用变分方法求解大变形对称弹性力学问题

Large Deformation Symmetrical Elasticity Problems Solved by the Variational Method

文中以经典力学的数学理论和陈氏定理为基础,用变分的方法求解大变形对称弹性力学问题,得出了以瞬时位形为基准的位能广义变分原理和余能广义变分原理,以及两个变分原理的等价性;此外,还给出了以瞬时位形为基准的动力学问题的广义变分原理.

In this paper, based on the mathematical theory of classical mechanics and Chen's theorem[1], the variational method[2] is used in the study of large deformation symmetrical elasticity problems. The generalized variational principles of potential energy and complementary energy based on the instantaneous configuration are obtained, and the equivalence between the two principles is proved. Besides, the generalized variational principles of dynamical problems based on the ins an-taneous configuration are also given.