SECTION7SUPERELEMENTANALYSISTABLEOFCONTENTSSection

PageWHATISASUPERELEMENT? 7-9ADVANTAGESOFSUPERELEMENTANALYSIS 7-10DISADVANTAGESOFSUPERELEMENTANALYSIS 7-12HOWARESUPERELEMENTSDEFINEDINMSC.NASTRAN? 7-13MAINBULKDATASUPERELEMENTDEFINITION 7-15MAINBULKDATAGRIDPOINTPARTITIONING 7-16BULKDATAUSEDTODEFINEPARTS 7-17BULKDATAUSEDTODEFINESUPERELEMENTS 7-18BULKDATAUSEDTOCONNECTPARTS 7-19SEBNDRYENTRYelementBoundary-PointDefinition 7-20SECONCTENTRY 7-21SEEXCLDENTRY 7-23SEBULKENTRY 7-24SAMPLEPROBLEM-STEELSTAMPING 7-26SAMPLEPROBLEM—STEELSTAMPINGSAMPLESUPERELEMENT1 7-28TABLEOFCONTENTSSection

PageSAMPLEPROBLEM—STEELSTAMPINGSESETENTRIESFORMAIN BULKDATASUPERELEMENTS 7-33PARTITIONEDSOLUTIONS 7-34THEORYOFSTATICCONDENSATION 7-36CONVENTIONALANALYSIS 7-38SUPERELEMENTANALYSIS 7-41BULKDATAFORSTATICLOADSONSUPERELEMENTS 7-48SINGLE-POINTCONSTRAINSTSONSUPERELEMENTS 7-50MPCsANDRIGIDELEMENTSINSUPERELEMENTS 7-52RIGIDCONNECTIONOFTWOSUPERELEMENTS 7-53SUPERELEMENTCASECONTROLCOMMANDS 7-54SUPERCOMMAND 7-55EXPANDEDVERSUSCONDENSED 7-56SUPERCOMMANDEXAMPLE—ONELOADINGCONDITION 7-58MULTIPLELOADINGCONDITIONSINSUPERELEMENTCASE CONTROL–OPTION1 7-59TABLEOFCONTENTSSection

PageMULTIPLELOADINGCONDITIONSINSUPERELEMENTCASECONTROL–OPTION2 7-60REASONSTOUSEOPTION2FORMULTIPLELOADINGS 7-62MULTIPLELOADINGS–SAMPLEOFOPTION1 7-63MULTIPLELOADINGS–SAMPLEOFOPTION2 7-64PARAMETERSINCASECONTROL 7-65SAMPLESUPERELEMENTSTATICRUNINPUT 7-66SAMPLESUPERELEMENTSTATICRUNINPUT—USINGPARTS 7-68SUPERELEMENTREDUCTIONMETHODSAVAILABLEINDYNAMICANALYSIS 7-71DEGREESOFREDUCTION 7-72COMPARISONOFREDUCTIONMETHODS 7-73ADVANTAGESOFEACHREDUCTIONMETHOD 7-74CALCULATIONOFNORMALMODESUSINGSTATICREDUCTIONONLY 7-75CALCULATIONOFNORMALMODESUSINGDYNAMICREDUCTION FORSUPERELEMENT 7-76TABLEOFCONTENTSSection

Page“FIXEDBOUNDARY”SOLUTIONS(PARAM,FIXEDB,-1) 7-78PROCEDURESFORSUPERELEMENTDYNAMICREDUCTION 7-79SPECIFICATIONOFFIXEDANDFREEBOUNDARYDEGREESOFFREEDOM 7-81REFERENCESFORCMS 7-82SUPERELEMENTDYNAMICSEXAMPLE 7-83APPENDIX–THECRAIG-BAMPTONMEDTHOD–HAND-SOLVEDEXAMPLE 7-100DEFAULTCMSMETHOD“FIXEDBOUNDARY”CMS 7-101SOLUTIONBYHAND 7-104SOLUTIONUSINGMSC.NASTRANSOL103 7-114SELECTEDOUTPUTFROMMSC.NASTRAN 7-115TABLEOFCONTENTSSection

