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1、华中科技大学硕士学位论文AbstractThisworkissupportedbytheNaturalScienceFoundationofChina‗Astudyoftopologyandshapeoptimizationundergeometricconstraintsforcontinuumstructure‘(Grants:No.50975107).Existingstructuraloptimizationmethodsarewithincertainlimitstosolvetheproblem
2、oftheintegrationoftopologyoptimization,shapeoptimizationandsizingoptimization.Thispaperpresentsalevelset-basedmethodtocharacterizethegeometricfeatures,andasizingoptimizationforgeometricconstraintscanbeachievedaswellassimultaneouslytopologicalshapeoptimizat
3、ion.Furthermore,themethodissuccessfullyextendedtothecompliantmechanismdesign,andstructuraldynamicsoptimaldesign.Firstly,thefundamentaltheoryofstandardlevelsetmethodandparameterizedlevelsetmethodarediscussed,aswellastheiradvantagesanddisadvantages.Basedonth
4、isformula,inordertoaddresstheproblemofsizingdesignorpositiondesignforregularholes,aparameterizationlevelset-basedsizingoptimizationmethodisproposedbyconsideringtheregularholesasthegeometricconstraints.Inthismethod,theadvantageoftheimplicitrepresentationand
5、parameterizedexpressionisfullytakenintoaccount,andprovidestheprerequisitefortheconstructionofunifiedoptimizationmodel.Secondly,aunifiedoptimizationmodelisbuiltbycombiningthetopologicalshapeoptimizationmodelwiththesizingoptimizationmodel,andfurtherinferredt
6、hesensitivityanalysisresultsforoptimizationcriterionmethod.Atthesametime,somenumericalskillsarestudiedtosolvethenumericalproblemsinthepresentmethod,suchastheinterferedissueandtolerancezoneforregularholes.Thirdly,Inordertoaddresstheproblemofzigzagboundaryin
7、topologyoptimizationusingtheConventionalFiniteElementMethod(CFEM),anextendedFiniteElementMethod(XFEM)isintroducedintothepresentedunifiedoptimizationmodel.TheXFEMschemehasahighaccuracyinboundaryelements,whichgreatlyincreasedthesmoothnessoftheboundaryandsave
8、dthecomputingtime,theconvergencepropertyandtheconvergenceefficiencyofthealgorithmarealsoimproved.Finally,theunifiedoptimizationmethodisappliedtodesignanewLEDarm,theII华中科技大学硕士学位论文influenceoftopology,shapeandsi
