A complementarity eigenproblem in the stability analysis of finite dimensional elastic systems with frictional contact

A. Pinto da Costa, I. Figueiredo, J. Júdice and J. Martins

Abstract

In this paper a mixed complementarity eigenproblem (MCEICP) is formulated and a method is proposed for its numerical solution. This mathematical problem is motivated by the study of divergence instabilities of static equilibrium states of finite dimensional mechanical systems with unilateral frictional contact. The complementarity eigenproblem is solved by transforming it into a non-monotone mixed complementarity problem (MCP), with is then solved using the algorithm PATH. The proposed method is used to study some small sized examples and some large finite element problems.