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arXiv · 2410.22356

Sensitivity analysis and optimal control for a friction problem in the linear elastic model

Loïc Bourdin·Fabien Caubet·Aymeric Jacob de Cordemoy
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Abstract

This paper investigates, without any regularization procedure, the sensitivity analysis of a mechanical friction problem involving the (nonsmooth) Tresca friction law in the linear elastic model. To this aim a recent methodology based on advanced tools from convex and variational analyses is used. Precisely we express the solution to the so-called Tresca friction problem thanks to the proximal operator associated with the corresponding Tresca friction functional. Then, using an extended version of twice epi-differentiability, we prove the differentiability of the solution to the parameterized Tresca friction problem, characterizing its derivative as the solution to a boundary value problem involving tangential Signorini's unilateral conditions. Finally our result is used to investigate and numerically solve an optimal control problem associated with the Tresca friction model.

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Loïc Bourdin, Fabien Caubet, Aymeric Jacob de Cordemoy. 2024-10-16. Sensitivity analysis and optimal control for a friction problem in the linear elastic model. https://arxiv.org/abs/2410.22356

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