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1、Copyrightc2004TechSciencePresscmes,vol.5,no.6,pp.477-495,2004TheGeneralizedInterpolationMaterialPointMethodS.G.Bardenhagen12andE.M.Kober3Abstract:TheMaterialPointMethod(MPM)discreteIncomputationalsolidmechanicstheFiniteElementsolutionprocedureforcomputationalsolidmec
2、hanicsMethod(FEM)(see,e.g.[Johnson(1987)])hasbeenisgeneralizedusingavariationalformandaPetrovverysuccessfullyappliedtoawiderangeofproblemsGalerkindiscretizationscheme,resultinginafamilyofwithgoodresults.However,bodyfixedFEMmeshescanmethodsnamedtheGeneralizedInterpolati
3、onMaterialbedifficultandtimeconsumingtogenerateforcomplexPoint(GIMP)methods.Thegeneralizationpermitsiden-threedimensionalobjects.Further,meshdistortionas-tificationwithaspectsofotherpointornodebaseddis-sociatedwithlargedeformationscompromisessolutioncretesolutiontechniq
4、ueswhichdonotuseabodyfixedaccuracy,ultimatelyrequiringremeshing.Thesedif-grid,i.e.themeshlessmethods.Similaritiesarenotedficultieshavespurredthedevelopmentofalternatedis-andsomepracticaladvantagesrelativetosomeofthesecretizationstrategieswhichavoidmeshdistortionbydis-me
5、thodsareidentified.Examplesareusedtodemon-cretizingatpointsandnevermaintainingabodyfixedstrateandexplainnumericalartifactnoisewhichcanbemesh.expectedinMPMcalculations.Thisnoiseresultsinnon-Quiteanumberofmeshlessmethodshavebeende-physicallocalvariationsatthematerialpoint
6、s,whereveloped.Someofthewaysinwhichthemethodsdifferconstitutiveresponseisevaluated.Itisshowntodestroyincludewhetherornotatemporarymeshisusedinthetheexplicitsolutioninonecase,andseriouslydegradeitsolutionprocedure,whetherthediscretizationprocedureinanother.Historydepen
7、dent,inelasticconstitutivelawsbeginswiththedifferentialequationsoraweakform,andcanbeexpectedtoevolveerroneouslyandreportinac-intheconstructionandsupportofthepointweightingcuratestressstatesbecauseofnoisyinput.Thenoiseisfunctions.Inarecentreviewarticle,[Belytschko,Kro-
8、duetothelackofsmoothnessoftheinterpolationfunc-ngauz,Organ,Fleming,andKrysl(1996)],similaritiestions,andoccursduetomaterialp
