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1、INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERING,VOL.14,961-986(1979)LARGEDISPLACEMENTANALYSISOFTHREE-DIMENSIONALBEAMSTRUCTURESKLAUS-JURGENBATHEtANDSAIDBOLOURCHItDepartmentofMechanicalEngineering,MassachusettsinstituteofTechnology,Massachusetts,USA.SUM
2、MARYAnupdatedLagrangianandatotalLagrangianformulationofathree-dimensionalbeamelementarepresentedforlargedisplacementandlargerotationanalysis.Itisshownthatthetwoformulationsyieldidenticalelementstiffnessmatricesandnodalpointforcevectors,andthattheupdatedLag
3、rangianformulationiscomputationallymoreeffective.Thisformulationhasbeenimplementedandtheresultsofsomesampleanalysesaregiven.INTRODUCTIONThepossibilityofpracticalstaticanddynamicnonlinearanalysisofstructureshasduringrecentyearsprogressedsubstantially,duetot
4、heeffectiveuseofdigitalcomputersoperatingonfiniteelementrepresentationsofthestructures.Toenablegeneralnonlinearanalysisthedevelop-mentofversatilegeometricandmaterialnonlinearfiniteelementsisinmuchneed,andamongtheseelementstheuseofaneffectivethree-dimension
5、albeamelementisveryimportant.Sincethefirstapplicationsofcomputerstononlinearanalysisofstructures,variousnonlinearbeamelementshavebeenpresented.*-"Thelargenumberofpublicationsonnonlinearanalysisofbeamstructuresis,atleastpartially,duetothefactthatvariouskine
6、maticnonlinearformulationscanbeemployed,andthatatthistimeitisnotclearwhichformulationismosteffective.Thedifficultyofobtainingeffectivesolutionsisparticularlypronouncedintheanalysisofthree-dimensionalbeamstructures.Namely,consideringabeamelementitisnotedtha
7、tageneralthree-dimensionalnonlinearbeamformulationisnotasimpleextensionofatwo-dimensionalformulation,becauseinthree-dimensionalanalysislargerotationshavetobeaccountedforthatarenotvectorquantities.Inthedevelopmentofageometricallynonlinearbeamelement,basical
8、lyanupdatedLagrangianoratotalLagrangianformulationcanbeemployed.12,13Theseformulationsmustbeimplementedusingappropriatedisplacementinterpolationfunctions.Consideringthechoiceofthesefunctionsitisrecognizedthat
