The goal of this paper is to improve the performance of an electric motor by modifying the
geometry of a specific part of the iron core of its rotor. To be more precise, the objective is to …

Mathematical analysis and numerical solutions of problems with unknown shapes or
geometrical domains is a challenging and rich research field in the modern theory of the …

The topological derivative method is recognized as a robust numerical technique in
engineering applications such as topology optimization, inverse problems, imaging …

We study distributed and boundary integral expressions of Eulerian and Fréchet shape
derivatives for several classes of nonsmooth domains such as open sets, Lipschitz domains …

We consider the shape-topological control of a singularly perturbed variational inequality.
The geometry-dependent state problem that we address in this paper concerns a …

The topological sensitivity analysis for the heterogeneous and anisotropic elasticity problem
in two-dimensions is performed in this work. The main result of the paper is an analytical …

A simple analytical expression for crack nucleation sensitivity analysis is proposed relying
on the concept of topological derivative and applied within a two‐dimensional linear elastic …

A class of non-smooth and non-convex optimization problems with penalty constraints linked
to variational inequalities is studied with respect to its shape differentiability. The specific …

We consider an elastic body with a rigid inclusion and a crack located at the boundary of the
inclusion. It is assumed that nonpenetration conditions are imposed at the crack faces which …

An elastic body weakened by small cracks is considered in the framework of unilateral
variational problems in linearized elasticity. The frictionless contact conditions are …