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FiniteElementAnalyticalTechniquesandApplicationstoStructuralDesignPage111FiniteElementAnalyticalFiniteElementAnalyticalFiniteElementAnalyticalFiniteElementAnalyticalFiniteElementAnalyticalTTTTTechniqechniqechniqechniqechniquesandApplicationstuesandApplicationstuesandApplicationstuesandApplicationstuesandApplicationstoooooStructuralDesignStructuralDesignStructuralDesignStructuralDesignStructuralDesignTawfikKhalilandPaulDuBoisAnalyticalsimulationofvehiclecrashworthinesshasevolvedoverthepast30years.Threetypesofmodelsareusedtosimulatevehiclestructures-LumpedParameter(LP)models,hybridmodels,andFiniteElement(FE)models.TheFEmodelscanbedividedintotwogroups:heuristicbeammodelsandcontinuummechanics-basedmodelswhichusebeam,solidandshellelements.Theprogressionofthesemodelsovertheyearsfollowedapatternofincreasinggeometricdetailssinceitwasrealizedthatasimpleanalyticalmodelofthecrashevent,developedandtunedtofitoneormoreparametersfromaspecifictest,doesnotensureaccuratepredictionforallimpactconditions.Infact,themostdetailedmodels(LPorFE)developedtodateshouldbeconsideredapproximationsofahighlycomplexnon-linearsystemthatisoftensubjecttolargeandunstableelastic-plasticdeformations.Obviously,advancesinunderstandingcomplexsystemperformancesuchascrashworthinesscanbeachievedbyincreasinglyincludingmoredetailsthatcapturerealisticvehiclekinematicsandloadsencounteredingeneralcrashconditions.ThischapterprovidesanoverviewoftheFEtechniquesusedinvehiclebodystructuraldevelopmenttosatisfythedesignconstraintsnecessaryforthevehicletomeetmyriadsafetyrequirementsexpectedofthevehiclestructureandtoassurevehiclecrashworthiness.Theanalyticaltoolsusedtoassessoccupantresponseincrashandhumantolerancetoimpactisaddressedinanotherchapter.Forcompleteness,recentmodelsthatintegratetheoccupant,restraintsystems,andvehiclestructureinasingleanalysiswillbediscussedinthischapter.3.1HistoricalBackgroundThehistoryofstructuralcrashworthinessanalysiscanbestbecharacterizedbytwoperiodsofhistoricaldevelopment:anearlyperiod,extendingfrom1970toVehicleCrashworthinessandOccupantProtectionPage112about1985;andasecondperiodbeginninginthemid-1980swiththeintroductionofsupercomputersandvectorizedexplicitfiniteelementcodes.Thefirstperiodwasessentiallyoneofgenesisandgrowth,aperiodoftrial,ofattemptingtodevelopsomeunderstandingofanextremelycomplexstructuralmechanicsproblem.Avarietyofnumericaltechniqueswereappliedtosimulatethedeformations,includingfoldingandbucklingofacarstructureduringthedecisivefirst50to100msofacrashtest.Approximatesolutionswereobtainedbyspring-massmodelingofthevehicle[1,2],anapproachoriginatedintheaerospaceindustry.Alternatively,solutionswereobtainedbyusingbeamelementmodelsinconjunctionwithnonlinearjointformulations[3,4,5]thatprovedverysuccessfulonnumerousoccasions,butrequiredarelativelyhighdegreeofskillandexperiencefromtheanalyst.Therewerealsoattemptstoobtainsolutionsbasedonfirstprinciplesbymodelingthecarbodyasacontinuum,andthus,automatingthetaskofattributingdiscretizedstiffnessvaluestothestructuralcomponents.Someofthisworkwasbasedonquasi-staticbeamelementformulation[6],implicitFEtechniques[7,8,9],finitedifferencemethods[10],implicit/explicitFEformulations[11]and,explicitFEtimeintegration[12].Itappearsthatthefirstcrashmodel[13]simulatedahead-oncollisionofavehiclefrontstructurewitharigidwall,usingthecomputercodeDYCASTwithanimplicitsolver[8].Inthismodel,thelefthalfofthevehiclewasrepresentedby504membranetriangular,beam,bar,andspringelements.Haug[11]discussedthedevelopmentofanimplicit-explicitintegrationFEPAM-CRASHcode,whichwasthenappliedtoanalyzetheresponseofanA-pillar,andnexttotherightfrontquarterofaunit-bodypassengervehiclestructure.Thequasi-staticanalysiswasaccomplishedbyaniterativeincrementalforce/displacementanalysis.ThetheoreticalbackgroundforimplicitFEformulationandanassociatedcodeforcrashanalysiswerepresentedbyArgyrisetal[9].Thedevelopedcodewasappliedtocalculatetheimpactresponseofavehiclefrontstructure,devoidofengine,transmissionanddriveline,whenitimpactedarigidbarrierfromaninitialvelocityof13.4m/s.Thesolutionaccountedformaterialstrainhardeningandrateeffects,andprovidedstructuraldeformations.Otherthanthethreeexamplesmentionedabove,theapplicationofimplicitFEsolverstocrashanalysisdidnotproceedbeyondthatpoint,primarilyduetoitsinabilitytoaccountforcontactandfoldingofthinsheetmetalstructuresandduetoexcessivedemandsoncomputerhardwarestorageandspeed.Someofthesedevelopmentsalreadycontainedtheessentialfeaturesthatmakeupthecoreofanycrashanalysissoftwaretoday.TheycombinedtimeintegrationFiniteElementAnalyticalTechniquesandApplicationstoStructuralDesignPage113withshellelements,node-to-segmentcontactforcetransmissions,andplanestresselasto-plasticity.Sincethesearestillthebasicalgorithmsusedintoday’sanalysisenvironment,itisnotsurprisingthatasearlyas1973,verygoodanalyticalresultswereobtainedonvehiclesubstructures.Thecontinuumapproach,however,remainedmainlyintheprovinceofresearch,sincethegoaloffull-vehiclesimulationcouldnotbeachievedwithsufficientaccuracyduetothelimitednumberof