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 systematic 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 identifled 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. CLC numbers: 0176; 0343 Document code: A