Shape optimization in contact mechanics using a penalty approach (Bastien Chaudet, UNIGE)

20.05.2022 10:30 – 11:30

Contact mechanics is the branch of continuum mechanics which studies the behaviour of solids that are in contact with each other. The physical non-penetration condition between the solids results in an inequality on the boundary of the domain. Therefore the associated mathematical formulation takes the form of a variational inequality. From the shape optimization point of view, this is not really convenient as such formulations are very difficult to differentiate with respect to the shape. Here, we focus on a well-known regularized formulation (the so-called "penalty formulation") obtained using a penalty approach, which enables us to get rid of the inequality. However, this new formulation remains not linear, nor differentiable.
In this talk, we begin with introducing the main notions related to shape optimization and to the contact problem. Then, we present an approach based on directional derivatives to get around the non-differentiability of the penalty formulation. Especially, we derive sufficient conditions for the solution to be shape differentiable. This allows us to develop a gradient-based shape optimization algorithm, built on these derivatives. Finally, in order to validate the approach, we test our algorithm on two-dimensional and three-dimensional benchmarks.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire d'analyse numérique

entrée libre