Analysis of two-dimensional mixed-mode crack problems by finite element alternating method

A finite element alternating method is presented and applied to analyze two-dimensional linear elastic mixed-mode fracture problems with single or multiple cracks. The method involves the iterative superposition of the finite element solution of a bounded uncracked plate and the analytical solution of an infinite two-dimensional plate with a crack subjected to arbitrary normal and shear loadings. The normal and shear residual stresses evaluated at the location of fictitious cracks are fitted by appropriate polynomials through the least-squares method. Based on those coefficients of the determined polynomials, the mixed-mode stress intensity factors can be calculated accurately. The interaction effects among cracks are also considered. This method provides a highly efficient way to deal with two-dimensional fracture problems.