Postbuckling analysis of multi-layered graphene sheets under non-uniform biaxial compression

Farajpour, Ali; Solghar, Alireza Arab; Shahidi, Alireza

doi:10.1016/j.physe.2012.10.028

Cited by 59 publications

(11 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, nonlinear nonlocal models [245][246][247] and nonlinear continuum models incorporating surface effects [248,249] have been developed in the literature to analyse the sizedependent post-buckling of nanoplates. 25…”

Section: 4c Size-dependent Buckling Of Nanoplatesmentioning

confidence: 99%

A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

Self Cite

212

View full text Add to dashboard Cite

Understanding the mechanical behaviour of nanostructures is of great importance due to their applications in nanodevices such as in nanomechanical resonators, nanoscale mass sensors, electromechanical nanoactuators and nanogenerators. Due to the difficulties of performing accurate experimental measurements at nanoscales and the high computational costs associated with the molecular dynamics simulations, the continuum modelling of nanostructures has attracted a considerable amount of attention. Since size influences have a crucial role in the mechanics of structures at nanoscale levels, classical continuum-based theories have been modified to incorporate these effects. Among various modified continuum-based theories, the nonlocal elasticity and the nonlocal strain gradient elasticity have been employed to estimate the mechanical behaviour of nanostructures. In this review paper, first these two modified elasticity theories are briefly explained. Then, the nonlocal motion equations for different nanostructures including nanorods, nanorings, nanobeams, nanoplates and nanoshells are derived. Several papers which reported on the size-dependent mechanical behaviour of nanostructures using modified continuum models are reviewed. Furthermore, important results reported on the vibration, bending and buckling of nanostructures as well as the results of size-dependent wave propagation analyses are discussed.

show abstract

Section: 4c Size-dependent Buckling Of Nanoplatesmentioning

confidence: 99%

A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

Self Cite

212

View full text Add to dashboard Cite

show abstract

“…where subscript NL and L were used to indicate nonlocal parameters. The potential energy of external loads could be defined as follows (Farajpour et al, 2013)…”

Section: H/lxmentioning

confidence: 99%

A novel one-variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on Eringen’s nonlocal differential law

Malikan

Nguyen

2018

WJE

View full text Add to dashboard Cite

CitationMalikan, M., and Nguyen, V. (2018) 'A novel one-variable firstorder shear deformation theory for biaxial buckling of a sizedependent plate based on Eringen's nonlocal differential law"', World Journal of Engineering, 15(5), pp.633-645. AbstractPurpose -This paper presents a new One Variable First-order Shear Deformation Theory (OVFSDT) using nonlocal elasticity concepts for buckling of graphene sheets. Design/methodology/approach -The FSDT had errors in its assumptions due to assuming constant shear stress distribution along thickness of the plate, even though by using shear correction factor (SCF) it has been slightly corrected, the errors have been remained due to the fact that the exact value of SCF has not already been accurately identified. By utilizing two-variable first-order shear deformation theories these errors decreased further by removing the SCF. In order to consider nanoscale effects on the plate, the Eringen's nonlocal elasticity theory was adopted. The critical buckling loads were computed by Navier's approach. The obtained numerical results were then compared with previous studied results using molecular dynamics simulations and other plate theories for validation which also showed the accuracy and simplicity of the proposed theory. Findings -In comparing the biaxial buckling results of the proposed theory with the two-variable shear deformation theories and exact results, it revealed that the two-variable plate theories were not appropriate for the investigation of asymmetrical analyses. Originality/value -A formulation for FSDT was innovated by reconsidering its errors in order to improve the FSDT for investigation of mechanical behavior of nanoplates.

show abstract

“…Substitution of the parameters given in Appendix A into equation (11) leads to the non-classical governing differential equations of motion in terms of displacement field as follow…”

Section: Preliminariesmentioning

confidence: 99%

“…In these applications, nanostructure-dependent size effects are often considerable. To capture such small scale effects on the mechanical responses, modified continuum elasticity theories have been introduced and applied in various researches [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Postbuckling behavior of circular higher-order shear deformable nanoplates including surface energy effects

Sahmani

Bahrami

Aghdam

et al. 2015

Applied Mathematical Modelling

View full text Add to dashboard Cite

Please cite this article as: S. Sahmani, M. Bahrami, M.M. Aghdam, R. Ansari, Postbuckling behavior of circular higher-order shear deformable nanoplates including surface energy effects, Appl. Math. Modelling (2014), doi: http://dx. AbstractThe effects of surface energy are generally ignored in traditional continuum elasticity. However, due to the high surface to volume ratio in nanostructures, this is not the case for them. In this work, the nonlinear postbuckling characteristics of circular nanoplates are predicted in the presence of surface energy effects including surface elasticity and residual surface tension. For this objective, Gurtin-Murdoch elasticity theory is implemented into the classical higher-order shear deformation plate theory. In order to satisfy the balance conditions on the surfaces of nanoplate, it is assumed the normal stress of the bulk is distributed cubically through the thickness of nanoplate. Hamilton's principle in conjunction with von Karman geometric nonlinearity is utilized to derive non-classical nonlinear governing differential equations of motion and related boundary conditions. Afterwards, an efficient numerical methodology based generalized differential quadrature (GDQ) method is carried out using the shifted ChebyshevGauss-Lobatto grid points to discretize the governing partial differential equations. Then, the Galerkin's method is employed to reduce the set of nonlinear equations into a time-varying set of ordinary differential equations of Duffing type. At the end, the pseudo arc-length continuation technique is utilized in order to obtain the solution of the parameterized equation.

show abstract

Postbuckling analysis of multi-layered graphene sheets under non-uniform biaxial compression

Cited by 59 publications

References 40 publications

A review on the mechanics of nanostructures

A review on the mechanics of nanostructures

A novel one-variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on Eringen’s nonlocal differential law

Postbuckling behavior of circular higher-order shear deformable nanoplates including surface energy effects

Contact Info

Product

Resources

About