弹性力学的广义变分原理

突破传统的势能密度与余能密度的数学形式,利用拉氏乘子法,建立了三类独立自变函数的广义泛函及其广义变分原理,以及各类新型的二类和一类独立自变函数的泛函及其变分原理。并证明了胡鹫原理,Hellinger-Reissner原理和广义余解原理,实质上都是二类独立自变函数的广义变分原理。

Generalized Variational Principles of Elasticity

We brack through the tradilionat forms of potential energy density and complementary energy density to establish the generalized functionals and the generalized variational principles belonging to three independent argument functions by use of Lagrange multiplier method and we derived new forms of the functionals and new forms of the variational principles belonging to one or two independent argument functions.In the course of the discussion we proved that Hu-Washizu's principle,H'ellinger-Reissner's principle and the generalized principle of Complementary energy2] are the generalized varialional principles belonging to two independent argument functions in essence.