Molding direction constraints in structural optimization via a level-set method

Grégoire Allaire (1, 2) , François Jouve (3) , Georgios Michailidis (4)

1 DeFI - Shape reconstruction and identification
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 LJLL - Laboratoire Jacques-Louis Lions
4 SIMaP - Science et Ingénierie des Matériaux et Procédés

In the framework of structural optimization via a level-set method, we develop an approach to handle the directional molding constraint for cast parts. A novel molding condition is formulated and a penalization method is used to enforce the constraint. A first advantage of our new approach is that it does not require to start from a feasible initialization, but it guarantees the convergence to a castable shape. A second advantage is that our approach can incorporate thickness constraints too. We do not adress the optimization of the casting system, which is considered a priori defined. We show several 3d examples of compliance minimization in linearized elasticity under molding and minimal or maximal thickness constraints. We also compare our results with formulations already existing in the literature.

Mots clés: molding; shape and topology optimization; level set

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

Grégoire Allaire, François Jouve, Georgios Michailidis. Molding direction constraints in structural optimization via a level-set method. Variational Analysis and Aerospace Engineering, Springer, pp.1-39, 2016, 978-3-319-45680-5. ⟨10.1007/978-3-319-45680-5⟩. ⟨hal-01242945⟩