AIAA Papers Volume Issue 1992 [Doi 10.2514%2F6.1992-4732] PATEL, H. -- [American Institute of Aeronautics and Astronautics 4th Symposium on Multidisciplinary Analysis and Optimization

8/12/2019 AIAA Papers Volume Issue 1992 [Doi 10.2514%2F6.1992-4732] PATEL, H. -- [American Institute of Aeronautics and Astronautics 4th Symposium on Multidisci

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MULTIDISCIPLINARY DESIGN OPT IhIIZATION WITHSUPERELEM ENTS I S ;CISC/NA4STRAN

ABSTRACT

Introduction1 1 1 ~ 1)a1)( r pres( nt5 t l ~ c ( d i ~ ~ i q wf ri~~rIt,idisci~ li~~i~ryle-sig~ropt i ~ ~ ~ i z a to11 ~ v i t1 \ ~ ~ p f ~ ~ ~ c l e ~ n e n t so r sulxt r ~ ~ i t ~ ~ r v s )ll.\IS('/S.ZS.L I i ~ \ N . 11rcapxljility lrlay used for csam plc.i l l t \ I ( . aut o l~ ~at r t llcsigrr of a large, structure rnotlr.let1 withsrrpewler~~er~t~s .or ~ninimumweight sltbject to a set of I)e-l iavio~~rall ~ ditlc, constra ints in a n ~~rltitlisc iplinar yesignenviro~rn~rwt.hr. ar l \a~f agr,f using a s~~ per elm wntiodrlover it n o n - s l ~ p c r e l c ~ ~ l e ~ ~ trrod~1ll tlesig~r opt i~u izat ion st,llat only superslernents affected by the design process haveto be rsgrneratetl during thc search for the optirnal design.\Vhcreas, for t h s 1lol1-snperclerne11tmodel, t h e wl~ole t ruc-tnrc has to he regeneratrd, which results in a si~bstant,ial~ w n a ly i l l cornpnter tirne.

Design srmsitivity analysis and optimization first, intro-tl~~cccln Version 66 of MS('/N/\Srl'R..\N, was originally lim-ited to t,hr residual structurt,. In Vrrsion 67, the designsensitivity capability was extended to upstream superele-r~wnts I ] ant1 in Versior~68, the sensitivity capal~ ility orupstrcarn su pereler ner~ts as extended to inclntle des-ign01)-tirnization in a rnnltidisciplinary design er~vironmcnt,.ThesuIjportc:tl solntion disciplines are: aeroelasticity. bucklir~g.frequency response, transimt response, normal rrlocles andstatics. \iersion 68 is in development at MSC; ant1 earlierversions are commerically available.

Copyright 992by the American Instituteof Aeronautics IncAll rights reserved.

Th e method usctl in hlS( /NASl 11AN for compu t-ing sensitiv ity coefficient,\ (o r gra tlirn ts), called th e scmi-analyt ical rnetliod, is rnhancctl to inclutlc tllc cor ~cept ofsupcrelcments. Tllc superc~li:nwirt. q~ ~il ihr inr ncluatiorr arcdilfcreritiatcd r~sirlg finite diffwmc e tccllniqui~ o i.o1 11~ )11 t~thc change i n th sys ten~olut,ior~. h e r c d ~ ~ i t i o ~ ~ecllniqueused in the analysis phase to reduce the su pc ~r ~l (~ nl r~ r~ ttiff-ness. Illass, tlal~lping lid load matrices is also used i l l thesellsit ivity colnpu tations. First or tlrr respolrw scnsitiviticsarc im~ rlp ntd 1bi11g f urward fi ~~ it clifFrrr~nc.c ~ ~ I ( V I I ( \ .

J)esign \~iriahlrys botl i shalw ar ~tl iz i~r g) an I)c tlc~tirretllocally for a snl~er c~l( ~rnc n~r ca~r ji. l i ~ l k d c . 1 . 0 5 ~xi~l)r~.cl (~-rrlcmt Ijol l~itlari cs. I hc sizing varial)lvs r an I o ally rtxal fieldspecified on a propert,y bl ~l k ata entry . For sllape vari;ll)l(.s,the tjasis vector conccyt is utilizrd, wllcrc tlre slrnpc rrari-ablcs arc scalar rnr~ltpliers of thv hasis vwtors. 1)ilfbrvnts l l a p ~ ectors may bc xpccilicd. witir t hr assu~rlptiorr .liatthe optirllal design can bc c~xp rcsx d s a lincar colr~l,iirntionof t h e hasis vt~-tors. ksign rwponscs [nay hc I IQIII an ofthe s l~l)po~tet loll~tiondisciplines. u ~ t lrlal- t~olistriri~~etlfor I~otlr j)rirlrary a d wc.onrlary (i~~lagclsf pri~rlar?.) u-pereler~icvts.

