Surface parameterization complex geometry
Among thin-walled structures, including building structures and constructions, shells of complex geometry are effective in their rigidity and strength characteristics, which are also distinguished by architectural harmony. For a wider application of shells of complex geometry, it is necessary to rel...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Peoples’ Friendship University of Russia (RUDN University)
2022-12-01
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| Series: | Structural Mechanics of Engineering Constructions and Buildings |
| Subjects: | |
| Online Access: | https://journals.rudn.ru/structural-mechanics/article/viewFile/33413/21662 |
| _version_ | 1811175275129470976 |
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| author | Samat N. Yakupov Guzial Kh. Nizamova |
| author_facet | Samat N. Yakupov Guzial Kh. Nizamova |
| author_sort | Samat N. Yakupov |
| collection | DOAJ |
| description | Among thin-walled structures, including building structures and constructions, shells of complex geometry are effective in their rigidity and strength characteristics, which are also distinguished by architectural harmony. For a wider application of shells of complex geometry, it is necessary to reliably assess their stress-strain state. In this case, an integral part of the calculation is the parametrization stage of the median surface of shells of complex geometry. There are shells of complex geometry of canonical and non-canonical forms. For shells of non-canonical shape, the median surface cannot be defined by analytical formulas. At the same time, difficulties arise at the stage of specifying (parameterizing) the shape of the median surface. The task becomes more complicated when the shell fragment has a complex contour and one or more surface points have fixed coordinates. For building structures, this is, for example, the presence of additional internal supports. Information about the spline version of the FEM is presented. Some well-known parametrization methods are noted. The approach of parametrization of a minimal surface of a complex shape bounded by four curved contours and a given (fixed) coordinate of one inner point of the surface is considered. An algorithm for constructing a spatial network, as well as determining coordinates, metric tensor components and Christoffel symbols necessary for solving parametrization problems in the spline version of the finite element method is described. |
| first_indexed | 2024-04-10T19:34:32Z |
| format | Article |
| id | doaj.art-80ec7eb268814dd79642c32fd4bc63d8 |
| institution | Directory Open Access Journal |
| issn | 1815-5235 2587-8700 |
| language | English |
| last_indexed | 2024-04-10T19:34:32Z |
| publishDate | 2022-12-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | Structural Mechanics of Engineering Constructions and Buildings |
| spelling | doaj.art-80ec7eb268814dd79642c32fd4bc63d82023-01-30T09:11:48ZengPeoples’ Friendship University of Russia (RUDN University)Structural Mechanics of Engineering Constructions and Buildings1815-52352587-87002022-12-0118546747410.22363/1815-5235-2022-18-5-467-47420957Surface parameterization complex geometrySamat N. Yakupov0https://orcid.org/0000-0003-0047-3679Guzial Kh. Nizamova1https://orcid.org/0000-0002-7193-9125Federal Research Center “Kazan Scientific Center of Russian Academy of Sciences”Peoples’ Friendship University of Russia (RUDN University)Among thin-walled structures, including building structures and constructions, shells of complex geometry are effective in their rigidity and strength characteristics, which are also distinguished by architectural harmony. For a wider application of shells of complex geometry, it is necessary to reliably assess their stress-strain state. In this case, an integral part of the calculation is the parametrization stage of the median surface of shells of complex geometry. There are shells of complex geometry of canonical and non-canonical forms. For shells of non-canonical shape, the median surface cannot be defined by analytical formulas. At the same time, difficulties arise at the stage of specifying (parameterizing) the shape of the median surface. The task becomes more complicated when the shell fragment has a complex contour and one or more surface points have fixed coordinates. For building structures, this is, for example, the presence of additional internal supports. Information about the spline version of the FEM is presented. Some well-known parametrization methods are noted. The approach of parametrization of a minimal surface of a complex shape bounded by four curved contours and a given (fixed) coordinate of one inner point of the surface is considered. An algorithm for constructing a spatial network, as well as determining coordinates, metric tensor components and Christoffel symbols necessary for solving parametrization problems in the spline version of the finite element method is described.https://journals.rudn.ru/structural-mechanics/article/viewFile/33413/21662complex geometryfixed surface pointparametrizationnetwork construction algorithmspatial coordinatesmetric tensor componentschristoffel symbols |
| spellingShingle | Samat N. Yakupov Guzial Kh. Nizamova Surface parameterization complex geometry Structural Mechanics of Engineering Constructions and Buildings complex geometry fixed surface point parametrization network construction algorithm spatial coordinates metric tensor components christoffel symbols |
| title | Surface parameterization complex geometry |
| title_full | Surface parameterization complex geometry |
| title_fullStr | Surface parameterization complex geometry |
| title_full_unstemmed | Surface parameterization complex geometry |
| title_short | Surface parameterization complex geometry |
| title_sort | surface parameterization complex geometry |
| topic | complex geometry fixed surface point parametrization network construction algorithm spatial coordinates metric tensor components christoffel symbols |
| url | https://journals.rudn.ru/structural-mechanics/article/viewFile/33413/21662 |
| work_keys_str_mv | AT samatnyakupov surfaceparameterizationcomplexgeometry AT guzialkhnizamova surfaceparameterizationcomplexgeometry |