surface sail and the ribs are fabric mem-branes. The upper surface sail is cut from a 0.75ounce per square yard nylon cloth while the lowersurface sail and the ribs are cut from a 6 ounces persquare yard Dacron®, cloth. Samples from bothcloths were cut and tested to determine the mechani-cal properties required for the analysis. The aver-age properties are shown in Table 1.

Using Equation (1), and reference area of 11,714sq. feet and air density of .00238 slug per sq. foot,the flight velocity was found to be 117.2 feet per sec-ond.

The flight velocity was fed to the aerodynamic rou-tine along with other geometric parameters to gen-erate element pressures for the 1 .Og loading condi-tion.

Table 1. Average mechanical properties of sail cloths

Breaking StrengthFill Direction

Warp Direction

Linear Modulus of ElasticityFill Direction

Warp Direction

Nylon(pounds/inch)

29.052.0

150.0254.0

Dacron®(pounds/inch)

235.0214.0

1575.01080.0

The rigid frame was assumed to be made of ahigh strength aluminum alloy.

Applied loads

The flexible wing was analyzed for a 1 .Og loadingcondition. Equating the inertia forces to the aerody-namic forces in a steady gliding path, the flight ve-locity can be determined as2:

V = {(2/p) (W/S) (C 2 + C 2) -°5} °:L D

0)

Where C = lift coefficientL

C = drag coefficientD

p = air mass density

W = total weight of the system

S = wing reference area

The total weight of the wing system (wing plus pay-load) was estimated to be 135,000 pounds. The liftand drag coefficients obtained from wind tunnel testdata of a similar wing were taken to be 0.7 and .0875,respectively for an angle of attack of 9.25 degrees.

Finite element model

A finite element model (FEM) of one half section(symmetric section) of the wing is shown in Figure4. The model was created using PATRAN3 and thenconverted into ANSYS4 input data. Triangular areaelements were used for the fabric cloth to satisfy thelarge deflection requirement of the code. The rigidframe was modeled using line elements. The com-pleted model consisted of 1,392 nodes and 2,769elements.

Since the FEM node coordinates were used by theaerodynamic routine, a modeling and numberingscheme was devised so that the transferred FEMdata can be readily used. The entire model wasdivided into nodal lines where each nodal line rep-resented the air foil shape of the wing. The first nodenumber starts at the root chord trailing edge and in-creases in an ascending order from the lower sur-face to the upper surface in the clockwise direction.A line joining the first node and the last node definesthe air foil shape. The numbering order then movesto the next chord in the spanwise direction. The tipof the wing was given a finite width to maintain theairfoil shape for the entire span of the wing.

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Symmetric boundary conditions were imposed onthe root chord. The junction of the leading edge sparand the cross tube was supported in the vertical di-rection to simulate the cable support.

Generation of aerodynamic loading

The aerodynamic routine generated pressure coef-ficients for each control point and subsequently foreach grid point of the FEM. Geometric coordinates,flight velocity, angle of attack, and air density wereinput to the aerodynamic routine. The routine, ob-tained from Reference 5, is based on the vortex-panel method applied to an airfoil of arbitrary thick-ness and camber. The finite wing approximationsas well as compressibility, viscous, and interferenceeffects are not included in the problem formulation.Following is a brief content of the problem formula-tion. The reader is advised to consult Chapter 5 ofReference 5 for complete description on the sub-ject.

The vortex-panel method introduced in the problemhas the feature that the circulation density on eachpanel varies linearly from one corner to the otherand is continuous across the corner, as shown inFigure 5. The Kutta condition is easily incorporatedin this formulation, and the numerical computationis stable unless a large number of panels is chosenon an airfoil with cusped trailing edge. The panelsare assumed planer and are named in the clock-wise direction, starting from the trailing edge. Thecondition that the airfoil be a streamline is met ap-proximately by applying the condition of zero nor-mal velocity component at "control points", speci-fied as the midpoints of the panels.

In the presence of a uniform flow VM at an angle ofattack a and m vortex panels, the velocity potentialat the ilh control point (x,,^) is:

is a distance s. measured from the leading edge ofthe panel. The integration is performed along theentire panel from (X.,Y) to (Xj+1,Yj+1).

Satisfying the boundary condition, and carrying outthe involved differentiation and integration, the un-known circulation densities can be determined. Fromthis data the tangential component of the dimension-less velocity at each panel surface is determined.The local pressure coefficient at the ilh control pointis then given by:

Several FORTRAN utility routines were utilized toconvert the control point pressure coefficients to gridpoint pressures and subsequently to the elementpressures that are required for the finite elementanalysis.

Due to the absence of finite wing approximations,the total lift produced by the routine will be higherthan the actual. This is because no spanwise varia-tion of pressure is present as opposed to elliptical orarbitrary distribution present in reality. In order toovercome this problem, the angle of attack and theflight velocity responsible for the lift were adjusted toobtain the correct lift force. The stagnation pressureinside the wing, however, was calculated based onthe true flight velocity.

For the 1.0g loading condition, this resulted in anadjusted angle of attack of 8.0 degrees and an ad-justed velocity of 85.5 feet per second for a total liftof approximately 151 ,000 pounds. The lift value wasfound about 12 percent higher than the required forthe 1 .Og condition. For preliminary design analysis,this was considered acceptable.

