凑合反推法和弹性理论中的多变量广义变分原理

详细介绍了如何应用凑合反推法(semi-inverse method)构造弹性理论中的两类独立变量的广义变分原理(包括熟知的Hellinger-Reissner变分原理,Hu-Washizu变分原理)及三类独立变量的广义变分原理(钱伟长广义变分原理) 。应用凑合反推法还可以清楚地看出各变量之间的约束关系,从而再一次证明了Hu-Washizu变分原理实际上是两类独立变量的广义变分原理。

Semi-Inverse Method and Generalized Variational Principles With Multi-Variables in Elasticity

Semi-inverse method,which is an integration and an extension of Hu's try-and-error method,Chien's veighted residual method and Liu's systematiic method,is proposed to establish generalized variational principles with multi-variables without any variational crisis phenomenon.The method is to construct an energy trial-functional with an unknown function F,which can be readilyi-dentified by making the trial-functional stationary and using known constraint equations.As a result generalized variational principles with two kinds of independent variables(such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle)and generalized variational principles with three kinds of independent variables(such as Chien's generalized variational principles)in elasticity have been deduced without using Lagrange multiplier method.By semi-inverse method,the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables,stress-strain relations are still its constraints.