Simulation of unilateral constrained systems with many bodies

Nowadays the theory of multi-body systems including unilateral constraints is quite well established. However, the tendency towards more and more detailed and complex models may not be compensated with increasing computer power. In fact the growing computational effort demands for improved numerical methods in order to solve large systems. In this paper a time-stepping method is proposed for the computation of multi-body systems with many unilateral constraints. Stability and accuracy are discussed with respect to the given discretisation. In order to handle many contacts an iterative algorithm is applied based on a Gauss-Seidel relaxation scheme. A numerical example shows the efficiency of the relaxation scheme in comparison with Lemke's method and an Augmented Lagrangian approach.