Further study of the equivalent theorem of Hellinger-Reissner and Hu-Washizu variational principles

In this paper, it has been pro ved that the well_known Hu_Washizu variational principle is a pseudo_generalized variational principle(pseudo_GVP). The stationary conditions of its functional may satisfy all its field equations and boundary conditions if all the variables in the functional are considered as independent variations, but there might exi st some kinds of constraints. Some new pseudo_GVPs are established to distinguis h them from genuine ones by the so_called inverse Lagrange multiplier method. Th e constrained Hu_Washizu principle, therefore, is proved to be equivalent with t he Hellinger_Reissner principle under the constraints of stress_strain relations .