Thickness control in structural optimization via a level set method

Grégoire Allaire (1, 2) , François Jouve (3) , Georgios Michailidis (2)

1 DeFI - Shape reconstruction and identification
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 LJLL - Laboratoire Jacques-Louis Lions

In the context of structural optimization via a level-set method we propose a framework to handle geometric constraints related to a notion of local thickness. The local thickness is calculated using the signed distance function to the shape. We formulate global constraints using integral functionals and compute their shape derivatives. We discuss diff erent strategies and possible approximations to handle the geometric constraints. We implement our approach in two and three space dimensions for a model of linearized elasticity. As can be expected, the resulting optimized shapes are strongly dependent on the initial guesses and on the speci fic treatment of the constraints since, in particular, some topological changes may be prevented by those constraints.

Mots clés: thickness control; level-set method; signed distance function; shape and topology optimization

Domaines: Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

Grégoire Allaire, François Jouve, Georgios Michailidis. Thickness control in structural optimization via a level set method. Structural and Multidisciplinary Optimization, 2016, 53, pp.1349-1382. ⟨hal-00985000v2⟩