Continuation of the static contact problem with Coulomb friction

• ID: 2643, RIV: 10132747
• ISSN: not specified, ISBN: 978-80-7372-821-2
• source: SNA'12, Seminar on Numerical Analysis
• keywords: Coulomb friction; continuation; path following
• authors: Vladimír Janovský, Radek Kučera
• authors from KNM: Janovský Vladimír

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.