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Numerical approximation for a non-linear membrane problem |
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| Authors: | Nabil Kerdid Abdelkader Sa?¨di |
| Institution: | a College of Computer and Information Sciences, Imam University, Riyadh, Saudi Arabia b Laboratoire Jacques-Louis Lions, UPMC Univ Paris 06, UMR 7598, F-75005 Paris, France c Laboratoire Jacques-Louis Lions, CNRS, UMR 7598, F-75005 Paris, France d Institut de Recherche Mathématique Avancée, Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg, France |
| Abstract: | We present a numerical study of large deformations of non-linearly elastic membranes. We consider the non-linear membrane model obtained by Le Dret and Raoult using Γ-convergence, in the case of a Saint Venant-Kirchhoff bulk material. We consider conforming P1 and Q1 finite element approximations of the membrane problem and use a non-linear conjugate gradient algorithm to minimize the discrete energy. We present numerical tests including membranes subjected to live pressure loads. |
| Keywords: | Non-linear elasticity Membranes/thin films Finite element approximation |
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