[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.12989/scs.2015.18.2.425

Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect

Chaht, Fouzia Larbi (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Kaci, Abdelhakim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Houari, Mohammed Sid Ahmed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Beg, O. Anwar (Gort Engovation-Propulsion, Nanomechanics and Biophysics)
Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)

Publication Information

Steel and Composite Structures / v.18, no.2, 2015 , pp. 425-442 More about this Journal

Abstract

This paper addresses theoretically the bending and buckling behaviors of size-dependent nanobeams made of functionally graded materials (FGMs) including the thickness stretching effect. The size-dependent FGM nanobeam is investigated on the basis of the nonlocal continuum model. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a sinusoidal variation of all displacements through the thickness without using shear correction factor. The material properties of FGM nanobeams are assumed to vary through the thickness according to a power law. The governing equations and the related boundary conditions are derived using the principal of minimum total potential energy. A Navier-type solution is developed for simply-supported boundary conditions, and exact expressions are proposed for the deflections and the buckling load. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and stability responses of the FGM nanobeam are discussed in detail. The study is relevant to nanotechnology deployment in for example aircraft structures.

Keywords

nanobeam; nonlocal elasticity theory; bending; buckling; stretching effect; functionally graded materials; navier solution; aspect ratio;

Citations & Related Records

Times Cited By KSCI : 8 (Citation Analysis)

