On Nonlinearly Elastic Membranes under Compression  

作　　者：Karim TRABELSI 

机构地区：[1]Centre de Mathématiques Appliquées (CMAP),Ecole Polytechnique,91128 Palaiseau cedex,France

出　　处：《Chinese Annals of Mathematics,Series B》2006年第4期379-392,共14页数学年刊（B辑英文版）

摘　　要：The classical equations of a nonlinearly elastic plane membrane made of Saint Venant-Kirchhoff material have been justified by Fox, Raoult and Simo （1993） and Pantz （2000）. We show that, under compression, the associated minimization problem admits no solution. The proof is based on a result of non-existence of minimizers of non-convex functionals due to Dacorogna and Marcellini （1995）. We generalize the application of their result from Diane elasticity to three-dimensional Diane membranes.

关 键 词：Nonlinear elasticity MINIMIZATION QUASICONVEXITY Quasiconvex envelope Rank- 1-convexity 

分 类 号：O175.2[理学—数学]