62
2 Size-Dependent Theories of Beams, Plates and Shells
106. Civalek, O., Demir, C.: Bending analysis of microtubules using nonlocal Euler-Bernoulli
beam theory. Appl. Math. Model. 35, 2053–2067 (2011)
107. Mustapha, K.B., Zhong, Z.W.: Free transverse vibration of an axially loaded non-prismatic
single-walled carbon nanotube embedded in a two-parameter elastic medium. Comput. Mater.
Sci. 50, 742–751 (2010)
108. Li, C., Lim, C.W., Yu, J.L., Zeng, Q.C.: Analytical solutions for vibration of simply supported
nonlocal nanobeams with an axial force. Int. J. Struct. Stab. Dyn. 11(2), 257–271 (2011)
109. Ghannadpour, S.A.M., Mohammadi, B., Fazilati, J.: Bending, buckling and vibration problems
of nonlocal Euler beams using Ritz method. Compos. Struct. 96, 584–589 (2013)
110. Ansari, R., Ramezannezhad, H., Gholami, R.: Nonlocal beam theory for nonlinear vibrations
of embedded multiwalled carbon nanotubes in thermal environment. Nonlinear Dyn. 67,
2241–2254 (2012)
111. Fang, B., Zhen, Y.X., Zhang, C.P., Tang, Y.: Nonlinear vibration analysis of double-walled
carbon nanotubes based on nonlocal elasticity theory. Appl. Math. Model. 37, 1096–1107
(2013)
112. Simsek, M.: Large amplitude free vibration of nanobeams with various boundary conditions
based on the nonlocal elasticity theory. Compos. B Eng. 56, 621–628 (2014)
113. Bagdatli, S.M.: Non-linear vibration of nanobeams with various boundary condition based
on nonlocal elasticity theory. Compos. B Eng. 80, 43–52 (2015)
114. Simsek, M.: Nonlocal effects in the free longitudinal vibration of axially functionally graded
tapered nanorods. Comput. Mater. Sci. 61, 257–265 (2012)
115. Nguyen, N.T., Kim, N.I., Lee, J.: Analytical solutions for bending of transversely or axially
FG nonlocal beams. Steel. Compos. Struct. 17, 639–663 (2014)
116. Niknam, H., Aghdam, M.M.: A semi analytical approach for large amplitude free vibration and
buckling of nonlocal FG beams resting on elastic foundation. Compos. Struct. 119, 452–462
(2014)
117. Ebrahimi, F., Salari, E.: Thermo-mechanical vibration analysis of nonlocal temperaturedependent FG nanobeams with various boundary conditions. Compos. B Eng. 78, 272–290
(2015)
118. Ebrahimi, F., Salari, E.: Nonlocal thermo-mechanical vibration analysis of functionally graded
nanobeams in thermal environment. Acta Astronaut. 113, 29–50 (2015)
119. Nejad, M.Z., Hadi, A.: Eringen’s non-local elasticity theory for bending analysis of bidirectional functionally graded Euler-Bernoulli nano-beams. Int. J. Eng. Sci. 106, 1–9 (2016)
120. Nejad, M.Z., Hadi, A., Rastgoo, A.: Buckling analysis of arbitrary two-directional functionally
graded Euler-Bernoulli nano-beams based on nonlocal elasticity theory. Int. J. Eng. Sci. 103,
1–10 (2016)
121. Nazemnezhad, R., Hosseini-Hashemi, S.: Nonlocal nonlinear free vibration of functionally
graded nanobeams. Compos. Struct. 110, 192–199 (2014)
122. El-Borgi, S., Fernandes, R., Reddy, J.N.: Non-local free and forced vibrations of graded
nanobeams resting on a non-linear elastic foundation. Int. J. Non-Linear Mech. 77, 348–363
(2015)
123. Shafiei, N., Kazemi, M., Safi, M., Ghadiri, M.: Nonlinear vibration of axially functionally
graded non-uniform nanobeams. Int. J. Eng. Sci. 106, 77–94 (2016)
124. Zhang, Y.Q., Liu, G.R., Wang, J.S.: Small-scale effects on buckling of multiwalled carbon
nanotubes under axial compression. Phys. Rev. B. 70, 205430–6 (2004)
125. Li, R., Kardomateas, G.A.: Thermal buckling of multi-walled carbon nanotubes by nonlocal
elasticity. J. Appl. Mech. Trans. ASME. 74, 399–405 (2007)
126. Li, R., Kardomateas, G.A.: Vibration characteristics of multiwalled carbon nanotubes embedded in elastic media by a nonlocal elastic shell model. J. Appl. Mech. Trans. ASME. 74,
1087–1094 (2007)
127. Wang, Q., Varadan, V.K.: Application of nonlocal elastic shell theory in wave propagation
analysis of carbon nanotubes. Smart. Mater. Struct. 16, 178–191 (2007)
128. Hu, Y.G., Liew, K.M., Wang, Q., He, X.Q., Yakobson, B.I.: Nonlocal shell model for elastic
wave propagation in single- and double-walled carbon nanotubes. J. Mech. Phys. Sol. 56,
3475–3485 (2008)
2 Size-Dependent Theories of Beams, Plates and Shells
106. Civalek, O., Demir, C.: Bending analysis of microtubules using nonlocal Euler-Bernoulli
beam theory. Appl. Math. Model. 35, 2053–2067 (2011)
107. Mustapha, K.B., Zhong, Z.W.: Free transverse vibration of an axially loaded non-prismatic
single-walled carbon nanotube embedded in a two-parameter elastic medium. Comput. Mater.
