Techno Press


Steel and Composite Structures   Volume 26, Number 6, March25 2018, pages 663-672
DOI: http://dx.doi.org/10.12989/scs.2018.26.6.663
 
Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory
Amin Hadi, Mohammad Zamani Nejad, Abbas Rastgoo and Mohammad Hosseini

 
Abstract     [Full Text]
    This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.
 
Key Words
    Euler-Bernoulli nano-beams; buckling analysis; consistent couple-stress theory; Three-directional functionally graded materials (TDFGMs); size effect; generalized differential quadrature method (GDQM)
 
Address
(1) Amin Hadi, Abbas Rastgoo:
School of Mechanical Engineering, University of Tehran, Tehran, Iran;
(2) Mohammad Zamani Nejad:
Department of Mechanical Engineering, Yasouj University, P.O. Box: 75914-353, Yasouj, Iran;
(3) Mohammad Hosseini:
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
 

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