论文标题
周期性均质化的应力公式和二元性方法
Stress formulation and duality approach in periodic homogenization
论文作者
论文摘要
本文介绍了所谓的“细胞问题”的几种不同公式，该制度是在均质理论中产生的部分微分方程的系统，但要遵守周期性边界条件。在主要未知的是位移，应力或菌株以及几种不同的配方作为最小化问题的情况下，介绍了细胞问题的变分制剂。还提出了两个双重配方，一个配方在压力压力上，另一个在应变应力中。相应的Lagrangians可以基于交替方向用于数值优化算法。
This paper describes several different formulations of the so-called "cellular problem" which is a system of partial differential equations arising in the theory of homogenization, subject to periodicity boundary conditions. Variational formulations of the cellular problem are presented where the main unknown is the displacement, the stress or the strain, as well as several different formulations as minimization problems. Two dual formulations are also presented, one in displacement-stress and another one in strain-stress. The corresponding Lagrangians may be used in numerical optimization algorithms based on alternated directions.
