Stress State of Elastic Thick-Walled Ring With Self-Balanced Pressures Distributed on Its Internal and External Borders
For the first time with the help of the theory of analytic functions and Kolosov-Muskhelishvili formulas the problem of the two-dimensional theory of elasticity for a thickwalled ring with the uneven pressures, acting on its borders, was solved. The pressure on the inner and outer boundaries is repr...
| Main Authors: | , |
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| Format: | Article |
| Language: | Russian |
| Published: |
Volgograd State University
2015-10-01
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| Series: | Vestnik Volgogradskogo Gosudarstvennogo Universiteta. Serija 1. Mathematica. Physica |
| Subjects: | |
| Online Access: | http://mp.jvolsu.com/index.php/en/component/attachments/download/461 |
| _version_ | 1828520248775540736 |
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| author | Kravchuk Aleksandr Stepanovich Kravchuk Anzhelika Ivanovna |
| author_facet | Kravchuk Aleksandr Stepanovich Kravchuk Anzhelika Ivanovna |
| author_sort | Kravchuk Aleksandr Stepanovich |
| collection | DOAJ |
| description | For the first time with the help of the theory of analytic functions and Kolosov-Muskhelishvili formulas the problem of the two-dimensional theory of elasticity for a thickwalled ring with the uneven pressures, acting on its borders, was solved. The pressure on the inner and outer boundaries is represented by Fourier series. The authors represent the two complex functions which solve boundary problem in the form of Laurent series. The logarithmic terms in these series are absent because the boundary problem has the self-balancing loads on each boundary of ring. The coefficients in the Laurent series are calculated by the boundary conditions. Firstly, the equations were obtained in the general form. But the hypothesis about even distributions of pressures at borders of ring was used for constructing an example. It leads to the fact that all coefficients of analytic functions represented in Laurent series have to be only real. As a solving example, the representation of pressures in equivalent hypotrochoids was used. The application of the computer algebra system Mathematica greatly simplifies the calculation of the distribution of stresses and displacements in ring. It does not require manual formal separation of real and imaginary parts in terms of Kolosov-Muskhelishvili to display the distribution of the physical parameters. It separates them only for calculated numbers with the help of built-in functions. |
| first_indexed | 2024-12-11T19:26:25Z |
| format | Article |
| id | doaj.art-452e4c22a4a9475ba0d55e824e42d14b |
| institution | Directory Open Access Journal |
| issn | 2222-8896 2409-1782 |
| language | Russian |
| last_indexed | 2024-12-11T19:26:25Z |
| publishDate | 2015-10-01 |
| publisher | Volgograd State University |
| record_format | Article |
| series | Vestnik Volgogradskogo Gosudarstvennogo Universiteta. Serija 1. Mathematica. Physica |
| spelling | doaj.art-452e4c22a4a9475ba0d55e824e42d14b2022-12-22T00:53:23ZrusVolgograd State UniversityVestnik Volgogradskogo Gosudarstvennogo Universiteta. Serija 1. Mathematica. Physica2222-88962409-17822015-10-014455610.15688/jvolsu1.2015.4.5Stress State of Elastic Thick-Walled Ring With Self-Balanced Pressures Distributed on Its Internal and External BordersKravchuk Aleksandr Stepanovich 0Kravchuk Anzhelika Ivanovna 1Belarusian State UniversityBelarusian State UniversityFor the first time with the help of the theory of analytic functions and Kolosov-Muskhelishvili formulas the problem of the two-dimensional theory of elasticity for a thickwalled ring with the uneven pressures, acting on its borders, was solved. The pressure on the inner and outer boundaries is represented by Fourier series. The authors represent the two complex functions which solve boundary problem in the form of Laurent series. The logarithmic terms in these series are absent because the boundary problem has the self-balancing loads on each boundary of ring. The coefficients in the Laurent series are calculated by the boundary conditions. Firstly, the equations were obtained in the general form. But the hypothesis about even distributions of pressures at borders of ring was used for constructing an example. It leads to the fact that all coefficients of analytic functions represented in Laurent series have to be only real. As a solving example, the representation of pressures in equivalent hypotrochoids was used. The application of the computer algebra system Mathematica greatly simplifies the calculation of the distribution of stresses and displacements in ring. It does not require manual formal separation of real and imaginary parts in terms of Kolosov-Muskhelishvili to display the distribution of the physical parameters. It separates them only for calculated numbers with the help of built-in functions.http://mp.jvolsu.com/index.php/en/component/attachments/download/461analytic functionsKolosov-Muskhelishvili formulascomplex numberselastic thick-walled ringuneven pressure |
| spellingShingle | Kravchuk Aleksandr Stepanovich Kravchuk Anzhelika Ivanovna Stress State of Elastic Thick-Walled Ring With Self-Balanced Pressures Distributed on Its Internal and External Borders Vestnik Volgogradskogo Gosudarstvennogo Universiteta. Serija 1. Mathematica. Physica analytic functions Kolosov-Muskhelishvili formulas complex numbers elastic thick-walled ring uneven pressure |
| title | Stress State of Elastic Thick-Walled Ring With Self-Balanced Pressures Distributed on Its Internal and External Borders |
| title_full | Stress State of Elastic Thick-Walled Ring With Self-Balanced Pressures Distributed on Its Internal and External Borders |
| title_fullStr | Stress State of Elastic Thick-Walled Ring With Self-Balanced Pressures Distributed on Its Internal and External Borders |
| title_full_unstemmed | Stress State of Elastic Thick-Walled Ring With Self-Balanced Pressures Distributed on Its Internal and External Borders |
| title_short | Stress State of Elastic Thick-Walled Ring With Self-Balanced Pressures Distributed on Its Internal and External Borders |
| title_sort | stress state of elastic thick walled ring with self balanced pressures distributed on its internal and external borders |
| topic | analytic functions Kolosov-Muskhelishvili formulas complex numbers elastic thick-walled ring uneven pressure |
| url | http://mp.jvolsu.com/index.php/en/component/attachments/download/461 |
| work_keys_str_mv | AT kravchukaleksandrstepanovich stressstateofelasticthickwalledringwithselfbalancedpressuresdistributedonitsinternalandexternalborders AT kravchukanzhelikaivanovna stressstateofelasticthickwalledringwithselfbalancedpressuresdistributedonitsinternalandexternalborders |