Sci. 50, 742–751 (2010)
108. Li, C., Lim, C.W., Yu, J.L., Zeng, Q.C.: Analytical solutions for vibration of simply supported
nonlocal nanobeams with an axial force. Int. J. Struct. Stab. Dyn. 11(2), 257–271 (2011)
109. Ghannadpour, S.A.M., Mohammadi, B., Fazilati, J.: Bending, buckling and vibration problems
of nonlocal Euler beams using Ritz method. Compos. Struct. 96, 584–589 (2013)
110. Ansari, R., Ramezannezhad, H., Gholami, R.: Nonlocal beam theory for nonlinear vibrations
of embedded multiwalled carbon nanotubes in thermal environment. Nonlinear Dyn. 67,
2241–2254 (2012)
111. Fang, B., Zhen, Y.X., Zhang, C.P., Tang, Y.: Nonlinear vibration analysis of double-walled
carbon nanotubes based on nonlocal elasticity theory. Appl. Math. Model. 37, 1096–1107
(2013)
112. Simsek, M.: Large amplitude free vibration of nanobeams with various boundary conditions
based on the nonlocal elasticity theory. Compos. B Eng. 56, 621–628 (2014)
113. Bagdatli, S.M.: Non-linear vibration of nanobeams with various boundary condition based
on nonlocal elasticity theory. Compos. B Eng. 80, 43–52 (2015)
114. Simsek, M.: Nonlocal effects in the free longitudinal vibration of axially functionally graded
tapered nanorods. Comput. Mater. Sci. 61, 257–265 (2012)
115. Nguyen, N.T., Kim, N.I., Lee, J.: Analytical solutions for bending of transversely or axially
FG nonlocal beams. Steel. Compos. Struct. 17, 639–663 (2014)
116. Niknam, H., Aghdam, M.M.: A semi analytical approach for large amplitude free vibration and
buckling of nonlocal FG beams resting on elastic foundation. Compos. Struct. 119, 452–462
(2014)
117. Ebrahimi, F., Salari, E.: Thermo-mechanical vibration analysis of nonlocal temperaturedependent FG nanobeams with various boundary conditions. Compos. B Eng. 78, 272–290
(2015)
118. Ebrahimi, F., Salari, E.: Nonlocal thermo-mechanical vibration analysis of functionally graded
nanobeams in thermal environment. Acta Astronaut. 113, 29–50 (2015)
119. Nejad, M.Z., Hadi, A.: Eringen’s non-local elasticity theory for bending analysis of bidirectional functionally graded Euler-Bernoulli nano-beams. Int. J. Eng. Sci. 106, 1–9 (2016)
120. Nejad, M.Z., Hadi, A., Rastgoo, A.: Buckling analysis of arbitrary two-directional functionally
graded Euler-Bernoulli nano-beams based on nonlocal elasticity theory. Int. J. Eng. Sci. 103,
1–10 (2016)
121. Nazemnezhad, R., Hosseini-Hashemi, S.: Nonlocal nonlinear free vibration of functionally
graded nanobeams. Compos. Struct. 110, 192–199 (2014)
122. El-Borgi, S., Fernandes, R., Reddy, J.N.: Non-local free and forced vibrations of graded
nanobeams resting on a non-linear elastic foundation. Int. J. Non-Linear Mech. 77, 348–363
(2015)
123. Shafiei, N., Kazemi, M., Safi, M., Ghadiri, M.: Nonlinear vibration of axially functionally
graded non-uniform nanobeams. Int. J. Eng. Sci. 106, 77–94 (2016)
124. Zhang, Y.Q., Liu, G.R., Wang, J.S.: Small-scale effects on buckling of multiwalled carbon
nanotubes under axial compression. Phys. Rev. B. 70, 205430–6 (2004)
125. Li, R., Kardomateas, G.A.: Thermal buckling of multi-walled carbon nanotubes by nonlocal
elasticity. J. Appl. Mech. Trans. ASME. 74, 399–405 (2007)
126. Li, R., Kardomateas, G.A.: Vibration characteristics of multiwalled carbon nanotubes embedded in elastic media by a nonlocal elastic shell model. J. Appl. Mech. Trans. ASME. 74,
1087–1094 (2007)
127. Wang, Q., Varadan, V.K.: Application of nonlocal elastic shell theory in wave propagation
analysis of carbon nanotubes. Smart. Mater. Struct. 16, 178–191 (2007)
128. Hu, Y.G., Liew, K.M., Wang, Q., He, X.Q., Yakobson, B.I.: Nonlocal shell model for elastic
wave propagation in single- and double-walled carbon nanotubes. J. Mech. Phys. Sol. 56,
3475–3485 (2008)