动态摩擦接触问题的统一原对偶主动集方法

Fixed Point Theory and Applications Pub Date : 2022-08-30 DOI:10.1186/s13663-022-00729-4

Abide, Stéphane, Barboteu, Mikaël, Cherkaoui, Soufiane, Dumont, Serge

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引用次数: 1

摘要

本文提出了一种半光滑牛顿法和一种原始对偶主动集策略来求解带摩擦的动态接触问题。利用半光滑牛顿法，将库仑摩擦接触条件转化为与准优化问题相关的不动点问题。该方法基于原始对偶活动集(PDAS)策略的使用。这里的主要思想是找到正确的节点子集$\mathcal{A}$，这些节点是处于接触状态(活动)的，而不是处于接触状态(不活动)的。对于每一种情况，非线性边界条件都被合适的线性边界条件所取代。通过对超弹性问题和刚性颗粒材料的数值实验，验证了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Unified primal-dual active set method for dynamic frictional contact problems

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Unified primal-dual active set method for dynamic frictional contact problems

In this paper, we propose a semi-smooth Newton method and a primal-dual active set strategy to solve dynamical contact problems with friction. The conditions of contact with Coulomb’s friction can be formulated in the form of a fixed point problem related to a quasi-optimization one thanks to the semi-smooth Newton method. This method is based on the use of the primal-dual active set (PDAS) strategy. The main idea here is to find the correct subset $\mathcal{A}$ of nodes that are in contact (active) opposed to those which are not in contact (inactive). For each case, the nonlinear boundary condition is replaced by a suitable linear one. Numerical experiments on both hyper-elastic problems and rigid granular materials are presented to show the efficiency of the proposed method.

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来源期刊

Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.