Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
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ISSN 0021-8928
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IssuesArchive of Issues2017-3pp.236-247

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E.V. Rashidova and B.V. Sobol, "An equilibrium internal transverse crack in a composite elastic half-plane," J. Appl. Math. Mech. 81 (3), 236-247 (2017)
Year 2017 Volume 81 Issue 3 Pages 236-247
DOI 10.1016/j.jappmathmech.2017.08.016
Title An equilibrium internal transverse crack in a composite elastic half-plane
Author(s) E.V. Rashidova (Don State Technical University, Rostov-on-Don, Russia,
B.V. Sobol (Don State Technical University, Rostov-on-Don, Russia)
Abstract The problem of the stress concentration in the vicinity of the crack tips for a crack of finite length located perpendicular to the interface of two elastic bodies - a half-plane and a strip - is considered. Using the method of generalized integral transforms, the problem reduces to solution of a singular integral equation with a Cauchy kernel. Limit cases of the problem are considered when the thickness of the strip is relatively small, equal to zero (free boundary of the half-plane), or indefinitely large (a composite plane). The solution of the integral equation is constructed by the collocation method and the small parameter method. With the aim of increasing the efficiency of the numerical method, an approximation of the regular part of the kernel in a special form is used. Values of the stress intensity factors of the normal stresses in the vicinity of crack tips are obtained for different combinations of the geometrical and physical parameters of the problem.
Received 04 March 2016
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