First. tach solution discipline is proressctl iili:rcn~ent,i~llyin th e analysis phases. Secon d, the design i.ons ~r.aint s lltltheir sensitivities are co~llpuied nc re~ ne ~~t all yor t.acll de-sign discipline. T hird, thc tlc sig ~~omt,ritints and serrsit,iv-ties for the various tlisciplines are nlergetl and co ~ ~ v e r t c ~ loan app roxima te tlesig~i notlcl. Finally, the opt i~ui zermod-ifies the approximate design model. The tl csi g~ ~rocess isiterative in nature , with t h e design variables and constraintsfor all superclenients considered sirnultancolrsly by thc op-t irnizrr.

D(-sign synthesis of large st,r uct, ~~ra lyst,en~se q u i r ~ sig-nificant coniputer resource allocation. Furtherlnore, man-agement of th e enormous da ta creat,ed during ma trix gc3n-eration places an unnecessary hurclen on th e analyst or rle-signer. To alleviate this burden, an atlvar~ced atabasc fea-t~11.cf MSCINA STRAN called th e multi-master teck~nic~uc~[2] is available, which provides t he facility for scgms nting thvtlataha se for effective utilizat ion of disk space. This p ermitsa solutio n by processing groups of supt.relenientsi r ~ rr ir~depentlentmanner arltl off~rs ractical data man-agtvllrnt for large rnotlcls.


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where the right hand side terms are known as pseudoloatls, resulting from t l lc design va.riahle pertu rbat ions. T heper turbat ion of the load a ~l t l t if fness matr ix i s carr ied ou t~ls ing f in ite di fference method a t the element level. Th epseudo loads have NDV x NLC columns, where NDV isthe number of independent design variables and NLC is thenum bcr of load cases. Tli r change in the system solution.A[:, can he eva lmte d using the same reduction method usedfor analysis.

First ortler response sensit ivit ies are then evaluated us-ing a forward finite difference scheme

where X - Design variable, GI is the solntion vectorAM- change in the analysis so lu t ion vector due to a per-turbat ion A.Y.

Eigenvalue Response Sensitivity Th e e ig en v a l~ l e e -sponse is a function of the g1ol)al structure antl , thereforeits sensit ivity is compute d a t the residual sup erelenlen t levelonly.

Consider the following eigenvalue problern:

c v h e l ~< stiff~lessm at r i x . il s the mass n iat r iz . Xis the squ are of th e natu ral frequency of vilxation antl 4is thc- dynarnic rnocle sha pe corresponding to e igenvalue A

If we consider a AX c11ange esulting in a Ali change inst i f fness and change in the mass , we obtain the cl langei l l X

Expanding this equation as a first order variation, pre-~l lu l t ip ly ing o th s ides by * and using equat ion (12) we

Note t l lat equation (14) is valid only for the case of dis-tinct eigenvalues.

In the superelement context, eigenvalue sensit ivityfor the k th eigenvalue of t he s t ruct ure i s s imply the s um ofth e co n t r ib u t io n t h a t each su p ere l em en t m ak es t o t h e k theigmva lue der ivat ive:

the model , excluding ex ternal superelements . k i s thekth eigenvector of j th superelement. Th e d efau l t Gu y anretlnction technique is exact for st iffness but approximatefor mass. Th e assum ption is tha t significant masses areassigned to th e boundary po in ts . Therefore, advanced re-duct ion techniques such as G eneralized Dynamic Re duct ion( G D R ) [7 ] or ("omponent M ode Synthesis (C'MS) [7 ] a r erecon~~nencleclo en h an ce t h e m ass m at r i x r ed u c t io n .