Reference
Cited By KSCI

1	Aifantis, E.C. (1999), "Strain gradient interpretation of size effects", Int. J. Fract., 95(1-4), 299-314. DOI
2	Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. DOI
3	Amara, K., Tounsi, A., Mechab, I. and Adda-Bedia, E.A. (2010), "Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field", Appl. Math. Model., 34(12), 3933-3942. DOI ScienceOn
4	Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2012), "Thermal buckling of functionally graded plates according to a four-variable refined plate theory", J. Therm. Stresses, 35(8), 677-694. DOI
5	Bachir Bouiadjra, R., Adda Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., Int. J., 48(4), 547-567. DOI
6	Baghdadi, H., Tounsi, A., Zidour, M. and Benzair, A. (2014), "Thermal effect on vibration characteristics of armchair and zigzag single walled carbon nanotubes using nonlocal parabolic beam theory", Fullerenes, Nanotubes and Carbon Nanostructures, 23(3), 266-272. DOI
7	Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos.: Part B, 60, 274-283. DOI
8	Benachour, A., Daouadji Tahar, H., Ait Atmane, H., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos.: Part B, 42(6), 1386-1394. DOI
9	Benatta, M.A., Mechab, I., Tounsi, A. and Adda Bedia, E.A. (2008), "Static analysis of functionally graded short beams including warping and shear deformation effects", Comput. Mater. Sci., 44(2), 765-773. DOI
10	Benguediab, S., Semmah, A., Larbi Chaht, F. Mouaz, S. and Tounsi, A. (2014), "An investigation on the characteristics of bending, buckling and vibration of nanobeams via nonlocal beam theory", Int. J. Comput. Methods, 11(6), 1350085. DOI
11	Besseghier, A., Tounsi, A., Houari, M.S.A., Benzair, A., Boumia, L. and Heireche, H. (2011), "Thermal effect on wave propagation in double-walled carbon nanotubes embedded in a polymer matrix using nonlocal elasticity", Physica E, 43(7), 1379-1386. DOI ScienceOn
12	Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N. and Boumia, L. (2008), "The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", J. Phys. D: Appl. Phys., 41(22), 225404. DOI
13	Berrabah, H.M., Tounsi, A., Semmah, A. and Adda Bedia, E.A. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., Int. J., 48(3), 351-365. DOI
14	Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15(6), 671-703. DOI
15	Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104. DOI ScienceOn
16	Boumia, L., Zidour, M., Benzair, A. and Tounsi, A. (2014), "A Timoshenko beam model for vibration analysis of chiral single-walled carbon nanotubes", Physica E, 59, 186-191. DOI
17	Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33. DOI
18	El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. DOI ScienceOn
19	Bouremana, M., Houari, M.S.A., Tounsi, A., Kaci, A. and Adda Bedia, E.A. (2013), "A new first shear deformation beam theory based on neutral surface position for functionally graded beams", Steel Compos. Struct., Int. J., 15(5), 467-479. DOI ScienceOn
20	Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Methods, 11(6), 1350082. DOI
21	Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420. DOI
22	Eringen, A.C. (1967), "Theory of micropolar plates", Z. Angew. Math. Phys., 18, 12-30. DOI
23	Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. DOI
24	Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. DOI
25	Fekrar, A., El Meiche, N., Bessaim, A., Tounsi, A. and Adda Bedia, E.A. (2012), "Buckling analysis of functionally graded hybrid composite plates using a new four variable refined plate theory", Steel Compos. Struct., Int. J., 13(1), 91-107. DOI ScienceOn
26	Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49(4), 795-810. DOI
27	Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140(2), 374-383. DOI
28	Gafour, Y., Zidour, M., Tounsi, A., Heireche, H. and Semmah, A. (2013), "Sound wave propagation in zigzag double-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory", Physica E, 48, 118-123. DOI ScienceOn
29	Gurtin, M.E., Weissmuller, J. and Larche, F. (1998), "A general theory of curved deformable interfaces in solids at equilibrium", Philos. Mag. A, 78(5), 1093-1109. DOI
30	Harik, V.M. and Salas, M.D. (2003), Trends in Nanoscale Mechanics, Analysis of Nanostructured Materials and Multiscale Modeling, Kluwer Academic Publishers.
