Bending Analysis of Multi-Layered Graphene Sheets Under Combined Non-Uniform Shear and Normal Tractions
محورهای موضوعی : Engineering
M.M Alipour
1
(Department of Mechanical Engineering, University of Mazandaran, Babolsar, Iran)
M Shaban
2
(Mechanical Engineering Department, Faculty of Engineering, Bu-Ali Sina University, Hamadan, Iran)
کلید واژه: Graphene, Multilayer, Nonlocal, Shear and normal traction,
چکیده مقاله :
Bending analysis of multilayer graphene sheets (MLGSs) subjected to non-uniform shear and normal tractions is presented. The constitutive relations are considered to be non-classical based on nonlocal theory of elasticity. Based on the differential transformation method, numerical illustrations are carried out for circular and annular geometries. The effects of nano scale parameter, radius of circular and annular graphene sheet, number of layers as well as distance between layers in the presence of van der Waals interaction forces are investigated. In addition, the effects of different boundary conditions are also examined. The numerical results show that above mentioned parameters have significant effects on the bending behavior of MLGSs under the action of non-uniform shear and normal tractions.
[1] Chang W. J., Lee H. L., 2014, Mass detection using a double-layer circular graphene-based nanomechanical resonator, Journal of Applied Physics 116(3): 034303.
[2] Gheshlaghi B., Hasheminejad S. M., 2013, Size dependent damping in axisymmetric vibrations of circular nanoplates, Thin Solid Films 537: 212-216.
[3] Gibson R. F., Ayorinde E. O., Wen Y. F., 2007, Vibrations of carbon nanotubes and their composites: A review, Composites Science and Technology 67(1): 1-28.
[4] Behfar K., Naghdabadi R., 2005, Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium, Composites Science and Technology 65(7-8): 1159-1164.
[5] Behfar K., Seifi P., Naghdabadi R., Ghanbari J., 2006, An analytical approach to determination of bending modulus of a multi-layered graphene sheet, Thin Solid Films 496(2): 475-480.
[6] Eringen A. C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54(9): 4703.
[7] Rafiee R., Moghadam R. M., 2014, On the modeling of carbon nanotubes : A critical review, Composites Part B 56: 435-449.
[8] Eringen A. C., 2002, Nonlocal Continuum Field Theories, Springer.
[9] Lim C. W., 2010, On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: equilibrium, governing equation and static deflection, Applied Mathematics and Mechanics 31(1):37-54.
[10] Babaei H., Shahidi A. R., 2011, Vibration of quadrilateral embedded multilayered graphene sheets based on nonlocal continuum models using the Galerkin method, Acta Mechanica Sinica 27: 967-976.
[11] Duan W. H., Wang C. M., 2007, Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory, Nanotechnology 18: 385704.
[12] Lim C. W., Li C., Yu J. L., 2012, Free torsional vibration of nanotubes based on nonlocal stress theory, Journal of Sound and Vibration 331(12): 2798-2808.
[13] Murmu T., Pradhan S. C., 2009, Small-scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model, Physica E: Low-Dimensional Systems and Nanostructures 41(8):1628-1633.
[14] Pradhan S. C., Phadikar J. K., 2009, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration 325: 206-223.
[15] Radić N., Jeremić D., Trifković S., Milutinović M., 2014, Buckling analysis of double-orthotropic nanoplates embedded in Pasternak elastic medium using nonlocal elasticity theory, Composites Part B 61: 162-171.
[16] Zenkour A. M., Sobhy M., 2013, Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium, Physica E: Low-Dimensional Systems and Nanostructures 53: 251-259.
[17] Wang Y. Z., Li F. M., 2012, Static bending behaviors of nanoplate embedded in elastic matrix with small scale effects, Mechanics Research Communications 41: 44-48
[18] Narendar S., Gopalakrishnan S., 2011, Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory, Acta Mechanica 223(2):395-413.
[19] Bedroud M., Nazemnezhad R., 2015, Axisymmetric / asymmetric buckling of functionally graded circular / annular Mindlin nanoplates via nonlocal elasticity, Physica E: Low-Dimensional Systems and Nanostructures 43(10):1820-1825.
[20] Farajpour A., Danesh M., Mohammadi M., 2011, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: Low-Dimensional Systems and Nanostructures 44(3): 719-727.
[21] Malekzadeh P., Farajpour A., 2012, Axisymmetric free and forced vibrations of initially stressed circular nanoplates embedded in an elastic medium, Acta Mechanica 223(11): 2311-2330.
[22] Bedroud M., Hosseini-Hashemi S., Nazemnezhad R., 2013, Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity, Acta Mechanica 224(11): 2663-2676.
[23] Bedroud M., Nazemnezhad R., 2015, Axisymmetric / asymmetric buckling of functionally graded circular / annular Mindlin nanoplates via nonlocal elasticity, Meccanica 50:1791-1806.
[24] Shaban M., Alibeigloo A., 2014, Static analysis of carbon nano-tubes based on shell model by using three-dimensional theory of elasticity, Journal of Computational and Theoretical Nanoscience 11: 1954-1961.
[25] Shaban M., Alibeigloo A., 2014, Three dimensional vibration and bending analysis of carbon nano- tubes embedded in elastic medium based on theory of elasticity, Latin American Journal of Solids and Structures 11: 2122-2140.
[26] Shaban M., Alipour M. M., 2011, Semi-analytical solution for free vibration of thick functionally graded plates rested on elastic foundation with elastically restrained edge, Acta Mechanica Sinica 24(4): 340-354.
[27] Alipour M. M., Shariyat M., Shaban M., 2010, A semi-snalytical solution for free vibration and modal stress analyses of circular plates resting on two-parameter elastic foundations, Journal of Solid Mechechanics 2(1): 63-78.
[28] Alipour M. M., Shariyat M., 2010, Stress analysis of two-directional FGM moderately thick constrained circular plates with non-uniform load and substrate stiffness distributions, Journal of Solid Mechechanics 2(4): 316-331.
[29] Alipour M. M., Shariyat M., 2011, A power series solution for free vibration of variable thickness mindlin circular plates with two-directional material heterogeneity and elastic foundations, Journal of Solid Mechechanics 3(2): 183-197.
[30] Saidi A. R., Rasouli A., Sahraee S., 2009, Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory, Composite Structures 89(1):110-119.
