[Un résultat d'existence à un problème dynamique de contact sans frottement en élasticité]
Le but de ce travail est de présenter un résultat d'existence au problème dynamique de contact sans frottement entre un corps élastique et une fondation rigide. La preuve est basée sur cinq étapes fondamentales : une discrétisation en temps du problème qui mène à un problème à solution unique ; la construction de plusieurs séquences ; le traitement de la condition de contact au moyen d'un multiplicateur de Lagrange dont les propriétés d'orthogonalité nous permettent d'obtenir des estimations à priori et donc, obtenir la convergence des séquences ; finalement on passe à la limite pour obtenir une solution faible du problème continu.
The purpose of this work is to present an existence result for the dynamic frictionless contact problem between an elastic body and a rigid foundation. The proof is based on five fundamental steps: a discretization in time which leads to a discretized problem with unique solution; the construction of functions approximating a solution of the problem; the treatment of the contact condition by means of a Lagrange multiplier whose orthogonality properties allow us to get a priori estimates; the convergence of said functions and, finally, the pass to the limit obtaining a weak solution of the continuous problem.
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@article{CRMATH_2006__343_5_355_0,
author = {Mar{\'\i}a Teresa Cao and Peregrina Quintela},
title = {Existence of solutions for a dynamic {Signorini's} contact problem},
journal = {Comptes Rendus. Math\'ematique},
pages = {355--360},
publisher = {Elsevier},
volume = {343},
number = {5},
year = {2006},
doi = {10.1016/j.crma.2006.07.004},
language = {en},
}
María Teresa Cao; Peregrina Quintela. Existence of solutions for a dynamic Signorini's contact problem. Comptes Rendus. Mathématique, Volume 343 (2006) no. 5, pp. 355-360. doi : 10.1016/j.crma.2006.07.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.07.004/
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