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Advances in Mathematical Physics
Volume 2016, Article ID 3845362, 12 pages
http://dx.doi.org/10.1155/2016/3845362
Research Article

The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity

Ilia Vekua Institute of Applied Mathematics, Ivane Javakhishvili Tbilisi State University, University Street 2, 0186 Tbilisi, Georgia

Received 14 August 2015; Revised 19 January 2016; Accepted 31 January 2016

Academic Editor: Mikhail Panfilov

Copyright © 2016 Roman Janjgava. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a two-dimensional system of differential equations of the moment theory of elasticity. The general solution of this system is represented by two arbitrary harmonic functions and solution of the Helmholtz equation. Based on the general solution, an algorithm of constructing approximate solutions of boundary value problems is developed. Using the proposed method, the approximate solutions of some problems on stress concentration on the contours of holes are constructed. The values of stress concentration coefficients obtained in the case of moment elasticity and for the classical elastic medium are compared. In the final part of the paper, we construct the approximate solution of a nonlocal problem whose exact solution is already known and compare our approximate solution with the exact one. Supposedly, the proposed method makes it possible to construct approximate solutions of quite a wide class of boundary value problems.