Generalized Kelvin solution based boundary element method for crack problems in multilayered solids

Abstract

This paper presents a new boundary element method (BEM) for linear elastic fracture mechanics in three-dimensional multilayered solids. The BEM is based on a generalized Kelvin solution. The generalized Kelvin solution is the fundamental singular solution for a multilayered elastic solid subject to point concentrated body-forces. For solving three-dimensional elastic crack problems in a finite region, a multi-region method is also employed in the present BEM. For crack problems in an infinite space, a large finite body is used to approximate the infinite body. In addition, eight-node traction-singular boundary elements are used in representing the displacements and tractions in the vicinity of a crack front. The incorporation of the generalized Kelvin solution into the boundary integral formulation has the advantages in elimination of the element discretization at the interfaces of different elastic layers. Three numerical examples are presented to illustrate the proposed method for the calculation of stress intensity factors for cracks in layered solids. The results obtained using the proposed method are well compared with the existing results available in the relevant literature. © 2002 Elsevier Science Ltd. All rights reserved.