Thesis for the Degree of学位论文

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1、ThesisfortheDegreeofLicentiateofPhilosofyStochasticOptimizationofStructuralTopologyAntonEvgrafovDepartmentofMathematicsChalmersUniversityofTechnologyandGöteborgUniversityGöteborg,Sweden2002StochasticOptimizationofStructuralTopologyAntonEvgrafovcAntonEvgrafov,2002I

2、SSN0347–2809/No2002:32DepartmentofMathematicsChalmersUniversityofTechnologyandGöteborgUniversitySE-41296GöteborgSwedenTelephone+46(0)31–7721000AboutthecoverCoverartiscT.Saur,

 
CoverartreprintedwithpermissionfromT.Saur.Chalmer

3、sUniversityofTechnologyGöteborg,Sweden2002ABSTRACTThisworkaddressestheproblemofhierarchicaldecision-makingunderuncertaintyand,morespecicaly,itsapplicationsinmechanicalengineer-ing.Themotivationforthisstudycomesfromtheneedtobuildcost-effectivestructuresthatarerobu

4、stundervaryingconditions;failuretotakeuncertaintyintoaccountmayleadeithertoveryexpensiveorveryinefcientdesigns.Weareprimarilyconcernedwiththerobustdesign(includingthepos-sibilityofmodifyingthetopology)oftruss-likestructuresinunilateralcontactand/orincludingmember

5、sthatareabletosustainonlytensileforces.Theproblemisformulatedandstudiedasastochasticbilevelpro-grammingproblem,whichallowsustotakeboththerandomnessandthehierarchicalnatureofdesignoptimizationproblemsintoaccount.Threeparticularquestionsarestudied:(i)theapproximatio

6、nofthenon-differentiabletopologyoptimizationproblemswithasequenceofsim-pler,differentiable,sizingoptimizationproblems;(ii)therobustnessoftheoptimaldesignswithrespecttoerrorsinthemodellingofuncer-tainty;and(iii)thediscretizationoftheinnite-dimensionalstochasticstr

7、ucturaloptimizationproblems,orapproximationwithasequenceofnite-dimensionaloptimizationproblems.Within(i),wegeneralizetheknownapproximationresultstothestochasticsetting,butthemaincontributionisanewapproximationmethodforstochasticstressconstrainedweightminimization

8、problembasedontheideaofpenaltyfunctions.Withrespectto(ii),weshowtherobustnessoftheoptimalsolutionstothestochasticcompliancemin-imizationproblem,andwepro