Publication ahead of print Issue ESAIM: COCV DOI 10.1051/cocv/2009013 Published online 18 June 2009

ESAIM: COCV
DOI: 10.1051/cocv/2009013

A penalty method for topology optimization subject to a pointwise state constraint

Samuel Amstutz

Laboratoire d'Analyse Non Linéaire et Géométrie, Faculté des Sciences, 33 rue Louis Pasteur, 84000 Avignon, France. samuel.amstutz@univ-avignon.fr

Received January 8, 2008. Revised November 21, 2008. Published online June 18, 2009.

Abstract
This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.

Mathematics Subject Classification. 49Q10, 49Q12, 49M30, 35J05

Key words: Topology optimization, topological derivative, penalty methods, pointwise state constraints


© EDP Sciences, SMAI 2009

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