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首页> 外文期刊>Applications of Mathematics >APPROXIMATION AND NUMERICAL REALIZATION OF 3D CONTACT PROBLEMS WITH GIVEN FRICTION AND A COEFFICIENT OF FRICTION DEPENDING ON THE SOLUTION
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APPROXIMATION AND NUMERICAL REALIZATION OF 3D CONTACT PROBLEMS WITH GIVEN FRICTION AND A COEFFICIENT OF FRICTION DEPENDING ON THE SOLUTION

机译：具有给定摩擦并且取决于解决方案的摩擦系数的3D接触问题的逼近和数值实现

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摘要

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 F which depends on a solution. It is shown that a solution exists for a large class of F and is unique provided that 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.
机译：本文考虑了在公共表面上的摩擦，给出了由刚性半空间单边支撑的弹性体的3D接触问题的分析，逼近和数值实现。摩擦服从最简单的Tresca模型（先验地给出滑移边界），但是摩擦系数F取决于解。结果表明，存在大量的F的解，并且唯一的条件是F是Lipschitz连续且Lipschitz连续性的模数足够小。通过有限元离散化该问题，并建立了离散解的收敛性。最后，描述了实现数值的方法，并通过几个模型实例说明了该方法的有效性。

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