31	Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Adda Bedia, E.A. (2008a), "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity", Physica E., 40(8), 2791-2799. DOI
32	Heireche, H., Tounsi, A. and Benzair, A. (2008b), "Scale effect on wave propagation of double-walled carbon nanotubes with initial axial loading", Nanotechnology, 19, 185703. DOI
33	Heireche, H., Tounsi, A., Benzair, A. and Mechab, I. (2008c), "Sound wave propagation in single - carbon nanotubes with initial axial stress", J. Appl. Phys., 104, 014301. DOI ScienceOn
34	Hemmatnezhad, M. and Ansari, R. (2013), "Finite element formulation for the free vibration analysis of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory", J. Theor. Appl. Phys., 7, 1-10. DOI
35	Levinson, M. (1981), "A new rectangular beam theory", J. Sound Vib., 74(1), 81. DOI
36	Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111. DOI
37	Janghorban, M. and Zare, A. (2011), "Free vibration analysis of functionally graded carbon nanotubes with variable thickness by differential quadrature method", Physica E, 43(9), 1602-1604. DOI
38	Klouche Djedid, I., Benachour, A., Houari, M.S.A., Tounsi, A. and Ameur, M. (2014), "A n-order four variable refined theory for bending and free vibration of functionally graded plates", Steel Compos. Struct., Int. J., 17(1), 21-46. DOI
39	Lim, C.W. and Wang, C.M. (2007), "Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams", J. Appl. Phys., 101, 054312. DOI
40	Lu, P., Lee, H.P., Lu, C. and Zhang, P.Q. (2007), "Application of nonlocal beam models for carbon nanotubes", Int. J. Solids Struct., 44(16), 5289-5300. DOI
41	Maachou, M., Zidour, M., Baghdadi, H., Ziane, N. and Tounsi, A. (2011), "A nonlocal Levinson beam model for free vibration analysis of zigzag single-walled carbon nanotubes including thermal effects", Solid State Commun., 151(20), 1467-1471. DOI ScienceOn
42	Mahi, A., Adda Bedia, E.A., Tounsi, A. and Mechab, I. (2010), "An analytical method for temperaturedependent free vibration analysis of functionally graded beams with general boundary conditions", Compos. Struct., 92(8), 1877-1887. DOI ScienceOn
43	Murmu, T. and Pradhan, S.C. (2009a), "Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM", Physica E, 41(7), 1232-1239. DOI
44	Menaa, R., Tounsi, A., Mouaici, F., Mechab, I., Zidi, M. and Adda Bedia, E.A. (2012), "Analytical solutions for static shear correction factor of functionally graded rectangular beams", Mech. Adv. Mater. Struct., 19(8), 641-652. DOI
45	Mukherjee, S. and Aluru, N.R. (2006), "Applications in micro- and nanoelectromechanical systems", Engrg. Anal. Bound. Elem. 30, 909. DOI
46	Murmu, T. and Adhikari, S. (2012), "Non local elasticity based vibration of initially pre-stressed coupled nanobeam systems", Eur. J. Mechanics A-Solids, 34, 52-62. DOI
47	Murmu, T. and Pradhan, S.C. (2009b), "Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Comput. Mater. Sci., 46(4), 854-859. DOI
48	Mustapha, K.B. and Zhong, Z.W. (2010a), "The thermo-mechanical vibration of a single-walled carbon nanotube studied using the Bubnov-Galerkin method", Physica E., 43(1), 375-381. DOI
49	Mustapha, K.B. and Zhong, Z.W. (2010b), "Free transverse vibration of an axially loaded non-prismatic single-walled carbon nanotube embedded in a two-parameter elastic medium", Comput. Mater. Sci., 50(2), 742-751. DOI
50	Naceri, M., Zidour, M., Semmah, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2011), "Sound wave propagation in armchair single walled carbon nanotubes under thermal environment", J. Appl. Phys., 110, 124322. DOI ScienceOn
51	Pijaudier-Cabot, G. and Bazant, Z. (1987), "Nonlocal damage theory", ASCE J. Eng. Mech., 113(10), 1512-1533. DOI
52	Narendar, S. and Gopalakrishnan, S. (2011a), "Critical buckling temperature of single-walled carbon nanotubes embedded in a one-parameter elastic medium based on nonlocal continuum mechanics", Physica E, 43(6), 1185-1191. DOI
53	Narendar, S. and Gopalakrishnan, S. (2011b), "Nonlocal wave propagation in rotating nanotube", Results Phys., 1(1), 17-25. DOI
54	Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41(3-5), 305-312. DOI
55	Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", ASME J. Appl. Mech., 51(4), 745-752. DOI
56	Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288. DOI
57	Reddy, J.N. and Pang, S.D. (2008), "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103, 023511. DOI
