NONLINEAR DYNAMIC ANALYSIS OF COMPLEX STRUCTURES 复杂结构的非线性动力分析

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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