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1、硕士学ԡ论文AbstractTherearemanyuncertaintiesinpracticalengineeringproblems.Theaccuratemeasurement,analysisandcontrolforparameteruncertaintyandwherebyconductingcorrespondingreliabilitydesignareeffectivemeansofensuringthenormalfunctionsofproductsorstructuresundercomplexworkingconditi
2、ons.Currently,thetoolsofdescribinguncertaintyaremainlyprobabilisticmethod,fuzzymethodandintervalapproach.Thefirstorderreliabilitymethod(FORM)istheclassicandmostcommonlyusedmethodinthefieldofreliability,andithasbeenwidelyusedinstructuralanalysisanddesigninvariousindustrialfield
3、s.InFORM,theproblemofreliabilityanalysisisusuallyconvertedintoanoptimizationproblemtosolveforthereliabilityindexinthestandardnormalspace,basedonaprobabilitytransformation.ThekeyproblemofFORM-basedreliabilityanalysisisthusreducedtosolvingtheoptimizationproblem.Aseriesofalgorith
4、msaimedatsolvingthisoptimizationproblemhavebeendeveloped.Inthispaper,wedosomeworktosolvethestructuralreliabilityproblems.Themaincontentsofthispaperareasfollows:(1)Inthispaper,forthestructuralreliabilityproblems,weintroduceanewperformancemeasureapproachbasedonthehomotopyanalysi
5、s,denotedastheHOMOmethod.FirstweestablishtheKarush–Kuhn–Tucker(KKT)conditionofthestructuralreliabilityproblems,thenconstructthecorrespondinghomotopyequations,andapplytheβ-conepath-trackingalgorithmtosolvetheequations.Finally,severalnumericalexamplesandanengineeringapplicationa
6、reprovidedtovalidatetheeffectivenessofthepresentmethod.Severalexamplesareprovidedtoshowthatthemethodhasrobustconvergenceinsolvingthelimit-statefunctionsofdifferentdegreenonlinearity.(2)Inthispaper,weintroduceanewapproachbasedonhomotopyanalysistotheRBDOproblems.Firstwetransform
7、theRBDObasedontheperformancemeasureapproach,thentheoptimizationistransformedintodeterministicoptimization.Lastweapplyhomotopyanalysistosolvetheoptimization.Finally,numericalexamplesareprovidedtoverifytheeffectivenessofthismethod.Severalexamplesareprovidedtoshowthattheapproach,
8、establishedinourpaper,hasgoodprecisionandconvergenceinsolving