PageEXTERNALSUPERELEMENTS 7-117CREATINGANEXTERNALSUPERELEMENT 7-118ATTACHINGANEXTERNALSUPERELEMENT 7-120DATARECOVERYFORANEXTERNALSUPERELEMENT 7-122ATTACHINGANEXTERNALSUPERELEMENT 7-123SAMPLEPROBLEM 7-125SAMPLEPROBLEMUSINGMATRIXDB 7-126SAMPLEPROBLEMUSINGDMGIOP2PROGRAM 7-132

WHATISASUPERELEMENT?PhysicalandmathematicalrepresentationPhysical–asuperelementisasubstructure:afiniteelementmodelofaportionofastructureMathematical–thephysicalmodelisreplacedwith“boundarymatrices”:loads,mass,damping,andstiffnessreducedfromtheinteriorpointstotheexteriororboundarypointsWhenamodelisdividedintosuperelements,itisbesttothinkofeachsuperelementashavingit’sownuniquebulkdataset(internally).Eachsuperelementisprocessedandthefiniteelementmodelisreplacedbyreducedmatriceswhichrepresentthemass,damping,stiffnessandloadingsonthesuperelementasseenbyanyadjacentpartsofthemodelOnceasuperelementisprocessed,thebulkdatausedtodefineit,alongwithallmatricesusedinprocessingitarenotneededuntilperformingdatarecoveryonthesuperelement,orperformingmodificationsonit.Thisdatamaybe“archived”toreducediskusage.ThereducedmatricesareusedtoreplacethephysicalmodelofthesuperelementADVANTAGESOFSUPERELEMENTANALYSISLargeproblems(i.e.,allowssolvingproblemsthatexceedyourhardwarecapabilities)LessCPUorwallclocktimeperrun(reducedrisksinceeachsuperelementmaybeprocessedindividually)Partialredesignrequiresonlypartialsolution(cost).AllowsmorecontrolofresourceusagePartitionedinputdesirableOrganizationRepeatedcomponentsPartitionedoutputdesirableOrganizationComprehensionComponentsmaybemodeledbysubcontractors.ADVANTAGESOFSUPERELEMENTANALYSIS(Cont.)Multi-stepreductionfordynamicanalysisZooming(orglobal-localanalysis)Allowsforefficientconfigurationstudies(“Whatif...”)DISADVANTAGESOFSUPERELEMENTANALYSISIncreasedoverheadduetoDMAPcompilationanddatabasemanipulationandstorageMandatorystaticcondensationmaycancelothercostsavingsforsmallmodels.Allsuperelementsmustbelinear.Approximationsmustbemadeindynamicsformassanddampingthroughstatic,componentmode,orgeneralizeddynamicreduction.HOWARESUPERELEMENTSDEFINEDINMSC.NASTRAN?Superelementsareidentifiedusingnumbers(SEID).Eachsuperelement(SEID>0)isdefinedwithitsownsetofgrids,elements,constraints,loads,etc.TherearetwowaystodefinesuperelementsinMSC.NASTRAN,MainBulkDataSuperelementsandPARTS(notcurrentlysupportedfornonlinearanalysis),whichallowpartitionedinputfiles.MainBulkDatasuperelementsareeasiestthoughtofasa“cookie–cutter”approach.Alldataprovidedinthe“MainBulkData”section(Betweenthe“BEGINBULK”andeitherthefirst“BEGINSUPER=i”orENDDATAentry)ispartitioned(divided)intoaseparatesetforeachsuperelementbasedonGRIDpointassignmentsmadebytheuserPartitionedbulkdatasuperelements(PARTs)aredefinedinseparate(self–contained)sectionsoftheinputfile.TheseparatePARTsare“assembled”togetherbasedoncoincidentpoints.EachPARTisdefinedina“self–contained”sectionwhichbeginswitha“BEGINSUPER=i”entryandendswitheitherthenext“BEGINSUPER=j”entryoftheENDDATAHOWARESUPERELEMENTSDEFINEDINMSC.NASTRAN?Theresidualstructureisasuperelementthatcontainsgridpoints,elements,etc.(intheMainBulkData),whicharenotassignedtoanyothersuperelement.Lastsuperelement(SEID=0)tobeprocessedSuperelementonwhichtheassemblyanalysis(nonlinear,transientresponse,frequencyresponse,buckling,systemmodes,etc.)isperformedAsuperelementmayalsobedefinedasanimageofasuperelementorobtainedfromoutsideMSC.NASTRAN.MAINBULKDATASUPERELEMENTDEFINITIONEachsuperelement(SEID>0)definedintheMainBulkDatasectionisdefinedwithitsownsetofgrids,elements,constraints,loads,etc.Interiorgridpointsareassigned(partitioned)toasuperelementbytheuser.Exteriorgridpoints,elements,loads,andconstraintsareautomaticallypartitionedbytheprogrambasedoninteriorgridpointassignments.MAINBULKDATAGRIDPOINTPARTITIONINGBulkDataEntriesOnlyinteriorpointsneedtobedefined.SESETtakesprecedenceoverGRID.Fortheexampleshownabove,GridPoint47willbelongtotheresidualstructure(SEID=0).Elements,constraints,loads,etc.,areautomaticallypartitioned.SESET“THRU”optionallows“opensets.”P(pán)ointsnotassignedtoanysuperelementbelongtotheresidualstructurebydefault.Amodelwithnogridpointassignmentsisdefinedasaresidualstructure-onlymodel.Superelementsareidentifiedbyaninteger.BULKDATAUSEDTODEFINEPARTSEachPARTisdefinedinaseparatesectionoftheinputfileThesectioncontainingthedataforaPARTwillbeginwith:BEGIN(BULK)SUPER=iwhereiisthesuperelementidtobedefinedbythefollowinginputThesectioncontainingthedataforaPARTwillendwitheither:BEGIN(BULK)SUPER=jwherejisthesuperelementdefinedinthenextsectionoftheinputfile

