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CONVERGENCE OF A CLASS OF SEMI-IMPLICIT TIME-STEPPING SCHEMES FOR NONSMOOTH RIGID MULTIBODY DYNAMICS

Bogdan Gavrea(gavrea***at***seas.upenn.edu)
Mihai Anitescu(anitescu***at***mcs.anl.gov)
Florian Potra(potra***at***math.umbc.edu)

Abstract: In this work we present a framework for the convergence analysis in a measure differential inclusion sense of a class of time-stepping schemes for multibody dynamics with contacts, joints, and friction. This class of methods solves one linear complementarity problem per step and contains the semi-implicit Euler method, as well as trapezoidallike methods for which second-order convergence was recently proved under certain conditions. By using the concept of a reduced friction cone, the analysis includes, for the first time, a convergence result for the case that includes joints. An unexpected intermediary result is that we are able to define a discrete velocity function of bounded variation, although the natural discrete velocity function produced by our algorithm may have unbounded variation.

Keywords: rigid body, contact dynamics, friction, measure differential inclusion, complementarity problems

Category 1: Complementarity and Variational Inequalities

Category 2: Applications -- Science and Engineering (Mechanical Engineering )

Category 3: Other Topics (Other )

Citation: Preprint ANL/MCS-1378-1006 Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, October, 2006

Download: [Postscript]

Entry Submitted: 11/30/2006
Entry Accepted: 12/01/2006
Entry Last Modified: 11/30/2006

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