Stochastic Finite Element Methods

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1、Chapter20StochasticFiniteElementMethodsMiguelA.Gutierrez´1andSteenKrenk21DelftUniversityofTechnology,Delft,TheNetherlands2TechnicalUniversityofDenmark,Lyngby,DenmarkStochasticfiniteelementsbelongtothelattersortof1Introduction657strategies.Finiteelementsarer

2、ecognizedasoneofthemostpowerfultechniquesforthenumericalsolutionofthepar-2RandomVariables658tialdifferentialequationsresultingfromthemathematical3StaticallyDeterminateProblems661modelingofsolidmechanicsproblems.Ifanyoftheinput4RepresentationofRandomFields6

3、63fieldsinvolvedintheanalysisexhibitsrandomlydistributed5BasicVariableSensitivityComputation667quantities,theresponsefieldwillberandomaswell.The6PerturbationTechnique668actualpropagationofrandomnesscanbestudiedbymeans7SpectralFormulation671offiniteelements.Th

4、ereexistdifferentpossibilitiesforthis8ReliabilityMethods676purpose,andthereforeonespeaksofstochasticfiniteele-mentmethods,wherethepluralnumberinmethodsis9StatusandOutlook680emphasized,ratherthanofthestochasticfiniteelementReferences680method.Twogeneraltypeso

5、fanalysiscanbecarriedoutbymeansofstochasticfiniteelements.Whenthepurpose1INTRODUCTIONoftheanalysisistoevaluatehowselectedcharacteristicsofthebasicrandomfieldsuchastheexpectationorthecovarianceinfluencethoseofaresponsefield,forexample,Whenaproblemofsolidmechani

6、csincludesuncertain-thedisplacementfield,onespeaksofuncertaintyanalysis.ties,itsmathematicalmodelingcanbeapproachedinWhenthepurposeofthecomputationsistoprovideanseveralways.Afirstpossibilitycouldbetoformulateaccurateapproximationoftheprobabilitydistributiono

7、fastochasticdifferentialequationtodescribetheprob-theresponsefieldgiventhatofthebasicfield,onespeakslem.However,theissuesrelatedtothenumericalsolu-ofreliabilityanalysis.Inthelattercase,specialattentionistionofstochasticdifferentialequationsconstituteafullpai

8、dtotheproperevaluationoftheprobabilitycontentofspecialitybythemselves.Adifferentstrategycanbethedistributiontails.adoptedsuchthatittakesadvantageofexistingnumericalThebasicaspectsofmodelingastochasticproblemb