Nonlocal Mechanical Buckling Analysis of Nano Single Layer Sheets Using Differential Quadrature method

Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

M.  Sadeghian ¹ (MSc. Student, Department of mechanics, Islamic Azad University, Mashhad Branch, Iran.)
M.  Jabbarzadeh ² (Assistant Professor, Department of mechanics, Islamic Azad University, Mashhad Branch, Iran.)

Received: 2016-01-19 Accepted : 2016-01-19 Published : 2014-02-20

Keywords: تئوری غیرموضعی الاستیسیته, روش مربعات دیفرانسیلی, کمانش مکانیکی, دایروی,

References:

[1]Taniguchi N., On the Basic Concept of Nanotechnology.Proceedings of the International Conference of Production Engineering, London, 1974, pp. 18-23.

[2] Ma M., Tu J.P., Yuan Y.F., Wang X.L., Li F., Mao K.F., Zeng Z.Y., Electrochemical Performance of ZnO Nanoplates as Anode Materials for Ni/Zn Secondary Batteries, Journal of Power Source, vol. 179, No. 1,  2008 , pp. 395-400.

[3] Agesen M., Sorensen V., Nanoplates and Their Suitability for Use as Solar Cells, Proceeding of Clean Technology, Boston Secondary Batteries, Journal of Power Source, vol. 179, No. 11, 2008, pp. 395-400.

[4]Yguerabide J., Yguerabide E. E.,Resonance Light Scattering Particles as Ultrasensitive Labels for Detection of Analytes in a wide Range of Applications, Journal of Cellular Biochemistry-Supplement, vol. 37, No. 37, 2011, pp. 71-81.

[5] Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Zhang Y., Dubonos S.V., Grigorieva I.V., Firsov A.A., Electric Field Effect in Atomically Thin Carbon Films. Science, vol. 306, No. 5696, 2004, pp. 666–669.

[6] Xu Z.P.,Buehler M.J. ,Geometry controls conformation of graphene sheets: membranes, ribbons, and scrolls, ACS-Nano, vol. 4, 2010, pp. 3869–3876.

[7] Chiu H.Y., Hung P., Postma H.W.Ch., Bockrath M.,Atomic-Scale Mass Sensing Using Carbon Nanotube Resonators, Nano Lett, vol. 8, 2008, pp. 4342–4346.

[8] Hernandez E., Goze C., Bernier P., Rubio A. , Elastic Properties of C and BxCyNz Composite Nanotubes. Physics Review Letters, vol. 80, 1998, pp. 4502–4505.

[9] Li C.Y., Chou T.W., Elastic wave velocities in single-walled carbon nanotubes, Physics Review B, vol. 73, 2006, pp. 245407.

[10]Li C., Chou T.W., Single-walled carbon nanotubes as ultrahigh frequency nano-mechanical resonators, Physics Review B, vol. 68, 2003, pp. 073405.

[11]Eringen. A.C, Nonlocal Continuum Field Theories, New york, Springer-Verlag, 2002.

[12] Fleck N.A., Hutchinson J.W.,Strain Gradient Plasticity, Advance applied mechanics, Vol.33, 1997, pp. 295-361.

[13]Yang F., Chong A.C.M., Lam D.C.C., Tong P.,Couple Stress Based Strain Gradient Theory for Elasticity, International journal of solid structures, vol. 39, 2002, pp. 2731-2743.

[14] Parnes A., Chiskis J., Buckling of nano-fibre reinforced composites: a re-examination of elastic buckling. Mechanical Physics Solids, vol. 50, 2002, pp. 855–879.

 

[15] Pradhan S. C., Murmu T.  ,Small Scale Effect on the Buckling of Single-Layered Graphene Sheets under Biaxial Compression via Nonlocal Continuum Mechanics, Computational Materials Science, vol. 47, 2009, pp. 268-274.

[16] Samaei A.T., Abbasion S., Mirsayar M.M., Buckling Analysis of a Single-Layer Graphene Sheet Embedded in an Elastic Medium Based on Nonlocal Mindlin Plate Theory, Mechanics Research Communications, vol. 38, 2011, pp. 481-485.

[17] Farajpour A., Danesh M., Mohammadi M., Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E, vol. 44, 2011, pp. 719–727.

[18] Narendar S., Gopalakrishnan S.,Critical buckling temperature of single-walled carbon nanotubes embedded in a one-parameter elastic medium based on nonlocal continuum mechanics, Physica E, vol. 43, 2011, pp.1185–1191.

[19] Lim C.W., Yang Q., Zhang J.B., Thermal buckling of nanorod based on non-local elasticity theory, International Journal of  Non-Linear Mechanics, vol. 47, 2012, pp. 496-505.

[20] Farajpour A., Shahidi A.R., Mohammadi M., Mohzoon M., Buckling of Orthotropic Micro/Nanoscale Plates under Linearly varying in-plane load via nonlocal continuum mechanics, Composite Structures, vol. 94, 2012, pp. 1605-1615.

[21] Prasanna Kumar T.J., Narendar S., Gopalakrishnan S., Thermal vibration analysis of monolayer graphene embedded in elastic medium based on nonlocal continuum mechanics. Composite Structures, vol. 100, 2013, pp. 332–342.

[22] Emam S.A., A general nonlocal nonlinear model for buckling of nanobeams.Applied Mathematical Modelling , vol. 37, 2013, pp. 6929–6939.

[23] Mohammadi M., , Farajpour A., Moradi A., Ghayour  M.,Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment.Composites: Part B, vol. 56, 2014, pp. 629–637.

[24]Sarrami-Foroushani S., Azhari M., Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects, Physica E, vol. 57, 2014,  pp. 83–95.

[25] Golmakania M.E., Rezatalab J., Nonuniform biaxial buckling of orthotropic nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory, Composite Structures, vol. 119, 2015, pp. 238–250.

[26] Farajpour A., Mohammadi M., Shahidi A.R., Mahzoon M. ,Axisymmetric Buckling of the Circular Graphene Sheets with the Nonlocal continuum plate model, Physica E, vol. 43, 2011, pp. 1820–1825.

[27]Karamooz Ravari M.R., Shahidi A.R., Axisymmetric buckling of the circular annular nanoplates using finite difference method, Meccanica, vol. 48, 2013, pp. 135–144.

[28]Bedroud M., Hosseini-Hashemi S., Nazemnezhad R., Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity, Acta Mechanics, vol. 224, 2013, pp. 2663-2676.

[29] Nosier A., Fallah F., Non-linear Analysis of Functionally Graded Circular Plates under Asymmetric Transverse Loading, International journal of non-Linear mechanics, vol. 44, 2009, pp. 928-942.

[30] Shu C., Differential Quadrature and Its Application in Engineering, 2000, Berlin, Springer.