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Contribution à l'étude mathématique et numérique des structures piézoélectriques en contact

Abstract : The topic of this thesis belongs both to applied mathematics and mechanics. It deals with the mathematical study of piezoelectric problems, i.e problems including a coupling between mechanical and electrical actions, involving contact and friction. We study the variational and numerical analysis of these problems. The thesis is structured in four parts. The first one contains the background in Mathematics and Mechanics needed in the rest of the manuscript. The second part deals with two static frictional contact problems between an electro-elastic body and a foundation. We provide the existence, uniqueness and continuons dependence of the solution of the primal problems, formulated in terms of displacement and electric potential fields. A dual formulation, in terms of stress and electric displacement fields is studied too, for which existence and uniqueness results are presented, as well. The third part concern two models of quasistatic piezoelectric contact. For each model we present existence results. The fourth part deals with the numerical analysis and simulations obtained by using Euler scheme in time and finite elements in space. We consider a static electro-elastic problem with normal compliance and friction for which we provide error estimates. The problem is written in the form of an augmented Lagrangian algorithm coupled with a generalized Newton method. Some two-dimensional simulations are presented in order to recover the error estimates. Similar results are also presented in the study of a quasistatic electro-viscoelastic problem contact.
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https://tel.archives-ouvertes.fr/tel-00192884
Contributor : Youssef Ouafik <>
Submitted on : Thursday, November 29, 2007 - 3:53:50 PM
Last modification on : Monday, March 21, 2016 - 5:31:44 PM
Long-term archiving on: : Monday, April 12, 2010 - 5:32:59 AM

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  • HAL Id : tel-00192884, version 1

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Youssef Ouafik. Contribution à l'étude mathématique et numérique des structures piézoélectriques en contact. Modélisation et simulation. Université de Perpignan, 2007. Français. ⟨tel-00192884⟩

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