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Theoretical analysis of discrete contact problems with Coulomb friction

Tomáš Ligurský — 2012

Applications of Mathematics

A discrete model of the two-dimensional Signorini problem with Coulomb friction and a coefficient of friction depending on the spatial variable is analysed. It is shown that a solution exists for any and is globally unique if is sufficiently small. The Lipschitz continuity of this unique solution as a function of as well as a function of the load vector f is obtained. Furthermore, local uniqueness of solutions for arbitrary > 0 is studied. The question of existence of locally Lipschitz-continuous...

Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution

Jaroslav HaslingerTomáš Ligurský — 2009

Applications of Mathematics

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 which depends on a solution. It is shown that a solution exists for a large class of and is unique provided that is Lipschitz continuous with a sufficiently small modulus of...

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