Bending of a circular disk: from cylinder to ultrathin membrane
The article discusses methods of mathematical modeling of the stress-strain state of a circular disc at various ratios of its thickness to radius, ranging from 1 to 10−3. For sufficiently thick plates, the solution of three-dimensional linear elasticity theory is used, for plates of medium thickness...
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| Format: | Article |
| Language: | English |
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Samara National Research University
2023-12-01
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| Series: | Вестник Самарского университета: Естественнонаучная серия |
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| Online Access: | https://journals.ssau.ru/est/article/viewFile/27148/10345 |
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| author | Sergey A. Lychev Alexander V. Digilov Nikita A. Pivovaroff |
| author_facet | Sergey A. Lychev Alexander V. Digilov Nikita A. Pivovaroff |
| author_sort | Sergey A. Lychev |
| collection | DOAJ |
| description | The article discusses methods of mathematical modeling of the stress-strain state of a circular disc at various ratios of its thickness to radius, ranging from 1 to 10−3. For sufficiently thick plates, the solution of three-dimensional linear elasticity theory is used, for plates of medium thickness — the solution of linear bending equations within the Kirchhoff – Love hypotheses and nonlinear equations of Foppl – von Karman, and for ultrathin plates — the nonlinear equations of Adkins – Rivlin – Green. A comparative analysis of the solutions has been conducted, and ranges of relative thickness have been identified in which the considered solutions adequately describe the deformation process. This result enables the selection of a method for mathematical modeling of the stress-strain state of circular plates used in microelectromechanical systems that is most suitable for their relative size. |
| format | Article |
| id | doaj-art-224b081d71f945388dfc4e76554dafa1 |
| institution | OA Journals |
| issn | 2541-7525 2712-8954 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Вестник Самарского университета: Естественнонаучная серия |
| spelling | doaj-art-224b081d71f945388dfc4e76554dafa12025-08-20T02:26:00ZengSamara National Research UniversityВестник Самарского университета: Естественнонаучная серия2541-75252712-89542023-12-012947710510.18287/2541-7525-2023-29-4-77-1058792Bending of a circular disk: from cylinder to ultrathin membraneSergey A. Lychev0https://orcid.org/0000-0001-7590-1389Alexander V. Digilov1https://orcid.org/0000-0001-6892-7740Nikita A. Pivovaroff2https://orcid.org/0009-0005-7149-4102Ishlinsky Institute for Problems in Mechanics RASIshlinsky Institute for Problems in Mechanics RASIshlinsky Institute for Problems in Mechanics RASThe article discusses methods of mathematical modeling of the stress-strain state of a circular disc at various ratios of its thickness to radius, ranging from 1 to 10−3. For sufficiently thick plates, the solution of three-dimensional linear elasticity theory is used, for plates of medium thickness — the solution of linear bending equations within the Kirchhoff – Love hypotheses and nonlinear equations of Foppl – von Karman, and for ultrathin plates — the nonlinear equations of Adkins – Rivlin – Green. A comparative analysis of the solutions has been conducted, and ranges of relative thickness have been identified in which the considered solutions adequately describe the deformation process. This result enables the selection of a method for mathematical modeling of the stress-strain state of circular plates used in microelectromechanical systems that is most suitable for their relative size.https://journals.ssau.ru/est/article/viewFile/27148/10345circular discshort cylinderthick platethin plateultrathin membraneclosed-form solutionfoppl – von karman equationsnonlinear membrane model |
| spellingShingle | Sergey A. Lychev Alexander V. Digilov Nikita A. Pivovaroff Bending of a circular disk: from cylinder to ultrathin membrane Вестник Самарского университета: Естественнонаучная серия circular disc short cylinder thick plate thin plate ultrathin membrane closed-form solution foppl – von karman equations nonlinear membrane model |
| title | Bending of a circular disk: from cylinder to ultrathin membrane |
| title_full | Bending of a circular disk: from cylinder to ultrathin membrane |
| title_fullStr | Bending of a circular disk: from cylinder to ultrathin membrane |
| title_full_unstemmed | Bending of a circular disk: from cylinder to ultrathin membrane |
| title_short | Bending of a circular disk: from cylinder to ultrathin membrane |
| title_sort | bending of a circular disk from cylinder to ultrathin membrane |
| topic | circular disc short cylinder thick plate thin plate ultrathin membrane closed-form solution foppl – von karman equations nonlinear membrane model |
| url | https://journals.ssau.ru/est/article/viewFile/27148/10345 |
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