Guidelines for the implementation of the CWELD and

FiniteElementsinAnalysisandDesign41(2004)193–210finelGuidelinesfortheimplementationoftheCWELDandACM2spotweldmodelsinstructuraldynamicsMatteoPalmonellaa,MichaelI.Friswellb,∗,JohnE.Mottersheadc,ArthurW.LeesaaSchoolofEngineering,UniversityofWalesSwansea,SingletonPark,SwanseaSA28PP,UKbDepartmentofAerospaceEngineering,UniversityofBristol,Queen’sBuilding,UniversityWalk,BristolBS81TR,UKcDepartmentofEngineering,UniversityofLiverpool,LiverpoolL693GH,UKReceived30November2003;accepted11April2004Availableonline10August2004AbstractOfthemanyspotweldmodelssuggestedintheliterature,CWELDandACM2arethemostwidelyusedinindustry.Theyarecoarsemodelswiththeimportantcharacteristicthattheyallowtheweldedplatestobemeshedindependently.Thismakesthemsuitableformodellinglargespotweldedstructuressuchasanautomotivebody-in-white.Althoughwidelyused,noguidelinesexistintheliteraturefortheirimplementation.Itisshowninthispaperthatthenaturalfrequenciesofthebenchmarkstructuresareverysensitivetosomeparameterscharacterisingthesemodels.Inpractice,oftenlittlecareisexercisedinsettingthevaluesoftheseparameterstobeclosetotheiroptimalvalues.InthispaperthetechniquesofmodelupdatinginstructuraldynamicsareusedtoanalyseandimproveCWELDandACM2models,andguidelinesaregivenfortheiroptimumimplementation.
2004ElsevierB.V.Allrightsreserved.Keywords:Spotwelds;CWELD;ACM2;Structuraldynamics1.IntroductionSpotweldsareusedextensivelyintheautomotiveindustrytojoinpanelstomakeautomotivebodies.Extensiveeffortsaremadetoaccuratelysimulatethesebodiesusingfiniteelementmodelling,andthesemethodsareusedtooptimisethedesigns.ThemostcommonlyusedfiniteelementmodelsofspotweldsaretheCWELDandACM2models[1].Thesemodelssharethegreatadvantageofnotconstrainingthe∗Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddress:[e-mail](M.I.Friswell).0168-874X/$-seefrontmatter
2004ElsevierB.V.Allrightsreserved.doi:10.1016/j.finel.2004.04.003194M.Palmonellaetal./FiniteElementsinAnalysisandDesign41(2004)193–210meshneartothespotwelds,andthusnoremeshingofthepanelstobejoinedisrequired.TheCWELDmodelhasonlyrecentlyappearedintheNASTRANelementlibrary,andiseasiertoimplementthantheACM2model.ThetrendistosubstitutetheACM2modelwithCWELD.Theaimofthispaperistoinvestigatetheaccuracythetwomodelsandtogiveguidelinesontheiruse.Despitethelargenumberofapplicationsofthesemodels,noguidelinesexistfortheirimplementation.Oneimportantissueisthemeshsizeoftheweldedplatesclosetospotweld.Thegroupofelementsinvolvedinthedefinitionofthespotweldmodeliscalledapatch,andoftentheareaandshapeofthesepatchesareverydifferentfordifferentspotwelds.Evenforasinglespotweld,theupperandlowerpatchesmayhaveverydifferentdimensions.Howeverthispaperwillshowthatthepatchareasignificantlyinfluencesthestiffnessofthestructure,andmeansthattheareassurroundingthespotweldsmustbemeshedwithcare.Anothercommonpracticeistomatchthebrickdimensionstothespotwelddiametersothatthebrickisinscribedonthecirclerepresentingthespotweld.Inrealitythespotwelddiameterdoesnotinfluencethestructure’sstiffness[2],whereasthebrickdimensionsdoinfluencethestiffnessofthemodel.Thuschangingthebricksizetomatchthespotwelddiameterisnotacceptable.InthispaperthetechniquesofmodelupdatinginstructuraldynamicswillbeusedtoimprovetheCWELDandACM2models,givingguidelinesfortheirimplementation.Forthispurposefivebenchmarkstructureshavebeenanalysedandupdatedusingsuitablespotweldparameters.2.CWELDandACM2modeldescriptionThespotweldmodelproposedbyFangetal.[3]isimplementedinNASTRANastheCWELDelement.TheCWELDelementismodelledwithaspecialshearflexiblebeam-typeelementwithtwonodes,andtwelvedegreesoffreedom.Iftheplatemesheswerecongruent,withnodesatthespotweldlocation,thenthebeamelementcouldbeusedtodirectlyconnectthetwoplates(providingtheplateelementsprovidesufficientrotationalstiffness).Forgeneralmeshesthenodesofthebeamareconnectedtoachosensetofnodesoftheplateitbelongsto.Theareaenclosedbythenodesofeachplatethatareattachedtothebeamelementarecalled“patches”.Fig.1showsatypicalpatchassociatedwithaspotweld,whereeachpatchconsistsof4elements.ThesixdegreesoffreedomofeachbeamnodeareconnectedtothethreeUpperpatchLowerpatchSpotweldelementFig.1.AschematicofthepatchassociatedwiththeCWELDspotweld.M.Palmonellaetal./FiniteElementsinAnalysisandDesign41(2004)193–210195RBE3elementsFig.2.AschematicofthepatchassociatedwiththeACM2spotweld.translationaldegreesoffreedomofeachplatenodewithconstraintsfromKirchoffshelltheory.Theseconnectionsyield12constraintequationsthatmaybeusedtogeneratemultipointconstraintsexplicitly,ortheconstraintsmaybeusedtoobtainthebeamstiffnessmatrixintermsoftheplatedegreesoffreedom.Heisereretal.[4]proposedthemodelknownasACM2(areacontactmodel2).ThemodelconsistsofabrickelementconnectingtheupperandlowerplatesviaRBE3elementsthatareavailableinNASTRAN.TheRBE3elementdistributestheappliedloadsthroughoutthemodel.ForcesandmomentsappliedtothebricknodesaredistributedtotheshellnodesinawaythatdependsontheRBE3geometryandweightfactorsassignedtotheshellnodes.Theweightsarethevaluesassumedbytheshapef