再论Hellinger-Reissner原理与Hu-Washizu原理之等价性

阐述了Hu-Washizu变分原理实际上是一个赝广义变分原理,即虽然其驻值条件满足所有的场方程及边界条件,但它存在某种约束.为了清楚说明问题,本文构造一些新的赝广义变分原理,用逆拉氏乘子法可以清楚地看出其约束关系,并进一步证明了Hu-Washizu变分原理和Helinger-Reisner变分原理之等价定理.

Further Study of the Equivalent Theorem of Hellinger-Reissner and Hu-Washizu Variational Principles

In this paper,it is proved that the well_known Hu_Washizu variational principle is a pseudo_generalized variational principle(pseudo_GVP),which is a functional whose stationary conditions would satisfy all its field equations and boundary conditions if all the variables in the functional were considered as independent variations, but in fact there might exist some kinds of constraints. Some new pseudo_GVPs are established to distinguish them from genuine ones by the so_called inverse Lagrange multiplier method. The constrained Hu_Washizu principle, therefore, is proved to be equivalent with the Hellinger_Reissner principle under the same constraints of stress_strain relations.