58	Roque, C.M.C., Ferreira, A.J.M. and Reddy, J.N. (2011), "Analysis of Timoshenko nanobeams with a nonlocal formulation and meshless method", Int. J. Eng. Sci., 49(9), 976-984. DOI
59	Saidi, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory", Steel Compos. Struct., Int. J., 15, 221-245. DOI ScienceOn
60	Sallai, B.O., Tounsi, A., Mechab, I., Bachir Bouiadjra, M., Meradjah, M. and Adda Bedia, E.A. (2009), "A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams", Comput. Mater. Sci., 44(4), 1344-1350. DOI
61	Tounsi, A., Heireche, H., Berrabah, H.M., Benzair, A. and Boumia, L. (2008), "Effect of small size on wave propagation in double-walled carbon nanotubes under temperature field", J. Appl. Phys., 104, 104301. DOI
62	Semmah, A., Tounsi, A., Zidour, M., Heireche, H. and Naceri, M. (2014), "Effect of chirality on critical buckling temperature of a zigzag single-walled carbon nanotubes using nonlocal continuum theory", Fullerenes, Nanotubes and Carbon Nanostructures, 23(6), 518-522. DOI
63	Song, J., Shen, J. and Li, X.F. (2010), "Effects of initial axial stress on waves propagating in carbon nanotubes using a generalized nonlocal model", Comput. Mater. Sci., 49(3), 518-523. DOI
64	Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. DOI
65	Tounsi, A, Semmah, A. and Bousahla, A.A. (2013a), "Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory", ASCE J. Nanomech. Micromech., 3(3), 37-42. DOI
66	Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013b), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11. DOI ScienceOn
67	Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013c), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. DOI
68	Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98, 124301. DOI
69	Wang, Q., Varadan, V.K. and Quek, S.T. (2006), "Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models", Phys Lett A, 357(2), 130-135. DOI
70	Wang, Q. and Liew, K.M. (2007), "Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures", Phys Lett A, 363(3), 236-242. DOI
71	Yaghoobi, H. and Fereidoon, A. (2014), "Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: An assessment of a simple refined nth-order shear deformation theory", Compos.: Part B, 62, 54-64. DOI
72	Yaghoobi, H. and Torabi, M. (2013a), "Post-buckling and nonlinear free vibration analysis of geometrically imperfect functionally graded beams resting on nonlinear elastic foundation", Appl. Math. Model., 37(18-19), 8324-8340. DOI
73	Yaghoobi, H. and Torabi, M. (2013b), "Exact solution for thermal buckling of functionally graded plates resting on elastic foundations with various boundary conditions", J. Therm. Stresses, 36(9), 869-894. DOI
74	Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: An analytical approach", Meccanica, 48(8), 2019-2035. DOI ScienceOn
75	Yang, F., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solids Struct., 39(10), 2731-2743. DOI
76	Yoon, J., Ru, C.Q. and Mioduchowski, A. (2003), "Vibration of an embedded multiwall carbon nanotube", Compos. Sci. Technol., 63(11), 1533-1542. DOI
77	Zhang, Y.Q., Liu, G.R. and Wang, J.S. (2004), "Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression", Phys. Rev. B., 70, 205430. DOI ScienceOn
78	Zhang, Y.Q., Liu, G.R. and Han, X. (2006), "Effect of small length scale on elastic buckling of multi-walled carbon nanotubes under radial pressure", Phys. Lett. A, 349(5), 370-376. DOI
79	Zhang, Y., Liu, G. and Han, X. (2005a), "Transverse vibrations of double-walled carbon nanotubes under compressive axial load", Phys. Lett. A., 340(1-4), 258-66. DOI ScienceOn
80	Zhang, Y.Q., Liu, G.R. and Xie, X.Y. (2005b), "Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity", Phys. Rev. B., 71, 195404. DOI ScienceOn
81	Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. DOI
82	Zidour, M., Benrahou, K.H., Semmah, A., Naceri, M., Belhadj, H.A., Bakhti, K. and Tounsi, A. (2012), "The thermal effect on vibration of zigzag single walled carbon nanotubes using nonlocal Timoshenko beam theory", Comput. Mater. Sci., 51(1), 252-260. DOI ScienceOn
83	Zidour, M., Daouadji, T.H., Benrahou, K.H., Tounsi, A., Adda Bedia, E.A. and Hadji, L. (2014), "Buckling analysis of chiral single-walled carbon nanotubes by using the nonlocal Timoshenko beam theory", Mech. Compos. Mater., 50(1), 95-104. DOI

