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Wind and Structures
  Volume 26, Number 4, April 2018 , pages 205-214

Analytical solution for scale-dependent static stability analysis of temperature-dependent nanobeams subjected to uniform temperature distributions
Farzad Ebrahimi and Ramin Ebrahimi Fardshad

    In this paper, the thermo-mechanical buckling characteristics of functionally graded (FG) size-dependent Timoshenko nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution for the first time. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form and the material properties are assumed to be temperature-dependent. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal governing equations are derived based on Timoshenko beam theory through Hamilton\'s principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate critical buckling temperature results of the FG nanobeams as compared to some cases in the literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as material distribution profile, small scale effects and aspect ratio on the critical buckling temperature of the FG nanobeams in detail. It is explicitly shown that the thermal buckling of a FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.
Key Words
    thermal buckling; Timoshenko beam theory; functionally graded material; nonlocal elasticity theory
Farzad Ebrahimi: Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin P.O.B. 16818-34149, Iran
Ramin Ebrahimi Fardshad: Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

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