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ArticleOriginal scientific text

Title

Topology optimization of systems governed by variational inequalities

Authors 1

Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

Abstract

This paper deals with the formulation of the necessary optimality condition for a topology optimization problem of an elastic body in unilateral contact with a rigid foundation. In the contact problem of Tresca, a given friction is governed by an elliptic variational inequality of the second order. The optimization problem consists in finding such topology of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. The topological derivative of the cost functional is calculated and a necessary optimality condition is formulated. The calculated topological derivative is also used in the numerical algorithm to find a descent direction by inserting voids in the domain occupied by the body. Numerical examples are provided.

Keywords

ENG
variational inequality, topology optimization

Bibliography

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2010/30/2
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Pages:
237-252
Main language of publication
English
Received
2009-11-25
Published
2010

DOI: 10.7151/dmdico.1122

Exact and natural sciences