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The membrane shell model in nonlinear elasticity: A variational asymptotic derivation. (English) Zbl 0844.73045

Summary: fe 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 \(\Gamma\)-limit of the sequence of three-dimensional energies.

MSC:

74K15 Membranes
74B20 Nonlinear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
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