or ENDDATAwhichindicatestheendoftheinputfileTheBulkDataforeachPARTmustbe’self–contained’Itmustcontainalldatadefiningelements,properties,materials,andloadingsforthatPARTDifferentPARTsmayusethesameidnumbersforelementsandGRIDpoints,sinceeachisina“self–contained”inputsection.BULKDATAUSEDTODEFINESUPERELEMENTSIDtest,problemSOL101CENDTITLE=SAMPLEINPUTFILEDEMONSTRATINGPARTINPUTSUBCASE1LOAD=1DISP=ALLBEGINBULK$$MAINBULKDATA–maybeomittedifdesired$containsdatadefiningresidualstructureandalsoanyMainBulkData$superelements$$anysuperelementsdefinedinthissectionwillbedefinedby$usingSESETentriesorfield9ontheGRIDentries$BEGINSUPER=1$$modeldataforPART1$BEGINSUPER=2$$modeldataforPART2$ENDDATASampleinputstreamBULKDATAUSEDTOCONNECTPARTSSincePARTsare“self–contained”,itisnecessaryto“connect”themtoeachotherandtheMainBulkDatasuperelementsTheProgramwillautomaticallydeterminecoincidentgridpointsbetweeneachPARTandanyotherPARTsorMainBulkDatasuperelementsIfdesired,theautomaticconnectionlogicmaybemodifiedoroverriddenbyusingthefollowingentriesintheMainBulkDatasectionSEBNDRY–definesasetofpointsforaPARTwhichmaybeusedintheautomaticsearchforattachmentsSECONCT–Allowsdefinitionofatoleranceforconnectionand(ifdesired)manuallistingofthegridpointsbeingconnectedSEEXCLD–AllowsyoutoprovidealistofpointstobeexcludedfromtheboundarysearchSEBULK–the“METHOD”fieldonthisentrycontrolswhethertheAUTOorMANUALconnectionlogicisused.SEBNDRYENTRYDefinesalistofgridpointsinapartitionedsuperelementfortheautomaticboundarysearchbetweenaspecifiedsuperelementorbetweenallothersuperelementsinthemodel.Format:

Example1:

Example2:

Field Contents SEIDA SuperelementIdentificationnumber.SeeRemark2.(Integer0) SEIDB SuperelementIdentification.SeeRemark3.(Integer0orCharacter “All”;Default=“ALL”) GIDAI IdentificationnumberofaboundarygridpointinsuperelementSEIDA.

