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The Axisymmetric Distribution of Stresses in an Infinite Elastic Solid Containing a Flat Annular Crack under Internal Pressure
Author(s) -
Shibuya T.,
Nakahara I.,
Koizumi T.
Publication year - 1975
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19750550707
Subject(s) - stress intensity factor , internal pressure , rotational symmetry , displacement (psychology) , radius , crack tip opening displacement , geometry , mechanics , mathematical analysis , mathematics , fourier series , plane (geometry) , deformation (meteorology) , stress (linguistics) , materials science , physics , fracture mechanics , composite material , psychology , linguistics , philosophy , computer security , computer science , psychotherapist
The authors analyze the axisymmetric distribution of stress in an infinite elastic solid containing a flat annular crack under internal pressure which is one of three‐part mixed boundary value problems. Assuming that the deformation on the crack surface is continuous, we may represent it by Fourier series, and reduce the problem to the solution of an infinite system of algebraic equations. The displacement and stress components obtained are given by series involving infinite integrals. In particular, the integrals on the crack plane are expressed in terms of Gaußian hypergeometric functions. The radial distributions of the displacement and the stress components and the variations of the stress intensity factors at the crack tips with the ratio of the inner to the outer radius of the crack are shown graphically.