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Mathematical Problems in Engineering
Volume 2009, Article ID 132980, 10 pages
Research Article

Dual Boundary Element Method Applied to Antiplane Crack Problems

Department of Mathematics & Computer Science Education, Taipei Municipal University of Education, Taipei 10048, Taiwan

Received 23 February 2009; Revised 7 July 2009; Accepted 3 August 2009

Academic Editor: Angelo Luongo

Copyright © 2009 Wei-Liang Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.