Remarks: 1.SEBNDRYmayonlybespecifiedinthemainBulkDataSectionandisnot recognizedaftertheBEGINSUPER=n. 2.SEIDAANDSEIDBmayreferencepartitionedsuperelementsorsuperelementsin themainBulkDataSectionSECONCTENTRYExplicitlydefinesgridandscalarpointconnectionproceduresforapartitionedsuperelement.Format: Example:

Field Contents SEIDA PartitionedsuperelementIdentificationnumber.SeeRemark2. (Integer>0) SEIDB IdentificationnumberofsuperelementforconnectiontoSEIDA. (Integer0) TOL Locationtolerancetobeusedwhensearchingfororchecking boundarygridpoints.(Real;Default=10E–5) LOC Coincidentlocationcheckoptionformanualconnection. (Character;“YES”or“NO”;Default=“YES”) GIDAI Identificationnumberofagridorscalarpointinsuperelement SEIDA,whichwillbeconnectedtoGIDBI. GIDBI Identificationnumberofagridorscalarpointinsuperelement SEIDB,whichwillbeconnectedtoGIDAI.SECONCTENTRY(Cont.)Remarks: 1.SECONCTcanonlybespecifiedinthemainBulkData SectionandisignoredaftertheBEGINSUPER=n command. 2.TOLandLOCcanbeusedtooverridethedefaultvalues specifiedontheSEBULKentries. 3.Thecontinuationentryisoptional. 4.The(GIAI,GIBI)pairmustbothbegridsorscalarpoints. 5.Allsixdegreesoffreedomofgridpointswillbedefinedas boundarydegreesoffreedom.SEEXCLDENTRYDefinesgridsthatwillbeexcludedduringtheattachmentofapartitionedsuperelement.Format: Example:

Field Contents SEIDA PartitionedsuperelementIdentificationnumber.SeeRemark2. (Integer>0) SEIDB SuperelementIdentification.(Integer>0orCharacter=“ALL”) GIDAI IdentificationnumberofagridinsuperelementSEIDAtobe executedfromconnectiontosuperelementSEIDB. Remarks: 1.SEEXCLDcanonlybespecifiedinthemainBulkDataSectionandis ignoredaftertheBEGINSUPER=ncommand. 2.SEIDAandSEIDBmayreferencepartitionedsuperelementsor superelementsdefinedinthemainBulkDataSection.SEBULKENTRYDefinessuperelementboundarysearchoptionsandarepeated,mirrored,orcollectorsuperelement.Format:Example:Field ContentsSEID Superelementidentificationnumber.(Integer0)TYPE Superelementtype.(Character;NoDefault) PRIMARY Primary REPEAT Identical MIRROR Mirror COLLCTR Collector EXTERNAL ExternalRSEID Identificationnumberofthereferencesuperelement,usedifTYPE “REPEAT”and“MIRROR”.(Integer0;Default0)METHOD Methodtobeusedwhensearchingforboundarygridpoints.(Character: “AUTO”or“MANUAL”;Default=“AUTO”)TOL Locationtolerancetobeusedwhensearchingforboundarygridpoints. (Real;Default10E–5)LOC Coincidentlocationcheckoptionformanualconnectionoption. (Character:“YES”or“NO”;Default=“YES”)SEBULKENTRY(Cont.)Remarks:1.TheTYPE=“REPEAT”or“MIRROR”doesnotincludesuperelementsupstreamofthereferencesuperelement.Arepeatedormirroredsuperelementcanhaveboundaries,loads,constraints,andreductionproceduresthataredifferentthanthereferencesuperelement.2.METHOD=“MANUAL”requiresSECONCTentries.SEBNDRYandSEEXCLD,whichreferenceSEID,willproduceafatalmessage.3.SECONCT,SEBNDRY,andSEEXCLDentriescanbeusedtoaugmentthesearchprocedureand/oroverridetheglobaltolerance.4.Forcombinedautomaticandmanualboundarysearch,theMETHOD=“AUTO”shouldbespecifiedandconnectionsshouldbespecifiedonaSECONCTentry.5.TOLandLOCarethedefaultvaluesthatcanbemodifiedbetweentwosuperelementsbyprovidingtherequiredtoleranceontheSECONCTentry.6.TYPE=“MIRROR”alsorequiresspecificationofaSEMPLNentry.7.TYPE=“COLLCTR”indicatesacollectorsuperelement,whichdoesnotcontainanygridsorscalarpoints.8.ForTYPE=“EXTERNAL”,seealsoPARAM,EXTOUT,etc.descriptioninSection6oftheMSC.NASTRANQuickReferenceGuide.SAMPLEPROBLEM-STEELSTAMPINGSAMPLEPROBLEM-STEELSTAMPING(Cont.)GridPoints1and2fixedMaterialproperties:Steelt=0.05”E=29x106psi

