68
2 Size-Dependent Theories of Beams, Plates and Shells
245. Eremeyev, V.A., Lebedev, L.P.: Mathematical study of boundary-value problems within the
framework of Steigmann-Ogden model of surface elasticity. Contin. Mech. Thermodyn. 28,
407–422 (2016)
246. Simsek, M., Reddy, J.N.: A unified higher order beam theory for buckling of a functionally
graded microbeam embedded in elastic medium usingmodified couple stress theory. Compos.
Struct. 101, 47–58 (2013)
247. 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)
248. Limkatanyu, S., Ponbunyanon, P., Prachasaree, W., Kuntiyawichai, K., Kwon, M.: Correlation
between beam on Winkler-Pasternak foundation and beam on elastic substrate medium with
inclusion of microstructure and surface effects. J. Mech. Sci. Tech. 28, 3653–3665 (2014)
249. Gao, X.L., Zhang, G.Y.: A non-classical Kirchhoff plate model incorporating microstructure,
surface energy and foundation effects. Contin. Mech. Thermodyn. 28, 195–213 (2016)
250. Lim, C.W., He, L.H.: Size-dependent nonlinear response of thin elastic films with nano-scale
thickness. Int. J. Mech. Sci. 46, 1715–1726 (2004)
251. Lu, P., He, L.H., Lee, H.P., Lu, C.: Thin plate theory including surface effects. Int. J. Solids
Struct. 43, 4631–4647 (2006)
252. Lu, C.F., Wu, D.Z., Chen, W.Q.: Nonlinear responses of nanoscale FGM films including the
effects of surface energies. IEEE Trans. Nanotech. 10, 1321–1327 (2011)
253. Wang, K.F., Wang, B.L.: Effects of residual surface stress and surface elasticity on the nonlinear free vibration of nanoscale plates. J. Appl. Phys. 112, 013520-1–013520-6 (2012)
254. Lazopoulos, K.A.: On bending of strain gradient elastic micro-plates. Mech. Res. Commun.
36, 777–783 (2009)
255. Michael, J.: Lachut, John, E.: Sader effect of surface stress on the stiffness of cantilever plates.
Phys. Rev. Lett. 99(20), e206102 (2007)
256. Rouhi, H., Ansari, R., Darvizeh, M.: Size-dependent large amplitude vibration analysis of
nanoshells using the Gurtin-Murdoch model. Int. J. Nanosci. Nanotech. 13, 241–252 (2017)
257. Wang, Q.: Wave propagation in carbon nanotubes via nonlocal continuum mechanics. J. Appl.
Phys. 98, 124301 (2005)
258. Wang, Q., Varadan, V.K.: Vibration of carbon nanotubes studied using nonlocal continuum
mechanics. Smart Mater. Struct. 15, 659–666 (2006)
259. 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)
260. Wang, C.M., Zhang, Y.Y., He, X.Q.: Vibration of nonlocal Timoshenko beams. Nanotech. 18,
105401–9 (2007)
261. Wang, C.M., Kitipornchai, S., Lim, C.W., Eisenberger, M.: Beam bending solutions based on
nonlocal Timoshenko beam theory. J. Eng. Mech. 134, 475–481 (2008)
262. Wang, Q., Liew, K.M.: Application of nonlocal continuum mechanics to static analysis of
micro- and nano- structures. Phys. Lett. A. 363, 236–242 (2007)
263. Lu, P., Lee, H.P., Lu, C., Zhang, P.Q.: Application of nonlocal beam models for carbon
nanotubes. Int. J. Sol. Struct. 44, 5289–52300 (2007)
264. Reddy, J.N., Pang, S.D.: Nonlocal continuum theories of beams for the analysis of carbon
nanotubes. J. Appl. Phys. 103, 023511–16 (2008)
265. Murmu, T., Pradhan, S.C.: Buckling analysis of a single-walled carbon nanotube embedded
in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using
DQM. Phys E. 41, 1232–1239 (2009)
266. Ansari, R., Gholami, R., Darabi, M.A.: Thermal buckling analysis of embedded single-walled
carbon nanotubes with arbitrary boundary conditions using the nonlocal timoshenko beam
theory. J. Therm. Stresses. 34, 1271–1281 (2011)
267. Pradhan, S.C., Murmu, T.: Small-scale effect on vibration analysis of single-walled carbon
nanotubes embedded in an elastic medium using nonlocal elasticity theory. J. Appl. Phys.
