Half‐Plane Crack Under Normal Load: Complete Solution
Publication: Journal of Engineering Mechanics
Volume 119, Issue 11
Abstract
A half‐plane flat crack in a transversely isotropic elastic space subjected to arbitrary normal load is considered. An exact closed‐form solution is obtained in terms of elementary functions to the complete field of stresses and displacements in the whole space due to a point force loading. Both transversely isotropic and purely isotropic cases are considered. The solution is based on the results previously reported by the first writer. The transversely isotropic solution does not seem to have been reported in the literature. The isotropic case was considered by Ufliand who used the integral transform approach. A comparison with his results shows exact correspondence. Explicit formulas are also given for the stress intensity factor, as well as for the stresses and displacements in the plane of the crack.
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References
1.
Elliott, H. A. (1948). “Three‐dimensional stress distribution in hexagonal aeolotropic crystals.” Proc. Cambridge Philisophical Society, Cambridge, England, 44, 522–533.
2.
Fabrikant, V. I. (1989). Applications of potential theory in mechanics. Selection of new results. Kluwer Academic, Boston, Mass.
3.
Kit, G. S., and Khai, M. V. (1989). The potential method in three‐dimensional problems of the thermoelasticity of bodies with cracks. Naukova Dumka, Kiev, Ukraine (in Russian).
4.
Ufliand, I. S. (1967). Integral transforms in the theory of elasticity. 2nd Ed., Nauka, Leningrad, Russia (in Russian).
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Copyright © 1993 American Society of Civil Engineers.
History
Received: Aug 10, 1992
Published online: Nov 1, 1993
Published in print: Nov 1993
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