Mixed mode BEM analysis of multiple curvilinear cracks in the general anisotropic solids by the crack tip singular element

We consider multiple curvilinear cracks in the two-dimensional general anisotropic solids and establish a computationally effective technique to determine the stress intensity factors accurately. Each curvilinear crack is represented by a collection of straight crack elements and the crack opening displacement (COD) by the continuous distribution of the dislocation dipoles. The crack element located next to the crack tip is called the crack tip singular element (CTSE), where the known √r crack tip opening displacement and the 1/√r stress singularity is mathematically built in the interpolation of the COD using the Chebyshev polynomials. The regular crack elements away from the crack tip use the quadratic polynomial interpolation for the CODs.Simple analytical formulas for the displacement, traction, and the stress intensity factor (SIF) contributions for the CTSE are developed in terms of its own COD coefficients. Since the SIFs are obtained during the main processing no post processing is required; a distinct advantage over the powerful quarter-point element. Numerical results are given for several multiple curvilinear crack problems to demonstrate the accuracy and simplicity of the technique.