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221. Yan, Z., Jiang, L.Y.: Surface effects on the electromechanical coupling and bending behaviours
of piezoelectric nanowires. J. Phys. D-Appl. Phys. 44, 075404 (2011)
222. Yan, Z., Jiang, L.Y.: The vibrational and buckling behaviors of piezoelectric nanobeams with
surface effects. Nanotech. 22, 245703 (2011)
223. Li, Y.H., Fang, B., Zhang, J.H., Song, J.Z.: Surface effects on the wrinkling of piezoelectric
films on compliant substrates. J. Appl. Phys. 110, 114303 (2011)
224. Maranganti, R., Sharma, N.D., Sharma, P.: Electromechanical coupling in nonpiezoelectric
materials due to nanoscale size effects: Green’s function solutions and embedded inclusions.
Phys. Rev. B 74, 014110 (2006)
225. Majdoub, M.S., Sharma, P., Cagin, T.: Dramatic enhancement in energy harvesting for a
narrow range of dimensions in piezoelectric nanostructures. Phys. Rev. B 78, 121407 (2008)
226. Eliseev, E.A., Morozovska, A.N., Glinchuk, M.D., Blinc, R.: Spontaneous flexoelectric/flexomagnetic effect in nanoferroics. Phys. Rev. B 79, 165433 (2009)
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piezoelectric nanowire. Smart Mater. Struct. 21, 115024 (2012)
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surface effects. Nanotech. 18, 295701 (2007)
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232. Zhou, L.G., Huang, H.: Are surfaces elastically softer or stiffer? Appl. Phys. Lett. 84, 1940
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233. Streitz, F.H., Cammarata, R.C., Sieradzki, K.: Surface-stress effects on elastic properties. I.
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235. Guo, J.G., Zhao, Y.P.: The size-dependent elastic properties of nanofilms with surface effects.
J. Appl. Phys. 98, 074306 (2005)
236. Gao, X.L., Zhang, G.Y.: A non-classical Mindlin plate model incorporating microstructure,
surface energy and foundation effects. Proc. R. Soc. A: Math. Phys. Eng. Sci. 472(2191),
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237. Winkler, E.: Die Lehre von der Elasticitaet und Festigkeit. Verlag von H. Dominicus, Prague,
Czech Republic (1867)
238. Filonenko-Borodich, M.M.: Some approximate theories of the elastic foundation. Sci. Not.
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242. Feng, Z.H., Cook, R.D.: Beam elements on two-parameter elastic foundations. J. Eng. Mech.
109, 1390–1402 (1983)
243. Eisenberger, M., Clastornik, J.: Beams on variable two-parameter elastic foundation. J. Eng.
Mech. 113, 1454–1466 (1987)
244. Khajeansari, A., Baradaran, G.H., Yvonnet, J.: An explicit solution for bending of nanowires
lying on Winkler-Pasternak elastic substrate medium based on the Euler-Bernoulli beam
theory. Int. J. Eng. Sci. 52, 115–128 (2012)
67
220. Huang, G.Y., Yu, S.W.: Effect of surface piezoelectricity on the electromechanical behaviour
of a piezoelectric ring. Phys. Stat. Sol. B-Basic 243, R22–R24 (2006)
221. Yan, Z., Jiang, L.Y.: Surface effects on the electromechanical coupling and bending behaviours
of piezoelectric nanowires. J. Phys. D-Appl. Phys. 44, 075404 (2011)
222. Yan, Z., Jiang, L.Y.: The vibrational and buckling behaviors of piezoelectric nanobeams with
surface effects. Nanotech. 22, 245703 (2011)
223. Li, Y.H., Fang, B., Zhang, J.H., Song, J.Z.: Surface effects on the wrinkling of piezoelectric
films on compliant substrates. J. Appl. Phys. 110, 114303 (2011)
224. Maranganti, R., Sharma, N.D., Sharma, P.: Electromechanical coupling in nonpiezoelectric
materials due to nanoscale size effects: Green’s function solutions and embedded inclusions.
Phys. Rev. B 74, 014110 (2006)
225. Majdoub, M.S., Sharma, P., Cagin, T.: Dramatic enhancement in energy harvesting for a
narrow range of dimensions in piezoelectric nanostructures. Phys. Rev. B 78, 121407 (2008)
226. Eliseev, E.A., Morozovska, A.N., Glinchuk, M.D., Blinc, R.: Spontaneous flexoelectric/flexomagnetic effect in nanoferroics. Phys. Rev. B 79, 165433 (2009)
227. Liu, C.C., Hu, S.L., Shen, S.P.: Effect of flexoelectricity on electrostatic potential in a bent
piezoelectric nanowire. Smart Mater. Struct. 21, 115024 (2012)
228. Guo, J.G., Zhao, Y.P.: The size-dependent bending elastic properties of nanobeams with
surface effects. Nanotech. 18, 295701 (2007)
229. Villain, P., Beauchamp, P., Badwi, K.F., Goudeau, P., Renault, P.O.: Scr. Mater. 50, 1247
(2004)
230. Wolf, D.: Surface-stress-induced structure and elastic behavior of thin films. Appl. Phys. Lett.
58, 2081 (1991)
231. Liang, H., Upmanyu, M.: Size-dependent elasticity of nanowires: Nonlinear effects. Phys.
Rev. B 71, 241403 (2005)
232. Zhou, L.G., Huang, H.: Are surfaces elastically softer or stiffer? Appl. Phys. Lett. 84, 1940
(2004)
233. Streitz, F.H., Cammarata, R.C., Sieradzki, K.: Surface-stress effects on elastic properties. I.
Thin metal films. Phys. Rev. B 49, 10699 (1994)
234. Dingreville, R., Qu, J., Cherkaoui, M.: Surface free energy and its effect on the elastic behavior
of nano-sized particles, wires and films. J. Mech. Phys. Sol. 53, 1827 (2005)
235. Guo, J.G., Zhao, Y.P.: The size-dependent elastic properties of nanofilms with surface effects.
J. Appl. Phys. 98, 074306 (2005)
236. Gao, X.L., Zhang, G.Y.: A non-classical Mindlin plate model incorporating microstructure,
surface energy and foundation effects. Proc. R. Soc. A: Math. Phys. Eng. Sci. 472(2191),
20160275 (2016)
237. Winkler, E.: Die Lehre von der Elasticitaet und Festigkeit. Verlag von H. Dominicus, Prague,
Czech Republic (1867)
238. Filonenko-Borodich, M.M.: Some approximate theories of the elastic foundation. Sci. Not.
Moskow Nat. Univ. Mech. 46, 3–18 (1940). (in Russian)
239. Pasternak, P.L.: On a New Method of Analysis of an Elastic Foundation by Means of Two
Foundation Constants. Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture,
Moscow (1954). (in Russian)
240. Kerr, A.D.: Elastic and viscoelastic foundation models. ASME J. Appl. Mech. 31, 491–498
(1964)
241. Vlasov, V.Z.: Beams, Plates and Shells on Elastic Foundations. Jerusalem, Israel (1966)
242. Feng, Z.H., Cook, R.D.: Beam elements on two-parameter elastic foundations. J. Eng. Mech.
109, 1390–1402 (1983)
243. Eisenberger, M., Clastornik, J.: Beams on variable two-parameter elastic foundation. J. Eng.
Mech. 113, 1454–1466 (1987)
244. Khajeansari, A., Baradaran, G.H., Yvonnet, J.: An explicit solution for bending of nanowires
lying on Winkler-Pasternak elastic substrate medium based on the Euler-Bernoulli beam
theory. Int. J. Eng. Sci. 52, 115–128 (2012)