Плоский напружений стан для смуги, що ослаблена тріщиною

Abstract

The plane stress elastic infinite strip problem of a finite longitudinal crack is investigated. The method that can be applied to calculate the stress state and the displacements for an infinite and semi-infinite strip with the longitudinal crack and arbitrary configuration of the boundary conditions is proposed. The main advantage of this method lies in the absence of necessity for use of the apparatus of the matrix differential calculus. Initial problem is reduced to the one-dimensional boundary value problem with the help of the generalized scheme of the integral transform method. By using the inverse integral Fourier transform, the one-dimensional problem is reduced to solving of the system of singular integral equations on a finite interval. The solution of this system was constructed with the help of the method of orthogonal polynomials by means of the second kind Chebyshev polynomials series expansion of the unknown functions. A graph of dependence of the stress intensity factor (SIF) on the geometric parameters of the problem is plotted. It is shown that the SIF for the case of the said strip tends to the SIF for the case of an infinite plane as the width of the strip approaches infinity.