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Pré-Publication, Document De Travail Année : 2023

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

Loïc Bourdin
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Fabien Caubet

Résumé

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 et 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)

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  • HAL Id : hal-04127512 , version 6

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Loïc Bourdin, Fabien Caubet, Aymeric Jacob de Cordemoy. Sensitivity analysis and optimal control for a contact problem with friction in the linear elastic model. 2024. ⟨hal-04127512v6⟩
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