105, 124306–9 (2009)
2 Size-Dependent Theories of Beams, Plates and Shells
245. Eremeyev, V.A., Lebedev, L.P.: Mathematical study of boundary-value problems within the
framework of Steigmann-Ogden model of surface elasticity. Contin. Mech. Thermodyn. 28,
407–422 (2016)
246. Simsek, M., Reddy, J.N.: A unified higher order beam theory for buckling of a functionally
graded microbeam embedded in elastic medium usingmodified couple stress theory. Compos.
Struct. 101, 47–58 (2013)
247. 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)
248. Limkatanyu, S., Ponbunyanon, P., Prachasaree, W., Kuntiyawichai, K., Kwon, M.: Correlation
between beam on Winkler-Pasternak foundation and beam on elastic substrate medium with
inclusion of microstructure and surface effects. J. Mech. Sci. Tech. 28, 3653–3665 (2014)
249. Gao, X.L., Zhang, G.Y.: A non-classical Kirchhoff plate model incorporating microstructure,
surface energy and foundation effects. Contin. Mech. Thermodyn. 28, 195–213 (2016)
250. Lim, C.W., He, L.H.: Size-dependent nonlinear response of thin elastic films with nano-scale
thickness. Int. J. Mech. Sci. 46, 1715–1726 (2004)
251. Lu, P., He, L.H., Lee, H.P., Lu, C.: Thin plate theory including surface effects. Int. J. Solids
Struct. 43, 4631–4647 (2006)
252. Lu, C.F., Wu, D.Z., Chen, W.Q.: Nonlinear responses of nanoscale FGM films including the
effects of surface energies. IEEE Trans. Nanotech. 10, 1321–1327 (2011)
253. Wang, K.F., Wang, B.L.: Effects of residual surface stress and surface elasticity on the nonlinear free vibration of nanoscale plates. J. Appl. Phys. 112, 013520-1–013520-6 (2012)
254. Lazopoulos, K.A.: On bending of strain gradient elastic micro-plates. Mech. Res. Commun.
36, 777–783 (2009)
255. Michael, J.: Lachut, John, E.: Sader effect of surface stress on the stiffness of cantilever plates.
Phys. Rev. Lett. 99(20), e206102 (2007)
256. Rouhi, H., Ansari, R., Darvizeh, M.: Size-dependent large amplitude vibration analysis of
nanoshells using the Gurtin-Murdoch model. Int. J. Nanosci. Nanotech. 13, 241–252 (2017)
257. Wang, Q.: Wave propagation in carbon nanotubes via nonlocal continuum mechanics. J. Appl.
Phys. 98, 124301 (2005)
258. Wang, Q., Varadan, V.K.: Vibration of carbon nanotubes studied using nonlocal continuum
mechanics. Smart Mater. Struct. 15, 659–666 (2006)
259. 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)
260. Wang, C.M., Zhang, Y.Y., He, X.Q.: Vibration of nonlocal Timoshenko beams. Nanotech. 18,
105401–9 (2007)
261. Wang, C.M., Kitipornchai, S., Lim, C.W., Eisenberger, M.: Beam bending solutions based on
nonlocal Timoshenko beam theory. J. Eng. Mech. 134, 475–481 (2008)
262. Wang, Q., Liew, K.M.: Application of nonlocal continuum mechanics to static analysis of
micro- and nano- structures. Phys. Lett. A. 363, 236–242 (2007)
263. Lu, P., Lee, H.P., Lu, C., Zhang, P.Q.: Application of nonlocal beam models for carbon
nanotubes. Int. J. Sol. Struct. 44, 5289–52300 (2007)
264. Reddy, J.N., Pang, S.D.: Nonlocal continuum theories of beams for the analysis of carbon
nanotubes. J. Appl. Phys. 103, 023511–16 (2008)
265. Murmu, T., Pradhan, S.C.: Buckling analysis of a single-walled carbon nanotube embedded
in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using
DQM. Phys E. 41, 1232–1239 (2009)
266. Ansari, R., Gholami, R., Darabi, M.A.: Thermal buckling analysis of embedded single-walled
carbon nanotubes with arbitrary boundary conditions using the nonlocal timoshenko beam
theory. J. Therm. Stresses. 34, 1271–1281 (2011)
267. Pradhan, S.C., Murmu, T.: Small-scale effect on vibration analysis of single-walled carbon
nanotubes embedded in an elastic medium using nonlocal elasticity theory. J. Appl. Phys.
105, 124306–9 (2009)