Modélisation et méthodes de décomposition de domaines pour des problèmes de contact

Abstract : This PhD thesis treats the mathematical modelization of thin layers and the domain decomposition methods in contact mechanics.\\
The first part is dedicated to a quasistatic contact problem with non local Coulomb friction law between an elastic body and a thin layer. After establishing an existence theorem, we define a critical ratio between the geometrical and the elastic parameters. For this ratio, we establish rigorously a limit contact law by making the layer thickness tends to zero.\\
The second part is devoted to some ``natural'' domain decomposition methods in contact problems. This method consists of retaining the natural interface between two bodies as a numerical interface for the domain decomposition. Firstly, we study a contact problem without friction between two elastic bodies (Signorini problem) for which we propose and prove the convergence of a Neumann-Dirichlet algorithm. This result is then generalized to a contact problem with Coulomb friction. At last, we propose and prove the convergence of a ``Neumann-Neumann'' decomposition algorithm for a Signorini problem.
Some numerical results give confidence to the validity of the theoretical results.
Document type :
Theses
Mathematics. INSA de Lyon, 2004. French


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Contributor : Jalila Sabil <>
Submitted on : Friday, March 17, 2006 - 12:32:31 PM
Last modification on : Friday, March 17, 2006 - 4:54:11 PM

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Jalila Sabil. Modélisation et méthodes de décomposition de domaines pour des problèmes de contact. Mathematics. INSA de Lyon, 2004. French. <tel-00011970>

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