A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams

2016 ◽  
Vol 4 (4) ◽  
pp. 251-264 ◽  
Author(s):  
Boumediene Kheroubi ◽  
Abdelnour Benzair ◽  
Abdelouahed Tounsi ◽  
Abdelwahed Semmah
Keyword(s):  
Beam Theory ◽  
Nonlocal Beam

POSTBUCKLING OF NANO RODS/TUBES BASED ON NONLOCAL BEAM THEORY

2009 ◽  
Vol 01 (02) ◽  
pp. 259-266 ◽  
Author(s):  
C. M. WANG ◽  
Y. XIANG ◽  
S. KITIPORNCHAI
Keyword(s):  
Differential Equation ◽  
Scale Effect ◽  
Shooting Method ◽  
Beam Theory ◽  
Length Scale ◽  
Small Length ◽  
Concentrated Load ◽  
Small Length Scale ◽  
Nano Rods ◽  
Nonlocal Beam

This paper is concerned with the postbuckling problem of cantilevered nano rods/tubes under an end concentrated load. Eringen's nonlocal beam theory is used to account for the small length scale effect. The governing equation is derived from statical and geometrical considerations and Eringen's nonlocal constitutive relation. The nonlinear differential equation is solved using the shooting method for the postbuckling load and the buckled shape. By comparing with the classical postbuckling solutions, the sensitivity of the small length scale effect on the buckling load and buckled shape may be observed. It is found that the small length scale effect decreases the postbuckling load and increases the deflection of the rod.

A NEW NONLOCAL BEAM THEORY WITH THICKNESS STRETCHING EFFECT FOR NANOBEAMS

2013 ◽  
Vol 12 (04) ◽  
pp. 1350025 ◽  
Author(s):  
ABDELOUAHED TOUNSI ◽  
SOUMIA BENGUEDIAB ◽  
MOHAMMED SID AHMED HOUARI ◽  
ABDELWAHED SEMMAH
Keyword(s):  
Shear Deformation ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Dynamic Responses ◽  
Theoretical Development ◽  
Small Scale ◽  
Small Scale Effect ◽  
Nonlocal Beam

This paper presents a new nonlocal thickness-stretching sinusoidal shear deformation beam theory for the static and vibration of nanobeams. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and it accounts for both shear deformation and thickness stretching effects by a sinusoidal variation of all displacements through the thickness without using shear correction factor. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanobeam are derived using Hamilton's principle. The effects of nonlocal parameter, aspect ratio and the thickness stretching on the static and dynamic responses of the nanobeam are discussed. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the bending and dynamic behaviors of complex-nanobeam-system such as complex carbon nanotube system.

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