A boundary weak singularity elimination method for multilayer structures

Abstract 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.