Varying parameterization of an ellipsoidal thin shell with FEM-based implementation
This article describes an algorithm developed for the finite element analysis of the stressstrain state of a shell that takes the shape of a triaxial ellipsoid with varying parameterization of its mid-surface. A quadrangular fragment of the shell mid-surface with nodal unknowns in the form of displa...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2023-11-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/6 |
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| author | Yu. V. Klochkov A. P. Nikolaev O. V. Vakhnina T. A. Sobolevskaya A. Sh. Dzhabrailov M. Yu. Klochkov |
| author_facet | Yu. V. Klochkov A. P. Nikolaev O. V. Vakhnina T. A. Sobolevskaya A. Sh. Dzhabrailov M. Yu. Klochkov |
| author_sort | Yu. V. Klochkov |
| collection | DOAJ |
| description | This article describes an algorithm developed for the finite element analysis of the stressstrain state of a shell that takes the shape of a triaxial ellipsoid with varying parameterization of its mid-surface. A quadrangular fragment of the shell mid-surface with nodal unknowns in the form of displacements and their first derivatives along the curvilinear coordinates was used as the discretization element.When approximating the displacements through the nodal values, two variants were considered. In the first variant, the known approximating functions were applied to each component of the displacement vector of the internal point of the finite element through the nodal values of the same component. In the second variant, the approximating expressions were used directly for the expression of the displacement vector of the internal point of the finite element through the vector unknowns of the nodal points. After the coordinate transformations, each component of the displacement vector of the internal point of the finite element was expressed through the nodal values of all components of the nodal unknowns. The approximating expressions of the required displacements of the internal point of the finite element also include the parameters of the curvilinear coordinate system used in the calculations.The high efficiency of the developed algorithm was confirmed by the results of the numerical experiments. |
| format | Article |
| id | doaj-art-787aa7501eaf476c9d65d70ee004341d |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-787aa7501eaf476c9d65d70ee004341d2025-02-02T23:06:08ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982023-11-011651496710.26907/2541-7746.2023.1.49-675Varying parameterization of an ellipsoidal thin shell with FEM-based implementationYu. V. Klochkov0A. P. Nikolaev1O. V. Vakhnina2T. A. Sobolevskaya3A. Sh. Dzhabrailov4M. Yu. Klochkov5Volgograd State Agrarian UniversityVolgograd State Agrarian UniversityVolgograd State Agrarian UniversityVolgograd State Agrarian UniversityVolgograd State Agrarian UniversityVolgograd State Technical UniversityThis article describes an algorithm developed for the finite element analysis of the stressstrain state of a shell that takes the shape of a triaxial ellipsoid with varying parameterization of its mid-surface. A quadrangular fragment of the shell mid-surface with nodal unknowns in the form of displacements and their first derivatives along the curvilinear coordinates was used as the discretization element.When approximating the displacements through the nodal values, two variants were considered. In the first variant, the known approximating functions were applied to each component of the displacement vector of the internal point of the finite element through the nodal values of the same component. In the second variant, the approximating expressions were used directly for the expression of the displacement vector of the internal point of the finite element through the vector unknowns of the nodal points. After the coordinate transformations, each component of the displacement vector of the internal point of the finite element was expressed through the nodal values of all components of the nodal unknowns. The approximating expressions of the required displacements of the internal point of the finite element also include the parameters of the curvilinear coordinate system used in the calculations.The high efficiency of the developed algorithm was confirmed by the results of the numerical experiments.https://uzakufismat.elpub.ru/jour/article/view/6shell with ellipsoidal mid-surfacesurface parameterizationfinite element modelinvariant interpolation of required quantities |
| spellingShingle | Yu. V. Klochkov A. P. Nikolaev O. V. Vakhnina T. A. Sobolevskaya A. Sh. Dzhabrailov M. Yu. Klochkov Varying parameterization of an ellipsoidal thin shell with FEM-based implementation Учёные записки Казанского университета: Серия Физико-математические науки shell with ellipsoidal mid-surface surface parameterization finite element model invariant interpolation of required quantities |
| title | Varying parameterization of an ellipsoidal thin shell with FEM-based implementation |
| title_full | Varying parameterization of an ellipsoidal thin shell with FEM-based implementation |
| title_fullStr | Varying parameterization of an ellipsoidal thin shell with FEM-based implementation |
| title_full_unstemmed | Varying parameterization of an ellipsoidal thin shell with FEM-based implementation |
| title_short | Varying parameterization of an ellipsoidal thin shell with FEM-based implementation |
| title_sort | varying parameterization of an ellipsoidal thin shell with fem based implementation |
| topic | shell with ellipsoidal mid-surface surface parameterization finite element model invariant interpolation of required quantities |
| url | https://uzakufismat.elpub.ru/jour/article/view/6 |
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