加权能量驻值定理及其权函数

本文构造了加权广义势能和加权广义余能等两个泛函,并使它们成为驻值,建立了加权广义势能驻值定理和加权广义余能驻值定理。并发现在第一个定理中,应力边界权函数应等于内部权函数,但位移边界函数独立;在第二个定理中,位移边界权函数应等于内部权函数,但应力边界权函数独立。

THE THEOREM OF STATIONARY VALUE OF WEIGHTED ENERGY AND ITS WEIGHTING FUNCTIONS

This paper presents two energy functionals which are made as stationary values. Thus, the theorem of stationary value of weighted generalized potential energy and the theorem of stationary value of weighted generalized complementary energy are established. In the first theorem, the stress boundary weighting function must be equal to the internal weighting function while the displacement boundary weighting function is independen; and in the (?)econd theorem, the displacement boundary weighting function must be equal to the internal weighting function while the stress boundary weighting function is independent.