References
293
174. Sun, Z.H., Wang, X.X., Soh, A.K., Wu, H.A., Wang, Y.: Bending of nanoscale structures:
inconsistency between atomistic simulations and strain gradient elasticity solution. Comput.
Mater. Sci. 40, 108–113 (2007)
175. Andreev, A.N., Nemirovskii, Y.V.: Multilayered Anisotropic Shells and Plates: Bend, Stability,
Vibration. Nauka, Novosibirsk (2001)
176. Awrejcewicz, J., Krysko-Jr., V.A., Yakovleva, T.V., Krysko, V.A.: Noisy contact interactions
of multi-layer mechanical structures coupled by boundary conditions. J. Sound Vib. 369,
77–86 (2016)
177. Srinivasa, A.R., Reddy, J.N.: A model for a constrained, finitely deforming, elastic solid with
rotation gradient dependent strain energy, and its specialization to von Kármán plates and
beams. J. Mech. Phys. Solids 61(3), 873–885 (2013)
178. Park, S.K., Gao, X.L.: Variational formulation of a modified couple stress theory and its
application to a simple shear problem. Z. Angew Math. Phys. 59, 904–917 (2008)
179. Yang, J., Ono, T., Esashi, M.: Energy dissipation in submicrometer thick single-crystal silicon
cantilevers. J. Microelectromech. Syst. 11(6), 775–783 (2002)
180. Mindlin, R.D.: Influence of couple-stresses on stress concentrations. Exp. Mech. 3, 1–7 (1963)
181. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)
182. Polizzotto, C.: Gradient elasticity and nonstandard boundary conditions. Int. J. Solids Struct.
40, 7399–7423 (2003)
183. Wang, C.M., Zhang, Y.Y., Ramesh, S.S., Kitipornchai, S.: Buckling analysis of micro- and
nano-rods/tubes based on nonlocal Timoshenko beam theory. J. Phys. D: Appl. Phys. 39,
3904–3909 (2006)
184. Wang, Q.: Wave propagation in carbon nanotubes via nonlocal continuum mechanics. J. Appl.
Phys. 98, 124301 (2005)
185. Santos, A., Reddy, J.N.: Vibration of Timoshenko beams using non-classical elasticity theories. Shock Vib. 19(3), 251–256 (2012)
186. Reddy, J.N., Arbind, A.: Bending relationships between the modified couple stress-based
functionally graded Timoshenko beams and homogeneous Bernoulli–Euler beams. A. Ann.
Solid Struct. Mech. 3(1), 15–26 (2012)
187. Kahrobaiyan, M.H., Asghari, M., Ahmadian, M.T.: A Timoshenko beam element based on
the modified couple stress theory. Int. J. Mech. Sci. 79, 75–83 (2014)
188. Thai, H.T., Vo, T.: A size-dependent functionally graded sinusoidal plate model based on a
modified couple stress theory. Compos. Struct. 96, 376–383 (2013)
189. Alashti, R.A., Abolghasemi, A.H.: A size-dependent Bernoulli-Euler beam formulation based
on a new model of couple stress theory. IJE Trans. C: Asp. 27(6), 951–960 (2014)
190. Chen, W., Li, X.: A new modified couple stress theory for anisotropic elasticity and microscale
laminated Kirchhoff plate model. Arch. Appl. Mech. 84, 323–341 (2014)
191. Mohammad-Abadi, M., Daneshmehr, A.R.: Modified couple stress theory applied to dynamic
analysis of composite laminated beams by considering different beam theories. Int. J. Eng.
Sci. 87, 83–102 (2015)
192. Shafiei, N., Kazemi, M., Fatahi, L.: Transverse vibration of rotary tapered microbeam based
on modified couple stress theory and generalized differential quadrature. Mech. Adv. Mater.
Struct. 24(3), 240–252 (2015)
193. Rajneesh, K.: Response of thermoelastic beam due to thermal source in modified couple stress
theory. Comput. Methods Sci. Technol. 22(2), 95–101 (2016)
194. Khorshidi, M.A., Shariati, M., Emam, S.A.: Postbuckling of functionally graded nanobeams
based on modified couple stress theory under general beam theory. Int. J. Mech. Sci. 110,
160–169 (2016)
195. Abazari, A.M., Safavi, S.M., Rezazadeh, G., Villanueva, L.G.: Modelling the size effects on
the mechanical properties of micro/nano structures. Sensors 15, 28543–28562 (2015)
196. Tsiatas, G.C., Yiotis, A.J.: Size effect on the static, dynamic and buckling analysis of
orthotropic Kirchhoff-type skew micro-plates based on a modified couple stress theory: comparison with the nonlocal elasticity theory. Acta Mech. 226, 1267–1281 (2015)
293
174. Sun, Z.H., Wang, X.X., Soh, A.K., Wu, H.A., Wang, Y.: Bending of nanoscale structures:
inconsistency between atomistic simulations and strain gradient elasticity solution. Comput.
