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

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2012-3pp.324-329

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A.N. Zlatin, "Exact solutions of the mixed axisymmetric problem of the torsion of an elastic space containing a spherical crack," J. Appl. Math. Mech. 76 (3), 324-329 (2012)
Year 2012 Volume 76 Issue 3 Pages 324-329
Title Exact solutions of the mixed axisymmetric problem of the torsion of an elastic space containing a spherical crack
Author(s) A.N. Zlatin (St Petersburg, Russia, anzlat@yandex.ru)
Abstract The problem of the torsion of an elastic space, weakened by a spherical crack, is reduced to a system of paired summation equations in first-order associated Legendre functions. It is assumed that the load, applied to the crack surface, can also be represented in the form of a series in associated Legendre functions. Using special differential operators, this system is reduced to permitting an exact elementary solution of a system of equations in Legendre polynomials. Two examples are given. The solution is compared with a known result in the literature. The problem of the effect of curvature of the surface on the stress intensity factor is investigated.
Received 10 May 2011
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