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Journal Articles Journal de Mathématiques Pures et Appliquées Year : 2008

Dimensional reduction for energies with linear growth involving the bending moment

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.

Dates and versions

hal-00265696 , version 1 (19-03-2008)

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Jean-François Babadjian, Elvira Zappale, Hamdi Zorgati. Dimensional reduction for energies with linear growth involving the bending moment. Journal de Mathématiques Pures et Appliquées, 2008, 90 (6), pp.520-549. ⟨10.1016/j.matpur.2008.07.003⟩. ⟨hal-00265696⟩
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