Publication at Faculty of Mathematics and Physics |
2012
Abstract
Let be a linearly elastic body supported by a rigid foundation along the contact boundary. We consider the static contact problems with Coulomb friction.
In particular, we will investigate a discrete version of this problem. This may be understood as FEM-approximation of the continuous problem.
Under generic assumptions, there exists a solution for any data. A difficulty comes from the fact that the solution may not be unique.
In order to find the non unique solutions, we explore continuation (path-following) techniques: Note that the classical continuation techniques fail, since the problem is not smooth. Nevertheless, it is piecewise-smooth and we can exploit this feature in the continuation algorithm.