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A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2022-3pp.644-651

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Zhong Chen, Rongguo Zhao, Jingxiang Wu, and Nan JI, "Timoshenko Beam Theory for Buckling of Nanocolumn Free-Standing on an Elastic Substrate," Mech. Solids. 57 (3), 644-651 (2022)
Year 2022 Volume 57 Number 3 Pages 644-651
DOI 10.3103/S0025654422030104
Title Timoshenko Beam Theory for Buckling of Nanocolumn Free-Standing on an Elastic Substrate
Author(s) Zhong Chen (College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, China)
Rongguo Zhao (College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, China; Key Laboratory of Dynamics and Reliability of Engineering Structures of College of Hunan Province, Xiangtan University, Xiangtan 411105, China, zhaorongguo@xtu.edu.cn)
Jingxiang Wu (College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, China; Key Laboratory of Dynamics and Reliability of Engineering Structures of College of Hunan Province, Xiangtan University, Xiangtan 411105, China)
Nan JI (College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, China)
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.
Keywords Timoshenko beam theory, buckling, critical length, elastic substrate, self-weight
Received 04 November 2021Revised 12 January 2022Accepted 21 January 2022
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