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Structural Engineering and Mechanics Volume 71, Number 6, September25 2019 , pages 669-682 DOI: https://doi.org/10.12989/sem.2019.71.6.669 |
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Nonlinear thermal buckling of bi-directional functionally graded nanobeams |
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Yang Gao, Wan-shen Xiao and Haiping Zhu
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| Abstract | ||
| We in this article study nonlinear thermal buckling of bi-directional functionally graded beams in the theoretical frameworks of nonlocal strain graded theory. To begin with, it is assumed that the effective material properties of beams vary continuously in both the thickness and width directions. Then, we utilize a higher-order shear deformation theory that includes a physical neutral surface to derive the size-dependent governing equations combining with the Hamilton\'s principle and the von Kármán geometric nonlinearity. It should be pointed out that the established model, containing a nonlocal parameter and a strain gradient length scale parameter, can availably account for both the influence of nonlocal elastic stress field and the influence of strain gradient stress field. Subsequently, via using a easier group of initial asymptotic solutions, the corresponding analytical solution of thermal buckling of beams is obtained with the help of perturbation method. Finally, a parametric study is carried out in detail after validating the present analysis, especially for the effects of a nonlocal parameter, a strain gradient length scale parameter and the ratio of the two on the critical thermal buckling temperature of beams. | ||
| Key Words | ||
| Bi-directional FGMs; Nonlocal strain gradient theory; Nonlinear thermal buckling | ||
| Address | ||
| Yang Gao, Wan-shen Xiao: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China Haiping Zhu: School of Computing, Engineering and Mathematics, Western Sydney University, Locked, Bag 1797, Penrith, NSW 2751, Australia | ||