Abstract A Γ -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.
Dimensional reduction for energies with linear growth involving the bending moment / Babadjian J., F; Zappale, Elvira; Zorgati, H.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 1776-3371. - 90, n. 6:(2008), pp. 520-549. [doi.org/10.1016/j.matpur.2008.07.003]
Dimensional reduction for energies with linear growth involving the bending moment
ZAPPALE, ELVIRA;
2008
Abstract
Abstract A Γ -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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.