A simplified model for elastic thin shells

Article type: Research Article

Authors: Blanchard, Dominique^; | Griso, Georges

Affiliations: Université de Rouen, UMR 6085, 76801 Saint Etienne du Rouvray Cedex, France. E-mails: [email protected], [email protected] | Laboratoire J.-L. Lions–CNRS, Boîte courrier 187, Université Pierre et Marie Curie, 4 place Jussieu, 75005 Paris, France. E-mail: [email protected]

Note: [] Corresponding author. E-mail: [email protected].

Abstract: We introduce a simplified model for the minimization of the elastic energy in thin shells. This model is not obtained by an asymptotic analysis. The nonlinear simplified model admits always minimizers by contrast with the original one. We show the relevance of our approach by proving that the rescaled minimum of the simplified model and the rescaled infimum of the full model have the same limit as the thickness tends to 0. The simplified energy can be expressed as a functional acting over fields defined on the mid-surface of the shell and where the thickness remains as a parameter.

Keywords: nonlinear elasticity, shells

DOI: 10.3233/ASY-2011-1057

Journal: Asymptotic Analysis, vol. 76, no. 1, pp. 1-33, 2012