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1、PeterWriggersNonlinearFiniteElementMethods123Prof.Dr.PeterWriggersLeibnizUniversitatHannover¨Fakultatf¨urMaschinenbau¨InstitutfurKontinuumsmechanik¨Appelstr.1130167HannoverGermanywriggers@ikm.uni-hannover.deISBN:978-3-540-71000-4e-ISBN:978-3-540-71001-1LibraryofCongressControlNumber:200893329
2、7c2008Springer-VerlagBerlinHeidelbergThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicati
3、onofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw.Theuseofgeneraldescriptivenames,registerednames,tradema
4、rks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Coverdesign:WMXDesignGmbH,HeidelbergPrintedonacid-freepaper987654321springer.comPrefaceDuringthelastdecade,themethodoffinitee
5、lements(FEM)hasproventobeauniversaltoolfortheanalysisofcomplexstructuresinengineer-ing.Withincreasingcomputingpower,differentnonlinearproblemscanbetreatednowadays.Thisbookdescribes,besidesthephysicalandmathematicalbackgroundofthefiniteelementmethod,specialdiscretizationtechniquesandalgorithmswh
6、ichhavetobeappliedfornonlinearproblemsofsolidmechanics.Thisin-cludesthenecessarybasicsofcontinuummechanics,constitutiveequationsforengineeringmaterialsandvariationalprinciplesaswellasthematrixfor-mulationofFEMwithrespecttodifferentconfigurationsandthedevelopmentofalgorithmsforthesolutionofthere
7、sultingnonlinearalgebraicequationsystems.Furthermore,timedependentproblemsarediscussedfornonlin-eardynamicalsystemsandconstitutiveequations.Sincenonlinearproblemsexhibitsingularitiesalsoformulationsareincludedwhichfacilitateacompu-tationoflim
