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Summary: A matrix-free cone complementarity approach for solving large-scale,
nonsmooth, rigid body dynamics
Preprint ANL/MCS-P1692-1109
A.Tasora a
M.Anitescu b
aUniversit`a degli Studi di Parma, Dipartimento di Ingegneria Industriale, 43100 Parma, Italy, tasora@ied.unipr.it
bMathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA,
anitescu@mcs.anl.gov
Abstract
This paper proposes an iterative method that can simulate mechanical systems featuring a large number of contacts and joints
between rigid bodies. The numerical method behaves as a contractive mapping that converges to the solution of a cone comple-
mentarity problem by means of iterated fixed-point steps with separable projections onto convex manifolds. Since computational
speed and robustness are important issues when dealing with a large number of frictional contacts, we have performed special
algorithmic optimizations in order to translate the numerical scheme into a matrix-free algorithm with O(n) space complexity and
easy implementation. A modified version, that can run on parallel computers is discussed. A multithreaded version of the method
has been used to simulate systems with more than a million contacts with friction.
Key words: Large-scale multibody, contact, friction, cone complementarity problem
1. Introduction
Many engineering problems involve unilateral con-
tacts between rigid bodies, for instance, in simulations
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