Dimensional reduction for energies with linear growth involving the bending moment

Jean-François Babadjian (1) , Elvira Zappale (2) , Hamdi Zorgati (3)

1 EDP - Equations aux Dérivées Partielles
2 Università degli Studi di Salermo
3 Département de mathématiques [Tunis]

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.

Mots clés: Dimension reduction; Γ-convergence; Functions of bounded variation; Tangent measures

Domaines: Equations aux dérivées partielles [math.AP]

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⟩