Design Optimization Solution2T he design scwsit,ivity and opt.imization procedu re inb I S ( / N A S r l 1 i A N Version 8 is available in SOL 200 as t . r u c t u r ~ t lolution sequence . This i s a mu l t icl i sci l inary su-p w e l e n i c n t s o l ~ ~ t i o nequenc e supporting th e following disci-plines: aeroelast ,ic, buckling, eigenvalue, frequency response(d i rect o r rnodal ) , s tat ics and t ransien t response (moda lo n ly ) .

6 User InterfaceT he de sign op t,i~ niz ati on ulk d ata entries i l lt .rotlucetl inb I S ( ' / N A S T K t Z N [ ] for the r lon-s t~pereleme~i tapa.l)ilityare unmodif ied , wi th t he except ion of th e D ESOBJ a.ndD RE SP l bu lk cla. ta en t r ies . Th e DESO BJ en t ry , which spec-i fies th e ob je ct ive response, has a new field for specifying asnperelement ID. The DRESPl en t ry used for def in ing adesign response, allows specification of supere lemen t ID forvolume and weight responses. Th e design entries are brieflydescr ibed in Table 1 .

Table 1 . Bulk Data Entr ies

DESO BJ Design objec tiveDESVXR Drsien variableI ) L INI< Design variable linkingI)OPTF'RLI I O~tirnization~aran letersD K E S P 1 Response quantityDHF'\P: Svnthetic remonseDSC'HEEN 1 ('onstraint screening dataI Tahlr ronstantsI)C.(;RID Design variable to grid relationI)VPRI


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8.1 Seventy Two Bar Truss7 Mult i Master TechniqueTllc tlat,abase segmen tation feature of M S( /NASrYR.4N isan e xtrem ely powerfnl and versat.ile procedure available forsolvirrg very large, models which are subjrtct to colrstraintso n disk spa.ce and C P U availability. This feature enables apiece-meal solut ion by process ing groups of ~u ~ er e l cn le n tsna s t a n d a l o ~ washion. Normally, all processing informa tionfor s up e ~ le m e n t s s s to re d in the DB ALL da ta ba se s e t,(dbset). The datablocks can be retlirectetl to different filesby using a num ber of location PAR AMete rs. Th e two mostcomnlonly used are DBU P and DBDN .DBUP th e location where upst ream processing infor-

mation is stored a.ncl is only needed for data recoveryfor th e supere lem e~i t This dbse t i s typica l ly verylarge.

DBDN th e location where downstrea m processing isstore d. T he reduced clamping, mass, s tiffness and loadmatrices a re stored here. This dbset is small and isonly needed when processing any superelement whichis downs tream of th e current supere lement .

Th e da tabase for each supere lement or group of supere le-nients is par t i t ioned in to a ups t ream dbse t (D BU P) conta in-ing da t a required for da t a recovery and a downs tream d hse t(DR DN ) which conta ins the bare minimum of informat ionfor downs tream process ing. Th e individual da tabases a rethen a t tached to the downs tream s teps us ing the DBLO-CATE capability [ 2 ] .This enables incremental or even con-cnrre nt processing of sup erelements s ince each group of supere lements has i t s own independent da tab ase .

For design sensitivity and optimization in SOL 200, t h esuperelernen ts of interest can be processed at the user s t l is-cretion with th e aid of the SEDV and SERESI case controlentries [ I. Thu s only th e necessary dbse ts have to be onl ine .Since t,h is i s a ~ na nu al rocedure the opt imiza t ion phase islimited to a s il~ gle lesign cycle. Th e user has th e optionof rnanually updating the designed grids arid properties; orusi r~g he DHJ,O(~ A I E feat,ure for restart ,ing t ,he tlrs ig~ i 1 -t imizat,ion task

8 Illustrative ExamplesTh e fol lowing exam ple de mons t ra t e t he me thod-ology of designing structtlre modeled with superelements.Al l problc~nswere run on an IBM R S / 6 0 0 0 (M ode l 9 5 0 ) . Afil~ ite ifference step size of 1.0E - 4 was used for t,h e tlesignsellsit ivit y calcu lation s.

