Boundary Element Analysis for Mode III Crack Problems of Thin-Walled Structures from Micro- to Nano-Scales

Abstract

This paper develops a new numerical framework for mode III crack problems of thin-walled structures by integrating multiple advanced techniques in the boundary element literature. The details of special crack-tip elements for displacement and stress are derived. An exponential transformation technique is introduced to accurately calculate the nearly singular integral, which is the key task of the boundary element simulation of thin-walled structures. Three numerical experiments with different types of cracks are provided to verify the performance of the present numerical framework. Numerical results demonstrate that the present scheme is valid for mode III crack problems of thin-walled structures with the thickness-to-length ratio in the microscale, even nanoscale, regime.