带裂纹薄板弯曲问题的边界元法分析

Boundary Element Analysis for Cracked Plate Bending Problem

本文得到了薄板弯曲问题的边界积分方程以及与之等价的泛函极值问题,讨论了裂纹薄板的奇异性,得到了裂纹薄板在奇异点附近的奇异主项,提出了一种用奇异主项作为插值基函数的奇异边界元法来计算裂纹薄板的弯曲问题,并给出了初步的误差分析。

In this paper, We discuss singularity of cracked plate, obtain the boundary integral equations of plate and singular main terms of cracked plate. A new method which uses singular main terms as interpolation functions is presented. The numerical results show that the new method is valid for cracked plate bending problem, and error estimation is also discused.