From differential calculus to 0-1 topological optimization. (English) Zbl 1139.49039

Summary: The topological asymptotic expansion gives the variation of a cost function when a small hole is created in a domain. This approach leads to very powerful algorithms in topological optimization. Unfortunately, these asymptotic expansions are obtained with the use of complicated mathematical tools. The goal of this paper is to provide a straightforward way to derive a topological asymptotic expansion using a classical gradient. We will illustrate this general approach by some numerical experiments for the elasticity and the Stokes problems.


49Q10 Optimization of shapes other than minimal surfaces
49Q12 Sensitivity analysis for optimization problems on manifolds
74P05 Compliance or weight optimization in solid mechanics
74P10 Optimization of other properties in solid mechanics
74P15 Topological methods for optimization problems in solid mechanics
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