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

Issue		ESAIM: COCV Volume 16, Number 3, July-September 2010


Page(s)		523 - 544
DOI		10.1051/cocv/2009013
Published online		18 June 2009

ESAIM: COCV 16 (2010) 523-544

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: 8 January 2008
Revised: 21 November 2008

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.

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