Penny-shaped crack simulation with a single high order smooth boundary element

Abstract

Based on Lagrange interpolation polynomials, the penny-shaped cracks placed on but not limited to flat surface are simulated with a single high order smooth boundary element in the present work. By taking advantage of geometrical features of circular shape such as the symmetry and periodicity, the smoothness within the element is realized by repeated use of real nodes for interpolation in both the radial and circumferential directions of the element using high order shape functions, so that the end node/line effects existing in conventional low order elements have been removed. In the application of the boundary element method (BEM) for crack problems, the hyper-singular integrals are treated with the aid of the technique of shape function manipulations. The near hyper-singular integrals are treated with the tangential distance transformations together with the subdivision techniques. The crack-related parameters including the crack opening displacements (COD), the stresses ahead of crack tip, the stress intensity factors (SIF) and the T-stresses are computed under various loads and compared with the analytical solutions in the numerical examples, showing the accuracy, efficiency and effectiveness of the proposed high order smooth crack element.