Torsion problem: stress statement and solution by the boundary element method
The formulation of the problem of torsion regarding stresses and its solution by the boundary elements method are described. The main advantage of the problem formulation in stresses is direct determination of stresses in the cross-section, unlike the classical formulation, when the result of the ap...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Peoples’ Friendship University of Russia (RUDN University)
2023-11-01
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| Series: | Structural Mechanics of Engineering Constructions and Buildings |
| Subjects: | |
| Online Access: | https://journals.rudn.ru/structural-mechanics/article/viewFile/36834/22787 |
| _version_ | 1797450794385014784 |
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| author | Vladimir V. Lalin Daniil A. Semenov |
| author_facet | Vladimir V. Lalin Daniil A. Semenov |
| author_sort | Vladimir V. Lalin |
| collection | DOAJ |
| description | The formulation of the problem of torsion regarding stresses and its solution by the boundary elements method are described. The main advantage of the problem formulation in stresses is direct determination of stresses in the cross-section, unlike the classical formulation, when the result of the approximate solution is the Prandtl stress function values, and the determination of stresses is brought down to numerical differentiation. The boundary integral equation of the second kind is obtained to formulate the problem with respect to stresses. The procedure for solving the problem by the boundary elements method is described, the system of solving equations is compiled. Solutions of test problems on torsion of rods with rectangular and channel cross-sections are presented. Comparison of the calculation results with known analytical solutions illustrates the reliability and permissible engineering accuracy of the obtained solutions. |
| first_indexed | 2024-03-09T14:45:43Z |
| format | Article |
| id | doaj.art-b7ab0632409e44e393ea1b7e26feb9df |
| institution | Directory Open Access Journal |
| issn | 1815-5235 2587-8700 |
| language | English |
| last_indexed | 2024-03-09T14:45:43Z |
| publishDate | 2023-11-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | Structural Mechanics of Engineering Constructions and Buildings |
| spelling | doaj.art-b7ab0632409e44e393ea1b7e26feb9df2023-11-27T08:50:12ZengPeoples’ Friendship University of Russia (RUDN University)Structural Mechanics of Engineering Constructions and Buildings1815-52352587-87002023-11-0119433934810.22363/1815-5235-2023-19-4-339-34820998Torsion problem: stress statement and solution by the boundary element methodVladimir V. Lalin0https://orcid.org/0000-0003-3850-424XDaniil A. Semenov1https://orcid.org/0000-0002-9144-1412Peter the Great St. Petersburg Polytechnic UniversityPeter the Great St. Petersburg Polytechnic UniversityThe formulation of the problem of torsion regarding stresses and its solution by the boundary elements method are described. The main advantage of the problem formulation in stresses is direct determination of stresses in the cross-section, unlike the classical formulation, when the result of the approximate solution is the Prandtl stress function values, and the determination of stresses is brought down to numerical differentiation. The boundary integral equation of the second kind is obtained to formulate the problem with respect to stresses. The procedure for solving the problem by the boundary elements method is described, the system of solving equations is compiled. Solutions of test problems on torsion of rods with rectangular and channel cross-sections are presented. Comparison of the calculation results with known analytical solutions illustrates the reliability and permissible engineering accuracy of the obtained solutions.https://journals.rudn.ru/structural-mechanics/article/viewFile/36834/22787elastic rod torsionpoisson’s equationintegral representation of stressesboundary integral equationintegral equation of the second kind |
| spellingShingle | Vladimir V. Lalin Daniil A. Semenov Torsion problem: stress statement and solution by the boundary element method Structural Mechanics of Engineering Constructions and Buildings elastic rod torsion poisson’s equation integral representation of stresses boundary integral equation integral equation of the second kind |
| title | Torsion problem: stress statement and solution by the boundary element method |
| title_full | Torsion problem: stress statement and solution by the boundary element method |
| title_fullStr | Torsion problem: stress statement and solution by the boundary element method |
| title_full_unstemmed | Torsion problem: stress statement and solution by the boundary element method |
| title_short | Torsion problem: stress statement and solution by the boundary element method |
| title_sort | torsion problem stress statement and solution by the boundary element method |
| topic | elastic rod torsion poisson’s equation integral representation of stresses boundary integral equation integral equation of the second kind |
| url | https://journals.rudn.ru/structural-mechanics/article/viewFile/36834/22787 |
| work_keys_str_mv | AT vladimirvlalin torsionproblemstressstatementandsolutionbytheboundaryelementmethod AT daniilasemenov torsionproblemstressstatementandsolutionbytheboundaryelementmethod |