Dual Boundary Element Method Applied to Antiplane Crack Problems

Abstract

This paper is concerned with an efficient dual boundary element method for 2d crack problems under antiplane shear loading. The dual equations are the displacement and the traction boundary integral equations. When the displacement equation is applied on the outer boundary and the traction equation on one of the crack surfaces, general crack problems with anti-plane shear loading can be solved with a single region formulation. The outer boundary is discretised with continuous quadratic elements; however, only one of the crack surfaces needs to be discretised with discontinuous quadratic elements. Highly accurate results are obtained, when the stress intensity factor is evaluated with the discontinuous quarter point element method. Numerical examples are provided to demonstrate the accuracy and efficiency of the present formulation.

Relative Performance of Three Mesh-Reduction Methods in Predicting Mode III Crack-Tip Singularity

“…As in the preceding reference, no necessity of discretizing traction-free crack surface exists and, upon comparing with FEM and some literature results, efficiency of the approach is established. Analysis of mode III cracks using a dual BEM, consisting of both displacement and traction boundary integral equations, is presented by Wu (2009). The method has an obvious advantage of having to work with a single region formulation, with the displacement equation applied at the outer boundary discretized with continuous quadratic elements while the traction equation is applied to only one of the crack surfaces discretized with discontinuous quadratic elements.…”

Numerical Solution for an Epicycloid Crack

“…Integral transform method to the solution of a Fredholm integral equation of second kind and numerical approach was implemented by Kassir [12,13] in solving the rectangular crack problem, while the classic collocation and Galerkin methods were applied by Ioakimidis [14] for solving the plane crack problem subjected to normal load, whereas a perturbation analysis and the complex potential method [15] were performed by Cotterell and Rice [16] to obtain the stress intensity factors for the curved and kinked crack subject to arbitrary tractions in an explicit and simple form. Recently, Wu [17] proposed the dual boundary element method to solve the antiplane crack problem, whilst Georgiadis and Gourgiotis [18] advocated distributed dislocation technique in solving crack problems within Cosserat elasticity with constrained rotations. Motivated by the work of Lazzarin and Zappalorto [19], Lazzarin et al [20] investigated the stress fields close to a rectangular hole in a plate of finite thickness.…”