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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 of our method and our theoretical results.
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https://hal-univ-pau.archives-ouvertes.fr/hal-03848645
Contributor : Aymeric Jacob de Cordemoy Connect in order to contact the contributor
Submitted on : Thursday, November 10, 2022 - 7:30:01 PM
Last modification on : Monday, November 14, 2022 - 11:40:20 AM

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  • HAL Id : hal-03848645, version 1

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Samir Adly, Loïc Bourdin, Fabien Caubet, Aymeric Jacob de Cordemoy. Shape optimization for variational inequalities: the scalar Tresca friction problem. 2022. ⟨hal-03848645⟩

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