胡-鹫变分原理与Hellinger-Reissner变分原理非等价性的证明及其他

PROOF ABOUT NON-EQUIVALENCE OF HU-WASHIZU AND HELLINGER-REISSNER VARIATIONAL PRINCIPLFS AND OTHERS

本文以传统的Lagrange乘子法证明了胡-鹫原理中的泛函具有3类独立变量,胡-鹫原理与Hellinger-Reissner变分原理的关系是包含与被包含关系;本文还从Hellinger-Reissner变分原理出发建立了线弹性力学的又一广义变分原理,说明对于同一物理问题存在着并不唯一的泛函;作者还对如何建立广义变分原理提出建议。

In this paper, it is proved by means of lagrange multiplier method that there are three kinds of functions independent to each ofher in Hu-Washizu variational principle. Hellinger-Rcissner variational principle is inclvdcd in Hu-Washizu variational principle; another generalized variational principle in linear elasticity is found from Hellinger-Reissner variational principle. It is proved that for a given problem of physics, there may be many functionals; the way how to establish generalized variational principles is advanced.