The Membrane Shell Model in Nonlinear Elasticity: A Variational Asymptotic Derivation

  • H. Le Dret
  • A. Raoult
Conference paper

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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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • H. Le Dret
    • 1
  • A. Raoult
    • 2
  1. 1.Laboratoire d’Analyse NumériqueUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.Laboratoire de Modélisation et CalculUniversité Joseph FourierGrenoble Cedex 9France

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