SEMI-INVERSE METHOD AND GENERALIZED VARIATIONAL PRINCIPLES WITH MULTI-VARIABLES IN ELASTICITY

Semiinverse method, which is an integration and an extension of Hu's tryanderror method, Chien's veighted residual method and Liu's systematic method, is proposed to establish generalized variational principles with multivariables 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 wellknown HellingerReissner variational principle and HuWashizu 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 semiinverse method, the author has also proved that HuWashizu principle is actually a variational principle with only two kinds of independent variables, stressstrain relations are still its constraints.