非线性弹性理论余能原理的注记

A NOTE ON THE COMPLEMENTARY ENERGY PRINCIPLE IN NONLINEAR ELASTICITY

指出非线性弹性理论中余能原理泛函中的位移场可由变分约束方程，即平衡方程和力的边界条件解出为Ｋｉｒｃｈｈｏｆ第二应力张量的函数．仅以应力张量为独立变分量的纯粹的余能原理是存在的．通过一般一维问题及三维情形简例。

It is shown that the displacement vector in the functional of complementary energy principle for nonlinear elasticity can be represented by the second Kirchhoff stress tensor through solving the constraint equations of the functional: the equation of equilibrium and the surface traction condition.There exists a pure complementary energy principle with only one argument,the stress tensor.A generalized one dimensional problem and a simple example for three dimensional case are given to demonstrate the analysis.