Quadrilateral element in mixed FEM for analysis of thin shells of revolution
The purpose of study is to develop an algorithm for the analysis of thin shells of revolution based on the hybrid formulation of finite element method in two dimensions using a quadrilateral fragment of the middle surface as a discretization element. Nodal axial forces and moments, as well as compon...
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| Format: | Article |
| Language: | English |
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Peoples’ Friendship University of Russia (RUDN University)
2023-03-01
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| Series: | Structural Mechanics of Engineering Constructions and Buildings |
| Subjects: | |
| Online Access: | https://journals.rudn.ru/structural-mechanics/article/viewFile/34423/22057 |
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| author | Yuriy V. Klochkov Valeria A. Pshenichkina Anatoliy P. Nikolaev Olga V. Vakhnina Mikhail Yu. Klochkov |
| author_facet | Yuriy V. Klochkov Valeria A. Pshenichkina Anatoliy P. Nikolaev Olga V. Vakhnina Mikhail Yu. Klochkov |
| author_sort | Yuriy V. Klochkov |
| collection | DOAJ |
| description | The purpose of study is to develop an algorithm for the analysis of thin shells of revolution based on the hybrid formulation of finite element method in two dimensions using a quadrilateral fragment of the middle surface as a discretization element. Nodal axial forces and moments, as well as components of the nodal displacement vector were selected as unknown variables. The number of unknowns in each node of the four-node discretization element reaches nine: six force variables and three kinematic variables. To obtain the flexibility matrix and the nodal forces vector, a modified Reissner functional was used, in which the total specific work of stresses is represented by the specific work of membrane forces and bending moments of the middle surface on its membrane and bending strains, and the specific additional work is determined by the specific work of membrane forces and bending moments of the middle surface. Bilinear shape functions of local coordinates were used as approximating expressions for both force and displacement unknowns. The dimensions of the flexibility matrix of the four-node discretization element were found to be 36×36. The solution of benchmark problem of analyzing a truncated ellipsoid of revolution loaded with internal pressure showed sufficient accuracy in calculating the strength parameters of the studied shell. |
| first_indexed | 2024-04-09T17:38:57Z |
| format | Article |
| id | doaj.art-df4420db287a4512af654e48cf9b9833 |
| institution | Directory Open Access Journal |
| issn | 1815-5235 2587-8700 |
| language | English |
| last_indexed | 2024-04-09T17:38:57Z |
| publishDate | 2023-03-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | Structural Mechanics of Engineering Constructions and Buildings |
| spelling | doaj.art-df4420db287a4512af654e48cf9b98332023-04-17T09:42:06ZengPeoples’ Friendship University of Russia (RUDN University)Structural Mechanics of Engineering Constructions and Buildings1815-52352587-87002023-03-01191647210.22363/1815-5235-2023-19-1-64-7220975Quadrilateral element in mixed FEM for analysis of thin shells of revolutionYuriy V. Klochkov0https://orcid.org/0000-0002-1027-1811Valeria A. Pshenichkina1https://orcid.org/0000-0001-9148-2815Anatoliy P. Nikolaev2https://orcid.org/0000-0002-7098-5998Olga V. Vakhnina3https://orcid.org/0000-0001-9234-7287Mikhail Yu. Klochkov4https://orcid.org/0000-0001-6751-4629Volgоgrad State Agrarian UniversityVolgograd State Technical UniversityVolgоgrad State Agrarian UniversityVolgоgrad State Agrarian UniversityVolgograd State Technical UniversityThe purpose of study is to develop an algorithm for the analysis of thin shells of revolution based on the hybrid formulation of finite element method in two dimensions using a quadrilateral fragment of the middle surface as a discretization element. Nodal axial forces and moments, as well as components of the nodal displacement vector were selected as unknown variables. The number of unknowns in each node of the four-node discretization element reaches nine: six force variables and three kinematic variables. To obtain the flexibility matrix and the nodal forces vector, a modified Reissner functional was used, in which the total specific work of stresses is represented by the specific work of membrane forces and bending moments of the middle surface on its membrane and bending strains, and the specific additional work is determined by the specific work of membrane forces and bending moments of the middle surface. Bilinear shape functions of local coordinates were used as approximating expressions for both force and displacement unknowns. The dimensions of the flexibility matrix of the four-node discretization element were found to be 36×36. The solution of benchmark problem of analyzing a truncated ellipsoid of revolution loaded with internal pressure showed sufficient accuracy in calculating the strength parameters of the studied shell.https://journals.rudn.ru/structural-mechanics/article/viewFile/34423/22057four-node discretization elementstress-strain stateflexibility matrix |
| spellingShingle | Yuriy V. Klochkov Valeria A. Pshenichkina Anatoliy P. Nikolaev Olga V. Vakhnina Mikhail Yu. Klochkov Quadrilateral element in mixed FEM for analysis of thin shells of revolution Structural Mechanics of Engineering Constructions and Buildings four-node discretization element stress-strain state flexibility matrix |
| title | Quadrilateral element in mixed FEM for analysis of thin shells of revolution |
| title_full | Quadrilateral element in mixed FEM for analysis of thin shells of revolution |
| title_fullStr | Quadrilateral element in mixed FEM for analysis of thin shells of revolution |
| title_full_unstemmed | Quadrilateral element in mixed FEM for analysis of thin shells of revolution |
| title_short | Quadrilateral element in mixed FEM for analysis of thin shells of revolution |
| title_sort | quadrilateral element in mixed fem for analysis of thin shells of revolution |
| topic | four-node discretization element stress-strain state flexibility matrix |
| url | https://journals.rudn.ru/structural-mechanics/article/viewFile/34423/22057 |
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