The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity
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 so...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/3845362 |
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| author | Roman Janjgava |
| author_facet | Roman Janjgava |
| author_sort | Roman Janjgava |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fe06e5485b4c48c1904ab081800d040a |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-fe06e5485b4c48c1904ab081800d040a2025-02-03T05:47:24ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/38453623845362The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of ElasticityRoman Janjgava0Ilia Vekua Institute of Applied Mathematics, Ivane Javakhishvili Tbilisi State University, University Street 2, 0186 Tbilisi, GeorgiaWe 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.http://dx.doi.org/10.1155/2016/3845362 |
| spellingShingle | Roman Janjgava The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity Advances in Mathematical Physics |
| title | The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity |
| title_full | The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity |
| title_fullStr | The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity |
| title_full_unstemmed | The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity |
| title_short | The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity |
| title_sort | approximate solution of some plane boundary value problems of the moment theory of elasticity |
| url | http://dx.doi.org/10.1155/2016/3845362 |
| work_keys_str_mv | AT romanjanjgava theapproximatesolutionofsomeplaneboundaryvalueproblemsofthemomenttheoryofelasticity AT romanjanjgava approximatesolutionofsomeplaneboundaryvalueproblemsofthemomenttheoryofelasticity |