Published Paper
Inserted: 18 feb 2009
Journal: JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES.
Volume: 90
Number: 6
Pages: 520-549
Year: 2008
Abstract:
A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.
Keywords: Dimensional Reduction, relaxation, Functions of Bounded Variations, Radon measures