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Journal of Convex Analysis 16 (2009), No. 2, 351--365
Copyright Heldermann Verlag 2009

The Cosserat Vector in Membrane Theory: a Variational Approach

Guy Bouchitté
Dép. de Mathématiques, Université du Sud-Toulon-Var, 83957 La Garde, France

Irene Fonseca
Dept. of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.

M. Luísa Mascarenhas
Dep. de Matemática, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal

In a previous article of the authors [J. Elasticity 73 (2004) 75--99] a model of nonlinear membrane was studied, where the external surface loading induces a density of bending moment. Due to the special form of the applied surface forces, the emerging Cosserat vector, resulting from the 3D-2D dimension reduction, was restricted to a class of two dimensional functions. In this paper the full 3D dependence of the Cosserat vector is analyzed via Γ-convergence techniques.

Keywords: Dimension reduction, Gamma-convergence, relaxation, quasiconvexity, bending effect.

MSC: 35E99, 35M10, 49J45, 74B20, 74K15, 74K20, 74K35

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