Axisymmetric finite cylinder with rigid ends and a circumferential edge crack

Durucan, Ayşe Ruşen
An axisymmetric finite cylinder with rigid ends and a circumferential edge crack is considered in this study. The finite cylinder is under the action of uniformly distributed loads at two rigid ends. Material of the finite cylinder is assumed to be linearly elastic and isotropic. This finite cylinder problem is solved by considering an infinite cylinder containing an internal ring-shaped crack located at z=0 plane and two penny-shaped rigid inclusions located at z=±L planes. General expressions of the infinite cylinder problem are obtained by solving Navier equations with Fourier and Hankel transforms. This infinite cylinder problem is then converted to the target problem by letting the radius of the rigid inclusions approach the radius of the cylinder and letting the outer edge of the crack approach the surface of the cylinder. Consequently, these rigid inclusions form the rigid ends and internal crack form the circumferential edge crack resulting in the problem of a finite cylinder with rigid ends having an edge crack. The problem is reduced to a set of three singular integral equations. These singular integral equations are converted to a system of linear algebraic equations with the aid of Gauss-Lobatto and Gauss-Jacobi integration formulas and are solved numerically.


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Citation Formats
A. R. Durucan, “Axisymmetric finite cylinder with rigid ends and a circumferential edge crack,” M.S. - Master of Science, Middle East Technical University, 2010.