=0.3

=0.283lb/in3(weightdensity)Appliedloads1psipressureonsquareportionsNormalforceof2lbonGrids93and104Opposingnormalforceof2lbonGrids93and104SAMPLEPROBLEM—STEELSTAMPING

SAMPLESUPERELEMENT1SAMPLEPROBLEM–STEELSTAMPING(Cont.)Grids1and2arefixedSteel D=.06” E=20x106psi D=.3

=.283lb./In3(weightdensity)AppliedLoadsPressureonsquareportionsof1psiNormalforceof2lbonGridspoints93and104Opposingnormalforcesof2lbonGridpoints93and104MODELDEFINITIONFORSAMPLEPROBLEMBEGINBULK$$*******************************************************************$BASICMODELDEFINITION-SAMEFORALLRUNS$*******************************************************************$GRDSET,,,,,,,6GRID,1,,-.4,0.,0.,,123456GRID,3,,-.4,0.9,0.=,*2,=,=,*.9,===1GRID,2,,.4,0.,0.,,123456GRID,4,,.4,0.9,0.=,*2,=,=,*.9,===1GRID,9,,-3.6,3.6,0.=,*1,=,*.8,===8GRID,19,,-3.6,4.4,0.=,*1,=,*.8,===8GRID,29,,-3.6,5.2,0.GRID,30,,-2.8,5.2,0.GRID,31,,2.8,5.2,0.GRID,32,,3.6,5.2,0.GRID,33,,-5.2,6.,0.=,*1,=,*.8,===4GRID,39,,1.2,6.,0.=,*1,=,*.8,===4GRID,45,,-5.2,6.8,0.=,*1,=,*.8,===4GRID,51,,1.2,6.8,0.=,*1,=,*.8,===4GRID,57,,-5.2,7.6,0.=,*1,=,*.8,===4GRID,63,,1.2,7.6,0.=,*1,=,*.8,===4GRID,69,,-5.2,8.4,0.=,*1,=,*.8,===4GRID,75,,1.2,8.4,0.=,*1,=,*.8,===4GRID,81,,-5.2,9.2,0.=,*1,=,*.8,===4GRID,87,,1.2,9.2,0.=,*1,=,*.8,===4GRID,93,,-5.2,10.,0.=,*1,=,*.8,===4GRID,99,,1.2,10.,0.=,*1,=,*.8,===4MODELDEFINITIONFOR

SAMPLEPROBLEM(Cont.)$$ELEMENTS$CQUAD4,1,1,1,2,4,3=,*1,=,*2,*2,*2,*2=1CQUAD4,4,1,7,8,14,13CQUAD4,6,1,9,10,20,19=,*1,=,*1,*1,*1,*1=2CQUAD4,5,1,13,14,24,23CQUAD4,10,1,14,15,25,24=*1,=,*1,*1,*1,*1=2CQUAD4,14,1,19,20,30,29CQUAD4,15,1,29,30,36,35CQUAD4,16,1,27,28,32,31CQUAD4,17,1,31,32,42,41CQUAD4,18,1,33,34,46,45=,*1,=,*1,*1,*1,*1=3CQUAD4,23,1,45,46,58,57=,*1,=,*1,*1,*1,*1=3CQUAD4,28,1,57,58,70,69=,*1,=,*1,*1,*1,*1=3CQUAD4,33,1,69,70,82,81=,*1,=,*1,*1,*1,*1=3CQUAD4,38,1,81,82,94,93=,*1,=,*1,*1,*1,*1=3CQUAD4,43,1,39,40,52,51=,*1,=,*1,*1,*1,*1=3CQUAD4,48,1,51,52,64,63=,*1,=,*1,*1,*1,*1=3CQUAD4,53,1,63,64,76,75=,*1,=,*1,*1,*1,*1=3CQUAD4,58,1,75,76,88,87=,*1,=,*1,*1,*1,*1=3CQUAD4,63,1,87,88,100,99=,*1,=,*1,*1,*1,*1=3MAT1,1,30.+6,,.3,.283PARAM,WTMASS,.00259PSHELL,1,1,.05,1,,1$$LOADINGS$$LOADCASE1-PRESSURELOAD$PLOAD2,101,-1.,18,THRU,42PLOAD2,101,-1.,43,THRU,67$MODELDEFINITIONFOR