This e lementary problem from reference [5] s modeled withtwo superelements (see Figure 1 . Elements 1-30 are as -s igned to supere lement 1 a nd the re ma inde r 31-72 are bydefaul t assigned to th e res idual supere lement . Th e des ignobjec t ive is to m inimize the weight of th e s t ruc ture subjec tt o displacement and stress constraints . Th e design vari-ables are the cross-sectio~ lal reas of th e bars, w ith mem bersl inked to enforce symm etry . Th e design da ta is given in t hetable below:

Ta b le 2.Objec t iveCons tra in ts

Ies ign Da ta for Seventy-Two Bar T russWeightDisplacement - 0 . 2 5 ~ n C l 2 0 . 2 5 ~ ~ ~(Gr ids 1-4)Stress ( p s z ) - 2 5 E 3 u ~ 2 5 E 3(Elements 1-72)Minimum Area 0.01in2

De5ignVariable1235678910111213141516

TableElements

3. Final D esign for Seventy-T wo Bar T russl l 2 \

eight 11Max. Cons tra in t

C o m ~ a r i s o n f t he f in al d e s i ~ n alues in tab le 3 indicatesth at th e final design variable values for the supere lementmodel agree c losely wi th th e non-superelement m odel . Thi sis to be expected since the accuracy of the static responsevalues and their corresponding sensitivities are not affected(within numerica l roundoff) by the s ta t ic condensa t ion pro-cedure used in reducing the superelement matrices.


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8 2 Intermediate Complexity WingTh e design t,ask for th is rnoclcl (originally an AS PROSmodel) is t,o demonstrat e t he multidisciplinary design ( stat -ics antl normal rnotles) of a wing stri~cture 6] rnodcledwith superclen~ents.The s truc ture is partitioned chordwiseinto t,hrce supereler ~rents sec Figurc 2): with a cantileveredbountlary i~ontlitionat thi, root. All thr w si~perc~l er~~e ntsh a w sizing variables and constraints. The structure is mod-clid usir~g1-D (mass a11d rod) and 2-D (plate and shearpane l) elcmm t ty11c.s. Th e graphitr-epoxy wing skins are~ nod i ~ l rdi th corr~~~ositelat,e (~lenli~nt s.n t l th i~ l~ickni,ssof i,acl~ ly gror~ p or each clement tlesignetl in d ep c~ ~t lr ~~ tl y.Rot,h top antl hotton1 wing skins lor the same ply oriiwta-t i o ~ ~I I C ir~kcati o c>~~f ol~c) . ~ ~ ~ n l c ~ t r ~ .nt1 t v pl ) o~ . ic~ l l i~-tioils ilr( 11i liI l i x ~ d . 11~w i ~ ~ gi~rfaceb rc c.o nr~ c~t idithtlrr ~ ,ot l \ ~ ~ t lP cross-srctiorlal arr as a rc si,lectcd as tlr-iiguvarial)lr~s.711e spar s antl webs are nl otl i~l (d sing tllc shearparlols arrtl th e thiclincss of t,he ele me~ lts re also part ofthe il(~sig~lcdroptrtir7s. 7 11 ~~ .s a total of 153 i~ltlt-l)cn-tliwt sizi~lglr>sigu variahlrs. I he ~ving s s u l ~ j ~ c td t w ostat ic loatl caws ri~prcsent t ivi, of a s u h o ~ ~ i crlcl a slipcr-sonic air loatl. The ~lolrstructuralmass of t,hc str11ctrn.e is

~not lclc( l 1sing invariant corlc~rntratcilmasses. A ~uini rnun~\vtxight (lcsign is sought s l ~ l ~ j r c to a set of static constrai~rth(vo~r-;llisc.s t rcw ant1 ply Hill-la ilure illtliccs) ant1 the, secondcigeuvalue (t orsional) is constrailled to be above 40 IIz. Thetlefar~l t :uyan reduction procedure is used with th e 1,anc-zos rigen\raluc extraction rnethod. Thc co n v ~ . ~inearizationmethod for constrairlt approximation is s~le ctk d or all theresponse ttypes. Fiual designs for thc no~l-sujjerclcmentver-s11s supe rele ~rlr ntmodels are as follows:

Table 1 Fmal Des~gns or Intermed~nte( ornplex~ t ng

The final es~gnq fol the 5uperelernent models ngreec lowl) w~ th he non-superelement model. In spection of the


