Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory

Based on the nonlocal elasticity theory, buckling analysis of the nano-beams made of two-directional functionally graded materials (FGM) with small scale effects is carried out. To the best of the authors’ knowledge, so far all previous solutions to the buckling analysis of arbitrary FGM Euler–Berno...

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Published in	International journal of engineering science Vol. 103; pp. 1 - 10
Main Authors	Nejad, Mohammad Zamani, Hadi, Amin, Rastgoo, Abbas
Format	Journal Article
Language	English
Published	Elsevier Ltd 01.06.2016
Subjects	Buckling Buckling analysis Constants Euler–Bernoulli nano-beams Functionally gradient materials GDQM Materials selection Mathematical analysis Mathematical models Nanostructure Nonlocal elasticity Nonlocal theory Size effect Two-directional functionally graded materials GDQM Two-directional functionally graded materials Nonlocal theory Buckling analysis Euler–Bernoulli nano-beams Size effect
Online Access	Get full text
ISSN	0020-7225 1879-2197
DOI	10.1016/j.ijengsci.2016.03.001

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Abstract	Based on the nonlocal elasticity theory, buckling analysis of the nano-beams made of two-directional functionally graded materials (FGM) with small scale effects is carried out. To the best of the authors’ knowledge, so far all previous solutions to the buckling analysis of arbitrary FGM Euler–Bernoulli nano-beams have addressed the case of properties varying in one direction only. The novelty of the current work is to present a solution by taking into account the variation of properties in two-directional functionally graded materials with arbitrary functions. The material properties obey the arbitrary function in thickness and length direction. The governing equations are obtained, employing the principle of minimum potential energy. Generalized differential quadrature method (GDQM) is selected in order to analyze the nonlocal beams with arbitrary boundary conditions along them to obtain the critical buckling load of FG nano-beam. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. Finally, some numerical results are presented to study the effects of material length scale parameter and inhomogeneity constant on size dependent critical buckling load.
AbstractList	Based on the nonlocal elasticity theory, buckling analysis of the nano-beams made of two-directional functionally graded materials (FGM) with small scale effects is carried out. To the best of the authors’ knowledge, so far all previous solutions to the buckling analysis of arbitrary FGM Euler–Bernoulli nano-beams have addressed the case of properties varying in one direction only. The novelty of the current work is to present a solution by taking into account the variation of properties in two-directional functionally graded materials with arbitrary functions. The material properties obey the arbitrary function in thickness and length direction. The governing equations are obtained, employing the principle of minimum potential energy. Generalized differential quadrature method (GDQM) is selected in order to analyze the nonlocal beams with arbitrary boundary conditions along them to obtain the critical buckling load of FG nano-beam. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. Finally, some numerical results are presented to study the effects of material length scale parameter and inhomogeneity constant on size dependent critical buckling load.
Author	Rastgoo, Abbas Hadi, Amin Nejad, Mohammad Zamani
Author_xml	– sequence: 1 givenname: Mohammad Zamani surname: Nejad fullname: Nejad, Mohammad Zamani email: m_zamani@yu.ac.ir, m.zamani.n@gmail.com organization: Mechanical Engineering Department, Yasouj University, P. O. Box: 75914-353, Yasouj, Iran – sequence: 2 givenname: Amin surname: Hadi fullname: Hadi, Amin organization: Mechanical Engineering Faculty, University of Tehran, Tehran, Iran – sequence: 3 givenname: Abbas surname: Rastgoo fullname: Rastgoo, Abbas organization: Mechanical Engineering Faculty, University of Tehran, Tehran, Iran
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Snippet	Based on the nonlocal elasticity theory, buckling analysis of the nano-beams made of two-directional functionally graded materials (FGM) with small scale...
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SubjectTerms	Buckling Buckling analysis Constants Euler–Bernoulli nano-beams Functionally gradient materials GDQM Materials selection Mathematical analysis Mathematical models Nanostructure Nonlocal elasticity Nonlocal theory Size effect Two-directional functionally graded materials
Title	Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory
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