74
2 Size-Dependent Theories of Beams, Plates and Shells
373. Thai, H.T., Kim, S.E.: A simple quasi-3D sinusoidal shear deformation theory for functionally
graded plates. Compos. Struct. 99, 172–180 (2013)
374. Ahouel, M., Houari, M.S.A., Bedia, E.A.A., Tounsi, A.: Size-dependent mechanical behavior
of functionally graded trigonometric shear deformable nanobeams including neutral surface
position concept. Steel. Compos. Struct. 20, 963–981 (2016)
375. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A., Mahmoud, S.R.: Bending and
buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams
including the thickness stretching effect. Steel. Compos. Struct. 18, 425–442 (2015)
376. Pour, H.R., Vossough, H., Heydari, M.M., Beygipoor, G., Azimzadeh, A.: Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential
quadrature method. Struct. Eng. Mech. 54, 1061–1073 (2015)
377. Sadatshojaei, E., Sadatshojaie, A., Fakhar, M.H.: Differential quadrature method for nonlocal
nonlinear vibration analysis of a boron nitride nanotube using sinusoidal shear deformation
theory. Mech. Adv. Mater. Struct. 23, 1278–1283 (2016)
378. Berrabah, H.M., Tounsi, A.L., Semmah, A., Adda Bedia, E.A.: Comparison of various refined
nonlocal beam theories for bending, vibration and buckling analysis of nanobeams. Struct.
Eng. Mech. 48, 351–365 (2013)
379. Thai, H.T., Choi, D.H.: Efficient higher-order shear deformation theories for bending and free
vibration analyses of functionally graded plates. Arch. Appl. Mech. 83, 1755–1771 (2013)
380. Ebrahimi, F., Barati, M.R.: A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment. Appl. Phys. A. 122, 792–806 (2016)
381. Mashat, D., Zenkour, A., Sobhy, M.: Investigation of vibration and thermal buckling of
nanobeams embedded in an elastic medium under various boundary conditions. J. Mech.
32, 277–287 (2016)
382. Thai, S., Thai, H.T., Vo, T.P., Patel, V.I.: A simple shear deformation theory for nonlocal
beams. Compos. Struct. (2017). https://doi.org/10.1016/j.compstruct.2017.03.022
383. Aghababaei, R., Reddy, J.N.: Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates. J. Sound Vib. 326, 277–289 (2009)
384. Pradhan, S.C.: Buckling of single layer graphene sheet based on nonlocal elasticity and higher
order shear deformation theory. Phys. Lett. A. 373, 4182–8 (2009)
385. Pradhan, S.C., Sahu, B.: Vibration of single layer graphene sheet based on nonlocal elasticity
and higher order shear deformation theory. J. Comput. Theor. Nanosci. 7, 1042–50 (2010)
386. Ansari, R., Sahmani, S.: Prediction of biaxial buckling behavior of single-layered graphene
sheets based on nonlocal plate models and molecular dynamics simulations. Appl. Math.
Model. 37, 7338–7351 (2013)
387. Hosseini-Hashemi, S., Kermajani, M., Nazemnezhad, R.: An analytical study on the buckling
and free vibration of rectangular nanoplates using nonlocal third-order shear deformation
plate theory. Eur. J. Mech. A Solids. 51, 29–43 (2015)
388. Daneshmehr, A., Rajabpoor, A., Pourdavood, M.: Stability of size dependent functionally
graded nanoplate based on nonlocal elasticity and higher order plate theories and different
boundary conditions. Int. J. Eng. Sci. 82, 84–100 (2014)
389. Daneshmehr, A., Rajabpoor, A., Hadi, A.: Size dependent free vibration analysis of nanoplates
made of functionally graded materials based on nonlocal elasticity theory with high order
theories. Int. J. Eng. Sci. 95, 23–35 (2015)
390. Narendar, S.: Buckling analysis of micro-/nano-scale plates based on two-variable refined
plate theory incorporating nonlocal scale effects. Compos. Struct. 93, 3093–3103 (2011)
391. Malekzadeh, P., Shojaee, M.: Free vibration of nanoplates based on a nonlocal two-variable
refined plate theory. Compos. Struct. 95, 443–452 (2013)
392. Narendar, S., Gopalakrishnan, S.: Scale effects on buckling analysis of orthotropic nanoplates
based on nonlocal two-variable refined plate theory. Acta Mech. 223, 395–413 (2012)
393. Sobhy, M.: Hygrothermal vibration of orthotropic double-layered graphene sheets embedded
in an elastic medium using the two-variable plate theory. Appl. Math. Model. 40, 85–99 (2016)
394. Sobhy, M.: Generalized two-variable plate theory for multi-layered graphene sheets with
arbitrary boundary conditions. Acta Mech. 225, 2521–2538 (2014)
2 Size-Dependent Theories of Beams, Plates and Shells
373. Thai, H.T., Kim, S.E.: A simple quasi-3D sinusoidal shear deformation theory for functionally
graded plates. Compos. Struct. 99, 172–180 (2013)
374. Ahouel, M., Houari, M.S.A., Bedia, E.A.A., Tounsi, A.: Size-dependent mechanical behavior
of functionally graded trigonometric shear deformable nanobeams including neutral surface
position concept. Steel. Compos. Struct. 20, 963–981 (2016)
375. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A., Mahmoud, S.R.: Bending and
buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams
including the thickness stretching effect. Steel. Compos. Struct. 18, 425–442 (2015)
376. Pour, H.R., Vossough, H., Heydari, M.M., Beygipoor, G., Azimzadeh, A.: Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential
quadrature method. Struct. Eng. Mech. 54, 1061–1073 (2015)
377. Sadatshojaei, E., Sadatshojaie, A., Fakhar, M.H.: Differential quadrature method for nonlocal
nonlinear vibration analysis of a boron nitride nanotube using sinusoidal shear deformation
theory. Mech. Adv. Mater. Struct. 23, 1278–1283 (2016)
378. Berrabah, H.M., Tounsi, A.L., Semmah, A., Adda Bedia, E.A.: Comparison of various refined
nonlocal beam theories for bending, vibration and buckling analysis of nanobeams. Struct.
