A geometrical-based contact algorithm using a barrier method

Most methods employed in the numerical solution of contact problems in fini te element simulations rely on equality-based optimization methods. Typical ly, a gap function which is non-differentiable at the point of contact is u sed in these kind of approaches. The gap function can be seen as the Macaul ay bracket of some distance function, where the latter is differentiable at the point of contact. In this article, we propose to use the distance func tion directly instead of using the gap function. This will give rise to a f ormulation involving inequality constraints. This approach eliminates the a rtificially introduced non-differentiability. To this end we propose a barr ier algorithm as the method of choice to solve the problem. The method orig inates in optimization literature, where convergence proofs for the method are available. Copyright (C) 2001 John Wiley & Sons, Ltd.