Zenkour, A., Ebrahimi, F., Barati, M. (2019). Buckling analysis of a size-dependent functionally graded nanobeam resting on Pasternak's foundations. International Journal of Nano Dimension, 10(2), 141-153.

Ashraf Zenkour; Farzad Ebrahimi; Mohammad Reza Barati. "Buckling analysis of a size-dependent functionally graded nanobeam resting on Pasternak's foundations". International Journal of Nano Dimension, 10, 2, 2019, 141-153.

Zenkour, A., Ebrahimi, F., Barati, M. (2019). 'Buckling analysis of a size-dependent functionally graded nanobeam resting on Pasternak's foundations', International Journal of Nano Dimension, 10(2), pp. 141-153.

Zenkour, A., Ebrahimi, F., Barati, M. Buckling analysis of a size-dependent functionally graded nanobeam resting on Pasternak's foundations. International Journal of Nano Dimension, 2019; 10(2): 141-153.

Buckling analysis of a size-dependent functionally graded nanobeam resting on Pasternak's foundations

^{1}Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.

^{2}Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt.

^{3}Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran.

Abstract

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobeam. The two-parameter elastic foundation model including linear Winkler's springs along with Pasternak's shear layer is in contact with the beam in deformation. Material properties of FG nanobeam are supposed to vary gradually along the thickness according to both power-law and Mori–Tanaka laws. Small-scale effect of Eringen's nonlocal elasticity theory has been considered. Nonlocal equilibrium equations are obtained based on the minimum potential energy principle and solved analytically. The accuracy of current method is examined by comparing current results with the available ones in literature. Effects of foundation parameters, gradient index, nonlocal parameter and slenderness ratio on buckling behavior of FG nanobeams are examined.

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