The membrane shell model in nonlinear elasticity: A variational asymptotic derivation
نویسندگان
چکیده
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. 1 Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France 2 Laboratoire de Modélisation et Calcul, Université Joseph Fourier, BP 53, 38041 Grenoble Cedex 9, France The membrane shell model in nonlinear elasticity 1
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