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Timoshenko Beam Theory for Buckling of Nanocolumn Free-Standing on an Elastic Substrate

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Abstract

In this paper, the buckling behaviour of a nanocolumn on an elastic substrate is studied by utilizing the Timoshenko beam theory. The governing equations considering self-weight are derived. The boundary conditions containing the rotational spring stiffness are given, and the Galerkin method is used to solve the numerical solution of the governing equations. The influence of the elastic substrate on the buckling of a nanocolumn is discussed. Compared with the Euler-Bernoulli beam theory, the numerical results obtained by the Timoshenko beam theory can more accurately describe the influence of self-weight on buckling. Simultaneously, the shear force significantly influences the buckling of the nanocolumn as the stiffness of the elastic substrate is significant.

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ACKNOWLEDGMENT

This work was supported by the National Natural Science Foundation of China (No. 52175255), the High-level Talent Gathering Project of Hunan Province (no. 2019RS1059), and the Research Project for Postgraduate Students of Hunan Province (no. CX20200648).

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Authors and Affiliations

  1. College of Civil Engineering and Mechanics, Xiangtan University, 411105, Xiangtan, China

    Zhong Chen, Rongguo Zhao, Jingxiang Wu & Nan JI

  2. Key Laboratory of Dynamics and Reliability of Engineering Structures of College of Hunan Province, Xiangtan University, 411105, Xiangtan, China

    Rongguo Zhao & Jingxiang Wu

Authors
  1. Zhong Chen
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  2. Rongguo Zhao
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Correspondence to Rongguo Zhao.

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Chen, Z., Zhao, R., Wu, J. et al. Timoshenko Beam Theory for Buckling of Nanocolumn Free-Standing on an Elastic Substrate. Mech. Solids 57, 644–651 (2022). https://doi.org/10.3103/S0025654422030104

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