弹性问题边界元法中内点应力的差分解

DIFFERENCE SOLUTION OF INTERNAL POINT STRESSES BY BEM

在弹性问题的边界元法中,内点应力算式较内点位移算式要复杂得多.因此增加了计算的工作量和难度,并且所计算的内点位移和应力数目的增加,还将影响到计算工作的经济性.本文尝试推出一种以边界元结合应变差分的方法,可以将内点应力的计算转化为对该内点及其两个邻点处位移的计算,从而使应力计算过程得以简化.本文还证明,通过适当选取内点及其两个邻点的间距,将使所求得的应力精度不低于由边界元法计算而得到的同一内点处的位移精度.

In the boundary element method ( BEM ) for elasticity, the formula for internal point stresses is much more complex than that for its displacements, thus making internal stresses computation more time-consuming and difficult. Furthermore, it is not economical with the increase of the number of the internal point stresses and displacements to be computed. In this article, a calculus is deduced combining BEM with difference and the computer program for internal point stresses is simplified. The calculus transforms the computation from the internal point stresses into displacements at the same point and other two adjacent points. By suitably selecting the distance between the internal point and its adjacent points, the accuracy of the internal point stresses computed by this calculus is not inferior to that of the displacement computed by BEM.