Aeroelastic analysis

m= Vjxcos a + y.sin a) - £ J (y(s.)/2n:)

tan-1 dS

Where circulation density is:

Y(SJ) = Y, + (Yi+1 - YJ)

As shown in Figure 5,of an arbitrary point on the jth panel of length S , which

represent coordinates

The aeroelastic analysis was performed accordingto the block diagram shown in. Figure 2. Elementpressures based on the undeformed shape of thewing were used for the first load step of the nonlin-ear finite element analysis. The ANSYS finite ele-ment code was utilized for the nonlinear analysis.Large deflection, stress stiffening, and tension only(for fabric) options were chosen to correctly repre-sent the elastic problem. The Newton-Raphsonmethod was chosen for the iterative process of solv-ing the nonlinear equations.

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The deflections produced in the converged solutionof the first load step analysis were used by the aero-dynamic routine to update the original element pres-sures. The nonlinear analysis was restarted and theupdated pressures were input as the second loadstep. The cycle was repeated once more after whichthe change in the deflections did not cause any ap-preciable change in the pressure values. No furtheranalysis was then required.

The results of the analysis can be seen in Figures 6through 11. Figure 6 shows the final deflected shapeof the wing. Stress contours for upper and lowersurfaces are shown in Figures 7 and 8, respectively.Maximum stresses, normal X or normal Y, are alsoindicated on these figures. Figures 9 through 11show plots of internal forces verses nodes of theleading edge spar. Nodes 3001 and 3028 are lo-cated at the leading edge root and tip of the wing,respectively.

CONCLUSIONS

It has been shown that aeroelastic analysis of glid-ing parachutes is possible using general purposefinite element codes and aerodynamic routines. Thesuggested procedure is not limited to ANSYS or theaerodynamic routine used here. In fact, the resultsof the above example can be improved if a betteraerodynamic routine can be utilized. Advantages ofusing powerful finite element codes for this type ofanalysis are many. For one, such codes possespowerful pre and post processing techniques veryuseful for detailed modeling and evaluation of endresults. Additionally, they allow the usage of direc-tional as well as nonlinear material properties thatare essential for fabric analysis. Choice of the non-linear equation solver and methods for achievingfaster convergence are also available to minimizethe total computational time. Restart capability andavailability of the updated stiffness matrix make itpossible to extend the static problem into an eigen-value or a dynamic problem.

However, the analyst should also be prepared forpossible difficulties. The problem may buckle andbecome unstable if the applied load increment is toobig for the structure to develop enough stiffness tospring back and resist the applied load. Conver-gence may not be achieved because a few elementsmay tend to oscillate above and below the conver-gence value. Even for a converged solution the re-

sults may turn out to be bad because of inadequatemesh transition regions. In such cases, a trial anderror approach, although costly and time consum-ing, may be required for a successful analysis. How-ever, with the continuing development of better ele-ments and solution techniques, such problems maydisappear in future.

REFERENCES

1. Thomas Chatzikonstantinou & E. Puskas, "Numerical Analysis of Three-Dimensional NonRigid Wings," AIAA-89-0907, April 1989.

2. T. W. Knacke," Parachute Recovery SystemsDesign Manual," First Edition, Para Publishing,Santa Barbara, California, 1992.

3. PATRAN Plus User Manual," Vols. I & II, PDAEngineering, Costa Mesa, California.

4. Gabriel J. Desalvo and Robert W. German,"ANSYS User's Manual," Vols. I & II, SwansonAnalysis Systems, Inc., Houston, Pennsylvania.

5. Arnold M. Kuethe and Chuen-Yen Chow, "Foundations of Aerodynamics," Forth Edition, JohnWiley &Sons, Inc., 1986.

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AERODYNAMIC FINITE ELEMENTROUTINE CODE

y k >I —— >" USER WRITTEN ————

pnnrnAM nni ITIMPP ^

\

Figure 1. Interaction between aerodynamic routine and finite element code

UNDEFORMEDSHAPE

INITIAL PRESSURES FIRST LOAD STEPANALYSIS

FIRST DEFORMEDSHAPE

^ REVISEDPRESSURES

^ SECOND LOADSTEP ANALYSIS

FINAL DEFORMEDSHAPE

FINAL REVISEDPRESSURES

FINAL LOAD STEPANALYSIS

CONVERGEDDEFLECTIONS ANDSTRESSES

Figure 2. Typical problem flow of wing aeroelastic analysis

Ram-Mr Inlet

Fa tele Hb*

Figure 3. Proposed design of the LRB recovery wing

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Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc.

Figure 4. Finite element model of the symmetric section

( X j -H, YJ-H) I <*sj

Panel J

Figure 5. Aerodynamic model of the wing airfoil

Figure 6. Final deflected shape of the wing section

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Y element

X element

Max. stress- 33 Ibs/inch

Figure 7. Stress contours - Normal X stress on upper surface

Y element

X element

Max. stress- 203 Ibs/inch

Figure 8. Stress contours - Normal Y stress on lower surface

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4OOOO

3OOOO -

20000 -

1OOOO -

- 1OOOO -

-2OOOO3OO 1 3 O 1 1 3O21

NODE NUMBERS3O28

Figure 9. Axial and shear forces in leading edge spar

2.0Oe-e

CO—Jzz;

1 .OOe--6 -

O.OOe~O

-co—ni—en—o>—CD—CD—CD—CD-

300 t 3O 1 I

NODE NUMBERS302 1 3O2S

Figure 10. Torque in leading edge spar

6.00e*e

-6.00e--e3OO 1 3O 1 1

NODE NUMBERS302 I 3O28

Figure 11. Moments in leading edge spar

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