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1、Computing69,239–263(2002)DigitalObjectIdentifier(DOI)10.1007/s00607-002-1459-8MatlabImplementationoftheFiniteElementMethodinElasticityJ.Alberty,Kiel,C.Carstensen,Vienna,S.A.Funken,KielandR.Klose,KielReceivedJune18,2001;revisedFebruary25,2002Publishedonline:December5,2002ÓSpringer-Ve
2、rlag2002AbstractAshortMatlabimplementationforP1andQ1finiteelements(FE)isprovidedforthenumericalsolutionof2dand3dproblemsinlinearelasticitywithmixedboundaryconditions.Anyadaptationfromthesimplemodelexamplesprovidedtomorecomplexproblemscaneasilybeperformedwiththegivendocumentation.Num
3、ericalexampleswithpostprocessinganderrorestimationviaanaveragedstressfieldillustratethenewMatlabtoolanditsflexibility.AMSSubjectClassification:65N30,65R20,73C50.Keywords:Finiteelementmethod,elasticity,Matlab.1.IntroductionUnlikecomplexblack-boxcommercialcomputercodes,thispaperprovides
4、asimpleandshortopen-boxMatlabimplementationofP1andQ1finiteelements(FE)forthenumericalsolutionsoflinearelasticityproblems.Insteadofcoveringallkindsofpossibleproblemsinonecode,theproposedtoolaimstobeplain,easytounderstand,andtomodify.Therefore,onlysimplemodelexamplesareincludedtobeada
5、ptedtowhateverisneededinthespiritof[1].Wepresentanerrorestimatorwhichillustratestheaccuracyofthenumericalcalculation.AdifferentapproachisrealizedbythecompanyComsolwiththefiniteelementpackageFemlab[7].Itisatoolforthesolutionofpartialdifferentialequationsofmanyphysicalphenomena,includin
6、gstructuralmechanics.Aspecialfeatureisthecomfortablemeshgeneratorandthepossibilitytocombinedifferentphysicalproblems.ThecodeiswrittenforthemostpartinMatlabandcanbemodified,exceptforthemeshgeneratorandthesolverfornonlinearproblems.Thebasisfunctionsinthefiniteelementmethodcanbechosentob
7、elinear,quadratic,cubicoroffourthorder.Thesolvercanuseadaptivityaswell.Theplanofourpaperisasfollows.Themodelproblem,theNavier-Lame´equations,withgeneralboundaryconditionsisdescribedinSect.2;theweakformulationanddiscretisationinSect.3.Theheartofthiscontributionisthedatarepresentatio
8、nofthetriangulation,theDir
