Shape optimization of a linearly elastic rolling structure under unilateral contact using Nitsche's method and cut finite elements

The main motivation of this work is to develop a numerical strategy for the shape optimization of a rolling elastic structure under contact with respect to a uniform rolling criterion. A first objective is to highlight the influence on the treatment of the contact terms. To do so, we present a numerical comparison between a penalty-based approach and the use of Nitsche's method which is known to have good consistency properties. A second task concerns the construction of an objective functional to force the uniform rolling criterion. Here, we present and compare two different strategies that will lead to quite similar results. All the numerical experiments proposed in this paper were performed using a fictitious domain approach coupled with a level set representation of the shape and the use of a cut finite element method to approximate the elastic equation.