When using boundary element analysis for thin walled structures, to ensure the computational accuracy, special considerations on the singular and nearly singular integrals are indispensible. The real issue about the singular and nearly singular integrals is how to remove the near singularity (for singular and nearly singular integrals) and singularity (for singular integrals only). The near singularity is caused by the location of the singular points or near singular points in the sub-regions which the integrals are performed. The performance of our method is as follows. For the singular integrals, a coordinate transformation at the singular point is employed to remove the singularities, by which the variables are also separated independently. Then, a derived sinh method is developed for removal of the near singularities. For the nearly singular integrals, a coordinate transformation at the nearest point is employed to separate the two variables. For each variable, sinh methods are constructed. Three numerical examples are proposed, considering a cube with coarse mesh, a plane structure and a simplified millstone of a vertical mill. It can be found that the results are in good agreement with the analytical solutions and FEM solutions.

当对薄壁结构使用边界元分析时，为了确保计算精度，对奇异积分和几乎奇异积分的特殊考虑是必不可少的。关于奇异和几乎奇异积分的真正问题是如何消除近奇异性（对于奇异积分和近奇异积分）和奇异性（仅对于奇异积分）。接近奇异点是由执行积分的子区域中奇异点或接近奇异点的位置引起的。我们方法的性能如下。对于奇异积分，采用奇异点处的坐标变换来消除奇异点，通过这些奇异点变量也可以独立分离。然后，开发了一种推导的正弦波方法来去除近奇点。对于接近奇异的积分，采用最近点的坐标转换来分离两个变量。对于每个变量，都构造了sinh方法。提出了三个数值示例，考虑了具有粗网格的立方体，平面结构和立式磨机的简化磨石。可以发现结果与分析解决方案和FEM解决方案非常吻合。