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Nonlocal layerwise theory for bending, buckling and vibration analysis of functionally graded nanobeams

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Abstract

In this paper, an efficient method is presented for the bending, buckling, and vibration analysis of functionally graded (FG) nanobeam based on nonlocal elasticity theory and Layerwise theory. The present method takes into account the transverse shear and normal strains of nanobeam and also the small-scale effect in modeling the mechanical behavior of nanobeams. The mechanical properties are assumed to vary continuously through the thickness of the nanobeam. The equations of motion are derived according to the nonlocal elasticity of Eringen and Hamilton’s principle. An analytical solution is presented for analysis of the bending, vibration and buckling of FG nanobeam for various boundary conditions. The results that are predicted by the proposed theory are validated by comparing with the results of other theories available in the literature. Numerical results are presented for bending, natural frequency, and buckling load of functionally graded nanobeams. In addition to flexural vibration modes, the thickness modes and natural frequencies are also predicted by the present theory. The effects of parameters such as length-to-thickness ratio, FG power-law index, nonlocal parameter, boundary conditions, and the number of numerical layers on the bending, natural frequency, and critical buckling load are investigated. It is seen that the present theory is an efficient and accurate method in predicting vibration, buckling, and bending of nanobeams.

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  1. Advanced Materials and Computational Mechanics Laboratory, Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran

    Mahsa Najafi & Isa Ahmadi

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  1. Mahsa Najafi
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  2. Isa Ahmadi
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Correspondence to Isa Ahmadi.

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Najafi, M., Ahmadi, I. Nonlocal layerwise theory for bending, buckling and vibration analysis of functionally graded nanobeams. Engineering with Computers 39, 2653–2675 (2023). https://doi.org/10.1007/s00366-022-01605-w

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  • DOI: https://doi.org/10.1007/s00366-022-01605-w

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