June 18,  19,  20   2003
 
 
 

12:00 AM - Friday, June 20, 2003 - Amphitheater Hermite

Grégoire Allaire

Centre de Mathématiques Apliquées
Ecole Polytechnique
91128 Palaiseau, France

gregoire.allaire@polytechnique.fr

Shape Optimization by the Level-Set Method

This is a joint work with F. Jouve and A.-M. Toader. The typical problem of structural optimization is to find the "best" structure which is, at the same time, of minimal weight and of maximum strength or which performs a desired deformation. In this context we propose a new numerical method of shape optimization based on a combination of the classical shape derivative and of the level-set method for front propagation. We implement this method in two and three space dimensions for a model of linear or non-linear elasticity. We consider various objective functions and constraints on the perimeter. The shape derivative is computed by an adjoint method. The cost of our numerical algorithm is moderate since the shape is captured on a fixed Eulerian mesh. Although this method is not specifically designed for topology optimization, it can easily handle topology changes. However, the resulting optimal shape is strongly dependent on the initial guess. We make some comparisons with the homogenization method for topology optimization.