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The membrane shell model in nonlinear elasticity: A variational asymptotic derivation

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Summary

We consider a shell-like three-dimensional nonlinearly hyperelastic body and we let its thickness go to zero. We show, under appropriate hypotheses on the applied loads, that the deformations that minimize the total energy weakly converge in a Sobolev space toward deformations that minimize a nonlinear shell membrane energy. The nonlinear shell membrane energy is obtained by computing the Γ-limit of the sequence of three-dimensional energies.

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Authors and Affiliations

  1. Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, 75252, Paris Cedex 05, France

    H. Le Dret

  2. Laboratoire de Modélisation et Calcul, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    A. Raoult

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  1. H. Le Dret
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Additional information

Communicated by Jerrold Marsden and Stephen Wiggins

This paper is dedicated to the memory of Juan C. Simo

This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan Simo.

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Le Dret, H., Raoult, A. The membrane shell model in nonlinear elasticity: A variational asymptotic derivation. J Nonlinear Sci 6, 59–84 (1996). https://doi.org/10.1007/BF02433810

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  • DOI: https://doi.org/10.1007/BF02433810

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