NASA Technical Memorandum 108519

Verification of Orthogrid FiniteElement Modeling Techniques

B.E. Steeve

October 1996

https://ntrs.nasa.gov/search.jsp?R=19970001271 2020-03-01T14:59:01+00:00Z

NASA Technical Memorandum 108519

Verification of Orthogrid FiniteElement Modeling TechniquesB.E. Steeve

Marshall Space Flight Center • MSFC, Alabama

National Aeronautics and Space AdministrationMarshall Space Flight Center ° MSFC, Alabama 35812

October 1996

TABLE OF CONTENTS

Page

INTRODUCTION .............................................................................................. 1

ORTHOGRID ................................................................................................... 1

FINITE ELEMENT MODELING ............................................................................ 2

Beam Model ............................................................................................ 2Shell and Beam Model ................................................................................ 3Shell Model ............................................................................................. 4

VERIFICATION ............................................................................................... 5

Test Article ............................................................................................. 5Loads .................................................................................................... 5Instrumentation ........................................................................................ 8

RESULTS ....................................................................................................... 8

Stiffness ................................................................................................ 9Strains ................................................................................................... 9

CONCLUSIONS ............................................................................................... 9

o,o

Ul

LIST OF ILLUSTRATIONS

Figure

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

Title Page

I-beam orthogrid structure .......................................................................... 1

Beam element orthogrid model .................................................................... 2

I-beam cross section ................................................................................ 2

Beam and shell element orthogrid model ......................................................... 3

Beam and shell element representation of I-beam section ...................................... 3

Shell element orthogrid model ..................................................................... 4

Shell element orthogrid model showing taper of web elements at each orthogrid node ..... 4

Shell element representation of I-beam section .................................................. 5

Orthogrid test article ................................................................................. 6

Typical strain gauge installation on interior members of orthogrid test article ............... 6

Strain gauge installation on side of orthogrid test article ........................................ 7

Normal load configuration ......................................................................... 7

Side load configuration ............................................................................. 8

Locations of strain gauge and displacement instrumentation ................................... 8

Normal load configuration deflection ............................................................. 10

Side load configuration deflection ................................................................. 10

Normal load configuration I-beam flange strain on members running across width ........ 11

Normal load configuration I-beam flange strain on members running along length ......... 11

Normal load configuration web strain on members running across width ................... 12

Normal load configuration web strain on members running along length .................... 12

Normal load configuration I-beam flange strain on members running across width ........ 13

Normal load configuration I-beam flange strain on members running along length ......... 13

Normal load configuration web strain on members running across width ................... 14

Normal load configuration web strain on members running along length .................... 14

iv

TECHNICAL MEMORANDUM

VERIFICATION OF ORTHOGRID FINITE ELEMENT MODELING TECHNIQUES

INTRODUCTION

Orthogrid structures are often used as a secondary mounting structure in aerospace designs where aregular to semiregular rectangular hole pattern is desired. Orthogrids are a strong, stiff, and relatively light-weight design solution. To maximize the stiffness while keeping the weight of an orthogrid structure low,I-beam sections are commonly used.

The stress analysis of such a structure is often performed using the finite element method. Whencreating a finite element model of an orthogrid structure, there are several possible techniques of varyingcomplexity that can be employed. These range from a simple beam model to a full-blown solid elementmodel. The choice of what technique to use depends on the availability of manpower, computer resources,and the desired level of results, both in accuracy and detail. This report looks at three modeling optionsand compares the results to experimental data.

ORTHOGRID

An orthogrid structure with I-beam sections is shown in figure 1. The structure is essentially twoseries of I-beams running orthogonal to each other and intersecting at nodes. Components are usuallymounted to the orthogrid at these nodes.

/-- Orthogrid Node

0 0 0

@@@@0 0 0

@@@@

@@0 0

@@0 0

@@0 0 0 0 0

@@@@@@

/

/Figure 1. I-beam orthogrid structure.

FINITE ELEMENT MODELING

A finite element model of an orthogrid structure can be constructed using several different tech-niques. Three techniques are investigated here. Each one possesses a significantly different level of com-plexity. All of the finite element modeling was performed using the ANSYS 5.1 program.

Beam Model

The simplest model, shown in figure 2, is constructed entirely of beam elements. The elementproperties are those of the I-beam section (fig. 3). The elements connect at a single node at each orthogridnode. The element properties do not vary to account for the change of the I-beam section around theorthogrid nodes.

Figure 2. Beam element orthogrid model.

IT' flanget

h

Z

Ir

webt

I

'flangew_

v y

A = (h-2*flange t)*webt+2*flange t*flangew

Iyy = 1/12*web t*(h-2*flange t) 3+

2*(1/12*flange w*flanget3+

flange w*flange (((h-flange t)/2)2)

IXX = 1/12*(h-2*flange t)*web t3+

2*(1/12*flange t*flange w3)

Figure 3. I-beam cross section.