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Super elemen ts 100, 101, 102 and 0 are identified for re-design, while superelements 200. '201, 202, and 300 are tobe l~ clcl ixed in tlie tlesigli task . T11e first two r un s cr eat et h e s r ~ p e r e l e n ~ e n tatrices for supert4emcmt groups A aridB. The t lowlis t ream information is direc ted to the DRDNd l ~ s e t s .Th e third run for superelement 0 (i.e. , residual), as-senihles the reduced matr ices of the ups tre am sup ere le ~ne nts(conta i l led in the DBDN dbsets ) and solves the sys tem m a-trices. T he ne st ru n reverses the process ortlcr antl goes upthe b ranch of group A to pe rfor n~ a ta recovery. T l ic f inalrun for design optimization attaches all dbsets created forsupere lement groups A ant l C . Superelement group B tlh-se ts are not required lxc ause they do not part icapte in thedesign process; i .e. , these supereleme nts do not have signvariables and/ or constrain ts, and are not downstrea.m of anydes igned supere lements . By a t taching only required dbsets ,

3 h lult,i-L evel S ~ ~ p f v l e n ~ e n tree the available disk space is used efficiently.

m r r u . LmS nm

4 Split L)at.al)asc.and i ts Atlvantagc~s

Cons ider t he run sequence i l lus tra ted in Figure 5 wherethe s l lpere lements are grouped as per the following:

Table 5 Supere lenlent GroupingGrou p Supere lement IDS

A 100, 101, 102

ConclusionsThe mult idisc ipl inary des ign opt imizat ion of s t ructuresmodeled with supere lements (or subs tructures) is demon-s tra ted in MSCJNASTRAN via example problems. T h efirst example, the Seventy-Two bar truss, is a relativelys ~ n a l l problem. Th e f ina l opt imal des igns for the su-perelement model agrees closely with the non-superelementmodel . Th e second example is the design of th e interm edia tecomplexity wing model subject to multidisciplinary designconstrain ts. Com para ble final designs for th e superelemen tmodels are obta ined. Since the mass matr ix reduct ion isapprox imate , the accuracy of th e e igenvalue response andi ts sens i t ivi ty is impacted. A defic iency in th e current im-plemen ta t ion is th a t m ode t racking is not avai lable . Con-s tra ined modes may change the ir order of occurrence asthe design is modified, and orthogonality checks need to bemade to automatica l ly cons tra in the user reques ted modes .For this example , the second mode was veri f ied to be thetors ional mode throu ghout the des ign psocess for both thesupere lement a nd non-supere lement models.

The efficiency of the design procedure can he improvedby exploi t ing the concurrent and/or para lle l process ing ca-pabi l i t ies of th e coniputer hardware and software . W ith th eaid of the mult i -mas ter method, concurrent process ing islxesent ly ava , ilable in M SCJN AST RAN .


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M TRIX GENER TION

3 M TRIX GENER TION SYSTEM SOLUTION

DBUP

5 DESIGN SENSITIVITY OPTIMIZ TION


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10 Acknowledgments

11 References1. Patel H . D., "Development of superelenient designsensi t ivity in MS CINA STRA N," Proceedings , 19 )1

hlSC World Users Conference, Los Angeles. C'A.,Xlarch 1991.

2. "Int ,roduction t V67 Seminar Notes ," T he M acNcal-Scliwentl lcr rorporation. Los Angeles, IA.. S ept em-1 cr 1991.

3 . Haftka K . T.. Gnrda l Z arid Iiarnat M. P.. H t m r rrfsof 5 2ruclr~rnlOpt i rr~i in t ion . i111werA c a t l e ~ r ~ i cublisl l-f.13, 10 10.

5. Arora 1 . arid Go\ril A. I i . , "An efficient method foroptirnal structural design by sul~st , ructur ing,"C orrr-p u t ~ r s crrrl .Strr~ctur.es.Vol. 7 p . 507-51,j .

7. ;ochel M. . A . "Hant l l ~ ooh o ~ upe l el ement Ana l y515. Th e AIac Neal S ch ne nd le~Corp o l a t ~ on . 982 .

8. hIoore G . .J. "MSCI/NASTRAN Design Sensit ivityand Optimization User 's Guide, Version 67," T h e;\ /lacNeal Schwendler C orpora tion, 1992.

Documents

AIAA Papers Volume Issue 1992 [Doi 10.2514%2F6.1992-4732] PATEL, H. -- [American Institute of Aeronautics and Astronautics 4th Symposium on Multidisciplinary Analysis and Optimization