Solution of a crack problem for an elastic strip by singular integral equations

In this study, Mode I crack problems for elastic strips weakened by latitudinal cracks are considered. Problems are reduced to a Cauchy type singular integral equation and the system of singular integral equations by using the basic equations of the elasticity theory and Fourier transform of Airy function. A quadratic approach is applied to a strip problem including N-cracks and the solution of the problem is reduced to solution of a system of linear algebraic equations. Normalized stress intensity factors at the edges of the crack along its propagation are calculated for the cases of N=1, N=2 ve N=3 under three different loading. To verify the validity of the results, the case of N=1 is approached by the Iterative method and Gauss Chebyshev formulas; and also N=2 is approached by Iterative method and Series method. It is aimed to analyze the crack interaction and the influence of relative thickness of strip and the effect of the mechanical orthotropic properties on the stress intensity factors. Keywords: Crack Problems, Gauss Quadrature Formulas, Iterative Method, Orthotropic Material, Series Method, Singular Integral Equations, Stress Intensity Factor.