Shell and Beam Model

The next model, shown in figure 4, better represents the three-dimensional nature of the structure.It uses shell elements to model the web of the 1-beam and offset beams to model the I-beam flanges. Thebeam elements have the same properties of an I-beam flange with the centroid of the flange offset from thenode locations by one half of the flange thickness (fig. 5). Like the beam model, the I-beam section doesnot vary at the orthogrid nodes.

!_>. i--.

....,.

I

J

<.i

-..>r_Z_...J

'F

o. •

iJ t "_rJF-_[..---T'_

Figure 4. Beam and shell element orthogrid model.

Figure 5.

T'I beam offset

h d _ _ web t

I I

Beam and shell element representation of I-beam section.

Shell Model

The third model is built using all shell elements. This model better represents the effect of thenodes. The radius of the I-beam flanges around the nodes are modeled, and the increased thickness of thewebs at the nodes is modeled by tapering the thickness of the web elements connected to the nodes to threetimes the nominal I-beam thickness (the value of three was chosen somewhat arbitrarily) (figs. 6 and 7).

Figure 6. Shell element orthogrid model.

Figure 7. Shell element orthogrid model showing taper of web elements at each orthogrid node.

4

A drawbackof thismodelis theoverlapof theflangeelementswith thewebelements(fig. 8).ANSYSdoesnothavethecapabilityto inputanoffsetdistancefor shellelementsfrom theirnodeloca-tions.Rigidelementscouldbeusedto createanoffset,but thisaddsadditionalmodelingcomplexityandwerenotused.Consequently,theI-beamsectionrepresentationof thismodelisnotentirelyaccurate.Themomentof inertia,Iyy, canbematchedwith theactualI-beaminertiaby adjustingthedistanced (aswasdonein this investigation).This leavestheoverallheightslightly lessthantheactualheight,whichproducesalowermaximumfiber stresson thetopandbottomsurfacesof theI-beam.In this investigation,thestress/strainvalueswereabout2 percentlessthanwhattheyshouldhavebeen.

--_ flangew 1"91---

h d web t

1,1Figure 8. Shell element representation of I-beam section.

VERIFICATION

To check the accuracy of the various orthogrid modeling techniques, a test was performed to pro-vide strain gauge data to compare with the finite element model predictions. An orthogrid panel wasinstrumented and then loaded in two different configurations. In one configuration, a load was appliednormal to the panel and, in the other, an in-plane load was applied to the side of the panel. The setup forboth configurations was designed so that the boundary conditions could be easily modeled.

Test Article

The orthogrid panel used in the test is shown in figure 9. All of the interior members were standardI-beam sections and the edges were rectangular sections. The section dimensions are listed in figures 10and 11. The panel was constructed from a single plate of aluminum 2219.

Loads

The two loading configurations are shown in figures 12 and 13. In the first configuration, a 2,500-lb normal load was applied at three points in the center of the panel. The load line was positioned such thatthe load at the three application points were equal. The load was reacted through a single point at eachcomer.

In the second configuration, a 5,000-1b in-plane load was applied along two lines on one side ofthe panel. The load was reacted on the other side through a line at each end.

The loads were applied incrementally, with data taken at every increment.

1-°000

20.7 in 0

J_°©

T2.11 in I

64.7 in _

0000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000©000000000000000000

Figure 9. Orthogrid test article.

1.375 _ 41_ 1.375

F__ -.-o.o__lHJ kro-,===xo¥,I J ! L.__j_

,_ +

-1--2.11

I

I I

I _ _ SXIY1

0.75 0.10

0.75

SXIY2

I I

X=Cell# Y=Side#

±

.10

CL

I

Figure 10. Typical strain gauge installation on interior members of orthogrid test article.

6

S1001

_'4_" 1.375 _ _ 1.375

S11010.50 t

0.25

Figure 11. Strain gauge installation on side of orthogrid test article.

Y

XA •

o_ f_

//////

Figure 12. Normal load configuration.

//////

X

Y

j///.

Figure 13. Side load configuration.

//

Instrumentation

Instrumentation of the test article included 32 strain gauges applied on the orthogrid members asshown in figure 14. The details of the gauge location on each member are shown in figures 10 and 11. Thegauges were oriented to measure the axial strain of the I-beam sections.

Two deflection transducers measured the deflection for each load configuration. The points of eachmeasurement are shown in figure 14.

D1 Side Load D2 Side LoadCell # Side #

Y

X 1 _N 1 N I

D1 Normal Load D2 Normal Load4

2

(!)

Figure 14. Locations of strain gauge and displacement instrumentation.

