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Exact solution for bending analysis of two-directional functionally graded Timoshenko beams

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Abstract

This paper studies the bending behavior of two-dimensional functionally graded (TDFG) beam based on the Timoshenko beam theory, where the material properties of the beam vary both in the length and thickness directions. By introducing a new auxiliary function, we simplify the coupled governing equations for the deflection and rotation to a single governing equation. Moreover, all physical quantities of interest can be expressed in terms of the auxiliary function. Then, the exact analytical solutions for bending of TDFG Timoshenko beams are derived for various boundary conditions. The influence of gradient indexes on the deflection and stress distribution of TDFG Timoshenko beams is discussed subjected to different transverse loadings, including uniformly distributed loading, linearly distributed loading and concentrated external loading. The introduced approach is of benefit to exact bending analysis of TDFG beams by employing other beam theories.

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Acknowledgements

The authors are very grateful to the reviewers for their valuable suggestions to improve the quality of the paper. This work was supported by Natural Science Foundation of Guangdong Province, PR China (Grant No. 2018A030313258).

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  1. School of Mathematics and Big Data, Foshan University, Foshan, 528000, Guangdong, China

    Yong Huang & Zheng-Yong Ouyang

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  1. Yong Huang
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  2. Zheng-Yong Ouyang
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Correspondence to Yong Huang.

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Huang, Y., Ouyang, ZY. Exact solution for bending analysis of two-directional functionally graded Timoshenko beams. Arch Appl Mech 90, 1005–1023 (2020). https://doi.org/10.1007/s00419-019-01655-5

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