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 Issues2008-6pp.724-737

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Total articles in the database: 10482
In Russian (ΟΜΜ): 9683
In English (J. Appl. Math. Mech.): 799

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L.M. Zubov and A.V. Stolpovskii, "A theory of dislocations and disclinations in elastic plates," J. Appl. Math. Mech. 72 (6), 724-737 (2008)
Year 2008 Volume 72 Issue 6 Pages 724-737
Title A theory of dislocations and disclinations in elastic plates
Author(s) L.M. Zubov (Rostov-on-Don, Russia, zubovl@yandex.ru)
A.V. Stolpovskii (Rostov-on-Don, Russia)
Abstract The problem of the stress state of a thin elastic plate, containing dislocations and disclinations, is considered using Kirchhoff's theory. The problem of the equilibrium of a multiply connected plate with Volterra dislocations with specified characteristics is formulated. The problem of the flexure of an annular slab resulting from a screw dislocation and a twisting disclination is solved. The solutions of problems of concentrated (isolated) dislocations and disclinations in an unbounded plate as well as the dipoles of dislocations and disinclinations are found. It is shown that a screw dislocation in a thin plate is equivalent to the superposition of two orthogonal dipoles of torsional disclinations. By taking the limit from a discrete set of defects to their continuous distribution, a theory of thin plates with distributed dislocations and disclinations is constructed. Solutions of problems of the flexure of circular and elliptic plates with continuously distributed disclinations are obtained. An analogy is established between the problem of the flexure of a plate with defects and the plane problem of the theory of elasticity with mass forces, and also between a plane problem with dislocations and disclinations and the problem of the flexure of a plate with specified distributed loads
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