Sensitivity Analysis of a Scalar Mechanical Contact Problem with Perturbation of the Tresca's Friction Law - Archive ouverte HAL Access content directly
Journal Articles Journal of Optimization Theory and Applications Year : 2022

Sensitivity Analysis of a Scalar Mechanical Contact Problem with Perturbation of the Tresca's Friction Law

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Loïc Bourdin
Fabien Caubet

Abstract

This paper investigates the sensitivity analysis of a scalar mechanical contact problem described by a boundary value problem involving the Tresca's friction law. The sensitivity analysis is performed with respect to right-hand source and boundary terms perturbations. In particular the friction threshold involved in the Tresca's friction law is perturbed, which constitutes the main novelty of the present work with respect to the existing literature. Hence we introduce a parameterized Tresca friction problem and its solution is characterized by using the proximal operator associated with the corresponding perturbed nonsmooth convex Tresca friction functional. Then, by invoking the extended notion of twice epi-differentiability depending on a parameter, 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 Signorini unilateral conditions. Finally numerical simulations are provided in order to illustrate our main result.
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Dates and versions

hal-03561843 , version 1 (08-02-2022)
hal-03561843 , version 2 (02-03-2022)

Identifiers

  • HAL Id : hal-03561843 , version 2

Cite

Loïc Bourdin, Fabien Caubet, Aymeric Jacob de Cordemoy. Sensitivity Analysis of a Scalar Mechanical Contact Problem with Perturbation of the Tresca's Friction Law. Journal of Optimization Theory and Applications, In press. ⟨hal-03561843v2⟩
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