摘要
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。
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.
出处
《应用数学和力学》
CSCD
北大核心
1999年第5期515-524,共10页
Applied Mathematics and Mechanics
关键词
弹性力学
变分原理
H-R原理
H-W原理
等价性
variational principles in elasticity
Hellinger_Reissner principle
Hu_Washizu principle
the semi_inverse method, trial_functional