Une approche intrinsèque d'un modèle non linéaire de la théorie des coques

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Original languageFrench
Pages (from-to)232-242
Journal / PublicationComptes Rendus Mathematique
Issue number2
Online published18 Jan 2017
Publication statusPublished - Feb 2017


We consider the model of a nonlinearly elastic “shallow” shell proposed by L.H. Donnell, V.Z. Vlasov, K.M. Mushtari & K.Z. Galimov, and W.T. Koiter. We show that the linearized change of curvature and nonlinear strain tensor fields appearing in the energy of this model can be taken as the sole unknowns of the problem, instead of the displacement field as is customary. In order to justify this “intrinsic approach” to this nonlinear model, we identify nonlinear compatibility conditions that these new unknowns must satisfy. These conditions are of Donati type, in the sense that they take the form of integral orthogonality relations against divergence-free tensor fields.