Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions
In this paper, a novel enriched three-node triangular element with the augmented interpolation cover functions is proposed based on the original linear triangular element for two-dimensional solids. In this enriched triangular element, the augmented interpolation cover functions are employed to enri...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/3/456 |
| _version_ | 1797486313942810624 |
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| author | Yancheng Li Sina Dang Wei Li Yingbin Chai |
| author_facet | Yancheng Li Sina Dang Wei Li Yingbin Chai |
| author_sort | Yancheng Li |
| collection | DOAJ |
| description | In this paper, a novel enriched three-node triangular element with the augmented interpolation cover functions is proposed based on the original linear triangular element for two-dimensional solids. In this enriched triangular element, the augmented interpolation cover functions are employed to enrich the original standard linear shape functions over element patches. As a result, the original linear approximation space can be effectively enriched without adding extra nodes. To eliminate the linear dependence issue of the present method, an effective scheme is used to make the system matrices of the numerical model completely positive-definite. Through several typical numerical examples, the abilities of the present enriched three node triangular element in forced and free vibration analysis of two-dimensional solids are studied. The results show that, compared with the original linear triangular element, the present element can not only provide more accurate numerical results, but also have higher computational efficiency and convergence rate. |
| first_indexed | 2024-03-09T23:32:24Z |
| format | Article |
| id | doaj.art-b01f15d3626242ebb2d7951a20f24ada |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:32:24Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b01f15d3626242ebb2d7951a20f24ada2023-11-23T17:07:48ZengMDPI AGMathematics2227-73902022-01-0110345610.3390/math10030456Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover FunctionsYancheng Li0Sina Dang1Wei Li2Yingbin Chai3Key Laboratory of High Performance Ship Technology, Wuhan University of Technology, Ministry of Education, Wuhan 430063, ChinaAir and Missile Defense College, Air Force Engineering University, Xi’an 710051, ChinaSchool of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, ChinaKey Laboratory of High Performance Ship Technology, Wuhan University of Technology, Ministry of Education, Wuhan 430063, ChinaIn this paper, a novel enriched three-node triangular element with the augmented interpolation cover functions is proposed based on the original linear triangular element for two-dimensional solids. In this enriched triangular element, the augmented interpolation cover functions are employed to enrich the original standard linear shape functions over element patches. As a result, the original linear approximation space can be effectively enriched without adding extra nodes. To eliminate the linear dependence issue of the present method, an effective scheme is used to make the system matrices of the numerical model completely positive-definite. Through several typical numerical examples, the abilities of the present enriched three node triangular element in forced and free vibration analysis of two-dimensional solids are studied. The results show that, compared with the original linear triangular element, the present element can not only provide more accurate numerical results, but also have higher computational efficiency and convergence rate.https://www.mdpi.com/2227-7390/10/3/456interpolation cover functionsfinite element methodsolid mechanicsfree and forced vibration analysislow order linear element |
| spellingShingle | Yancheng Li Sina Dang Wei Li Yingbin Chai Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions Mathematics interpolation cover functions finite element method solid mechanics free and forced vibration analysis low order linear element |
| title | Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions |
| title_full | Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions |
| title_fullStr | Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions |
| title_full_unstemmed | Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions |
| title_short | Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions |
| title_sort | free and forced vibration analysis of two dimensional linear elastic solids using the finite element methods enriched by interpolation cover functions |
| topic | interpolation cover functions finite element method solid mechanics free and forced vibration analysis low order linear element |
| url | https://www.mdpi.com/2227-7390/10/3/456 |
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