Shape optimization for variational inequalities: the scalar Tresca friction problem
Abstract
This paper investigates, without any regularization or penalization procedure, a shape optimization problem involving a simplified friction phenomena modeled by a scalar Tresca friction law. Precisely, using tools from convex and variational analysis such as proximal operators and the notion of twice epi-differentiability, we prove that the solution to a scalar Tresca friction problem admits a directional derivative with respect to the shape which moreover coincides with the solution to a boundary value problem involving Signorini-type unilateral conditions. Then we explicitly characterize the shape gradient of the corresponding energy functional and we exhibit a descent direction. Finally numerical simulations are performed to solve the corresponding energy minimization problem under a volume constraint which shows the applicability.
Cite
@article{arxiv.2410.11750,
title = {Shape optimization for variational inequalities: the scalar Tresca friction problem},
author = {Samir Adly and Loïc Bourdin and Fabien Caubet and Aymeric Jacob de Cordemoy},
journal= {arXiv preprint arXiv:2410.11750},
year = {2024}
}
Comments
30 pages