In this paper, a composite transformation method is developed to evaluate the singular and nearly singular boundary integrals in the boundary element analysis for multilayer thin structures. The composite transformation method is implemented as follows: Firstly, a sinh transformation method is developed to eliminate the influence of nearly singular integrals in the multilayer thin-structural problem; and then a complex transformation method is improved to deal with the weakly singular integrals. The complex transformation formulations of weakly singular integrals are derived from the composition of the (α, β) coordinate transformation and the sinh transformation in β direction. With this method for weakly singular integrals, the weak singularity in the radial direction and the potentially near singularity in the circumferential direction can be removed. Finally, the proposed transformation formulations of singular and nearly singular integrals are used to analyze multi-domain elasticity problem for multilayer thin structures. The numerical results for several examples are presented to demonstrate the computational accuracy of the proposed method.

在本文中，开发了一种复合变换方法来评估多层薄结构边界元分析中的奇异和近奇异边界积分。复合变换方法实现如下：首先，开发了一种sinh变换方法来消除多层薄结构问题中近奇异积分的影响；然后改进了一种复变换方法来处理弱奇异积分。弱奇异积分的复变换公式是由 ( α, β ) 坐标变换和β 中的 sinh 变换的组合推导出来的方向。使用这种弱奇异积分方法，可以去除径向弱奇异性和圆周方向潜在的近奇异性。最后，提出的奇异和近似奇异积分的变换公式用于分析多层薄结构的多域弹性问题。给出了几个例子的数值结果，以证明所提出方法的计算精度。