Comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress-strain state of thin shells
Relevance. To determine the stress-strain state (SSS) of thin-walled shells due to the complexity of obtaining numerical results, the theory of thin shells was developed with the introduction of the direct normal hypothesis to reduce the three-dimensional SSS to the two-dimensional one. With the mod...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Peoples’ Friendship University of Russia (RUDN University)
2018-12-01
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| Series: | Structural Mechanics of Engineering Constructions and Buildings |
| Subjects: | |
| Online Access: | http://journals.rudn.ru/structural-mechanics/article/viewFile/20423/16579 |
| _version_ | 1819106478110277632 |
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| author | Yuriy V Klochkov Anatoliy P Nikolaev Tatyana A Sobolevskaya Mikhail Yu Klochkov |
| author_facet | Yuriy V Klochkov Anatoliy P Nikolaev Tatyana A Sobolevskaya Mikhail Yu Klochkov |
| author_sort | Yuriy V Klochkov |
| collection | DOAJ |
| description | Relevance. To determine the stress-strain state (SSS) of thin-walled shells due to the complexity of obtaining numerical results, the theory of thin shells was developed with the introduction of the direct normal hypothesis to reduce the three-dimensional SSS to the two-dimensional one. With the modern development of digital technology and numerical methods of calculation, in particular the finite element method (FEM), it became possible to obtain numerical results without the use of the direct normal hypothesis, namely on the basis of the theory of elasticity in three-dimensional formulation even for thin shells. Aims. The aim of this work is to compare the efficiency of algorithms for the use of finite element stiffness matrices obtained on the basis of the theory of thin shells with the hypothesis of a straight normal and on the basis of the relations of the three-dimensional theory of elasticity. Methods. The results of comparative analysis of finite element calculations of thin shells using a two-dimensional sampling element in the form of a quadrangular fragment of the middle surface and a three-dimensional element in the form of an eight-node six-face are presented. The components of the displacement vector and their first derivatives were chosen as the nodal variable parameters. The functions of the form for both types of discretization elements were represented by products of Hermite polynomials of the third degree. Results. On the example of calculation of the cylindrical shell clamped at the ends it is shown that the two-dimensional statement in calculations of thin shells is adequate and allows to receive acceptable results at optimum costs of machine time. |
| first_indexed | 2024-12-22T02:38:46Z |
| format | Article |
| id | doaj.art-241b145d90804d028f737ee53ee401cb |
| institution | Directory Open Access Journal |
| issn | 1815-5235 2587-8700 |
| language | English |
| last_indexed | 2024-12-22T02:38:46Z |
| publishDate | 2018-12-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | Structural Mechanics of Engineering Constructions and Buildings |
| spelling | doaj.art-241b145d90804d028f737ee53ee401cb2022-12-21T18:41:41ZengPeoples’ Friendship University of Russia (RUDN University)Structural Mechanics of Engineering Constructions and Buildings1815-52352587-87002018-12-0114645946610.22363/1815-5235-2018-14-6-459-46617263Comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress-strain state of thin shellsYuriy V Klochkov0Anatoliy P Nikolaev1Tatyana A Sobolevskaya2Mikhail Yu Klochkov3Volgograd State Agricultural UniversityVolgograd State Agricultural UniversityVolgograd State Agricultural UniversityLomonosov Moscow state UniversityRelevance. To determine the stress-strain state (SSS) of thin-walled shells due to the complexity of obtaining numerical results, the theory of thin shells was developed with the introduction of the direct normal hypothesis to reduce the three-dimensional SSS to the two-dimensional one. With the modern development of digital technology and numerical methods of calculation, in particular the finite element method (FEM), it became possible to obtain numerical results without the use of the direct normal hypothesis, namely on the basis of the theory of elasticity in three-dimensional formulation even for thin shells. Aims. The aim of this work is to compare the efficiency of algorithms for the use of finite element stiffness matrices obtained on the basis of the theory of thin shells with the hypothesis of a straight normal and on the basis of the relations of the three-dimensional theory of elasticity. Methods. The results of comparative analysis of finite element calculations of thin shells using a two-dimensional sampling element in the form of a quadrangular fragment of the middle surface and a three-dimensional element in the form of an eight-node six-face are presented. The components of the displacement vector and their first derivatives were chosen as the nodal variable parameters. The functions of the form for both types of discretization elements were represented by products of Hermite polynomials of the third degree. Results. On the example of calculation of the cylindrical shell clamped at the ends it is shown that the two-dimensional statement in calculations of thin shells is adequate and allows to receive acceptable results at optimum costs of machine time.http://journals.rudn.ru/structural-mechanics/article/viewFile/20423/16579two-dimensional elementthree-dimensional elementthe nodal unknownsthe mesh discretization |
| spellingShingle | Yuriy V Klochkov Anatoliy P Nikolaev Tatyana A Sobolevskaya Mikhail Yu Klochkov Comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress-strain state of thin shells Structural Mechanics of Engineering Constructions and Buildings two-dimensional element three-dimensional element the nodal unknowns the mesh discretization |
| title | Comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress-strain state of thin shells |
| title_full | Comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress-strain state of thin shells |
| title_fullStr | Comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress-strain state of thin shells |
| title_full_unstemmed | Comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress-strain state of thin shells |
| title_short | Comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress-strain state of thin shells |
| title_sort | comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress strain state of thin shells |
| topic | two-dimensional element three-dimensional element the nodal unknowns the mesh discretization |
| url | http://journals.rudn.ru/structural-mechanics/article/viewFile/20423/16579 |
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