Application of Topology Size and Shape Optimization Methods in Polymer Metal Hybrid Structural.docx

Application of Topology Size and Shape Optimization Methods in Polymer Metal Hybrid Structural.docx

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ApplicationofTopologySizeandShapeOptimizationMethodsinPolymerMetalHybridStructural

ApplicationofTopology,SizeandShapeOptimizationMethodsinPolymerMetalHybridStructuralLightweightEngineering

Abstract

Applicationoftheengineeringdesignoptimizationmethodsandtoolstothedesignofautomotivebody-in-white（BIW）structuralcomponentsmadeofpolymermetalhybrid（PMH）materialsisconsidered.Specifically,theuseoftopologyoptimizationinidentifyingtheoptimalinitialdesignsandtheuseofsizeandshapeoptimizationtechniquesindefiningthefinaldesignsisdiscussed.TheoptimizationanalysesemployedwererequiredtoaccountforthefactthattheBIWstructuralPMHcomponentinquestionmaybesubjectedtodifferentin-serviceloadsbedesignedforstiffness,strengthorbucklingresistanceandthatitmustbemanufacturableusingconventionalinjectionover-molding.Thepaperdemonstratestheuseofvariousengineeringtools,i.e.aCADprogramtocreatethesolidmodelofthePMHcomponent,ameshingprogramtoensuremeshmatchingacrossthepolymer/metalinterfaces,alinear–staticanalysisbasedtopologyoptimizationtooltogenerateaninitialdesign,anonlinearstatics-basedsizeandshapeoptimizationprogramtoobtainedthefinaldesignandamold-fillingsimulationtooltovalidatemanufacturabilityofthePMHcomponent.

Keywords

Topology,Optimization,HybridStructural,LightweightEngineering

1.Introduction

Lightweightengineeringforautomobilesisprogressivelygaininginimportanceinviewofrisingenvironmentaldemandsandever-tougheremissionsstandards.Currenteffortsintheautomotivelightweightengineeringinvolveatleastthefollowingfivedistinctapproaches[1]:

（a）Requirementlightweightengineeringwhichincludeseffortstoreducethevehicleweightthroughreductionsincomponent/subsystemrequirements（e.g.areducedrequiredsizeofthefueltank）;（b）Conceptuallightweightengineeringwhichincludesthedevelopmentandimplementationofnewconceptsandstrategieswithpotentialweightsavingssuchastheuseofaself-supportingcockpit,astraightenginecarrier,etc.;（c）Designlightweightengineeringwhichfocusesondesignoptimizationoftheexistingcomponentsandsub-systemssuchastheuseofribsandcomplexcrosssectionsforenhancedcomponentstiffnessatareducedweight;（d）Manufacturinglightweightengineeringwhichutilizesnovelmanufacturingapproachestoreducethecomponentweightwhileretainingitsperformance（e.g.acombinedapplicationofspotweldingandadhesivebondingtomaintainthestiffnessofthejoinedsheet-metalcomponentswithreducedwallthickness）;and（e）Materiallightweightengineeringwhichisbasedontheuseofmaterialswithahighspecificstiffnessand/orstrengthsuchasaluminumalloysandpolymer-matrixcompositesorasynergisticuseofmetallicandpolymericmaterialsinahybridarchitecture（referredtoaspolymermetalhybrids,PMHs,intheremainderofthismanuscript）.Inthepresentwork,theproblemofintegrationoftheengineeringoptimizationmethodsandtoolsintotheaforementionedlightweightengineeringefforts,specificallyintoPMHtechnologyforbody-in-white（BIW）load-bearingautomotivecomponentsprocessedbytechniquessuchasinjectionover-molding[2]ormetalover-molding[3].Suchcomponentsaretypicallydesignedforstiffnessandbucklingresistanceandtheirperformanceisgreatlyaffectedbythedesignoftheplasticribbingstructureinjectionmoldedintoasheet-metalstamping.

Inconventionalautomotivemanufacturingpractice,metalsandplasticsarefiercecompetitors.ThePMHtechnologies,incontrast,aspiretotakefulladvantageofthetwoclassesofmaterialsbycombiningtheminasinglecomponent/sub-assembly.Thefirstexampleofasuccessfulimplementationofthistechnologicalinnovationinpracticewasreportedattheendof1996,whenthefrontendoftheAudiA6（madebyEcia,Audincourt/France）wasproducedasahybridstructure,combiningsheetsteelwithelastomer-modifiedpoly-amidePA6-GF30（DurethanBKV130fromBayer）.Akeyfeatureofhybridstructuresisthatthematerialsemployedcomplementeachothersothattheresultinghybridmaterialcanofferanenhancedoverallstructuralperformance.

Currently,PMHsarereplacingall-metalstructuresinautomotivefront-endmodulesatanacceleratedrateandarebeingusedininstrument-panelandbumpercross-beams,doormodules,andtailgatesapplications.Moreover,newPMHtechnologiesarebeing

introduced.

ThemainPMHtechnologiescurrentlybeingemployedintheautomotiveindustrycanbegroupedintothreemajorcategories:

（a）Injectionover-moldingtechnologies[2];（b）Metal-over-moldingtechnologiescombinedwithsecondaryjoiningoperations[3];and（c）Adhesively-bondedPMHs[4].AdetaileddescriptionforeachofthesegroupsofPMHmanufacturingtechnologiescanbefoundinourrecentwork[5].

