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1、INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERINGInt.J.Numer.Meth.Engng2013;95:529540Publishedonline25June2013inWileyOnlineLibrary(wileyonlinelibrary.com).DOI:10.1002/nme.4537Energyconservativepropertyofimpulse-basedmethodsforcollisionresolutionXHTang,APaluszny*,andR.W.ZimmermanDepartm
2、entofEarthScienceandEngineering,ImperialCollege,London,UKSUMMARYPhysicalaccuracy,numericalstability,andcomputationalspeedarecriticalfactorsinthesimulationofcolli-sions.Theimpulse-basedmethodmodelscollisionsinasystemofrigidbodiesinarelativelyreliableandfastmanner.Inthepresentpaper,evidence
3、ispresentedfortheenergy-conservingandmomentum-conservingpropertiesofthemethod.Twodifferentimpulse-basedapproachesarevalidatedusingnumericaltests.Anecessaryconditionisproposedfortheimpulse-basedmethodtobeenergyconservative.Resultsindicatethattheimpulse-basedmethodforcollisionsimulation,whi
4、chsatisfiestheproposedcondition,isenergyconservative.Copyright©2013JohnWiley&Sons,Ltd.Received22March2012;Revised7March2013;Accepted14May2013KEYWORDS:Impulse-basedmethod;energyconservation;linearmomentumconservation;collisionresolution1.INTRODUCTIONThesimulationofcollision-driveninteractio
5、nsinamulti-bodysystemisinstrumentalinmodelingscenariosforthepredictionandcontrolofindustrialprocessesandaddstotheunderstandingoftheircontrollingmechanisms.Ofteninvolvinghundredsofthousandstomillionsofinteractingbod-ies,simulationsmustconstantlyweighnumericalstability,physicalaccuracy,andc
6、omputationalspeed,iftheyaretobecomeindustrialtools.Thistrade-offisespeciallycriticalinthesimulationofrockfragmentationforminingengineering[1,2],andfortumblemillsinagriculture[3],forwhichgeometricrepresentationisbelievedtoplayadecisiveroleintheinteractionbehavior.Themainmethodsproposedtosi
7、mulatecontactsinarigidbodysystemincludeanalytic[4],penalty[5],andimpulse-basedmethods[6,7].Thepenaltymethod[8,9]transformsconstrainedoptimizationproblemsintoasetofnon-constrainedoptimizationproblemsbyiterativelycomputingaproperpenaltyparameterthatenforcescollisionsa
