Basedonalevelsetmodelandthehomogenizationtheory,anoptimizationalgorithmforfindingtheoptimalconfigurationofthemicrostructurewithspecifiedpropertiesisproposed,whichextendscurrentresearchonthelevelsetmethodforstructuretopologyoptimization.ThemethodproposedemploysalevelsetmodeltoimplicitlydescribethematerialinterfacesofthemicrostructureandaHamilton-Jacobiequationtocontinuouslyevolvethematerialinterfacesuntilanoptimaldesignisachieved.Meanwhile,themovingvelocitiesoflevelsetareobtainedbyconductingsensitivityanalysisandgradientprojection.Besides,howtohandletheviolatedconstraintsisalsodiscussedinthelevelsetmethodfortopologicaloptimization,andareturn-mappingalgorithmisconstructed.Numericalexamplesshowthatthemethodexhibitsoutstandingflexibilityofhandlingtopologicalchangesandfidelityofmaterialinterfacerepresentationascomparedwithotherconventionalmethodsinliteratures.
