Study of different strategies for splitting variables in multidisciplinary topology optimization

Rajae Aboulaich (1) , Abderrahmane Habbal (2, 3) , Noureddine Moussaid (1, 4)

1 LERMA - Laboratoire d'Etudes et Recherche en Mathématiques Appliquées
2 JAD - Laboratoire Jean Alexandre Dieudonné
3 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
4 Ecole Supérieure de Technologie d'Essaouira

This paper is devoted to the minimization of the thickness of an elastic structure under competitive loadings. We propose to determine an equilibrium thickness using game theory. We consider two loads exercised separately on two parts of the plate and we aim to optimize both compliances so we deal with a multiloading optimization problem. Firstly, the design variable is taken to be the thickness of the plate. In a second step, we assume that the thickness depends on two independent functions, that we consider as strategies. The multidisciplinary optimization problem is solved as a non-cooperative game and we determine a Nash equilibrium. Finally, some numerical simulations are presented and discuted.

Domaines: Optimisation et contrôle [math.OC]

Rajae Aboulaich, Abderrahmane Habbal, Noureddine Moussaid. Study of different strategies for splitting variables in multidisciplinary topology optimization. 2011. ⟨hal-00648701⟩