Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution. (English) Zbl 1212.65446

Haslinger, Jaroslav; Ligurský, Tomáš

Appl. Math., Praha 54, No. 5, 391-416 (2009).

Summary: The paper presents the analysis, approximation and numerical realization of 3D contact problems for an elastic body unilaterally supported by a rigid half space taking into account friction on the common surface. Friction obeys the simplest Tresca model (a slip bound is given a priori) but with a coefficient of friction \(\mathcal F\) which depends on a solution. It is shown that a solution exists for a large class of \(\mathcal F\) and is unique provided that \(\mathcal F\) is Lipschitz continuous with a sufficiently small modulus of the Lipschitz continuity. The problem is discretized by finite elements, and convergence of discrete solutions is established. Finally, methods for numerical realization are described and several model examples illustrate the efficiency of the proposed approach.

MSC:

65N30

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

unilateral contact and friction; solution-dependent coefficient of friction

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