Mater. Sci. 40, 108–113 (2007)
175. Andreev, A.N., Nemirovskii, Y.V.: Multilayered Anisotropic Shells and Plates: Bend, Stability,
Vibration. Nauka, Novosibirsk (2001)
176. Awrejcewicz, J., Krysko-Jr., V.A., Yakovleva, T.V., Krysko, V.A.: Noisy contact interactions
of multi-layer mechanical structures coupled by boundary conditions. J. Sound Vib. 369,
77–86 (2016)
177. Srinivasa, A.R., Reddy, J.N.: A model for a constrained, finitely deforming, elastic solid with
rotation gradient dependent strain energy, and its specialization to von Kármán plates and
beams. J. Mech. Phys. Solids 61(3), 873–885 (2013)
178. Park, S.K., Gao, X.L.: Variational formulation of a modified couple stress theory and its
application to a simple shear problem. Z. Angew Math. Phys. 59, 904–917 (2008)
179. Yang, J., Ono, T., Esashi, M.: Energy dissipation in submicrometer thick single-crystal silicon
cantilevers. J. Microelectromech. Syst. 11(6), 775–783 (2002)
180. Mindlin, R.D.: Influence of couple-stresses on stress concentrations. Exp. Mech. 3, 1–7 (1963)
181. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)
182. Polizzotto, C.: Gradient elasticity and nonstandard boundary conditions. Int. J. Solids Struct.
40, 7399–7423 (2003)
183. Wang, C.M., Zhang, Y.Y., Ramesh, S.S., Kitipornchai, S.: Buckling analysis of micro- and
nano-rods/tubes based on nonlocal Timoshenko beam theory. J. Phys. D: Appl. Phys. 39,
3904–3909 (2006)
184. Wang, Q.: Wave propagation in carbon nanotubes via nonlocal continuum mechanics. J. Appl.
Phys. 98, 124301 (2005)
185. Santos, A., Reddy, J.N.: Vibration of Timoshenko beams using non-classical elasticity theories. Shock Vib. 19(3), 251–256 (2012)
186. Reddy, J.N., Arbind, A.: Bending relationships between the modified couple stress-based
functionally graded Timoshenko beams and homogeneous Bernoulli–Euler beams. A. Ann.
Solid Struct. Mech. 3(1), 15–26 (2012)
187. Kahrobaiyan, M.H., Asghari, M., Ahmadian, M.T.: A Timoshenko beam element based on
the modified couple stress theory. Int. J. Mech. Sci. 79, 75–83 (2014)
188. Thai, H.T., Vo, T.: A size-dependent functionally graded sinusoidal plate model based on a
modified couple stress theory. Compos. Struct. 96, 376–383 (2013)
189. Alashti, R.A., Abolghasemi, A.H.: A size-dependent Bernoulli-Euler beam formulation based
on a new model of couple stress theory. IJE Trans. C: Asp. 27(6), 951–960 (2014)
190. Chen, W., Li, X.: A new modified couple stress theory for anisotropic elasticity and microscale
laminated Kirchhoff plate model. Arch. Appl. Mech. 84, 323–341 (2014)
191. Mohammad-Abadi, M., Daneshmehr, A.R.: Modified couple stress theory applied to dynamic
analysis of composite laminated beams by considering different beam theories. Int. J. Eng.
Sci. 87, 83–102 (2015)
192. Shafiei, N., Kazemi, M., Fatahi, L.: Transverse vibration of rotary tapered microbeam based
on modified couple stress theory and generalized differential quadrature. Mech. Adv. Mater.
Struct. 24(3), 240–252 (2015)
193. Rajneesh, K.: Response of thermoelastic beam due to thermal source in modified couple stress
theory. Comput. Methods Sci. Technol. 22(2), 95–101 (2016)
194. Khorshidi, M.A., Shariati, M., Emam, S.A.: Postbuckling of functionally graded nanobeams
based on modified couple stress theory under general beam theory. Int. J. Mech. Sci. 110,
160–169 (2016)
195. Abazari, A.M., Safavi, S.M., Rezazadeh, G., Villanueva, L.G.: Modelling the size effects on
the mechanical properties of micro/nano structures. Sensors 15, 28543–28562 (2015)
196. Tsiatas, G.C., Yiotis, A.J.: Size effect on the static, dynamic and buckling analysis of
orthotropic Kirchhoff-type skew micro-plates based on a modified couple stress theory: comparison with the nonlocal elasticity theory. Acta Mech. 226, 1267–1281 (2015)