Numerical approximation for a non-linear membrane problem

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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 P1and Q1finite 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. © 2008 Elsevier Ltd. All rights reserved.

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Kerdid, N., Le Dret, H., & Saïdi, A. (2008). Numerical approximation for a non-linear membrane problem. International Journal of Non-Linear Mechanics, 43(9), 908–914. https://doi.org/10.1016/j.ijnonlinmec.2008.06.007

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