The approximate solution of some plane boundary value problems of the moment theory of elasticity
type: Item
instance of: scholarly article
title: The approximate solution of some plane boundary value problems of the moment theory of elasticity
zbMATH Open document ID: 1462.74021
DOI: 10.1155/2016/3845362
author: R. Janjgava
published in: Advances in Mathematical Physics
publication date: 2018-10-17T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 74G70
zbMATH DE Number: 6957372
zbMATH Keywords: harmonic function
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: stress comcentration
zbMATH Keywords: hole
Wikidata QID: Q59122238
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/3845362
OpenAlex ID: W2290572395
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description: scientific article; zbMATH DE number 6957372