Finite Element Methods for Elasticity with Error-Controlled Discretization and Model Adaptivity

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1、Chapter2FiniteElementMethodsforElasticitywithError-controlledDiscretizationandModelAdaptivityErwinSteinandMarcusRuter¨UniversityofHannover,Hannover,Germanytheclassicalforceanddisplacementmethodsinlinear1Introduction5elasticstructuralanalysisderivedfr

2、omenergyprinciples.2NonlinearandLinearTheoryofElasticity7Thefirstfairlycomprehensiveengineeringtextbookon3VariationalProblemsandTheirFinitethefiniteelementmethodwaspublishedbyZienkiewiczElementDiscretizations16(1977).4ErrorEstimationandAdaptivityinLine

3、arizedThefirstchallenging2-DfiniteelementsolutionswiththeElasticity24displacementmethodusingbilineartriangles,forexample5CoupledaPosterioriModelandbyTurneretal.(1956),concernedplane-stressproblemsDiscretizationErrorEstimation40withcomplicatedgeometryan

4、dboundaryconditions,which6APosterioriErrorEstimationinFinitecouldrarelybesolvedbythefinitedifferencemethod.Elasticity46Thecomputersavailableinthemid-fifties,forexample7ConcludingRemarks54theIBM650ortheZuseZ21,permittedthedirectsolu-tionofabout100linear

5、symmetricalgebraicequationsorReferences55theiterativesolutionoflinearsymmetriceigenvalueprob-lemsoftheorder25,withoutapplyingspecialtrickswithmanyintermediatein-andoutputs.Theerrorcontrolofthe1INTRODUCTIONapproximatesolutionscouldbeperformedwithgloba

6、lorsectionalequilibriumconditionsusingintegratedstresses.Thefiniteelementmethod(FEM)wasinventedbyengi-Thissituationhaschangedconsiderablywiththeincreasingneersandmathematiciansfor1-Dand2-Delasticityprob-complexityoftheproblemsaswellasincreasingcomput-

7、lemswithfirstpublicationsbyCourant(1943)(onthevibra-ingpower.Nowadays,complexmechanicalsystemswithtionsofaBernoullibeam)andTurneretal.(1956)(ontheuptomillionsofdegreesoffreedom(dof)aresolvedusingshearstressfieldinadeltawingofanaircraft).Untiltoday,adva

8、ncedcomputertechnologiesandmultileveliterativemostapplicationsofthefiniteelementmethodinvarioussolvers.Anumberofinternationallyexperiencedgeneral-formshavebeeninlinearelasticstructuralmechanics.purposeprogramsareavailableandinstalledinvirtuallyArgyris