低阶奇异性边界单元法

A BOUNDARY ELEMENT METHOD WITH LOWER-ORDER SINGULARITY

本文所提出的低阶奇异性边界单元法,是以传统的边界单元法为基础,通过引入一个新的角变量,致使力的核函数由原来l/r的阶奇异性,降低为与位移核函数一样,仅具有Inr阶奇异性(r是场点与源点之间的距离)。从而推出新的边界积分方程,该方程具有较低奇异性,特别是在应力计算时,基本消除了原边界单元法的“边界层效应”——即原边界单元法在边界层附近的应力不能计算的现象。在本文中,还将对该新方法所编制的程序用于工程构件——300T压花机肘杆的强度分析,其结果与原边界单元法及光弹性实验结果有较好的一致性。

In this paper, a lower-order singular BEM based on original BEM is presented by introduccing a new variable of angle. In the new method, kernel of force is the same as kernel of displacement which is only singularity of InR ( R is the distance between a source and a field point ) . Hence, it results in a new BEM formulation, whose singularity is lower than that of the original BEM formulation. What's more, in calculating stress, it eliminates the boundary-layer effect in the main. A software which is based on lower-order singular formulation is used to analysis the bar of 300T coiningmachine, its result is coincident with that obtained by the original BEM and photo-elastic experiment.