SAMPLEPROBLEM(Cont.)$LOADCASE2-2POINTLOADSATCORNERS$FORCE,201,93,,2.,0.,0.,1.FORCE,201,104,,2.,0.,0.,1.$$LOADCASE3-OPPOSINGPOINTLOADSATCORNERS$FORCE,301,93,,2.,0.,0.,1.FORCE,301,104,,2.,0.,0.,-1.$*******************************************************************$ENDOFBASICMODELDEFINITION$*******************************************************************ENDDATASAMPLEPROBLEM—STEELSTAMPING

SESETENTRIESFORMAINBULKDATASUPERELEMENTS$FILESESET.DAT$$DEFINES.E.MEMBERSHIPOFGRIDPOINTSFORSINGLE–LEVELSUPERELEMEMT$SAMPLEPROBLEM$SESET,1,33,34,37,38SESET,1,45,THRU,50SESET,1,57,THRU,62SESET,1,69,THRU,74SESET,1,81,THRU,86SESET,1,93,THRU,98$SESET,2,39,40,43,44SESET,2,51,THRU,56SESET,2,63,THRU,68SESET,2,75,THRU,80SESET,2,87,THRU,92SESET,2,99,THRU,104$SESET,3,29,30$SESET,4,31,32$SESET,5,21,22SESET,5,9,THRU,12$SESET,6,25,26SESET,6,15,THRU,18$SESET,7,1,THRU,8$PARTITIONEDSOLUTIONSForeachsuperelement,itsdegrees-of-freedom(DOFs)aredividedintotwosubsets:ExteriorDOFs(calledtheA-set):DesignatestheanalysisDOFs,whichareretainedforsubsequentprocessing(forSuperelement1,GridPoints35and36)InteriorDOFs:DesignatestheDOFsthatarereducedoutduringsuperelementprocessingandareomittedinsubsequentprocessing(forSuperelement1ofthesampleproblem,GridPoints33,34,37,38,45–50,57–62,69–74,81–86,93–98).TheMainBulkDataispartitionedbysuperelement(althoughthefollowingoperationsareperformedusingtables,itiseasiertothinkofthemintermsoftheBulkData).AllBulkDatauniquetothesuperelementisremovedfromtheoriginalinputandplacedintoauniquesetforthesuperelement.BulkDatathatis‘shared’orusedbymorethanonesuperelement(ex:PSHELL,MAT1,etc.)iscopiedforeachapplicablesuperelement.PARTsarealreadyseparated.PARTITIONEDSOLUTIONS(Cont.)Foreachsuperelement,theprogramproducesadescriptioninmatrixtermsofitsbehaviorasseenattheboundaryorexteriordegreesoffreedom.Asetof‘G’-sizedmatricesisproducedforeachsuperelementbasedontheinputdata.Thesematricesarereduceddowntomatricesrepresentingthepropertiesofthesuperelementasseenbytheadjacent(attached)structure.Attheresidualstructure,theprogramcombinesandassemblestheboundarymatrices.TheBULKDATAfortheRESIDUALconsistsofall‘residual’MainBulkDatanotassignedtoanysuperelementplusanycommondata.Solvefortheresidualstructuredisplacements.Foreachsuperelement,expandboundary(exterior)displacementstoobtainitsinteriordisplacements.THEORYOFSTATICCONDENSATIONAftergeneratingmatricesandapplyingMPCsandSPCs,O-Set=Interiorpoints(tobecondensedoutbythereduction)A-Set=exterior(orboundary)points(whichareretainedfor furtheranalysis)PartitionExtractupperequationandpre-multiplyby