RESULTS

The results from the two tests, along with the predicted finite element results from the threemodels, are shown in figures 15 through 24. The incremental results indicate that the behavior of the panelwas linear with respect to the loading. This is shown by the deflection charts, figures 15 and 16. Thestrain results, figures 17 through 24, are given for the final maximum loading.

8

Stiffness

The shell model was the only one that accurately predicted the deflection behavior of the test panel.This model was within 5 percent of the normal load deflection and within 8 percent of the side loaddeflection. The other two models, on the other hand, did a poor job of matching the test data. For thenormal load configuration, the beam model was off by 20 percent and the beam and shell model was offby 16 percent. The predicted side load deflection was particularly poor, with both models off by more than100 percent. In each configuration, the two models over-predicted the deflections, indicating they are con-siderably less stiff than the actual orthogrid panel.

The low stiffness of the beam and the beam and shell models can be accounted for by the way theorthogrid nodes were modeled, or rather not modeled. Both of these models were modeled essentially asconstant section beams intersecting at a single node or line of nodes in the case of the beam and shellmodel. The effect of the extra material at each orthogrid node was not accounted for.

Strains

For the normal loading configuration, the highest strains occurred in the members running length-wise. All of the models did reasonably well in matching the strain gauge data from these members. Thebeam and shell model matched the two midline I-beam flange gauges most accurately, within 2 percent.The off-midline gauge closer to the nodes, SX023, was best matched by the shell model, within 1 percent,which can be attributed to the higher fidelity of this model around the nodes.

The strains in the members running across the width were very low. The models varied greatly inhow well they matched these strains. Since low-stressed areas are not critical design drivers, it is not veryimportant that the models match the test values at these areas in order to assess their performance

For the side-loading configuration, the highest strains occurred in the off-midline flange gauge,SX023. The shell model most closely matched the strain at this location, within 6 percent. The other twomodels exceeded the test values by 20 to 40 percent. The strain values at the other gauge locations werefairly low and, again, the model predictions varied, with none matching very well.

CONCLUSIONS

Based on this study, the shell model does the best job predicting the deflection behavior of anorthogrid structure. The nodes have a significant effect on the behavior of an orthogrid structure, whichthe beam and beam and shell models do not capture. It may be possible to alter these two models by modi-fying the beam section around the nodes to better model this effect.

All three models do reasonably well predicting strains due to normal loading. For side loading,only the shell model performed well in predicting the strains. The other two models tended to over-predictthe maximum strains in the flange by a significant amount. These two modeling techniques yield reason-able results between nodes but are conservative near the nodes.

This experiment shows that the best overall choice for modeling orthogrid is the shell elementmethod. This is especially true where deflections and stiffness are important. However, when model sizeand analysis time are important, which is usually the case, both the beam and beam and shell elementmethods provide reasonable to conservative results for a stress analysis. If the hardware is such that cap-turing the three dimensional nature of the structure is not important or poses no modeling difficulties, thenthe beam element method is probably sufficient. When the thickness of an orthogrid structure is moreimportant, such as when it has multiple interfaces to other hardware at different locations and planes, thenthe beam and shell element method will suffice.

9

_=

.==.O

Normal Load Deflection

500 1000 1500 2O00 25O0

_=_Tes_ D1 ......

_-"4-- Test D2 i ,

_Mo_m !

r'---,&-- seam _ 02 l

.-,,--_._,,s_,Mo_011L-.,II. - - Be_n & S_ea Mod_ D2 I

_--X'- She, Mo_ O2 j

Figure 15. Normal load configuration deflection.

i m

i

III 0.45

0.4

Side Load Deflection

O35

03

02

0.15

0.1

0.05

Test D1 !

--.._- - Test D2 i

_ Beam Model D1

- _-_-* Beam Model D2

---'_ Beam & Shel Model D1

i---IB-- Beam & Shel Model D2

[-- -X-- Shel Model D2 .....

0 1000 2000 3000 4000 5000 6000

Figure 16. Side load configuration deflection.

10

$2Ol I $2Ol 2 $2013

Normal Load I-Beam Flange Gage StrainWidthwise Members

$3011 $3012 $3013 $4011 $4o12 $4o13

0

Test

II She= Mode4

-100

-120

-140

Figure 17. Normal load configuration I-beam flange strain on members running across width.

0

Normal Load I-Beam Flange Gage Strain

Lengthwise Memberss:¢_2 s2_3 s30m sa_2 s3¢_ s4021 s_22 s4o23 s_0o_ $1101

ic

ii!!!i!ili!i!i!ili!ili!!!i!!!i!i_'_ _

Figure 18. Normal load configuration I-beam flange strain on members running along length.

11

100

Normal Load i-Beam Web Gage Strain

Widthwise Members

6o

40

_- 20

Z -20

-4O

-6O

-8O

-100

i

UBurn Model _;

eSheU _kx_ -- i

Figure 19. Normal load configuration web strain on members running across width.

