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 ass...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.展开更多
文摘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.
