BEM analysis of multilayer thin structures using a composite transformation method for boundary integrals

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 (alpha, beta) coordinate transformation and the sinh transformation in beta 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.

Automated summary

A composite transformation method was developed to evaluate singular and nearly singular boundary integrals in boundary element analysis for multilayer thin structures. The method uses sinh transformation to eliminate nearly singular integrals and improves complex transformation to handle weakly singular integrals. By combining (alpha, beta) coordinate transformation and sinh transformation, the method removes weak singularity in the radial direction and potentially near singularity in the circumferential direction. The proposed transformation formulations were used to analyze multi-domain elasticity problems for multilayer thin structures, with numerical results demonstrating computational accuracy.