Eng. Mech. 48, 351–365 (2013)
379. Thai, H.T., Choi, D.H.: Efficient higher-order shear deformation theories for bending and free
vibration analyses of functionally graded plates. Arch. Appl. Mech. 83, 1755–1771 (2013)
380. Ebrahimi, F., Barati, M.R.: A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment. Appl. Phys. A. 122, 792–806 (2016)
381. Mashat, D., Zenkour, A., Sobhy, M.: Investigation of vibration and thermal buckling of
nanobeams embedded in an elastic medium under various boundary conditions. J. Mech.
32, 277–287 (2016)
382. Thai, S., Thai, H.T., Vo, T.P., Patel, V.I.: A simple shear deformation theory for nonlocal
beams. Compos. Struct. (2017). https://doi.org/10.1016/j.compstruct.2017.03.022
383. Aghababaei, R., Reddy, J.N.: Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates. J. Sound Vib. 326, 277–289 (2009)
384. Pradhan, S.C.: Buckling of single layer graphene sheet based on nonlocal elasticity and higher
order shear deformation theory. Phys. Lett. A. 373, 4182–8 (2009)
385. Pradhan, S.C., Sahu, B.: Vibration of single layer graphene sheet based on nonlocal elasticity
and higher order shear deformation theory. J. Comput. Theor. Nanosci. 7, 1042–50 (2010)
386. Ansari, R., Sahmani, S.: Prediction of biaxial buckling behavior of single-layered graphene
sheets based on nonlocal plate models and molecular dynamics simulations. Appl. Math.
Model. 37, 7338–7351 (2013)
387. Hosseini-Hashemi, S., Kermajani, M., Nazemnezhad, R.: An analytical study on the buckling
and free vibration of rectangular nanoplates using nonlocal third-order shear deformation
plate theory. Eur. J. Mech. A Solids. 51, 29–43 (2015)
388. Daneshmehr, A., Rajabpoor, A., Pourdavood, M.: Stability of size dependent functionally
graded nanoplate based on nonlocal elasticity and higher order plate theories and different
boundary conditions. Int. J. Eng. Sci. 82, 84–100 (2014)
389. Daneshmehr, A., Rajabpoor, A., Hadi, A.: Size dependent free vibration analysis of nanoplates
made of functionally graded materials based on nonlocal elasticity theory with high order
theories. Int. J. Eng. Sci. 95, 23–35 (2015)
390. Narendar, S.: Buckling analysis of micro-/nano-scale plates based on two-variable refined
plate theory incorporating nonlocal scale effects. Compos. Struct. 93, 3093–3103 (2011)
391. Malekzadeh, P., Shojaee, M.: Free vibration of nanoplates based on a nonlocal two-variable
refined plate theory. Compos. Struct. 95, 443–452 (2013)
392. Narendar, S., Gopalakrishnan, S.: Scale effects on buckling analysis of orthotropic nanoplates
based on nonlocal two-variable refined plate theory. Acta Mech. 223, 395–413 (2012)
393. Sobhy, M.: Hygrothermal vibration of orthotropic double-layered graphene sheets embedded
in an elastic medium using the two-variable plate theory. Appl. Math. Model. 40, 85–99 (2016)
394. Sobhy, M.: Generalized two-variable plate theory for multi-layered graphene sheets with
arbitrary boundary conditions. Acta Mech. 225, 2521–2538 (2014)