Integral equations and Gauss-Chebyshev quadrature for planar rectangular cracks

摘要

This paper presents a modified form of the system of integral equations in the theory of planar cracks in space. This system is obtained by using the method of harmonic functions and then transformed to the form in which each integral equation is of similar type for all modes of loading. For a set of rectangular domains this equation is reduced to a special form suitable to use the Gauss-Chebyshev quadrature rule for the discretisation of the double singular integral as the Cartesian product of one-dimensional Gauss-Chebyshev rules. This provides high accuracy in the calculation of the fracture characteristics in planar crack problems. Here we demonstrate the high efficiency of the proposed algorithm by calculating the mode I stress intensity factors along the crack front for the rectangular cracks and the set of three rectangular cracks under different loads.