Fabio Botelho, Alexandre Molter
Published 2019-06-29Version 1
In this article we develop a duality principle and concerning numerical method for a shape optimization problem in elasticity. We consider the problem of finding the optimal shape for an elastic solid which minimizes its structural inner energy resulting from the action of external loads to be specified. The main results are obtained through standard tools of convex analysis and duality theory. We emphasize our algorithm do not include a filter to process the results, so that the result obtained is indeed a critical point for the original optimization problem. Finally, in the last section, we present some numerical examples concerning applications of the theoretical results established.
A duality principle for non-convex optimization in $\mathbb{R}^n$
Approximation of shape optimization problems with non-smooth PDE constraints
A shape optimization problem on planar sets with prescribed topology
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