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.
Highlights
The problem of a cracked body subjected to an antiplane shear loading had been studied extensively
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
We provide an efficient numerical procedure, based on the dual boundary element method DBEM, for antiplane shear loading problems
Summary
The problem of a cracked body subjected to an antiplane shear loading had been studied extensively. Paulino et al provided numerical solutions for a curved crack subjected to an antiplane shear loading in finite regions by using the boundary integral equation method. Ting et al provided numerical solutions for mode III crack problems by using the boundary element alternating method. Liu and Altiero provided numerical solutions for mode III crack problems using the boundary integral equation with linear approximation on displacements and stresses. The solution of general crack problems cannot be achieved with the direct application of the BEM, because the coincidence of the crack surfaces gives rise to a singular system of algebraic equations To overcome this shortcoming, we provide an efficient numerical procedure, based on the dual boundary element method DBEM , for antiplane shear loading problems. Numerical examples are provided to demonstrate the accuracy and efficiency of the present formulation
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