Let (BoundaryTransformation)

and (FixedBoundaryDisplacements) then (TotalInteriorDisplacements)THEORYOFSTATICCONDENSATION(Cont.)SubstituteexpressionforUointhelowerequationthen (BoundaryStiffness)and (BoundaryLoads)Solveforresidualstructure

(Boundarydisplacements)CONVENTIONALANALYSISFlowchartGenerationSolutionCONVENTIONALANALYSIS(Cont.)GenerationCONVENTIONALANALYSIS(Cont.)ApplyConstraintsandSolveSUPERELEMENTANALYSISFlowchartDOLABELAI=1,NSEPhaseIGenerationAssemblyReductionLABELAPhaseIISolutionDOLABELBI=1,NSEPhaseIIIDataRecoveryLABELBSUPERELEMENTANALYSIS(Cont.)Generation–SEID=1ResidualStructureSUPERELEMENTANALYSIS(Cont.)Reduction–SEID=1Eliminateconstraints:Computeboundarytransformation:

SUPERELEMENTANALYSIS(Cont.)Computeboundarystiffness:Computeboundaryloading:0SUPERELEMENTANALYSIS(Cont.)Similarly–SEID=20SUPERELEMENTANALYSIS(Cont.)ResidualStructureAssemblySolution0SUPERELEMENTANALYSIS(Cont.)DataRecovery–SEID=1Enforce(transform)boundarymotion.Computefixed-boundarymotion.Computetotalmotion.BULKDATAFORSTATICLOADSONSUPERELEMENTS MainBulkDataSuperelements:Loadsappliedtointeriorgridpointsareassignedtothesuperelement.Loadsappliedtoexteriorgridpointsareassignedtothemostdownstreamsuperelement,thatis,thesuperelementforwhichthegridpointisinterior.Loadsappliedtoelements(PLOADi)areassignedinthesamemanneraselements.

