Introduction to Finite Element M

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1、.1Overview1–1Chapter1:OVERVIEW1–2TABLEOFCONTENTSPage§1.1.WHERETHISMATERIALFITS1–3§1.1.1.ComputationalMechanics.............1–3§1.1.2.Staticsvs.Dynamics..............1–4§1.1.3.Linearvs.Nonlinear...............1–5§1.1.4.Discretizationmethods..............1–5§1.1.5.FEMVariants.............

2、....1–5§1.2.WHATDOESAFINITEELEMENTLOOKLIKE?1–6§1.3.THEFEMANALYSISPROCESS1–7§1.3.1.TheMathematicalFEM.............1–8§1.3.2.ThePhysicalFEM................1–9§1.3.3.SynergyofPhysicalandMathematicalFEM......1–9§1.4.INTERPRETATIONSOFTHEFINITEELEMENTMETHOD1–11§1.4.1.PhysicalInterpretation...

3、...........1–11§1.4.2.MathematicalInterpretation............1–12§1.5.KEEPINGTHECOURSE1–13§1.6.*WHATISNOTCOVERED1–13EXERCISES......................1–151–21–3§1.1WHERETHISMATERIALFITSThisbookisanintroductiontotheanalysisoflinearelasticstructuresbytheFiniteElementMethod(FEM).Itembodiesthre

4、eParts:IFiniteElementDiscretization:Chapters2-11.ThispartprovidesanintroductiontothediscretizationandanalysisofskeletalstructuresbytheDirectStiffnessMethod.IIFormulationofFiniteElements:Chapters12-20.Thispartpresentstheformulationofdisplacementassumedelementsinoneandtwodimensions.IIICom

5、puterImplementationofFEM:Chapters21-28.ThispartusesMathematicaastheimplementationlanguage.ThisChapterpresentsanoverviewofwherethebookfits,andwhatfiniteelementsare.§1.1.WHERETHISMATERIALFITSThefieldofMechanicscanbesubdividedintothreemajorareas:TheoreticalMechanicsApplied(1.1)ComputationalT

6、heoreticalmechanicsdealswithfundamentallawsandprinciplesofmechanicsstudiedfortheirintrinsicscientificvalue.Appliedmechanicstransfersthistheoreticalknowledgetoscientificandengineeringapplications,especiallyasregardstheconstructionofmathematicalmodelsofphysicalphenomena.Computationalmechani

7、cssolvesspecificproblemsbysimulationthroughnumericalmethodsimplementedondigitalcomputers.REMARK1.1Paraphrasinganoldjokeaboutmathematicians,onemaydefineacomputationalmechanicianasapersonwhosearchesforsolutionstogivenproblems,anappliedmechanicianasapersonwhosearchesforproblemsthatfi