Calculus of Variations and Geometric Measure Theory
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J. F. Babadjian - E. Zappale - H. Zorgati

Dimensional reduction for energies with linear growth involving the bending moment.

created by zappale on 18 Feb 2009


Published Paper

Inserted: 18 feb 2009

Volume: 90
Number: 6
Pages: 520-549
Year: 2008


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

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