Implementation of CPCT based BIEs for 3D elasticity and its application in fracture mechanics

The accurate evaluation of singular boundary integrals is a long-debated issue for the successful implementation of BIEs. In the past decades, various methods have been developed, among which the singularity subtraction technique (SST) has been proved to be a unified method for various orders of singularities. However, the accuracy of original SST is sensitive to element shape due to the near singularity caused by element shape distortion. In this paper, a new conformal polar coordinate transformation (CPCT) for quadrilateral elements is proposed to eliminate the shape effect. Besides, an improved sigmoidal transformation is introduced in the angular direction to assign Gauss points more reasonably. By combination of the two strategies with original SST, a more efficient and robust numerical integration scheme for singular integrals can be obtained. Several numerical examples including crack problems are presented to demonstrate the accuracy and feasibility to coarse meshes for CPCT based BIEs and dual BEM.