Abstract
We establish an existence theorem for the two-dimensional equations of a nonlinearly elastic “flexural” shell, recently justified by V. Lods and B. Miara by the method of formal asymptotic expansions applied to the corresponding three-dimensional equations of nonlinear elasticity. To this end, we show that the associated energy has at least one minimizer over the corresponding set of admissible deformations. The strain energy is a quadratic expression in terms of the “exact” change of curvature tensor, between the deformed and undeformed middle surfaces; the set of admissible deformations is formed by the deformations of the undeformed middle surface that preserve its metric and satisfy boundary conditions of clamping or simple support.
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