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1、PERGAMONComputersandStructures69(1998)719±738AreviewofhomogenizationandtopologyopimizationIIÐanalyticalandnumericalsolutionofhomogenizationequationsB.Hassani,E.Hinton*DepartmentofCivilEngineering,UniversityofWales,Swansea,SingletonPark,Swansea,SA28PP,U.K.Received28Ja
2、nuary1997;accepted28April1998AbstractThisisthesecondpartofathree-paperreviewofhomogenizationandtopologyoptimization.Inthe®rstpaper,wefocusedonthetheoryandderivationofthehomogenizationequations.Inthispaper,motivesforusingthehomogenizationtheoryfortopologicalstructural
3、optimizationarebrie¯yexplained.Dierentmaterialmodelsaredescribedandtheanalyticalsolutionofthehomogenizationequationsforthesocalled``ranklaminatecomposites''ispresented.The®niteelementformulationisexplainedforthematerialmodel,basedonamiscrostructureconsistingofanisotr
4、opicmaterialwithrectangularvoids.Usingtheperiodicityassumption,theboundaryconditionsarederivedandthehomogenizationequationsaresolved,andtheresultstobeusedintopologyoptimizationarepresented.Thethirdpaperdealswiththeuseofhomogenizationforstructuraltopologyoptimizationb
5、yusingoptimalitycriteriamethods.#1998ElsevierScienceLtd.Allrightsreserved.1.IntroductionStudyingthenatureofthetopologicalstructuralshapeoptimizationproblemsuggestsaspeci®candTopologicalstructuraloptimizationhasthecomplexdierentsortofparameterizationfromtheoutset:that
6、featuresofbothsizeandshaopeoptimizationpro-isthenaturalformulationofanin®nitenumberofblems.Oneofthedrawbacksofconventionalshapeholesofvaryingsize,whichimpliestheexistenceofaoptimizationbytheboundaryvariationmethodisthatspecialmicrostructure.Ithasalreadybeenproventhat
7、®naldesignsaretopologicallyequivalenttotheinitialinsomecases,havinga®nitenumberofdesignvari-ones.Normallythesetechniquesrequireseveral®niteablesdoesnotleadtotheoptimumsolution.Forelementre-meshingsintheoptimizationprocess.example,intheproblemofthicknessoptimizationof
8、aFurthermore,thedicultyofchangingthetopologylinearlyelasticplate,withmeancomplianceconsideredduringtheschemeincreasesthecomplexityo
