The whole crack singular element for 2-D boundary element analysis of multiple straight cracks in the general anisotropic solids

Abstract

We develop a singular crack element for the general anisotropic solids in two dimensions for the mixed mode boundary element analysis of multiple straight cracks. Given a normalized crack along an interval (–1, +1) on the X-axis, we represent the crack opening displacement (COD) by the continuous distribution of dislocation dipoles, which is interpolated by the Chebyshev polynomials with the √1 –  X² weight function. The analytical integration of the dislocation dipole distribution leads to a closed form displacement formula for the crack with the √r COD and the 1/√r stress singularity at its tips. In the BE solution, the stress intensity factors are determined, along with the unknown boundary displacements and tractions, without the post-processing. The proposed crack element, called the whole crack singular element (WCSE), drastically simplifies the mixed mode analysis of multiple straight cracks in the general anisotropic solids with no sacrifice of the accuracy.