SMALL SCALE EFFECT ON THE BUCKLING OF SINGLE-LAYERED GRAPHENE SHEETS UNDER BIAXIAL COMPRESSION VIA NONLOCAL CONTINUUM MECHANICS

In this article, the small scale effect on the buckling analysis of biaxially compressed single-layered graphene sheets (SLGS) is studied using nonlocal continuum mechanics. The nonlocal mechanics accounts for the small size effects when dealing with nano size elements such as graphene sheets. Using the principle of virtual work the governing equations are derived for rectangular nanoplates. Solutions for buckling loads are computed using differential quadrature method (DQM). It is shown that the nonlocal effect is quite significant in graphene sheets and has a decreasing effect on the buckling loads. When compared with uniaxially compressed graphene, the biaxially compressed one show lower influence of nonlocal effects for the case of smaller side lengths and larger nonlocal parameter values. This difference in behavior between uniaxial and biaxial compressions decreases as the size of the graphene sheets increases.

[1]  C. Wang,et al.  Exact Solutions for Buckling of Structural Members , 2004 .

[2]  H. P. Lee,et al.  Dynamic properties of flexural beams using a nonlocal elasticity model , 2006 .

[3]  M. Aydogdu.  AXIAL VIBRATION OF THE NANORODS WITH THE NONLOCAL CONTINUUM ROD MODEL , 2009 .

[4]  M. J. Abedini,et al.  A differential quadrature analysis of unsteady open channel flow , 2007 .

[5]  C. Bert,et al.  Application of differential quadrature to static analysis of structural components , 1989 .

[6]  C. Shu.  Differential Quadrature and Its Application in Engineering , 2000 .

[7]  J. Nakamura,et al.  Ballistic thermal conductance of a graphene sheet , 2007 .

[8]  K. Liew,et al.  PREDICTING NANOVIBRATION OF MULTI-LAYERED GRAPHENE SHEETS EMBEDDED IN AN ELASTIC MATRIX , 2006 .

[9]  Tony Murmu,et al.  Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM , 2009 .

[10]  Chien Ming Wang,et al.  Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes , 2006 .

[11]  Azim Eskandarian,et al.  Atomistic viewpoint of the applicability of microcontinuum theories , 2004 .

[12]  Tony Murmu,et al.  Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method , 2009 .

[13]  C. Wang,et al.  Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory , 2007 .

[14]  Lin Wang,et al.  The thermal effect on vibration and instability of carbon nanotubes conveying fluid , 2008 .

[15]  S. C. Pradhan,et al.  Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models , 2009 .

[16]  S. C. Pradhan,et al.  VIBRATION ANALYSIS OF NANO-SINGLE-LAYERED GRAPHENE SHEETS EMBEDDED IN ELASTIC MEDIUM BASED ON NONLOCAL ELASTICITY THEORY , 2009 .

[17]  S. Iijima.  Helical microtubules of graphitic carbon , 1991, Nature.

[18]  R. Naghdabadi,et al.  Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium , 2005 .

[19]  S. Kitipornchai,et al.  Pull-in instability of nano-switches using nonlocal elasticity theory , 2008 .

[20]  K. M. Liew,et al.  Continuum model for the vibration of multilayered graphene sheets , 2005 .

[21]  M T Ahmadian,et al.  Vibrational analysis of single-layered graphene sheets , 2008, Nanotechnology.

[22]  Lin Wang,et al.  Dynamical behaviors of double-walled carbon nanotubes conveying fluid accounting for the role of small length scale , 2009 .

[23]  A. Eringen.  On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves , 1983 .

[24]  P. Tong,et al.  Couple stress based strain gradient theory for elasticity , 2002 .

[25]  A. N. Sohi,et al.  Torsional buckling of carbon nanopeapods , 2007 .

[26]  M. Balkanski,et al.  ELASTIC PROPERTIES OF SINGLE-WALLED CARBON NANOTUBES , 2000 .

[27]  R. Bellman,et al.  DIFFERENTIAL QUADRATURE: A TECHNIQUE FOR THE RAPID SOLUTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS , 1972 .

[28]  Ado Jorio,et al.  UNUSUAL PROPERTIES AND STRUCTURE OF CARBON NANOTUBES , 2004 .

[29]  Tony Murmu,et al.  Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory , 2009 .

[30]  Abdelouahed Tounsi,et al.  Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity , 2008 .

[31]  Lin Wang,et al.  On vibration and instability of carbon nanotubes conveying fluid , 2008 .

[32]  Q. Han,et al.  Dynamic torsional buckling of a double-walled carbon nanotube embedded in an elastic medium , 2003 .

[33]  J. N. Reddy,et al.  Nonlocal continuum theories of beams for the analysis of carbon nanotubes , 2008 .

[34]  C. Wang,et al.  The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes , 2007, Nanotechnology.

[35]  A. Sakhaee-Pour,et al.  Elastic buckling of single-layered graphene sheet , 2009 .

[36]  R. Gibson,et al.  VIBRATIONS OF CARBON NANOTUBES AND THEIR COMPOSITES: A REVIEW , 2007 .

[37]  K. Liew,et al.  Resonance analysis of multi-layered graphene sheets used as nanoscale resonators , 2005, Nanotechnology.

[38]  C. Wang,et al.  Free vibration of nanorings/arches based on nonlocal elasticity , 2008 .