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1、T.Belytschko,Introduction,December16,1998CHAPTER1INTRODUCTIONbyTedBelytschkoNorthwesternUniversityCopyright19961.1NONLINEARFINITEELEMENTSINDESIGNNonlinearfiniteelementanalysisisanessentialcomponentofcomputer-aideddesign.Testingofprototypesisincreasin
2、glybeingreplacedbysimulationwithnonlinearfiniteelementmethodsbecausethisprovidesamorerapidandlessexpensivewaytoevaluatedesignconceptsanddesigndetails.Forexample,inthefieldofautomotivedesign,simulationofcrashesisreplacingfullscaletests,bothfortheevalu
3、ationofearlydesignconceptsanddetailsofthefinaldesign,suchasaccelerometerplacementforairbagdeployment,paddingoftheinterior,andselectionofmaterialsandcomponentcross-sectionsformeetingcrashworthinesscriteria.Inmanyfieldsofmanufacturing,simulationisspeed
4、ingthedesignprocessbyallowingsimulationofprocessessuchassheet-metalforming,extrusionofparts,andcasting.Intheelectronicsindustries,simulationisreplacingdrop-testsfortheevaluationofproductdurability.Forbothusersanddevelopersofnonlinearfiniteelementprog
5、rams,anunderstandingofthefundamentalconceptsofnonlinearfiniteelementanalysisisessential.Withoutanunderstandingofthefundamentals,ausermusttreatthefiniteelementprogramasablackboxthatprovidessimulations.However,evenmoresothanlinearfiniteelementanalysis,
6、nonlinearfiniteelementanalysisconfrontstheuserwithmanychoicesandpitfalls.Withoutanunderstandingoftheimplicationandmeaningofthesechoicesanddifficulties,auserisataseveredisadvantage.Thepurposeofthisbookistodescribethemethodsofnonlinearfiniteelementanal
7、ysisforsolidmechanics.Ourintentistoprovideanintegratedtreatmentsothatthereadercangainanunderstandingofthefundamentalmethods,afeelingforthecomparativeusefulnessofdifferentapproachesandanappreciationofthedifficultieswhichlurkinthenonlinearworld.Atthesa
8、metime,enoughdetailabouttheimplementationofvarioustechniquesisgivensothattheycanbeprogrammed.Nonlinearanalysisconsistsofthefollowingsteps:1.developmentofamodel;2.formulationofthegoverningequations;3.discretizationoftheequations;4.solutionoftheequatio
