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1、INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERINGInt.J.Numer.Meth.Engng2013;95:529540Publishedonline25June2013inWileyOnlineLibrary(wileyonlinelibrary.com).DOI:10.1002/nme.4537Energyconservativepropertyofimpulse-basedmethodsforcollisionresolutionXHTang,A
2、Paluszny*,andR.W.ZimmermanDepartmentofEarthScienceandEngineering,ImperialCollege,London,UKSUMMARYPhysicalaccuracy,numericalstability,andcomputationalspeedarecriticalfactorsinthesimulationofcolli-sions.Theimpulse-basedmethodmodelscollisionsinasystemofrigidb
3、odiesinarelativelyreliableandfastmanner.Inthepresentpaper,evidenceispresentedfortheenergy-conservingandmomentum-conservingpropertiesofthemethod.Twodifferentimpulse-basedapproachesarevalidatedusingnumericaltests.Anecessaryconditionisproposedfortheimpulse-ba
4、sedmethodtobeenergyconservative.Resultsindicatethattheimpulse-basedmethodforcollisionsimulation,whichsatisfiestheproposedcondition,isenergyconservative.Copyright©2013JohnWiley&Sons,Ltd.Received22March2012;Revised7March2013;Accepted14May2013KEYWORDS:Impulse-
5、basedmethod;energyconservation;linearmomentumconservation;collisionresolution1.INTRODUCTIONThesimulationofcollision-driveninteractionsinamulti-bodysystemisinstrumentalinmodelingscenariosforthepredictionandcontrolofindustrialprocessesandaddstotheunderstandi
6、ngoftheircontrollingmechanisms.Ofteninvolvinghundredsofthousandstomillionsofinteractingbod-ies,simulationsmustconstantlyweighnumericalstability,physicalaccuracy,andcomputationalspeed,iftheyaretobecomeindustrialtools.Thistrade-offisespeciallycriticalinthesi
7、mulationofrockfragmentationforminingengineering[1,2],andfortumblemillsinagriculture[3],forwhichgeometricrepresentationisbelievedtoplayadecisiveroleintheinteractionbehavior.Themainmethodsproposedtosimulatecontactsinarigidbodysystemincludeanalytic[4],penalty
8、[5],andimpulse-basedmethods[6,7].Thepenaltymethod[8,9]transformsconstrainedoptimizationproblemsintoasetofnon-constrainedoptimizationproblemsbyiterativelycomputingaproperpenaltyparameterthatenforcescollisionsa