Sensitivity analysis and optimal control for a friction problem in the linear elastic model - Université de Pau et des Pays de l'Adour
Journal Articles Applied Mathematics and Optimization Year : 2023

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

Loïc Bourdin
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Fabien Caubet

Abstract

This paper investigates, without any regularization procedure, the sensitivity analysis of a mechanical contact 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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Dates and versions

hal-04127512 , version 1 (13-06-2023)
hal-04127512 , version 2 (14-06-2023)
hal-04127512 , version 3 (20-06-2023)
hal-04127512 , version 4 (08-07-2023)
hal-04127512 , version 5 (03-08-2023)
hal-04127512 , version 6 (29-01-2024)
hal-04127512 , version 7 (02-08-2024)

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Cite

Loïc Bourdin, Fabien Caubet, Aymeric Jacob de Cordemoy. Sensitivity analysis and optimal control for a friction problem in the linear elastic model. Applied Mathematics and Optimization, 2023, 90 (1), pp.29. ⟨10.1007/s00245-024-10156-z⟩. ⟨hal-04127512v6⟩
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