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1、COMPUTERMETHODSINAPPLIEDMECHANICSANDENGINEERING71(1988)197-224NORTH-HOLLANDGENERATINGOPTIMALTOPOLOGIESINSTRUCTURALDESIGNUSINGAHOMOGENIZATIONMETHODMartinPhilipBENDS~EMathematicalInstitute,TheTechnicalUniversityofDenmark,DK-2800Lyngby,DenmarkandNoboruKIK
2、UCHIAppliedMechanicsDepartment,ComputationalMechanicsLaboratory,UniversityofMichigan,AnnArbor,MI48109,U.S.A.Received28March1988Optimalshapedesignofstructuralelementsbasedonboundaryvariationsresultsinfinaldesignsthataretopologicallyequivalenttotheinitia
3、lchoiceofdesign,andgeneral,stablecomputationalschemesforthisapproachoftenrequiresomekindofremeshingofthefiniteelementapproximationoftheanalysisproblem.Thispaperpresentsamethodologyforoptimalshapedesignwhereboththesedrawbackscanbeavoided.Themethodisrela
4、tedtomodernproductiontechniquesandconsistsofcomputingtheoptimaldistributioninspaceofananisotropicmaterialthatisconstructedbyintroducinganinfimumofperiodicallydistributedsmallholesinagivenhomogeneous,i~otropicmaterial,withtherequirementthattheresultings
5、tructurecancarrythegivenloadsaswellassatisfyotherdesignrequirements.Thecomputationofeffectivematerialpropertiesfortheanisotropicmaterialiscarriedoutusingthemethodofhomogenization.Computationalresultsarepresentedandcomparedwithresultsobtainedbyboundaryv
6、ariations.1.IntroductionShapeoptimizationoflinearlyelasticsUHctureshasbeenstudiedformorethanfifteenyearsandhasreachedalevelofmaturitythatmakesitviabletoimplementthemethodsinCAE(computeraidedengineering)systemsforproductionuse.Forexample,severalsoftware
7、vendorsoffiniteelementgeneral-purposeprogramsareintroducingmodulesofshapeoptimizationbasedonthesuccessfulimplementationofsensitivityanalysisforsizingdesignoptimizationproblemsinsuchcodes.However,shapeoptimizationisquitedifferentfromsizingproblems.Forsi
8、zingoptimizationproblems,oncesensitivityisknown,designmodifica-tionisrathersimple,andacorrespondingmodificationofafiniteelementmodelisstraightfor-ward.Computingsensitivityisthesameforshapesensitivityasforsizingproblemsiftheshapeofastruc
