Closed form solutions of bending Bi-directional functionally graded tapered beams using Euler and Timoshenko theories
This study focuses on developing closed-form analytical solutions for the bending analysis of bi-directional functionally graded tapered beams, a technically challenging area with limited existing solutions. Employing both Euler-Bernoulli and Timoshenko beam theories, the research provides a step-by...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Results in Engineering |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590123025002907 |
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| author | Omar K. Omar Mohammad Alshawabkeh H. Alkhatib |
| author_facet | Omar K. Omar Mohammad Alshawabkeh H. Alkhatib |
| author_sort | Omar K. Omar |
| collection | DOAJ |
| description | This study focuses on developing closed-form analytical solutions for the bending analysis of bi-directional functionally graded tapered beams, a technically challenging area with limited existing solutions. Employing both Euler-Bernoulli and Timoshenko beam theories, the research provides a step-by-step derivation methodology, validated through detailed formulations and computational tools such as Maple software. The analysis examines the effects of material gradation, geometric tapering, and shear deformation on beam behavior, offering comprehensive displacement and stress evaluations. Key findings reveal that Timoshenko theory yields more accurate results for shorter beams due to shear deformation, while variations in gradient indices, taper ratios, and axial parameters significantly influence deflection. For instance, increasing the material gradient index reduces deflection by up to 39%, and higher taper ratios decrease deflection by 58% in both theories. This work bridges theoretical and practical understanding, providing a valuable framework for educators and students to explore advanced beam mechanics and apply closed-form solutions in engineering education. |
| format | Article |
| id | doaj-art-83bbbe76e5b24aaa89102a849db1d192 |
| institution | Kabale University |
| issn | 2590-1230 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Engineering |
| spelling | doaj-art-83bbbe76e5b24aaa89102a849db1d1922025-02-09T05:01:04ZengElsevierResults in Engineering2590-12302025-03-0125104204Closed form solutions of bending Bi-directional functionally graded tapered beams using Euler and Timoshenko theoriesOmar K. Omar0Mohammad Alshawabkeh1H. Alkhatib2Mechanical Engineering Department, Al Hussein Technical University, Amman, JordanMechanical Engineering Department, Al Hussein Technical University, Amman, JordanSchool of Mechanical Engineering, Technological University Dublin, Dublin, Ireland; Dublin Energy Lab, Technological University Dublin, Dublin, Ireland; MaREI, the SFI Centre for Energy, Climate and Marine, Dublin, Ireland; Corresponding author at: School of Mechanical Engineering, Technological University Dublin, Dublin, Ireland.This study focuses on developing closed-form analytical solutions for the bending analysis of bi-directional functionally graded tapered beams, a technically challenging area with limited existing solutions. Employing both Euler-Bernoulli and Timoshenko beam theories, the research provides a step-by-step derivation methodology, validated through detailed formulations and computational tools such as Maple software. The analysis examines the effects of material gradation, geometric tapering, and shear deformation on beam behavior, offering comprehensive displacement and stress evaluations. Key findings reveal that Timoshenko theory yields more accurate results for shorter beams due to shear deformation, while variations in gradient indices, taper ratios, and axial parameters significantly influence deflection. For instance, increasing the material gradient index reduces deflection by up to 39%, and higher taper ratios decrease deflection by 58% in both theories. This work bridges theoretical and practical understanding, providing a valuable framework for educators and students to explore advanced beam mechanics and apply closed-form solutions in engineering education.http://www.sciencedirect.com/science/article/pii/S2590123025002907Closed form solutionTwo directional functionally graded materialTimoshenko beamEuler beamTapered beamTDFGM |
| spellingShingle | Omar K. Omar Mohammad Alshawabkeh H. Alkhatib Closed form solutions of bending Bi-directional functionally graded tapered beams using Euler and Timoshenko theories Results in Engineering Closed form solution Two directional functionally graded material Timoshenko beam Euler beam Tapered beam TDFGM |
| title | Closed form solutions of bending Bi-directional functionally graded tapered beams using Euler and Timoshenko theories |
| title_full | Closed form solutions of bending Bi-directional functionally graded tapered beams using Euler and Timoshenko theories |
| title_fullStr | Closed form solutions of bending Bi-directional functionally graded tapered beams using Euler and Timoshenko theories |
| title_full_unstemmed | Closed form solutions of bending Bi-directional functionally graded tapered beams using Euler and Timoshenko theories |
| title_short | Closed form solutions of bending Bi-directional functionally graded tapered beams using Euler and Timoshenko theories |
| title_sort | closed form solutions of bending bi directional functionally graded tapered beams using euler and timoshenko theories |
| topic | Closed form solution Two directional functionally graded material Timoshenko beam Euler beam Tapered beam TDFGM |
| url | http://www.sciencedirect.com/science/article/pii/S2590123025002907 |
| work_keys_str_mv | AT omarkomar closedformsolutionsofbendingbidirectionalfunctionallygradedtaperedbeamsusingeulerandtimoshenkotheories AT mohammadalshawabkeh closedformsolutionsofbendingbidirectionalfunctionallygradedtaperedbeamsusingeulerandtimoshenkotheories AT halkhatib closedformsolutionsofbendingbidirectionalfunctionallygradedtaperedbeamsusingeulerandtimoshenkotheories |