Dimensional reduction for energies with linear growth involving the bending moment

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

2007-11-05

arxiv.org/abs/0711.0591v2

Mathematics

Analysis of PDEs

26 pages

Scientific paper

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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