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
bouchitte@univ-tln.fr
Irene Fonseca
Dept. of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
fonseca@andrew.cmu.edu
M. Luísa Mascarenhas
Dep. de Matemática, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal
mascar@fct.unl.pt
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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