64
2 Size-Dependent Theories of Beams, Plates and Shells
150. Sari, M.S., Al-Kouz, W.G.: Vibration analysis of non-uniform orthotropic Kirchhoff plates
resting on elastic foundation based on nonlocal elasticity theory. Int. J. Mech. Sci. 114, 1–11
(2016)
151. Anjomshoa, A.: Application of Ritz functions in buckling analysis of embedded orthotropic
circular and elliptical micro/nano-plates based on nonlocal elasticity theory. Meccanica 48,
1337–1353 (2013)
152. Anjomshoa, A., Shahidi, A.R., Shahidi, S.H., Nahvi, H.: Frequency analysis of embedded
orthotropic circular and elliptical micro/nano-plates using nonlocal variational principle. J.
Sol. Mech. 7, 13–27 (2015)
153. Mohammadi, M., Farajpour, A., Moradi, A., Ghayour, M.: Shear buckling of orthotropic
rectangular graphene sheet embedded in an elastic medium in thermal environment. Compos.
B Eng. 56, 629–635 (2014)
154. Ashoori, A.R., Salari, E., Sadough Vanini, S.A.: Size-dependent thermal stability analysis of
embedded functionally graded annular nanoplates based on the nonlocal elasticity theory. Int.
J. Mech. Sci. 119, 396–411 (2016)
155. Park, S.K., Gao, X.L.: Bernoulli-Euler beam model based on a modified couple stress theory.
Micromech. Microeng. 16(11), 2355–2359 (2006)
156. Kong, S., Zhou, S., Nie, Z., Wang, K.: The size-dependent natural frequency of Bernoulli
Euler micro-beams. Int. J. Eng. Sci. 46, 427–437 (2008)
157. Kong, S., Zhou, S., Nie, Z., Wang, K.: Size effect on the buckling loads of slender columns
based on a modified couple stress theory. J. Mech. Streng. 31, 136–139 (2009)
158. Xia, W., Wang, L., Yin, L.: Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration. Int. J. Eng. Sci. 48, 2044–2053 (2010)
159. Simsek, M.: Nonlinear static and free vibration analysis of microbeams based on the nonlinear
elastic foundation using modified couple stress theory and He’s variational method. Compos.
Struct. 112, 264–272 (2014)
160. Wang, Y.G., Lin, W.H., Liu, N.: Nonlinear bending and post-buckling of extensible microscale
beams based on modified couple stress theory. Appl. Math. Model. 39, 117–127 (2015)
161. Wang, Y.G., Lin, W.H., Liu, N.: Nonlinear free vibration of a microscale beam based on
modified couple stress theory. Phys. E. 47, 80–85 (2013)
162. Farokhi, H., Ghayesh, M.H., Amabili, M.: Nonlinear dynamics of a geometrically imperfect
microbeam based on the modified couple stress theory. Int. J. Eng. Sci. 68, 11–23 (2013)
163. Togun, N., Bagdatli, S.M.: Size dependent nonlinear vibration of the tensioned nanobeam
based on the modified couple stress theory. Compos. B Eng. 97, 255–262 (2016)
164. Wang, Y.G., Lin, W.H., Zhou, C.L., Liu, R.X.: Thermal postbuckling and free vibration of
extensible microscale beams based on modified couple stress theory. J. Mech. 31, 37–46
(2014)
165. Ansari, R., Ashrafi, M.A., Arjangpay, A.: An exact solution for vibrations of postbuckled
microscale beams based on the modified couple stress theory. Appl. Math. Model. 39, 3050–
3062 (2015)
166. Asghari, M., Ahmadian, M.T., Kahrobaiyan, M.H., Rahaeifard, M.: On the size-dependent
behavior of functionally graded micro-beams. Mater. Des. 31, 2324–2329 (2010)
167. Akgoz, B., Civalek, O.: Free vibration analysis of axially functionally graded tapered
Bernoulli-Euler microbeams based on themodified couple stress theory. Compos. Struct. 98,
314–322 (2013)
168. Shafiei, N., Kazemi, M., Ghadiri, M.: Nonlinear vibration of axially functionally graded
tapered microbeams. Int. J. Eng. Sci. 102, 12–26 (2016)
169. Simsek, M.: Size dependent nonlinear free vibration of an axially functionally graded (AFG)
microbeam using He’s variational method. Compos. Struct. 131, 207–214 (2015)
170. Dehrouyeh-Semnani, A.M., Mostafaei, H., Nikkhah-Bahrami, M.: Free flexural vibration of
geometrically imperfect functionally graded microbeams. Int. J. Eng. Sci. 105, 56–79 (2016)
