Volumetric expressions of the shape gradient of the compliance in structural shape optimization

Matteo Giacomini (1, 2, 3) , Olivier Pantz (4) , Karim Trabelsi (3)

1 DeFI - Shape reconstruction and identification
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 IPSA - Institut Polytechnique des Sciences Avancées
4 LJAD - Laboratoire Jean Alexandre Dieudonné

In this article, we consider the problem of optimal design of a compliant structure under a volume constraint, within the framework of linear elasticity. We introduce the pure displacement and the dual mixed formulations of the linear elasticity problem and we compute the volumetric expressions of the shape gradient of the compliance by means of the velocity method. A preliminary qualitative comparison of the two expressions of the shape gradient is performed through some numerical simulations using the Boundary Variation Algorithm.

Mots clés: Shape optimization; Linear elasticity; Volumetric shape gradient; Compliance minimization; Pure displacement formulation; Dual mixed formulation

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

Matteo Giacomini, Olivier Pantz, Karim Trabelsi. Volumetric expressions of the shape gradient of the compliance in structural shape optimization. 2017. ⟨hal-01441943⟩