Proceedings of IMECE2008 ASME International Mechanical Engineering Congress and Exposition November 1-6, 2008, Boston, Massachusetts, USA IMECE2008-66766 DRAFT A GPU-BASED IMPLEMENTATION OF A CONE CONVEX COMPLEMENTARITY APPROACH FOR SIMULATING RIGIDBODY DYNAMICS WITH FRICTIONAL CONTACT Alessandro Tasora Dept. Mech. Engineering University of Parma Parma, Italy Email: tasora@ied.unipr.it Dan Negrut * Dept. Mech. Engineering University of Wisconsin, Madison, WI Email: negrut@wisc.edu Mihai Anitescu Math. and Comp. Sci. Division Argonne National Lab. Argonne, IL Email: anitescu@mcs.anl.gov ABSTRACT In the context of simulating the frictional contact dynam- ics of large systems of rigid bodies, this paper reviews a novel method for solving large cone complementarity problems by means of a fixed-point iteration algorithm. The method is an extension of the Gauss-Seidel and Gauss-Jacobi methods with overrelaxation for symmetric convex linear complementar- ity problems. Convergent under fairly standard assumptions, the method is implemented in a parallel framework by using a single instruction multiple data computation paradigm promoted by the Compute Unified Device Architecture library for graphical pro- cessing unit programming. The framework supports the analysis of problems with a large number of rigid bodies in contact. Sim- ulation thus becomes a viable tool for investigating the dynamics of complex systems such as ground vehicles running on sand, powder composites, and granular material flow. Introduction Approximating the time evolution of a multibody system in the presence of friction and contact/impact phenomena through numerical simulation continues to be a challenging task. For in- stance, results reported in [1] indicate that the most widely used * Address all correspondence to this author. commercial software package for multibody dynamics simula- tion has significant difficulties in handling the simple problem of a collection of balls falling in a box, whenever the number of balls becomes larger than 50; in fact, the problem becomes practically intractable when the number of bodies becomes larger than 100. Presented here is an algorithm that can robustly and efficiently approximate the dynamics of rigid bodies undergo- ing frictional contact [2]. Posing challenges of its own, the case of deformable frictional contact is extensively discussed in [3, 4] and falls outside the scope of this work. Two approaches are most often considered when simulat- ing the dynamics of a multibody system with frictional contact. First is the class of so-called penalty methods, where it is as- sumed that every time two rigid bodies come in frictional contact, the interaction can be represented by a collection of stiff springs combined with damping elements that act at the interface of the two bodies [5–8]. Implementing these regularization approaches requires little effort beyond that usually associated with devel- oping a multibody dynamics simulation code. Furthermore, this methodology can easily accommodate complex frictional con- tact mechanisms, as it allows for a large number of “tuning” pa- rameters that, in general, can be adjusted to control the dynam- ics of the frictional contact interaction. What has prevented the widespread use of this solution is the small step-size at which the 1 Copyright c  2008 by ASME