Problèmes de contact unilatéral avec frottement de Coulomb en élastostatique et élastodynamique. Etude mathématique et résolution numérique.

Abstract : The modelling of problems of contact leads to serious difficulties: conceptual, mathematical and data processing difficulties much more complex than those coming from the linear structural mechanics. Motivated by the fundamental role that the contact plays in applications of computational mechanics, we are interested in problems of unilateral contact and friction (static and dynamic) in small deformations. This thesis is devoted to the study of certain formulations and methods to solve this problem and breaks up into two great parts. The first one is devoted to the presentation of the hybrid discretization of unilateral contact problem with Coulomb friction. A formulation with a projection is developed and an existence and uniqueness result is given for the discrete problem. Different methods of solution are presented (Newton, iterative method, fixed points, Uzawa) and are compared in terms of number of iteration and robustness with respect to the coefficient of friction. The second part relates to the elastodynamic contact problem. Several algorithms (θ-method, Newmark, midpoint) are presented. New strategies are considered (Paoli and Schatzman scheme, scheme with an equivalent contact condition, scheme with equivalent mass matrix) to overcome the difficulties met with the previous schemes. The last method allows us to have energy conserving problem and to prove an existence result of a Lipschitz continuous solution for the discrete elastodynamic contact problem. These results are validated by numerical results.
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Submitted on : Thursday, March 9, 2006 - 11:51:07 AM
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Houari Boumediène Khenous. Problèmes de contact unilatéral avec frottement de Coulomb en élastostatique et élastodynamique. Etude mathématique et résolution numérique.. Mathématiques [math]. INSA de Toulouse, 2005. Français. ⟨tel-00011873⟩

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