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1、PartIIICourseM16:MaterialsModellingJ.C.TanIntroductiontotheFiniteElementMethodJan2006FiniteElementMethod(3Lectures)Dr.J.C.TanDr.J.C.TanLentTerm2006LentTerm2006-1-PartIIICourseM16:MaterialsModellingJ.C.TanIntroductiontotheFiniteElementMethodJan2006Lecture10Fini
2、teElementMethod(FEM)IGeneralintroductiontoFEM,FEterminologies,Discretisation,Directstiffnessmethod,1-Ddiscreteproblems,Simplespringstructures,Elementandglobalstiffnessrelations,Stiffnessmatrix,Complexspringsystems.(JCT)Lecture11FiniteElementMethodIISolutionpro
3、cedures,StepsintheFEmethod,2-Dtrussanalysis,Energymethods-Virtualworkprinciple,FEanalysisof2-Dcontinuum.(JCT)Lecture12FiniteElementMethodIIIConstantstrain2-Dtriangularelement,Elasticstrainsandstressesintriangularelement,Elasticconstantsmatrix,Relationbetweenno
4、dalforcesandelementstresses,Exampleproblem.(JCT)-2-PartIIICourseM16:MaterialsModellingJ.C.TanIntroductiontotheFiniteElementMethodJan20061.OverviewAllphysicalphenomenaencounteredinengineeringproblems,suchasmechanicsofmaterials,fluidflow,heattransfer,acousticsan
5、delectromagnetismcanbemodelledusingdifferentialequations,withasetofcorrespondingboundaryconditions(insteady-stateproblems)andinitialconditions(intransientproblems),seeFig.1.However,practicalengineeringproblemsaregenerallycomplicatedandcannotbesolvedusinganalyt
6、icalapproaches.Thesedifficultiesmayarisefromthecomplexnatureofthegoverningdifferentialequationsaddressed,thecomplexgeometryoftheproblem,orthedifficultboundaryconditions(BCs)andinitialconditionstobetakenintoaccount.Exactsolutionstosuchproblemsareoftennotavailab
7、le.Forsuchproblems,numericalapproachessuchasfinitedifferenceandfiniteelementmethodsarerequiredtoobtainapproximatesolutions.Inthisseriesoflectures,wewillfocusonthefiniteelementmethod(FEM),sometimesalsoknownasfiniteelementanalysisorFEA.Fig.1:Modellingofphysicalp
8、henomenonThebasicideabehindfiniteelementmethodistofirstdividethedomain(regiontobemodelled)intodiscreteconnectedparts,knownasfiniteelements.Theseelementsmaybeone-,two-orthree-dimens
