A singular element for three-dimensional fracture mechanics analysis

In this article, a singular boundary element for three-dimensional fracture mechanics analysis is presented. It is a nine-node quadratic element with plane geometry. These nodes are located at one quarter of the distance between two opposite sides of the element. Shape functions with a 1/,r singularity at the crack front are used to represent the tractions. The Stress Intensity Factors are computed as system unknowns appearing (except for a constant)as traction nodal values. Special attention is paid to the development of a simple and accurate integration approach for this singular element. The accuracy of the results obtained with the proposed element is demonstrated by solving several crack problems including edge and embedded cracks with different geometries. The element can be easily implemented and incorporated into existing quadratic boundary element codes. In a companion paper the element is formulated and used for fracture mechanics problems in transversely isotropic materials. Extension to other fields for which boundary element formulations exist, is quite simple.