On Lagrange multipliers in flexible multibody dynamics.pdf

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1、Comput.MethodsAppl.Mech.Engrg.195(2006)6993–7005www.elsevier.com/locate/cmaOnLagrangemultipliersinflexiblemultibodydynamicsBerndSimeonZentrumMathematikTUMu¨nchen,Boltzmannstr.3,D-85748Garching,GermanyReceived4October2004;receivedinrevisedform29April2005;a

2、ccepted29April2005AbstractTheLagrangemultipliertechniqueplaysakeyroleforthetreatmentofconstraintsinmultibodysystems.Incontrasttothewell-understoodrigidbodycase,theformulationofconstraintsforelasticbodiesrequiresspecialcare.Thispaperprovidesanintroduction

3、totheunderlyingmathematicaltheoryandshowswhichmodelsarewell-definedandwhicharequestionable.Additionally,estimatesontheinfluenceofperturbationsaregiven.Asimulationexampleillustratestheresults.Ó2005ElsevierB.V.Allrightsreserved.Keywords:Lagrangemultipliers;F

4、lexiblemultibodysystems;Constraints;Differential-algebraicequations(DAEs);Saddlepointproblems;Numericalsimulation1.IntroductionTheLagrangemultipliertechniqueplaysakeyroleinmodellingmechanicalsystemswithconstraints.Incaseofrigidbodysystems,thisapproachlead

5、stoawell-knownclassofdifferential-algebraicequations(DAEs),andduetotheresearcheffortsofthelast15years,existenceanduniquenessofsolutionsaswellasexcellentnumericalmethodshavebeenestab-lished.Butwhathappensifweconsidermoregeneralapplicationsthatcomprisealsoel

6、asticbodies?Suchflexiblemulti-bodysystemsconsistofbothrigidandelasticbodiesaswellasinterconnections.Jointsconstraintherelativemotionofpairsofbodieswhilespringsanddampersactascompliantelements.Flexiblemultibodysystemsaimatthegrowingsimulationdemandsinvehic

7、ledynamics,robotics,andinair-andspace-craftdevelopment.Theycombineconceptsandsolutiontechniquesfromstructuralmechanicsandfromrigidbodymechanics.Sinceelasticbodiesaregovernedbypartialdifferentialequations(PDEs)andrigidbodiesbyDAEs,themathe-maticalmodelofafl

8、exiblemultibodysystemisheterogeneousbynature.Onecouldalsospeakofacoupledsystemofdis-crete(rigidbodies)andcontinuum(elasticbodies)modelswheretheinterfaceorcouplingconditionsdeservespecialattention.ConcentratingontheLagrange