Boundary stress analysis using a new regularized boundary integral equation for three-dimensional elasticity problems

Abstract

This paper presents new regularized boundary integral equations (BIEs) for elastic displacement gradients in three dimensions and then combines them by the generalized Hooke’s law to calculate the boundary stress. In the new regularized BIEs, two special tangential vectors are designed with the normal vector to construct a transformation system. Based on this system, the displacement gradient in any direction can be transformed into a linear combination of the normal gradient and tangential gradients along the two special vectors. Moreover, a theorem related to some integral properties of the fundamental solution is introduced. Finally, the regularized indirect BIEs are developed by using the above-mentioned technique of linear combination and theorem. The proposed method has some advantages over the direct boundary element method, such as the relaxed continuity requirement of density function, no hypersingular integral, and being available to calculate the displacement gradient in any direction. The numerical implementation of the developed integral equation is provided, and the accuracy and convergence of the approach are also illustrated through four numerical examples.