Michel Jean

A Gauss-Seidel like algorithm to solve frictional contact problems

The purpose of this work is to present some mathematical and numerical results concerning an implicit method devoted to frictional contact problems. It has been implemented in a dynamical deep drawing simulation software (SIMEM3 Renault) where unilateral contact and dry friction is assumed between the metal sheet and the tools. The method may be viewed as a nonlinear block Gauss-Seidel algorithm. A convergence theorem is proved using nonsmooth analysis theory. Several numerical results are presented to illustrate the behaviour of this algorithm.

Some Computational Aspects of Structural Dynamics Problems with Frictional Contact

Contact and friction phenomena are common and very important in many fields of mechanical engineering. Recently, a significant research effort has been made to develop effective computational methods for finite element analysis of nonlinear problems in structural dynamics. This work may contribute to the discussion about different aspects of the implicit contact dynamics analysis. We begin with a brief presentation of the standard Newmark and Newton-Raphson approach. We propose several modifications to these schemes, presenting a set of first-order integration algorithms, and analyzing their numerical characteristics and utility in the numerical treatment of contact.

Dynamics of Rigid Bodies with Dry Friction and Partially Elastic Collisions

This paper deals with dynamical problems in the presence of unilateral contact and dry friction. Possible shocks may be either inelastic or partially elastic. The application in view is the motion of a collection of balls enclosed between walls and coming into contact with each other. A double time scale argument is evoked to justify the law governing shocks. It is observed that constraints are kinematically dependent. A numerical method is proposed and some computed examples are produced. Since the method proves efficient, one expects to deal in the future with a large number of balls, using a super computer, so as to generate the model of an aggregate. Everything in the sequel is presented in the two-dimensional setting.