# A Complementarity Eigenproblem in the Stability Analysis of Finite Dimensional Elastic Systems with Frictional Contact

• A. Pinto da Costa
• I. N. Figueiredo
• J. J. Júdice
• J. A. C. Martins
Chapter
Part of the Applied Optimization book series (APOP, volume 50)

## Abstract

In this paper a mixed complementarity eigenproblem (MCEIP) 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), which is then solved by using the algorithm PATH. The proposed method is used to study some small sized examples and some large finite element problems.

## Keywords

Complementarity contact friction eigenvalues instability

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## Authors and Affiliations

• A. Pinto da Costa
• 1
• I. N. Figueiredo
• 2
• J. J. Júdice
• 2
• J. A. C. Martins
• 1
1. 1.Dep. Eng. Civil and ICISTInst. Sup. TécnicoLisboaPortugal