Theobjectiveofthepresentworkistoextendtheaforementionedtwo-stepoptimizationapproachtoBIWloadbearingPMHcomponents.Atypicalall-metalBIWloadbearingcomponent,Figure1（a）,consistsoftwoflangedU-shapestampingsjoinedalongtheirmatchingflangesbyspot-welding（oftencomplementedbyadhesivebonding）.Whensuchanall-metalcomponentisreplacedwithaPMHcomponent,Figure1（b）,oneofitsstampingsisremovedandtheexterioroftheremainingstampingreinforcedusinganinjection-moldedthermoplasticrib-likestructure.Hence,theobjectiveofthepresentworkistoaddresstheoptimalarchitectureoftheribbingstructurewithrespecttodifferentloadingrequirements（axialcompression,bending,twisting）anddifferentdesignrequirements（e.g.stiffness,strength,bucklingresistance）.Theexamplesconsideredshowhowtopologyoptimizationmaybeusedtosuggestgoodinitialdesigns,butalsodemonstrateshowatopologyoptimizationfollowedbyadetailedsizeandshapeoptimizationmaybeusedtoprovideefficientdesignssatisfyingperformanceandmanufacturingconstraints.

Fig.1（a）Atwin-shellall-metalrearcross-roofmemberand（b）itspolymermetalhybridcounterpartconsistingasinglemetal-shellstampingandinjection-moldedplasticribbing.

Theorganizationofthepaperisasfollows:

Anoverviewofthebasicsoftopology,

sizeandshapeoptimizationmethodsispresentedandabriefdescriptionofthemaincomputationaltoolsusedinthepresentworkisgiveninSectionII.TheresultsobtainedinthepresentworkarepresentedanddiscussedinSectionIII.ThemainconclusionsresultingfromthepresentworkaresummarizedinSectionIV.

2.ComputationProcedure

2.1TheBasicsofStructuralTopology,SizeandShapeOptimization

Structuraloptimizationisaclassofengineeringoptimizationproblemsinwhichthe

evaluationofanobjectivefunction（s）orconstraintsrequirestheuseofstructural

analyses（typicallyafiniteelementanalysis,FEA）.Incompactform,theoptimization

problemcanbesymbolicallydefinedas:

Minimizetheobjectivefunctionf（x）

Subjecttothenon-equalityconstraintsg（x）<0andtotheequalityconstraints

h（x）=0

WherethedesignvariablesxbelongtothedomainD

where,ingeneral,g（x）andh（x）arevectorfunctions.Thedesignvariablesxformavectorofparametersdescribingthegeometryofaproduct.Forexample,x,f（x）

g（x）andh（x）canbeproductdimensions,productweight,astressconditiondefiningtheonsetofplasticyielding,andconstraintsonproductdimensions,respectively.

TopologyOptimization

Topologyoptimizationmethodsallowthechangesinthewaysubstructuresareconnectedwithinafixeddesigndomainandcanbeclassifiedas（a）discreteelement

（alsoknownasthegroundstructure）approach;and（b）continuumapproaches.Inthe

discreteelementapproach,thedesigndomainisrepresentedasafinitesetofpossible

locationsofdiscretestructuralmemberssuchastruss,frame,andpanels.Byvaryingthewidth/thicknessofeachmemberinthedesigndomainbetweenzero（inthiscasetheelementbecomesnonexistent）andacertainmaximumvalue,structureswithdifferentsizesandtopologiescanberepresented.Inthecontinuumapproach,thedesigndomainisrepresentedasthecontinuummixtureofamaterialand“void”andtheoptimaldesignisdefinedwithrespecttothedistributionsofthematerialdensitywithinthedesignspace.Sincethediscreteelementapproachutilizesacollectionofprimitivestructuralmembers,itallowseasyinterpretationoftheconceptualdesign.However,potentiallyoptimaltopologiesmaynotbeattainablebythenumberandtypesofpossiblememberlocationsdefinedinthedesigndomain.Thecontinuumapproach,ontheotherhand,doesnothavethislimitation,whileitmaybecomputationallymoreexpensive.Overthelastdecades,majoradvanceshavebeenreportedintheareaofthediscreteelementstructuraloptimization[6-10].

SizeOptimization

Withinsizeoptimizationapproach,thedimensionsthatdescribeproductgeometryare

usedasdesignvariables,x.Theapplicationofsizeoptimizationis,consequently,mostlyusedatthedetaileddesignstagewhereonlythefinetuningofproductgeometryisnecessary.Sizeoptimizationistypicallydoneinconjunctionwithfeature-basedvariationgeometry[11]whichisavailableinmanymodernCADprograms.Withpresent-dayavailabilityoffastpersonalcomputers,sizeoptimizationisrelativelyastraightforwardtaskandittypicallyrequiresnore-meshingofthefiniteelementmodelsduringoptimizationiterations.Adifficultymayarise,however,whenextremelylargefiniteelementmodelsorhighlynonlinearphenomenaneedtobeanalyzed,inwhichcasesurrogate（simplified）modelsaretypicallyemployed.

ShapeOptimization

Shapeoptimizationallowsthecha