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Comptes Rendus Mathématique
Volume 340, n° 1
pages 69-74 (janvier 2005)
Doi : 10.1016/j.crma.2004.11.016
Received : 20 October 2004 ;  accepted : 16 November 2004
Approximation numérique dʼun problème de membrane non linéaire
Numerical approximation for a nonlinear membrane problem

Nabil Kerdid a , Hervé Le Dret b , Abdelkader Saïdi c
a College of Computer Science and Information Systems, Imam University, Riyadh, Saudi Arabia 
b Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, boîte courrier 187, 75252 Paris cedex 05, France 
c Institut de recherche mathématique avancée, université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg, France 


On étudie numériquement les déformations dʼune membrane élastique non linéaire. On considère le modèle de membrane obtenu par Le Dret et Raoult par la méthode de Γ -convergence. Les déformations de la membrane minimisent une énergie non quadratique. On effectue une approximation du modèle par éléments finis conformes et on utilise un algorithme de gradient conjugué non linéaire pour minimiser lʼénergie discrétisée. Pour citer cet article : N. Kerdid et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).

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We study numerically the deformations of a nonlinearly elastic membrane. We consider the nonlinear membrane model obtained by Le Dret and Raoult using Γ -convergence. In this model, membrane deformations minimize a highly nonquadratic energy. We consider a conforming finite element approximation of the problem and use a nonlinear conjugate gradient algorithm to minimize the discrete energy. To cite this article: N. Kerdid et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The full text of this article is available in PDF format.

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