Study of static bending of functionally graded beams using analytical method
Email:
chitho.nguyen@lqdtu.edu.vn
Từ khóa:
Static bending response; Functionally graded composite beams; Two-parameter elastic foundation; Timoshenko's first-order shear deformation theory; Principle of virtual work
Tóm tắt
Beams made from variable mechanical properties materials are increasingly used in the fields of construction and transportation. The article presents a study on the static bending response of functionally graded composite beams resting on a two-parameter elastic foundation based on an exact solution. The material of the plate varies exponentially with the thickness variation. The calculations are formulated based on Timoshenko's first-order shear deformation theory, and the equilibrium equations of the beam are derived using the principle of virtual work. An analytical method is employed to derive expressions for displacement and rotation at any point along the beam. The reliability of the study is validated by comparison with previously published solutions. Furthermore, this study also investigates the effects of material, geometric, and elastic foundation parameters on the displacement and rotation responses of the composite beam. This research serves as a significant foundation for engineers in designing and manufacturing practical structuresTài liệu tham khảo
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[2]. V. T. A. Ninh, Fundamental frequencies of bidirectional functionally graded sandwich beams partially supported by foundation using different beam theories, Transport and Communications Science Journal, 72 (2021) 452-467. https://doi.org/10.47869/tcsj.72.4.5.
[3]. D.H. Duc, D.V. Thom, P.M. Phuc, Buckling analysis of variable thickness cracked nanoplatesconsiderting the flexoelectric effect, Transport and Communications Science Journal, 73 (2022) 470-485. https://doi.org/10.47869/tcsj.73.5.3.
[4]. D. M. Lan, N. D. Anh, P. V. Dong, D. V. Thom, Ö. Civalek, P. V. Minh, A new Galerkin method for buckling of sandwich nanobeams, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 29 (2024) 1-16.
https://doi.org/10.1177/09544062241304233
[5]. N.H. Nam, T.N. Canh, T.T. Thanh, T.V. Ke, V.D. Phan, D.V. Thom, Finite element modelling of a composite shell with shear connectors, Symmetry, 11 (2019) 527. https://doi.org/10.3390/sym11040527
[6]. N.C. Tho, N.T. Ta, D.V. Thom, New numerical results from simulations of beams and space frame systems with a tuned mass damper, Materials, 12 (2019) 1329. https://doi.org/10.3390/ma12081329
[7]. T Yu, TQ Bui, S Yin, DH Doan, CT Wu, T V. Do, S Tanaka, On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis, Composite Structures, 136 (2016) 684-695.
[8]. L. L. Ke, J. Yang, S. Kitipornchai, An analytical study on the nonlinear vibration of functionally graded beams, Meccanica, 45 (2010) 743-752. https://doi.org/10.1007/s11012-009-9276-1
[9]. S. E. Ghiasian, Y. Kiani, M. R. Eslami, Nonlinear thermal dynamic buckling of FGM beams, European Journal of Mechanics - A/Solids, 54 (2015) 232-242. https://doi.org/10.1016/j.euromechsol.2015.07.004
[10]. J. N. Reddy, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science, 45 (2007) 288–307. https://doi.org/10.1016/j.ijengsci.2007.04.004
[11]. S. C. Pradhan, Nonlocal finite element analysis and small scale effects of CNTs with Timoshenko beam theory, Finite Elements in Analysis and Design, 50 (2012) 8-20. https://doi.org/10.1016/j.finel.2011.08.008
[12]. Dao Manh Lan, Pham Van Dong, Luu Gia Thien, Bui Van Tuyen, Nguyen Trong Hai, Static Bending and Vibration of Composite Nanobeams Taking Into the Efect of Geometrical Imperfection, Journal of Vibration Engineering & Technologies, 12 (2024) 8685-8706. https://doi.org/10.1007/s42417-024-01384-2
[13]. W.Q. Chen, C.F. Lu, Z.G. Bian, A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation, Applied Mathematical Modelling, 28 (2004) 877-890. https://doi.org/10.1016/j.apm.2004.04.001
[14]. C.M. Wang, K.Y. Lam, X.Q. He, Exact solutions for Tiomoshenko beams on elastic foundations using Green’s functions, Mechanics of Structures and Machines, 26 (1998) 101-113. https://doi.org/10.1080/08905459808945422
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Nhận bài
08/06/2025
Nhận bài sửa
14/07/2025
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12/09/2025
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15/09/2025
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Kiểu trích dẫn
Nguyen Chi, T., Vu Van, H., Le Hong, H., Nguyen Huu, H., Pham Duc, T., & Dao Minh, T. (1757869200). Study of static bending of functionally graded beams using analytical method. Tạp Chí Khoa Học Giao Thông Vận Tải, 76(7), 928-938. https://doi.org/10.47869/tcsj.76.7.1
