Abstract
AbstractIn this study, a problem of a ring‐shaped crack contained in an infinitely long thick‐walled cylinder is considered. The problem is formulated for a transtropic (transversely isotropic) material by using integral transform technique under uniform load. The governing elasticity equation for the transtropic axisymmetric problem in cylindrical co‐ordinates was obtained in terms of a Love type stress function. Hankel and Fourier transforms were applied on the stress function because of the geometry of the configuration and boundary conditions. The stress function was expressed in terms of the governing equation. Using the boundary conditions, the problem reduced to a singular integral equation. This singular integral equation is solved by using the Gaussian Quadrature. Then the stress intensity factor at the crack tip was determined. The plastic zone widths are obtained by using the Dugdale model. The plastic zone widths are plotted for various ring‐shaped crack sizes and transtropic materials.
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Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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