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1、EARTHQUAKEENGINEERINGANDSTRUCTURALDYNAMICS,VOL.1,241-252(1973)NONLINEARDYNAMICANALYSISOFCOMPLEXSTRUCTURESE.L.WILSON~UniversityofCalifornia,Berkeley,CaliforniaI.FARHOOMAND$K.J.BATHESJohnBlumeandAssociates,SunFrancisco,CaliforniaUniversityofCalifornia,Berkeley,Ca
2、liforniaSUMMARYAgeneralstep-by-stepsolutiontechniqueispresentedfortheevaluationofthedynamicresponseofstructuralsystemswithphysicalandgeometricalnonlinearities.Thealgorithmisstableforalltimeincrementsandintheanalysisoflinearsystemsintroducesapredictableamountofe
3、rrorforaspecifiedtimestep.Guidelinesaregivenfortheselectionofthetimestepsizefordifferenttypesofdynamicloadings.Themethodcanbeappliedtothestaticanddynamicanalysisofbothdiscretestructuralsystemsandcontinuoussolidsidealizedasanassemblageoffiniteelements.Resultsofs
4、everalnonlinearanalysesarepresentedandcomparedwithresultsobtainedbyothermethodsandfromexperiments.INTRODUCTIONThedevelopmentofnumericalmethodsforthenonlinearanalysisofstructureshasattractedmuchattentionduringthepastseveralyears.1-6Mostoftheinvestigationshavebee
5、nconcernedwiththeanalysisofaparticulartypeofstructureandnonlinearity.Thepurposeofthispaperistopresentageneralsolutionschemeforthestaticanddynamicanalysisofanarbitraryassemblageofstructuralelementswithbothphysicalandgeometricalnonlinearities.Thestructuralelement
6、smaybebeamelementsortwo-andthree-dimensionalfiniteelementswhichareusedtoidealizecontinuoussolids.Therearevariousapproximationsinvolvedintherepresentationofacontinuousbodyasanassemblageoffiniteelements.'Inthispaperonlytheerrorsassociatedwiththesolutionofthediscr
7、etesystemnonlinearequationsofequilibriumarediscussed.Anincrementalformoftheequationsisgiven,whichcanbeusedtoobtainacheckofequilibriuminthedeformedconfiguration.Fordynamicanalysisanefficientalgorithmfortheintegrationoftheequationsofmotionisneeded.Variousdifferen
8、ttechniquesareinAsiswellknown,thecostofananalysisrelatesdirectlytothesizeofthetimestepwhichhastobeusedforstabilityandaccuracy.Inthispaperanunconditionallystableschemeisprese
