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1、ActaMech222,161173(2011)DOI10.1007/s00707-011-0512-0S.RashAhmadi·M.Sheikhlou·V.MahmoodGharebaghThermo-elastic/plasticsemi-analyticalsolutionofincompressiblefunctionallygradedsphericalpressurevesselunderthermo-mechanicalloadingReceived:18April2011/Publishedonline:3August2011©Springer-Verlag2

2、011AbstractInthispaper,numericalsolutionstoassesspartiallyplasticandfullyplasticdeformationbehaviorofafunctionallygradedsphericalpressurevesselarepresented.Themodulusofelasticityofthematerialisassumedtovarynonlinearlyintheradialdirectionandaxisymmetricdisplacementsandstressesinthefunc-tiona

3、llygradedsphericalvesselsubjectedtothermalloadinganduniforminternalpressurearedeterminedusingplasticitytheory.TrescasyieldcriterionanditsassociatedflowruleareusedtoformulatedifferentplasticregionsforanidealFGmaterial.Inthisway,thematerialpropertyvariesbyYoungsmodulusthatmaybeanarbitraryfunct

4、ionoftheradialcoordinate.Therefore,thematerialisassumedtobefunctionallygradedintheradialdirection.Hence,thegeneralanalyticalsolutionsofsuchequationsarenotavailable,thenumericalmethod(semi-analytical)isappliedandanewcollectionofequilibriumequationswithsmalldeflectionsispresented.Accordingly,t

5、heradialdomainisdividedintosomevirtualsub-domainsinwhichthepower-lawdistributionisusedforthethermomechanicalpropertiesoftheelementalcomponents.Byconsideringthenec-essarycontinuityconditionsbetweenadjacentsub-domains,jointlywiththeglobalboundaryconditions,asetoflineardifferentialequationsiso

6、btained.Solutionofthelineardifferentialequationsyieldsthethermoelasticresponsesforeachsub-domainasexponentialfunctionsoftheradialcoordinate.Subsequently,attributedtocentrifugalforce,resultsforthestress,strain,anddisplacementcomponentsalongtheradiusinelasticandplasticareaarepresented.1Introd

7、uctionRecently,theconceptoffunctionallygradedmaterials(FGM)hasbeenintroducedasathermalbarriermaterial.Inthelastdecade,suchmaterialshavebeenusedinmanyindustrialapplicationssubjectedtolargedifferencesofoperatingtemperatures.Gradually,FGMsprovetheirhighcapa