大变形对称弹性理论的广义变分原理

Generalized Variational Principles of Symmetrical Elasticity Problem of Large Deformation

本文以陈至达提出的变形几何非线性理论￣［１］为基础，应用Ｌａｇｒａｎｇｅ乘子法，对大变形对称弹性力学问题进行了研究，给出了相应的位能广义变分原理、余能广义变分原理，以及动力学问题的广义变分原理；同时，文中还证明了位能广义变分原理和余能广义变分原理的等价性。

This paper is based on the geometrical nonlinear theories of deformation presented by Chen Zhi-da[1],Lagrange's multiplier method is used to study the symmetry elasticty problems of large deformation. The general variational princi- ples of potential energy and complementary energy,and the general variation principle of dynamic problem have been proved.In the meantime it is also proved that the general variation principles of potential energy and complementary en-ergy are equivalent.