凑合反推法和弹性理论中的多变量广义变分原理

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

详细介绍了如何应用凑合反推法 (semi_inversemethod)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, 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 readily identified 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.