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Theses

Résultats de convergence pour les inéquations variationnelles et applications en mécanique du contact

Abstract : The topic of this thesis concerns some convergence results for variational inequalities with applications in the study of boundary value problems which describe the contact between a deformable body and a foundation. The thesis is divided into two parts. In the first part, we are interested in the analysis of quasivariational inequalities, with or without history-dependent operators, in Hilbert spaces. We prove some convergence results related to a perturbation of the set of constraints and a penalty method, as well. Moreover, for a class of history-dependent quasivariational inequalities we study a dual formulation for which we present existence, uniqueness and equivalence results. The second part is devoted to applications of these abstract results in the study of six contact problems with elastic, viscoelastic and viscoplastic materials, both in the static or quasistatic case. The contact conditions we consider are the Signorini condition, the normal compliance condition with unilateral constraint, the unilateral constraint condition with yield limit. Finally, we study a number of optimal control problems associated to some contact models. For these problems we provide existence and convergence results.
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https://tel.archives-ouvertes.fr/tel-01834598
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Submitted on : Tuesday, July 10, 2018 - 5:02:09 PM
Last modification on : Wednesday, July 11, 2018 - 1:14:08 AM
Long-term archiving on: : Tuesday, October 2, 2018 - 1:01:29 PM

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Ahlem Benraouda. Résultats de convergence pour les inéquations variationnelles et applications en mécanique du contact. Mathématiques générales [math.GM]. Université de Perpignan, 2018. Français. ⟨NNT : 2018PERP0009⟩. ⟨tel-01834598⟩

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