Grégoire Allaire (CMAP, Ecole Polytechnique, France)
“Geometrical constraints in the level set method for shape and topology optimization of structures”
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 or to molding direction. 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 different 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 specific treatment of the constraints since, in particular, some topological changes may be prevented by those constraints.
This is a joint work with François
Jouve and Georgios Michailidis.