In the numerical discretization for the models of multilayer thin structures, the elements with narrow strip shape may be appeared. When using the previous methods to integrate these elements, the potentially near singularity will arise in the circumferential direction. In this paper, a weak singularity elimination method for multilayer structures of 3D boundary element method is presented to accurately calculate weakly singular integrals. Its numerical implementation is divided into the following two parts: (1) (α, β) coordinate transformation is applied to deal with the weakly singular integral arising in boundary integral equation and separate out the integral in the circumferential direction (β direction); (2) Based on the integral form of β, a corresponding sinh transformation method is developed to eliminate the near singularity in β direction. Finally, the proposed transformation formulation is extended to multi-domain potential problem and applied to the boundary analysis for multilayer structures. Several numerical examples are given to verify the computational accuracy of the proposed method. And the numerical results are promising and encouraging.

在多层薄结构模型的数值离散化中，可能会出现窄条形单元。当使用以前的方法对这些元素进行积分时，可能会在圆周方向上出现近奇异点。本文提出了一种基于三维边界元法的多层结构弱奇异消除方法，以准确计算弱奇异积分。其数值实现分为以下两部分： (1)( α,β )坐标变换处理边界积分方程中出现的弱奇异积分，分离出圆周方向( β方向)的积分；(2) 基于β的积分形式，开发了相应的sinh变换方法来消除β方向的近奇点。最后，将所提出的变换公式扩展到多域潜在问题，并应用于多层结构的边界分析。给出了几个数值例子来验证所提出方法的计算精度。数值结果是有希望和令人鼓舞的。