Note:APLOADentrymaynotreferencetheinteriorpointsofmore thanonesuperelement. PartitionedSuperelements:AnyLoading–relatedentriesmustbedefinedinthepartitioneddata(intheareaoftheinputfilebeginningwith’BEGINSUPER=’) STATICLOADSONMAINBULKDATASUPERELEMENTS Example SESET,1,4,5,6Grids4,5,and6areinteriorpointstoSuperelement1.Point3isexteriortoSuperelement1.P2isassignedtoSuperelement0.WandP1isassignedtoSuperelement1.Superelement0Superelement1MAINBULKDATASUPERELEMENTSConstraintentriesappliedtotheinteriorpointsofasuperelementareassignedtothatsuperelement.Constraintentriesappliedtotheexteriorpointsofasuperelementare“sent”downstream.MultipleboundaryconditionsareallowedfortheresidualstructureonlyFormultipleboundaryconditions,placegridpointsthatwillbeconstrainedinteriortotheresidualstructure.EachsuperelementmayhaveonlyoneSPCsetperrun.PARTITTIONEDSUPERELEMENTSAllconstraint–relatedbulkdataentriesfortheinteriorpointsofaPARTmustbedefinedinthepartitionedbulkdata(BEGINSUPER=).SINGLE-POINTCONSTRAINSTSONSUPERELEMENTSSINGLE-POINTCONSTRAINSTSONSUPERELEMENTS(Cont.)SESET,1,4,5,6GridPoints4,5,and6areinteriortoSuperelement1.Point3isexteriortoSuperelement1.SPCat3isassignedtoSuperelement0.SPCat6isassignedtoSuperelement1.Superelement0Superelement1MPCsANDRIGIDELEMENTSINSUPERELEMENTSRigidelementsandMPCsthatconnectonlyinteriorpointsaremodeledconventionally.Dependentdegreesoffreedommaynotbeexterior.ForMPCsandrigidelementsthatconnecttwosuperelements,Placetheupstreamdegreesoffreedominthedependentset.Placethedownstreamdegreesoffreedomintheindependentset.MultiplemultipointconstraintconditionsareallowedfortheresidualstructureonlyFormultiplemultipointconstraints,placegridpointsthatwillbespecifiedontheseinteriortotheresidualstructure.EachsuperelementmayhaveonlyoneMPCsetperrun.(Note:MPCADDmaybeused.)RIGIDCONNECTIONOFTWOSUPERELEMENTSMETHOD1–RBARMETHOD2–MPC$ SEID GP1 GP2 GP3 ETC.SESET 1 11 12 13$ EID GA GB CNA CNB CMA CMBRBAR 100 3 11 123456 123456$ SEID GP1 GP2 GP3 ETC.SESET 1 11 12 13$ SID G C A G C AMPC 100 11 1 1. 3 1 –1.= = = *(1) = = *(1) ==(4)CSUPEXT13$ EID G1 G2PLOTEL 100 3 11orResidualStructure?SEID=1CBARRigidConnectionSUPERELEMENTCASECONTROLCOMMANDSSE-type(manualprocessing)–SEMG,SELG,SEKR,SELR,SEMR,SEDR,andSEALL–appearabovethefirstSUBCASEifusedControlsolutionsequenceexecutionMakenorequestsforloads,constraints,oroutputSEALLcombinesSEMG,SELG,SEKR,SELR,andSEMRNotnecessaryinSOL101andhigher(defaultisSEALL=ALL,whichimpliesthatallnecessaryprocessingwillbeperformed)Superelementprocessingordercontrol–appearabovethefirstSUBCASEifusedSEFINAL–Lastsuperelementstobeprocessedbeforeresidualstructure–notrecommendedSEEXCLUDE–SuperelementsnottobeassembleddownstreamCaseControlpartitioning–SUPERAssignsasubcase(s)toaspecificsuperelement(s)AppearsaboveorbelowsubcaselevelSUPERCOMMANDPartitions(assigns)asubcasetoasuperelement(s)Associatesasuperelement(s)withrequestsforparameters,loads,constraints,andoutputPre–V69–IftheCaseControlSectiondoesnotcontainaSUPERcommand,thenloads,constraints,andoutputrequestsareappliedtotheresidualstructureonly(theolddefaultwasSUPER=0).V69ThenewdefaultisSUPER=ALL.ifnoSUPERcommandispresent,thesubcasesareassumedtoapplytoALLsuperelements(ifanySUPERcommandsoccurintheCaseControl,thedefaultrevertstoSUPER=0forupwardcompatibility).TheSUPERcommandmayreferenceasuperelementoraSETofsuperelements.Note:TheSETIDmustbeuniquewithrespecttoanysuperelementIDs.FormofSUPERcommandSUPER=i,j wherei=superelementIDorsetofsuperelements j=loadsequencenumber(acounteronloadingconditions)EXPANDEDVERSUSCONDENSEDConventionalCaseControlExpandedCondensedSUBCASE10SET1=101THRU110DISP=1LOAD=100SUBCASE20SET1=101THRU110DISP=1LOAD=200SUBCASE30SET3=201THRU210DISP=3LOAD=200SET1=101THRU110SET3=201THRU210DISP=1LOAD=200SUBCASE10LOAD=100SUBCASE20SUBCASE30DISP=3EXPANDEDVERSUSCONDENSED(Cont.)SuperelementCaseControlExpanded–oneloadingconditionCondensed$modelwithsuperelements10,20,0DISP=ALLSUBCASE1$SE10SUPER=10LOAD=100SUBCASE2$SE20SUPER=20LOAD=100SUBCASE101$RESIDUALSTRUCTURESET999=0SUPER=999LOAD=100BEGINBULKSUBCASE1 DISP=ALL LOAD=100BEGINBULKSUPERCOMMANDEXAMPLE—ONELOADINGCONDITION$SEIDS1,2,3,4,5,0DISP=ALLSUBCASE10 SET101=1,4 SUPER=101 SPC=12SUBCASE20 SET103=2,5 SUPER=103 SET15=7,9 ELFOR=15 LOAD=9SUBCASE30 SUPER=0 ELSTRE=ALLMULTIPLELOADINGCONDITIONSINSUPERELEMENT

CASECONTROL–OPTION1AppearsidenticaltoconventionalCaseControlForeachloading,createonesubcase(usethedefaultSUPER=ALL)Option1requiresAllsuperelementsmustusethesameloading,SPC,andM