Spatial heterogeneity in 3D-2D dimensional reduction

被引:11
作者
Babadjian, JF [1 ]
Francfort, GA [1 ]
机构
[1] Univ Paris 13, Inst Galilee, LPMTM, F-93430 Villetaneuse, France
来源
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2005年 / 11卷 / 01期
关键词
dimension reduction; Gamma-convergence; equi-integrability; quasiconvexity; relaxation;
D O I
10.1051/cocv:2004031
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitte et al. (2002), the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as a problem of Gamma-convergence of the elastic energy, as the thickness tends to zero.
引用
收藏
页码:139 / 160
页数:22
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