References
63
129. Zhang, Y.Y., Wang, C.M., Duan, W.H., Xiang, Y., Zong, Z.: Assessment of continuum mechanics models in predicting buckling strains of single-walled carbon nanotubes. Nanotech. 20,
395707–8 (2009)
130. Rouhi, H., Ansari, R.: Nonlocal analytical Flugge shell model for axial buckling of doublewalled carbon nanotubes with different end conditions. Nano. 7, 1250018–10 (2012)
131. Sarvestani, H.Y.: Buckling analysis of curved nanotube structures based on the nonlocal shell
theory. Int. J. Multiscale Comput. Eng. 14, 45–54 (2016)
132. Lu, P., Zhang, P.Q., Lee, H.P., Wang, C.M., Reddy, J.N.: Non-local elastic plate theories. Proc.
R Soc. A Math. Phys. Eng. Sci. 463, 3225–3240 (2007)
133. Duan, W.H., Wang, C.M.: Exact solutions for axisymmetric bending of micro/nanoscale
circular plates based on nonlocal plate theory. Nanotech. 18, 385704–5 (2007)
134. Aksencer, T., Aydogdu, M.: Levy type solution method for vibration and buckling of
nanoplates using nonlocal elasticity theory. Phys. E. 43, 954–959 (2011)
135. Shakouri, A., Ng, T.Y., Lin, R.M.: Nonlocal plate model for the free vibration analysis of
nanoplates with different boundary conditions. J. Comput. Theor. Nanosci. 8, 2118–2128
(2011)
136. Pradhan, S.C., Murmu, T.: Small scale effect on the buckling of single-layered graphene
sheets under biaxial compression via nonlocal continuum mechanics. Comput. Mater. Sci.
47, 268–274 (2009)
137. Pradhan, S.C., Kumar, A.: Buckling analysis of single layered graphene sheet under biaxial
compression using nonlocal elasticity theory and DQ method. J. Comput. Theor. Nanosci. 8,
1325–1334 (2011)
138. Babaei, H., Shahidi, A.R.: Small-scale effects on the buckling of quadrilateral nanoplates
based on nonlocal elasticity theory using the Galerkin method. Arch. Appl. Mech. 81, 1051–
1062 (2011)
139. Farajpour, A., Danesh, M., Mohammadi, M.: Buckling analysis of variable thickness
nanoplates using nonlocal continuum mechanics. Phys. E. 44, 719–727 (2011)
140. Pradhan, S.C., Phadikar, J.K.: Small scale effect on vibration of embedded multilayered
graphene sheets based on nonlocal continuum models. Phys. Lett. A. 373, 1062–1069 (2009)
141. Shen, Z.B., Tang, H.L., Li, D.K., Tang, G.J.: Vibration of single-layered graphene sheet-based
nanomechanical sensor via nonlocal Kirchhoff plate theory. Comput. Mater. Sci. 61, 200–205
(2012)
142. Ansari, R., Shahabodini, A., Rouhi, H.: A nonlocal plate model incorporating interatomic
potentials for vibrations of graphene with arbitrary edge conditions. Curr. Appl. Phys. 15,
1062–1069 (2015)
143. Zhang, Y., Lei, Z.X., Zhang, L.W., Liew, K.M., Yu, J.L.: Nonlocal continuum model for
vibration of single- layered graphene sheets based on the element-free kp-Ritz method. Eng.
Anal. Bound. Elem. 56, 90–97 (2015)
144. Zhang, Y., Zhang, L.W., Liew, K.M., Yu, J.L.: Nonlocal continuum model for large deformation analysis of SLGSs using the kp-Ritz element-free method. Int. J. Non-Linear Mech. 79,
1–9 (2016)
145. Zhang, Y., Zhang, L.W., Liew, K.M., Yu, J.L.: Buckling analysis of graphene sheets embedded
in an elastic medium based on the kp-Ritz method and non-local elasticity theory. Eng. Anal.
Bound. Elem. 70, 31–39 (2016)
146. Ni, Z., Bu, H., Zou, M., Yi, H., Bi, K., Chen, Y.: Anisotropic mechanical properties of graphene
sheets from molecular dynamics. Phys. B Condens. Matter. 405, 1301–1306 (2010)
147. Pouresmaeeli, S., Fazelzadeh, S.A., Ghavanloo, E.: Exact solution for nonlocal vibration of
double- orthotropic nanoplates embedded in elastic medium. Compos. B Eng. 43, 3384–3390
(2012)
148. Mohammadi, M., Farajpour, A., Goodarzi, M., Heydarshenas, R.: Levy type solution for
nonlocal thermo- mechanical vibration of orthotropic mono-layer graphene sheet embedded
in an elastic medium. J. Solid Mech. 5, 116–132 (2013)
149. Mohammadi, M., Moradi, A., Ghayour, M., Farajpour, A.: Exact solution for thermomechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic
medium. Lat. Am. J. Sol. Struct. 11, 437–458 (2014)
63
129. Zhang, Y.Y., Wang, C.M., Duan, W.H., Xiang, Y., Zong, Z.: Assessment of continuum mechanics models in predicting buckling strains of single-walled carbon nanotubes. Nanotech. 20,
395707–8 (2009)
130. Rouhi, H., Ansari, R.: Nonlocal analytical Flugge shell model for axial buckling of doublewalled carbon nanotubes with different end conditions. Nano. 7, 1250018–10 (2012)
131. Sarvestani, H.Y.: Buckling analysis of curved nanotube structures based on the nonlocal shell
theory. Int. J. Multiscale Comput. Eng. 14, 45–54 (2016)
