On Variational Dimension Reduction in Structure Mechanics
On Variational Dimension Reduction in Structure Mechanics
复制标题
结构力学中的变分降维
DOI：
10.1007/s10659-014-9473-6
复制
发表时间：
2013
影响因子：
2
通讯作者：
P. Podio
中科院分区：
文献类型：
--
作者：
R. Paroni;P. Podio
薄结构的经典低维模型是基于对三维变形和/或应力场的某些先验假设，其性质不同，但都是由某些尺寸相对于其他尺寸的微小性引起的。近年来，为了严格证明这些先验假设，已经做了大量的工作，特别是，已经引入了几种技术，使降维严格。我们在这里回顾，并在一定程度上重新制定，这些技术共同的主要思想，使用一些显式的降维问题来解释我们想要做的点。
The classical low-dimensional models of thin structures are based on certain a priori assumptions on the three-dimensional deformation and/or stress fields, diverse in nature but all motivated by the smallness of certain dimensions with respect to others. In recent years, a considerable amount of work has been done in order to rigorously justify these a priori assumptions; in particular, several techniques have been introduced to make dimension reduction rigorous. We here review, and to some extent reformulate, the main ideas common to these techniques, using some explicit dimension-reduction problems to exemplify the points we want to make.