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1、INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERINGInt.J.Numer.Meth.Engng2000;00:1–6Preparedusingnmeauth.cls[Version:2002/09/18v2.02]Alinearlyimplicittrapezoidalmethodforintegratingstiffmultibodydynamicswithcontact,joints,andfrictionFlorianA.Potra1,MihaiAnitescu2∗,BogdanGavr
2、ea1,andJeffTrinkle31DepartmentofMathematics,UniversityofMaryland,BaltimoreCounty,2MathematicsandComputerScienceDivision,ArgonneNationalLaboratory,3DepartmentofComputerScience,RensselaerPolytechnicInstitute.SUMMARYWepresentahardconstraint,linearcomplementaritybased,methodforth
3、esimulationofstiffmultibodydynamicswithcontact,jointsandfriction.Theapproachusesalinearizationofthemodifiedtrapezoidalmethod,incorporatesaPoissonrestitutionmodelatcollision,andsolvesonlyonelinearcomplementarityproblempertimestepwhennocollisionsareencountered.Weprovethat,underc
4、ertainassumptions,themethodhasordertwo,afactthatisalsodemonstratedbyournumericalsimulations.Fortheunconstrained(ODE)case,themethodachievessecond-orderconvergenceandabsolutestabilitywhilesolvingonlyonelinearsystemperstep.WhenweuseaspecialapproximationoftheJacobianmatrixforthe
5、casewherethestiffforcesoriginateinspringsanddampersattachedtotwopointsinthesystem,thelinearcomplementarityproblemcanbesolvedforanyvalueofthetimestepandnumericalsimulationdemonstratethatthemethodisstifflystable.ThemethodwasimplementedinUMBRA,anindustrial-gradevirtualprototypings
6、oftware.SubjectIndex:65K10,90C33.Copyrightc2000JohnWiley&Sons,Ltd.keywords:MultibodyDynamics,RigidBodies,CoulombFriction,StiffMethods,LinearComplementarityProblems,LinearlyImplicitlyMethods1.IntroductionMechanicalsystemscomposedofnominallyrigidbodiesinteractingthroughfriction
7、alcontactsarepervasive,andinfact,areresponsibleforthehighlevelsofproductivityandlivingstandardenjoyedbycitizensofmodernindustrializedcountries.Themostobviousexampleofsuchmechanicalsystemsistheinternalcombustionengine,butmanyhuman-powereddevicesfallintothiscategorytoo.Spurred
8、byglobaleconomiccompetitionanddwindlingresources,companieshavebeguntouseana
