Mixed Finite Element Method for Multi-layer Elastic Contact Systems

TL;DR

This paper develops and analyzes a mixed finite element method for multi-layer elastic contact systems with Tresca friction, providing convergence proofs and numerical validation against existing methods.

Contribution

It introduces a novel mixed finite element approach for multi-layer elastic contact problems with Tresca friction, including convergence analysis and an algebraic dual algorithm.

Findings

The method converges theoretically under specified conditions.

Numerical experiments validate the method's effectiveness.

Comparison shows advantages over layer decomposition methods.

Abstract

With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent saddle point problems with interlayer Tresca friction conditions and the mixed finite element method are proposed and analyzed. Then, the convergence of the numerical solution of the mixed finite element method is theoretically proven, and the corresponding algebraic dual algorithm is given. Finally, through numerical experiments, the mixed finite element method is not only compared with the layer decomposition method, but also its convergence relationship with respect to the spatial discretization parameter $H$ is verified.