多体动力学和非线性有限元联合仿真

NAFEMSEuropeanConference:CoupledMBS-FEApplications:ANewTrendinSimulationNovember26-27,2013Frankfurt,GermanyANewSolutionForCoupledSimulationOfMulti-BodySystemsAndNonlinearFiniteElementModelsGiancarloCONTI,TanguyMERTENS,TariqSINOKROT(LMS,ASiemensBusiness)HiromichiAKAMATSU,HitoshiKYOGOKU,KojiHATTORI(NISSANMotorCo.,Ltd.)1IntroductionOneofthemostcommonchallengesforflexiblemulti-bodysystemsistheabilitytoproperlytakeintoaccountthenonlineareffectsthatarepresentinmanyapplications.Oneparticularcasewheretheseeffectsplayanimportantroleisthedynamicmodelingoftwistbeamaxlesincarsuspensions:thesecomponents,connectingleftandrighttrailingarmsanddesignedinawaythatallowsforlargetorsionaldeformations,cannotbemodeledasrigidbodiesandrepresentacriticalfactorforthecorrectpredictionofthefull-vehicledynamicbehavior.Themostcommonmethodstorepresenttheflexibilityofanypartinamulti-bodymechanismarebasedonmodalreductiontechniques,usuallyreferredtoasComponentModeSynthesis(CMS)methods,whichpredictthedeformationofabodystartingfromapreliminarymodalanalysisofthecorrespondingFEmesh.Severaldifferentmethodshavebeendevelopedandverified,butmostofthemcanbeconsideredasvariationsofthesameapproachbasedonalimitedsetofmodesofthestructure,calculatedwiththecorrectboundaryconditionsateachinterfacenodewiththerestofthemechanism,allowingtogreatlyreducethesizeofsystem’sdegreesoffreedomfromalargenumberofnodestoasmallsetofmodalparticipationfactors.Byproperlyselectingthenumberandfrequencyrangeofthemodes,aswellastheboundaryconditionsateachinterfacenode[1],itispossibletoaccuratelypredictthestaticanddynamicdeformationoftheflexiblebodywithremarkableimprovementsintermsofCPUtime:thismakesthesemethodsthestandardapproachtoreproducetheflexibilityofcomponentsinamulti-bodyenvironment.Still,animportantlimitationinherentlyliesintheirownfoundation:sincedisplacementsbasedonmodalrepresentationarebydefinitionlinear,anynonlinearphenomenacannotbecorrectlysimulated.Forexample,largedeformationsliketwistbeamtorsionduringhighlateralaccelerationcorneringmaneuverstypicallyleadtogeometricnonlinearities,preventinganylinearsolutionfromaccuratelypredictingmostofthesuspension’selasto-kinematiccharacteristicsliketoeanglevariation,wheelcenterposition,verticalstiffness.Onepossiblesolutiontoovercometheselimitationswhilestillworkingwithlinearmodalreductionmethodsisthesub-structuringtechnique[2]:thewholeflexiblebodyisdividedintosub-structures,whichareconnectedbycompatibilityconstraintspreventingtherelativemotionofthenodesthatliebetweentwoadjacentsub-structures.Standardcomponentmodesynthesismethodsareusedinformulatingtheequationsofmotion,whicharewrittenintermsofgeneralizedcoordinatesandmodalparticipationfactorsofeachsub-structure.Theideabehinditisthateachsub-portionofthewholeflexiblestructurewillundergosmallerdeformations,henceremaininginthelinearflexibilityrange.Byproperlyselectingthecuttingsectionsitisusuallypossibletoimprovetheaccuracyofresults(atleastintermsofnodaldisplacements:lessaccuracycanbeexpectedforstressandstraindistribution).Anotherlimitationofthesemethodsisthepreliminaryworkneededtore-arrangetheFEmesh,althoughsomeCAEproductsalreadyofferautomaticprocessesenablingtheusertoskipmostofthere-meshingtasksandhencereducingthemodelingefforts.Analternativeapproachtosimulatethebehaviorofnonlinearflexiblebodiesisbasedonaco-simulationtechniquethatusesaMulti-bodySystem(MBS)solverandanexternalnonlinearFiniteElementAnalysis(FEA)solver.UsingthistechniqueonecanmodeltheflexiblebodyintheexternalnonlinearFEAcodeandtherestofthecarsuspensionsystemintheMBSenvironment.TheloadsduetothedeformationofthebodyarecalculatedexternallybytheFEAsolverandcommunicatedtotheMBSsolveratdesignatedpointswheretheflexiblebodyconnectstotherestofthemulti-bodysystem.TheMBSsolver,ontheotherhand,calculatesdisplacementsandvelocitiesofthesepointsandcommunicatesthemtothenonlinearFEAsolvertoadvancethesimulation.Thisapproachdoesn’tsufferfromthelimitationsthatarisefromthelinearmodelingoftheflexibilityofabody.Thisleadstomoreaccurateresults,albeitatthepriceofmuchlargerCPUtime.Infact,simulationresultsarestronglyaffectedbythesizeofthecommunicationtimestepbetweenthetwosolvers:abetteraccuracy(andmorestablesolverconvergence)canbegenerallyobtainedbyusingsmallertimestepswhichrequirelargercalculationtimes,asshownalsoin[3].NAFEMSEuropeanConference:CoupledMBS-FEApplications:ANewTrendinSimulationNovember26-27,2013Frankfurt,Germany2OverviewoftheactivityThispaperpresentstheresultsofabenchmarkactivityperformedincollaborationwithNissanAutowhereanewFE-MBSvariable-stepco-simulationtechniquewasused:acouplingattheiterationlevelcurrentlyimplementedincommercialFEApackageLMSSAMCEFMecano[4]andgeneralpurposemulti-bodysystempackageLMSVirtual.LabMotion[5].InthistechniqueeachsolverusesitsownintegratorbutonlyoneNewtonsolverisused.InthiscaseonesolverisdesignatedasthemasterandwillberesponsibleforsolvingtheNewtoniterations.Thecouplediterationscontinueuntilbothsolverssatisfytheirownsolutiontolerancesandconvergenceisachieved.Theco-simulationprocessisorganizedbymeansofasuperviso