A Constraint- Stabilized Time-Stepping Approach for Rigid Multibody Dynamics with Joints, Contact and Friction

TitleA Constraint- Stabilized Time-Stepping Approach for Rigid Multibody Dynamics with Joints, Contact and Friction
Publication TypeReport
Year of Publication2002
AuthorsAnitescu, M, Hart, GD
Series TitleInt. J. Numer. Meth. Engng
Pagination1335-2371
Date Published10/2002
Other NumbersANL/MCS-P1002-1002
Abstract

<p>We present a method for achieving constraint stabilization for a linear-complementarity-based time-stepping scheme for multi-rigid-body dynamics with joints, contact and friction. The method requires the solution of only one linear complementarity problem per step. We show that under certain assumptions, that include the limited differentiability of the mappings governing the noninterpenetration and joint constraints; the pointed friction cone assumption; and at most linear growth of the external forces, the velocity is bounded for a sufficiently small size of the timestep over a fixed time-interval and the geometrical constraint infeasibility at step (l) is bounded above by a constant multiple of the square of the time-step and the square of the norm of the current value of the velocity. If, in addition, the velocity is uniformly bounded with respect to the time interval of the simulation, then the geometrical constraint infeasibility is bounded by the same bound irrespective of the time interval of the simulation.</p>

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