Normal Load I-Beam Web Gage Strain

Lengthwise Members

1500

-500

pT_jBBmm Mo_

BBeam & She, Mo_ :

_,s_, Mo_

-1000

-2OOO

Figure 20. Normal load configuration web strain on members running along length.

12

$2011

1200

1000

Side Load I-Beam Flange Gage StrainWidthwise Members

$2012 $2013 $3011 $3012 $3013 $4,011 $4012 $4013

8OO

Ai:

a_o

io_Yest: e,,,=_io,_ !i i

ps_=,_Mo__.

2OO

-200

1

Figure 21. Normal load configuration I-beam flange strain on members running across width.

4OO

Side Load I-Beam Flange Gage Strain

Lengthwise Members$2021 $2022 $2_3 $3(;21 $3_2 $3(_3 $4021 $4022 $4(_3 $1001 $1101

2OO

-200

o

-6OO

-8OO

-1000

-1200

I Model

Figure 22. Normal load configuration I-beam flange strain on members running along length.

13

Side Load I-Beam Web Gage StrainWidthwise Members

&,Sh_ Mod_ !

.120

-140

-160

Figure 23. Normal load configuration web strain on members running across width.

Side Load I-Beam Web Gage StrainLengthwise Members

100

mBsamMod_ i

m_ne_I Mod_ J i

!

-2OO

Figure 24. Normal load configuration web strain on members running along length.

14

APPROVAL

VERIFICATION OF ORTHOGRID FINITE ELEMENT MODELING TECHNIQUES

By B.E. Steeve

The information in this report has been reviewed for technical content. Review of any informationconcerning Department of Defense or nuclear energy activities or programs has been made by the MSFCSecurity Classification Officer. This report, in its entirety, has been determined to be unclassified.

.R.iuDirector, Structure_',arg:l Dynamics Laboratory

15

Form ApprovedREPORT DOCUMENTATION PAGE OMB No 0704-0188

Publicreportingbmdenfor thisoo41ectond itfform_icnis estimatedto average 1hourperresponse,includingthe timefor reviewinginstructions,searching existingdata sources,gathenngand maintainingthe data needed,and ¢omplelingand reviewingthe ¢oflectionof inlcematicn.Sendcommentsregardingthisburdenestimateor any otheraspectof thiscoUectionof inlonnalio,,including suggestions for reducingthis burden, to Washington HeadquartersSentices,Directoratefor IrdoanationOperationsand Reports,1215JelJemonDavis Highway,Suite1204, Arlington,Va 22202_, andto the Office of ManagementandBudget,PapenA,ork ReductionProject(0704-0188),Washington,DC 20503.

1. AGENCY USE ONLY (Leave Blank) 2. REPORT DATE 3 REPORT TYPE AND DATES COVEREDOctober 1996 Technical Memorandum

5 FUNDING NUMBERS4. TITLE AND SUBTITLE

Verification of Orthogrid Finite Element Modeling Techniques

6. AUTHOR(S)

B.E. Steeve

7. PERFORMING ORGANIZATION NAME(S)ANDADDRESS(ES)

George C. Marshall Space Flight Center

Marshall Space Flight Center, Alabama 35812

9. SPONSORING,%,IONITORINGAGENCYNAME(S)ANDADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

8 PERFORMING ORGANIZATON

REPORT NUMBERS

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

TM-I08519

11. SUPPLEMENTARYNOTES

Prepared by Structures and Dynamics Laboratory, Science and Engineering Directorate.

12a. DISTRIBUTION_VAILABILITYSTATEMENT

Unclassified-Unlimited

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

The stress analysis of orthogrid structures, specifically with I-beam sections, is

regularly performed using finite elements. Various modeling techniques are often used to

simplify the modeling process but still adequately capture the actual hardware behavior.

The accuracy of such 0short cuts6 is sometimes in question. This report compares three

modeling techniques to actual test results from a loaded orthogrid panel. The finite

element models include a beam, shell, and mixed beam and shell element model. Results

show that the shell element model performs the best, but that the simpler beam and beam

and shell element models provide reasonable to conservative results for a stress

analysis. When deflection and stiffness is critical, it is important to capture the

effect of the orthogrid nodes in the model.

14. SU_ECTTERMS

Orthogrid, finite element modeling

17. SECURITY CLASSIFICATION

Unclassified

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19 SECURITY CLASSIFICATION

OF ABSTRACT

Unclassified

15 NUMBER OF PAGES

18

16 PRICE CODE

NTIS

_.LIMITATIONOFABSTRACT

Unlimited

NSN 7540 - 01 - 280 - 5500 Standard Form 298 (Rev 2-89)PreserVed by ANSIStd. 23_-18