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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IssuesArchive of Issues2014-4pp.384-394

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Total articles in the database: 1813
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V.B. Penkov, L.V. Satalkina and A.S. Shulmin, "The use of the method of boundary states to analyse an elastic medium with cavities and inclusions," J. Appl. Math. Mech. 78 (4), 384-394 (2014)
Year 2014 Volume 78 Issue 4 Pages 384-394
Title The use of the method of boundary states to analyse an elastic medium with cavities and inclusions
Author(s) V.B. Penkov (Lipetsk, Russia, vbpenkov@Mail.Ru)
L.V. Satalkina (Lipetsk, Russia,
A.S. Shulmin (Lipetsk, Russia)
Abstract The analytical method of boundary states is developed and theoretically substantiated. A corollary of the Weierstrass theorem is proved according to which a function that is harmonic in a bounded, simply connected domain can be approximated by a series of homogeneous harmonic polynomials. A basis of the space of functions that are harmonic outside any neighbourhood of a point is constructed. An algorithm is developed for filling the basis of the space of the states of a multicavity elastic body. The method is used to solve a series of problems of determining of the stress-strain state of an unbounded elastic medium containing spherical cavities or inclusions with different boundary conditions: the boundary of the cavity is free (the Southwell problem), constrained or under conditions of contact with a rigid core. The effect of the width of the intercavity layer on the stress concentration is analysed in a non-axisymmetric problem with two cavities. The form of the relation between the mean-square discrepancy in the boundary conditions of the solution obtained and the number of elements in the basis is indicative of the numerical convergence of the solution of this problem.
Received 20 August 2012
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