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Two-dimensional elasticity solution for bending of functionally graded beams with variable thickness

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Abstract

This paper studies the stress and displacement distributions of functionally graded beam with continuously varying thickness, which is simply supported at two ends. The Young’s modulus is graded through the thickness following the exponential-law and the Poisson’s ratio keeps constant. On the basis of two-dimensional elasticity theory, the general expressions for the displacements and stresses of the beam under static loads, which exactly satisfy the governing differential equations and the simply supported boundary conditions at two ends, are analytically derived out. The unknown coefficients in the solutions are approximately determined by using the Fourier sinusoidal series expansions to the boundary conditions on the upper and lower surfaces of the beams. The effect of Young’s modulus varying rules on the displacements and stresses of functionally graded beams is investigated in detail. The two-dimensional elasticity solution obtained can be used to assess the validity of various approximate solutions and numerical methods for the aforementioned functionally graded beams.

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Acknowledgments

The project supported by “The natural science foundation of Jiangsu Province” (No. BK20130822) and China Postdoctoral Science Foundation funded project (No. 2011M501158). The authors also acknowledge the support from the National Natural Science Foundation of China (No. 51179063).

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Authors and Affiliations

  1. Department of Engineering Mechanics, Hohai University, Nanjing, 210098, People’s Republic of China

    Yepeng Xu & Tiantang Yu

  2. College of Civil Engineering, Nanjing Tech University, Nanjing, 211816, People’s Republic of China

    Ding Zhou

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  1. Yepeng Xu
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  2. Tiantang Yu
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  3. Ding Zhou
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Correspondence to Ding Zhou.

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Xu, Y., Yu, T. & Zhou, D. Two-dimensional elasticity solution for bending of functionally graded beams with variable thickness. Meccanica 49, 2479–2489 (2014). https://doi.org/10.1007/s11012-014-9958-1

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