BUCKLING OF NANO-RINGS/ARCHES BASED ON NONLOCAL ELASTICITY

2012 ◽  
Vol 04 (03) ◽  
pp. 1250025 ◽  
Author(s):  
C. M. WANG ◽  
Y. XIANG ◽  
J. YANG ◽  
S. KITIPORNCHAI
Keyword(s):  
Scale Effect ◽  
Nonlocal Elasticity ◽  
Radial Pressure ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Mode Shapes ◽  
Small Scale ◽  
Small Scale Effect ◽  
Bifurcation Buckling

This paper is concerned with the bifurcation buckling of nano-rings and nano-arches where the allowance for small scale effect is catered for by using Eringen's nonlocal theory of elasticity. Exact buckling solutions for nano-rings and nano-arches under uniform radial pressure are derived and the influence of small scale effect on the buckling pressures and mode shapes is investigated. The new results presented will be useful to engineers who are designing nano-rings and nano-arches to be used in MEMS and NEMS devices.

NONLOCAL THEORY FOR BUCKLING OF NANOPLATES

2011 ◽  
Vol 11 (03) ◽  
pp. 411-429 ◽  
Author(s):  
S. C. PRADHAN ◽  
J. K. PHADIKAR
Keyword(s):  
Elasticity Theory ◽  
Scale Effect ◽  
Nonlocal Elasticity ◽  
Plate Theory ◽  
Nonlocal Elasticity Theory ◽  
Nonlocal Theory ◽  
Theoretical Development ◽  
Small Scale ◽  
Classical Plate Theory ◽  
Small Scale Effect

Classical plate theory (CLPT) and first-order shear deformation plate theory (FSDT) of plates are reformulated using the nonlocal elasticity theory. Developed nonlocal plate theories have been applied to study buckling behavior of nanoplates. Nonlocal elasticity theory, unlike traditional elasticity theory introduces a length scale parameter into the formulation to take into account the discrete structure of the material to some extent. Both single-layered and multilayered nanoplates have been included in the analysis. Navier's approach has been used to obtain exact solutions for buckling loads for simply supported boundary conditions. Dependence of the small scale effect on various geometrical and material parameters has been investigated. Present study reveals the presence of significant small scale effect on the buckling response of nanoplates. The theoretical development and the numerical results presented in the present work are expected to promote the use of nonlocal theories for more accurate prediction of stability behavior of nanoplates and nanoshells.

Small Scale Effect on Boundary Conditions of Cantilever Single Carbon Nanotubes

2013 ◽  
Vol 275-277 ◽  
pp. 33-37
Author(s):  
Ming Li ◽  
Hui Ming Zheng ◽  
Luo Xia ◽  
Liu Yang
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Scale Effect ◽  
Nonlocal Elasticity ◽  
Small Scale ◽  
Euler Beam ◽  
Local Boundary ◽  
Local Boundary Condition ◽  
Small Scale Effect

In this paper, the boundary condition on free vibration of cantilever single-walled carbon nanotubes (SWCNTs) with Winkler elastic medium is investigated. The Euler beam theory with nonlocal elasticity is modeled as SWCNT. The analytical solution is derived and the numerical results show that the additional boundary conditions from small scale do not change natural frequencies. The reason is that the additional work made by the moment and shear force at the free end from small scale effect cancel each other, the boundary conditions due to local elasticity and nonlocal elasticity are also equivalent. Thus for simplicity, one can apply the local boundary condition to replace the small scale boundary condition.

CALIBRATION OF NONLOCAL SCALE EFFECT PARAMETER FOR BENDING SINGLE-LAYERED GRAPHENE SHEET UNDER MOLECULAR DYNAMICS

NANO ◽  
2012 ◽  
Vol 07 (05) ◽  
pp. 1250033 ◽  
Author(s):  
L. Y. HUANG ◽  
Q. HAN ◽  
Y. J. LIANG
Keyword(s):  
Molecular Dynamics ◽  
Elasticity Theory ◽  
Scale Effect ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Md Simulations ◽  
Small Scale ◽  
Graphene Sheets ◽  
Small Scale Effect ◽  
Effect Parameter

In this article, the small scale effect parameter e0 of single-layered graphene sheets (SLGSs) is calibrated for the bending problem. Taking the SLGSs as a rectangular plate, the normal displacement of the simply supported plate under concentrated force was analyzed by both nonlocal elasticity theory and molecular dynamics (MD) simulations, then the small scale effect parameter e0 of SLGSs with different size was obtained by matching the displacement of the nonlocal elasticity theory and that obtained from MD simulations. The results show that the value of e0 is not a constant but has a relationship with the size of SLGSs, and the relationship of armchair-graphene sheets and zigzag-graphene sheets is different.

Small-scale effect on the mechanical properties of metallic nanotubes

2012 ◽  
Vol 101 (9) ◽  
pp. 093109 ◽  
Author(s):  
Jin Zhang ◽  
Chengyuan Wang ◽  
Rajib Chowdhury ◽  
Sondipon Adhikari
Keyword(s):  
Mechanical Properties ◽  
Scale Effect ◽  
Small Scale ◽  
Small Scale Effect

Computing Buckling Characteristics of Double-Layered Graphene Film Embedded in an Elastic Foundation

2019 ◽  
Vol 19 (06) ◽  
pp. 1950065
Author(s):  
Zhengtian Wu ◽  
Yang Zhang ◽  
Weicheng Ma
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Graphene Film ◽  
Nonlocal Theory ◽  
Small Scale ◽  
Type Model ◽  
Classical Plate Theory ◽  
Buckling Behavior ◽  
Small Scale Effect ◽  
Simulation Results

Given the unique and extremely valuable properties, research has significantly focussed on graphene sheets (GSs). To premeditate the small-scale effect, the present work applies the nonlocal theory to study the buckling behavior of a double-layered GS (DLGS) embedded in an elastic foundation. To derive the equation, classical plate theory is adopted. For the elastic foundation, Pasternak-type model is used. In terms of buckling response, a meshless method is utilized to compute simulation results. Accordingly, we examine the effects of aspect ratio, geometry, boundary conditions and nonlocal parameters on the buckling responses of DLGSs.

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