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arXiv · 0711.0591

Dimensional reduction for energies with linear growth involving the bending moment

Jean-Francois Babadjian·Elvira Zappale·Hamdi Zorgati
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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.

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Jean-Francois Babadjian, Elvira Zappale, Hamdi Zorgati. 2007-11-05. Dimensional reduction for energies with linear growth involving the bending moment. https://arxiv.org/abs/0711.0591

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