粘性流体动力学有限元变分原理

ON THE VARIATOPNAL PRINCIPLES OF FEM IN THE DYNAMIC ANALYSIS OF VISCOUS FLUIDS

本文把建立有限元变分原理的一种新方法“N>2直接方法”从固体力学推广到流体力学,并用该方法把粘性流体动力学的广义功率消耗原理和广义变分原理发展成为有限元变分原理。还在论证中发现,相邻有限元交界面上的应力协调条件会自然地满足而无需引进任何拉民乘子。本文还建立了混合杂交非协调元的变分原理和广义变分原理,它解除了全部协调性约束条件和其它的边界性约束条件,但是并不增加待定的拉氏乘子,因此使有限元计算得到简化。本文结果可以作为粘性流体动力学有限元计算的基础定理。

In this paper, it presents an investigation that a new method 'N > 2 Direct Method' may be extended its application from the field of solid mechanics to the field of fluid mechanics to establish the variational principles of FEM for the latter. In the derivation, it is found that conditions of compatibility of the stresses on the interfaces of the elements are satisfied naturely and it is not necessary to introduce any Lagrange multiplies. Besides, the author also establish the variational principles of the mixed hybrid incompatible elements and its generalized variational principles. As a result, this formulation may reduce the computational work of the FEM computation greatly.