修正的变分原理与杂交边界元列式

MODIFIED VARIATIONAL PRINCIPLES AND HYBRID BOUNDERY ELEMENT FORMULATION IN ELASTOSTATICS

文章针对弹性静力学提出了几种修正的变分原理。与经典的变分原理不同的是,在修正的变分原理中,边界位移与边界面力和区域变量一起取作为独立的变量。修正的变分原理是建立杂交边界元公式的理论基础。利用文中提出的修正变分原理,建立了两种新型的杂交边界元列式。杂交边界元公式均具有对称的系数矩阵和易于与有限元耦合的特征。

In this paper several kinds of modified variational principles in elastostaties have been presented. The modified variational principles,in which boundary displacements and boundary tractions together with domain variables are taken as independent quantities with respect to variation,are different from the conventional variational principles.They are very usefel in formulating numerical models of elastostatics,espectially in formulating hybrid boundary element formulation.Using the modified variational principles presented,two types of new hybrid bound- ary element formulations have been presented,which give a symmetric matrix and are easily combined with finite element methods.