On the Development of a Modified Timoshenko Beam Element for the Bending Analysis of Functionally Graded Beams
This study examines the static bending behavior of functionally graded beams using a newly developed modified Timoshenko beam element. The mixed finite element formulation and Timoshenko beam theory serve as the foundation for the formulation of the proposed beam element. There are two nodes and two...
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| author | Mofareh Hassan Ghazwani Pham V. V. Vinh |
| author_facet | Mofareh Hassan Ghazwani Pham V. V. Vinh |
| author_sort | Mofareh Hassan Ghazwani |
| collection | DOAJ |
| description | This study examines the static bending behavior of functionally graded beams using a newly developed modified Timoshenko beam element. The mixed finite element formulation and Timoshenko beam theory serve as the foundation for the formulation of the proposed beam element. There are two nodes and two degrees of freedom in each node of the new beam element. The suggested element is free of shear locking, without the need for reduced or selective integrations, because of the mixed finite element formulation. Comparative results demonstrate high accuracy in computations, even with both regular and irregular meshes, as well as coarse and fine discretization. Because of its rapid convergence rate, the proposed element is an excellent tool for analyzing beam structures with complex geometries and load conditions. Several examples are provided to demonstrate the accuracy and high convergence of the proposed beam element. Additionally, the effects of various parameters, such as the power-law index and thickness-to-length ratio, on the bending behavior of functionally graded beams are investigated. The findings highlight the robustness and versatility of the developed beam element, which makes it a useful contribution to research into the computational mechanics of beam structures. |
| format | Article |
| id | doaj-art-8f19a0a438e1478fb8e4eaccc4e606fc |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-8f19a0a438e1478fb8e4eaccc4e606fc2025-01-10T13:18:10ZengMDPI AGMathematics2227-73902024-12-011317310.3390/math13010073On the Development of a Modified Timoshenko Beam Element for the Bending Analysis of Functionally Graded BeamsMofareh Hassan Ghazwani0Pham V. V. Vinh1Department of Mechanical Engineering, College of Engineering and Computer Sciences, Jazan University, P.O. Box 45124, Jazan 82917, Saudi ArabiaInstitute of Energy & Mining Mechanical Engineering, Nha Trang 57100, VietnamThis study examines the static bending behavior of functionally graded beams using a newly developed modified Timoshenko beam element. The mixed finite element formulation and Timoshenko beam theory serve as the foundation for the formulation of the proposed beam element. There are two nodes and two degrees of freedom in each node of the new beam element. The suggested element is free of shear locking, without the need for reduced or selective integrations, because of the mixed finite element formulation. Comparative results demonstrate high accuracy in computations, even with both regular and irregular meshes, as well as coarse and fine discretization. Because of its rapid convergence rate, the proposed element is an excellent tool for analyzing beam structures with complex geometries and load conditions. Several examples are provided to demonstrate the accuracy and high convergence of the proposed beam element. Additionally, the effects of various parameters, such as the power-law index and thickness-to-length ratio, on the bending behavior of functionally graded beams are investigated. The findings highlight the robustness and versatility of the developed beam element, which makes it a useful contribution to research into the computational mechanics of beam structures.https://www.mdpi.com/2227-7390/13/1/73Timoshenko beam theorybending analysisfinite element methodfunctionally graded material |
| spellingShingle | Mofareh Hassan Ghazwani Pham V. V. Vinh On the Development of a Modified Timoshenko Beam Element for the Bending Analysis of Functionally Graded Beams Mathematics Timoshenko beam theory bending analysis finite element method functionally graded material |
| title | On the Development of a Modified Timoshenko Beam Element for the Bending Analysis of Functionally Graded Beams |
| title_full | On the Development of a Modified Timoshenko Beam Element for the Bending Analysis of Functionally Graded Beams |
| title_fullStr | On the Development of a Modified Timoshenko Beam Element for the Bending Analysis of Functionally Graded Beams |
| title_full_unstemmed | On the Development of a Modified Timoshenko Beam Element for the Bending Analysis of Functionally Graded Beams |
| title_short | On the Development of a Modified Timoshenko Beam Element for the Bending Analysis of Functionally Graded Beams |
| title_sort | on the development of a modified timoshenko beam element for the bending analysis of functionally graded beams |
| topic | Timoshenko beam theory bending analysis finite element method functionally graded material |
| url | https://www.mdpi.com/2227-7390/13/1/73 |
| work_keys_str_mv | AT mofarehhassanghazwani onthedevelopmentofamodifiedtimoshenkobeamelementforthebendinganalysisoffunctionallygradedbeams AT phamvvvinh onthedevelopmentofamodifiedtimoshenkobeamelementforthebendinganalysisoffunctionallygradedbeams |