An Axisymmetric Infinite Cylinder with Two Cracks and a Rigid Inclusion


Abstract: This work considers the analysis of a cracked infinite cylinder with a rigid inclusion. The material of the cylinder is assumed to be linearly elastic and isotropic. The ends of the infinite cylinders are subjected to axial tension. Solution of this problem can be obtained by superposition of solutions for an infinite cylinder subjected to uniformly distributed tensile loads at infinity (I), and an infinite cylinder having a penny-shaped rigid inclusion at z = 0 and 2 penny-shaped cracks at z = \pm L (II). General expressions for the perturbation problem (II) are obtained by solving Navier equations using Fourier and Hankel transforms. Formulation of the problem is reduced to a system of 3 singular integral equations. By using the Gauss-Lobatto integration formula, these 3 singular integral equations are converted to a system of linear algebraic equations, which are solved numerically.

Keywords: Axisymmetric, Infinite cylinder, Penny-shaped crack, Rigid inclusion, Stress intensity factor

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