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1、INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERINGInt.J.Numer.Meth.Engng2013;95:529540Publishedonline25June2013inWileyOnlineLibrary(wileyonlinelibrary.com).DOI:10.1002/nme.4537Energyconservativepropertyofimpulse-basedmethodsforcollisionresolutionXH
2、Tang,APaluszny*,andR.W.ZimmermanDepartmentofEarthScienceandEngineering,ImperialCollege,London,UKSUMMARYPhysicalaccuracy,numericalstability,andcomputationalspeedarecriticalfactorsinthesimulationofcolli-sions.Theimpulse-basedmethodmodelscollisionsinasy
3、stemofrigidbodiesinarelativelyreliableandfastmanner.Inthepresentpaper,evidenceispresentedfortheenergy-conservingandmomentum-conservingpropertiesofthemethod.Twodifferentimpulse-basedapproachesarevalidatedusingnumericaltests.Anecessaryconditionispropos
4、edfortheimpulse-basedmethodtobeenergyconservative.Resultsindicatethattheimpulse-basedmethodforcollisionsimulation,whichsatisfiestheproposedcondition,isenergyconservative.Copyright©2013JohnWiley&Sons,Ltd.Received22March2012;Revised7March2013;Accepted14
5、May2013KEYWORDS:Impulse-basedmethod;energyconservation;linearmomentumconservation;collisionresolution1.INTRODUCTIONThesimulationofcollision-driveninteractionsinamulti-bodysystemisinstrumentalinmodelingscenariosforthepredictionandcontrolofindustrialpr
6、ocessesandaddstotheunderstandingoftheircontrollingmechanisms.Ofteninvolvinghundredsofthousandstomillionsofinteractingbod-ies,simulationsmustconstantlyweighnumericalstability,physicalaccuracy,andcomputationalspeed,iftheyaretobecomeindustrialtools.This
7、trade-offisespeciallycriticalinthesimulationofrockfragmentationforminingengineering[1,2],andfortumblemillsinagriculture[3],forwhichgeometricrepresentationisbelievedtoplayadecisiveroleintheinteractionbehavior.Themainmethodsproposedtosimulatecontactsin
8、arigidbodysystemincludeanalytic[4],penalty[5],andimpulse-basedmethods[6,7].Thepenaltymethod[8,9]transformsconstrainedoptimizationproblemsintoasetofnon-constrainedoptimizationproblemsbyiterativelycomputingaproperpenaltyparameterthatenforcescollisionsa
