SINGULAR p-VERSION FINITE ELEMENTS FOR STRESS INTENSITY FACTOR COMPUTATIONS

The Þnite element analysis of linear elastic fracture mechanics problems is complicated by the presence of the singular and Þnite non-singular stress distributions in the crack tip region. The availability of a constant stress term in addition to the singular term in the standard h-version singular Þnite elements is insu¦cient to model the Þnite nonsingular stress zone. A p-version singular Þnite element capable of modelling the higher-order non-singular stress terms in addition to the singular term and the constant term is presented. The formulation for the displacement substitution technique for computing the stress intensity factors using singular p-version triangular Þnite elements is developed. Unlike the standard h-version formulation, the stress intensity factors computed using the p-version displacement substitution technique do not depend on the speciÞc arrangement and length of the quarter point elements, and require simple mesh designs as well as fewer number of degrees of freedom. Numerical studies comparing the convergence of the stress intensity factors computed by the p-version method against other available alternatives such as the h-version method and the contour integral method are presented to demonstrate the e¤ectiveness of the present developments