132. Lu, P., Zhang, P.Q., Lee, H.P., Wang, C.M., Reddy, J.N.: Non-local elastic plate theories. Proc.
R Soc. A Math. Phys. Eng. Sci. 463, 3225–3240 (2007)
133. Duan, W.H., Wang, C.M.: Exact solutions for axisymmetric bending of micro/nanoscale
circular plates based on nonlocal plate theory. Nanotech. 18, 385704–5 (2007)
134. Aksencer, T., Aydogdu, M.: Levy type solution method for vibration and buckling of
nanoplates using nonlocal elasticity theory. Phys. E. 43, 954–959 (2011)
135. Shakouri, A., Ng, T.Y., Lin, R.M.: Nonlocal plate model for the free vibration analysis of
nanoplates with different boundary conditions. J. Comput. Theor. Nanosci. 8, 2118–2128
(2011)
136. Pradhan, S.C., Murmu, T.: Small scale effect on the buckling of single-layered graphene
sheets under biaxial compression via nonlocal continuum mechanics. Comput. Mater. Sci.
47, 268–274 (2009)
137. Pradhan, S.C., Kumar, A.: Buckling analysis of single layered graphene sheet under biaxial
compression using nonlocal elasticity theory and DQ method. J. Comput. Theor. Nanosci. 8,
1325–1334 (2011)
138. Babaei, H., Shahidi, A.R.: Small-scale effects on the buckling of quadrilateral nanoplates
based on nonlocal elasticity theory using the Galerkin method. Arch. Appl. Mech. 81, 1051–
1062 (2011)
139. Farajpour, A., Danesh, M., Mohammadi, M.: Buckling analysis of variable thickness
nanoplates using nonlocal continuum mechanics. Phys. E. 44, 719–727 (2011)
140. Pradhan, S.C., Phadikar, J.K.: Small scale effect on vibration of embedded multilayered
graphene sheets based on nonlocal continuum models. Phys. Lett. A. 373, 1062–1069 (2009)
141. Shen, Z.B., Tang, H.L., Li, D.K., Tang, G.J.: Vibration of single-layered graphene sheet-based
nanomechanical sensor via nonlocal Kirchhoff plate theory. Comput. Mater. Sci. 61, 200–205
(2012)
142. Ansari, R., Shahabodini, A., Rouhi, H.: A nonlocal plate model incorporating interatomic
potentials for vibrations of graphene with arbitrary edge conditions. Curr. Appl. Phys. 15,
1062–1069 (2015)
143. Zhang, Y., Lei, Z.X., Zhang, L.W., Liew, K.M., Yu, J.L.: Nonlocal continuum model for
vibration of single- layered graphene sheets based on the element-free kp-Ritz method. Eng.
Anal. Bound. Elem. 56, 90–97 (2015)
144. Zhang, Y., Zhang, L.W., Liew, K.M., Yu, J.L.: Nonlocal continuum model for large deformation analysis of SLGSs using the kp-Ritz element-free method. Int. J. Non-Linear Mech. 79,
1–9 (2016)
145. Zhang, Y., Zhang, L.W., Liew, K.M., Yu, J.L.: Buckling analysis of graphene sheets embedded
in an elastic medium based on the kp-Ritz method and non-local elasticity theory. Eng. Anal.
Bound. Elem. 70, 31–39 (2016)
146. Ni, Z., Bu, H., Zou, M., Yi, H., Bi, K., Chen, Y.: Anisotropic mechanical properties of graphene
sheets from molecular dynamics. Phys. B Condens. Matter. 405, 1301–1306 (2010)
147. Pouresmaeeli, S., Fazelzadeh, S.A., Ghavanloo, E.: Exact solution for nonlocal vibration of
double- orthotropic nanoplates embedded in elastic medium. Compos. B Eng. 43, 3384–3390
(2012)
148. Mohammadi, M., Farajpour, A., Goodarzi, M., Heydarshenas, R.: Levy type solution for
nonlocal thermo- mechanical vibration of orthotropic mono-layer graphene sheet embedded
in an elastic medium. J. Solid Mech. 5, 116–132 (2013)
149. Mohammadi, M., Moradi, A., Ghayour, M., Farajpour, A.: Exact solution for thermomechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic
medium. Lat. Am. J. Sol. Struct. 11, 437–458 (2014)