Sensitivity analysis and optimal control for a friction problem in the linear elastic model
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.
Keywords
Cite
@article{arxiv.2410.22356,
title = {Sensitivity analysis and optimal control for a friction problem in the linear elastic model},
author = {Loïc Bourdin and Fabien Caubet and Aymeric Jacob de Cordemoy},
journal= {arXiv preprint arXiv:2410.22356},
year = {2024}
}
Comments
37 pages. arXiv admin note: text overlap with arXiv:2410.11760, arXiv:2410.12315