171. Tsiatas, G.C.: A new Kirchhoff plate model based on a modified couple stress theory. Int. J.
Sol. Struct. 46(13), 2757–2764 (2009)
2 Size-Dependent Theories of Beams, Plates and Shells
150. Sari, M.S., Al-Kouz, W.G.: Vibration analysis of non-uniform orthotropic Kirchhoff plates
resting on elastic foundation based on nonlocal elasticity theory. Int. J. Mech. Sci. 114, 1–11
(2016)
151. Anjomshoa, A.: Application of Ritz functions in buckling analysis of embedded orthotropic
circular and elliptical micro/nano-plates based on nonlocal elasticity theory. Meccanica 48,
1337–1353 (2013)
152. Anjomshoa, A., Shahidi, A.R., Shahidi, S.H., Nahvi, H.: Frequency analysis of embedded
orthotropic circular and elliptical micro/nano-plates using nonlocal variational principle. J.
Sol. Mech. 7, 13–27 (2015)
153. Mohammadi, M., Farajpour, A., Moradi, A., Ghayour, M.: Shear buckling of orthotropic
rectangular graphene sheet embedded in an elastic medium in thermal environment. Compos.
B Eng. 56, 629–635 (2014)
154. Ashoori, A.R., Salari, E., Sadough Vanini, S.A.: Size-dependent thermal stability analysis of
embedded functionally graded annular nanoplates based on the nonlocal elasticity theory. Int.
J. Mech. Sci. 119, 396–411 (2016)
155. Park, S.K., Gao, X.L.: Bernoulli-Euler beam model based on a modified couple stress theory.
Micromech. Microeng. 16(11), 2355–2359 (2006)
156. Kong, S., Zhou, S., Nie, Z., Wang, K.: The size-dependent natural frequency of Bernoulli
Euler micro-beams. Int. J. Eng. Sci. 46, 427–437 (2008)
157. Kong, S., Zhou, S., Nie, Z., Wang, K.: Size effect on the buckling loads of slender columns
based on a modified couple stress theory. J. Mech. Streng. 31, 136–139 (2009)
158. Xia, W., Wang, L., Yin, L.: Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration. Int. J. Eng. Sci. 48, 2044–2053 (2010)
159. Simsek, M.: Nonlinear static and free vibration analysis of microbeams based on the nonlinear
elastic foundation using modified couple stress theory and He’s variational method. Compos.
Struct. 112, 264–272 (2014)
160. Wang, Y.G., Lin, W.H., Liu, N.: Nonlinear bending and post-buckling of extensible microscale
beams based on modified couple stress theory. Appl. Math. Model. 39, 117–127 (2015)
161. Wang, Y.G., Lin, W.H., Liu, N.: Nonlinear free vibration of a microscale beam based on
modified couple stress theory. Phys. E. 47, 80–85 (2013)
162. Farokhi, H., Ghayesh, M.H., Amabili, M.: Nonlinear dynamics of a geometrically imperfect
microbeam based on the modified couple stress theory. Int. J. Eng. Sci. 68, 11–23 (2013)
163. Togun, N., Bagdatli, S.M.: Size dependent nonlinear vibration of the tensioned nanobeam
based on the modified couple stress theory. Compos. B Eng. 97, 255–262 (2016)
164. Wang, Y.G., Lin, W.H., Zhou, C.L., Liu, R.X.: Thermal postbuckling and free vibration of
extensible microscale beams based on modified couple stress theory. J. Mech. 31, 37–46
(2014)
165. Ansari, R., Ashrafi, M.A., Arjangpay, A.: An exact solution for vibrations of postbuckled
microscale beams based on the modified couple stress theory. Appl. Math. Model. 39, 3050–
3062 (2015)
166. Asghari, M., Ahmadian, M.T., Kahrobaiyan, M.H., Rahaeifard, M.: On the size-dependent
behavior of functionally graded micro-beams. Mater. Des. 31, 2324–2329 (2010)
167. Akgoz, B., Civalek, O.: Free vibration analysis of axially functionally graded tapered
Bernoulli-Euler microbeams based on themodified couple stress theory. Compos. Struct. 98,
314–322 (2013)
168. Shafiei, N., Kazemi, M., Ghadiri, M.: Nonlinear vibration of axially functionally graded
tapered microbeams. Int. J. Eng. Sci. 102, 12–26 (2016)
169. Simsek, M.: Size dependent nonlinear free vibration of an axially functionally graded (AFG)
microbeam using He’s variational method. Compos. Struct. 131, 207–214 (2015)
170. Dehrouyeh-Semnani, A.M., Mostafaei, H., Nikkhah-Bahrami, M.: Free flexural vibration of
geometrically imperfect functionally graded microbeams. Int. J. Eng. Sci. 105, 56–79 (2016)
171. Tsiatas, G.C.: A new Kirchhoff plate model based on a modified couple stress theory. Int. J.
Sol. Struct. 46(13), 2757–2764 (2009)