9	Farzad Ebrahimi. (2016) Applied Physics A A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment / 122 (9)
1	K. Bouakkaz. (2016) Wind and Structures An analytical method for free vibration analysis of functionally graded sandwich beams / 23 (1) , 59
2	Farzad Ebrahimi. (2016) Advances in nano research An exact solution for buckling analysis of embedded piezo-electro-magnetically actuated nanoscale beams / 4 (2) , 65
3	Bachir Bouderba. (2016) Structural Engineering and Mechanics Thermal stability of functionally graded sandwich plates using a simple shear deformation theory / 58 (3) , 397
	Li Li. (2018) Composite Structures Nonlinear bending of a two-dimensionally functionally graded beam / 184 , 1049
	Mohammad Mahinzare. (2017) Microsystem Technologies Vibrational investigation of the spinning bi-dimensional functionally graded (2-FGM) micro plate subjected to thermal load in thermal environment /
3	Sidi Mohamed El-Hassar. (2016) Geomechanics and Engineering Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory / 10 (3) , 357
7	Hasti Hayati. (2017) Microsystem Technologies Coupled twist–bending static and dynamic behavior of a curved single-walled carbon nanotube based on nonlocal theory / 23 (7) , 2393
	Mohammad Reza Barati. (2017) Composite Structures A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate / 168 , 885
3	Yaghoub Tadi Beni. (2017) Journal of Low Frequency Noise, Vibration and Active Control Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality / 36 (3) , 277
4	A. Mirafzal. (2017) Applied Physics A Dynamic characteristics of temperature-dependent viscoelastic FG nanobeams subjected to 2D-magnetic field under periodic loading / 123 (4)
3	Thanh-Huong Trinh. (2016) Structural Engineering and Mechanics Post-buckling responses of elastoplastic FGM beams on nonlinear elastic foundation / 58 (3) , 515
	Korosh Khorshidi. (2016) International Journal of Mechanical Sciences Buckling analysis of functionally graded rectangular nano-plate based on nonlocal exponential shear deformation theory / 113 , 94
10	Farzad Ebrahimi. (2016) Applied Physics A On nonlocal characteristics of curved inhomogeneous Euler–Bernoulli nanobeams under different temperature distributions / 122 (10)
4	Abdelbaki Chikh. (2016) Structural Engineering and Mechanics Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory / 57 (4) , 617
5	S.H. Tagrara. (2015) Steel and Composite Structures On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams / 19 (5) , 1259
11	Farzad Ebrahimi. (2016) Applied Physics A Dynamic modeling of smart shear-deformable heterogeneous piezoelectric nanobeams resting on Winkler–Pasternak foundation / 122 (11)
10	Mohammad Arefi. (2017) The European Physical Journal Plus Size-dependent electro-magneto-elastic bending analyses of the shear-deformable axisymmetric functionally graded circular nanoplates / 132 (10)
4	Ismahene Belkorissat. (2015) Steel and Composite Structures On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model / 18 (4) , 1063
1	Kaddour Rakrak. (2016) Advances in nano research Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory / 4 (1) , 31
	Li Li. (2018) Composite Structures Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature / 184 , 1177
3	Habib Hebali. (2016) Steel and Composite Structures A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates / 22 (3) , 473
11	Farzad Ebrahimi. (2016) Applied Physics A Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams / 122 (11)
6	Lazreg Hadji. (2016) Wind and Structures Bending analysis of FGM plates using a sinusoidal shear deformation theory / 23 (6) , 543
	Fahimeh Mehralian. (2017) Physica B: Condensed Matter Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes / 514 , 61
1	Farzad Ebrahimi. (2017) Applied Physics A Vibration analysis of viscoelastic inhomogeneous nanobeams incorporating surface and thermal effects / 123 (1)
2	Javad Ehyaei. (2016) Advances in nano research Nonlocal vibration analysis of FG nano beams with different boundary conditions / 4 (2) , 85
4	Awda Chemi. (2015) Advances in nano research Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity / 3 (4) , 193
	M. H. Shojaeefard. (2018) Microsystem Technologies Free vibration and critical angular velocity of a rotating variable thickness two-directional FG circular microplate /
4	Abdelouahed Tounsi. (2016) Structural Engineering and Mechanics A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate / 60 (4) , 547
2	Hassen Ait Atmane. (2015) Steel and Composite Structures A computational shear displacement model for vibrational analysis of functionally graded beams with porosities / 19 (2) , 369
2	Fatima Bounouara. (2016) Steel and Composite Structures A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation / 20 (2) , 227
	Javad Marzbanrad. (2017) Microsystem Technologies Size-dependent hygro–thermo–electro–mechanical vibration analysis of functionally graded piezoelectric nanobeams resting on Winkler–Pasternak foundation undergoing preload and magnetic field /
4	Youcef Beldjelili. (2016) Smart Structures and Systems Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory / 18 (4) , 755
1	F. Chattibi. (2015) Steel and Composite Structures Thermomechanical effects on the bending of antisymmetric cross-ply composite plates using a four variable sinusoidal theory / 19 (1) , 93
9	Dharmendra Tripathi. (2016) Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine Peristaltic transport of bi-viscosity fluids through a curved tube: A mathematical model for intestinal flow / 230 (9) , 817
	Farzad Ebrahimi. (2017) Journal of Vibration and Control Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory / , 107754631771153
1	Merbouha Barka. (2016) Steel and Composite Structures Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation / 22 (1) , 91
7	Majid Ghadiri. (2016) Applied Physics A Influence of thermal and surface effects on vibration behavior of nonlocal rotating Timoshenko nanobeam / 122 (7)
5	Kada Draiche. (2016) Geomechanics and Engineering A refined theory with stretching effect for the flexure analysis of laminated composite plates / 11 (5) , 671
	Huu-Tai Thai. (2017) Composite Structures A review of continuum mechanics models for size-dependent analysis of beams and plates / 177 , 196
	Navvab Shafiei. (2017) Composite Structures Nonlinear thermal buckling of axially functionally graded micro and nanobeams / 168 , 428
	Li Li. (2017) International Journal of Mechanical Sciences Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects / 120 , 159
6	Farzad Ebrahimi. (2016) Smart Structures and Systems Thermal effects on nonlocal vibrational characteristics of nanobeams with non-ideal boundary conditions / 18 (6) , 1087
4	Djamel Ould Youcef. (2015) Advances in nano research On the bending and stability of nanowire using various HSDTs / 3 (4) , 177
5	Mama Ahouel. (2016) Steel and Composite Structures Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept / 20 (5) , 963
	M.A. Eltaher. (2016) Composite Structures Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs / 153 , 902
6	H Bakhshi Khaniki. (2017) Materials Research Express Buckling analysis of tapered nanobeams using nonlocal strain gradient theory and a generalized differential quadrature method / 4 (6) , 065003
5	Ahmed Boukhari. (2016) Structural Engineering and Mechanics An efficient shear deformation theory for wave propagation of functionally graded material plates / 57 (5) , 837
5	Farzad Ebrahimi. (2018) Mechanics of Advanced Materials and Structures Effect of three-parameter viscoelastic medium on vibration behavior of temperature-dependent non-homogeneous viscoelastic nanobeams in a hygro-thermal environment / 25 (5) , 361
2	Abdelmoumen Anis Bousahla. (2016) Structural Engineering and Mechanics On thermal stability of plates with functionally graded coefficient of thermal expansion / 60 (2) , 313
	H. Bakhshi Khaniki. (2018) Alexandria Engineering Journal Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method /
4	Fethi Mouaici. (2016) Wind and Structures Effect of porosity on vibrational characteristics of non-homogeneous plates using hyperbolic shear deformation theory / 22 (4) , 429
12	Farzad Ebrahimi. (2017) The European Physical Journal Plus Dynamic modeling of porous heterogeneous micro/nanobeams / 132 (12)
4	Khadidja Aissani. (2015) Structural Engineering and Mechanics A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium / 55 (4) , 743
12	Farzad Ebrahimi. (2016) Mechanics of Advanced Materials and Structures Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams / 23 (12) , 1379
3	Farzad Ebrahimi. (2016) Advances in nano research Analytical solution for nonlocal buckling characteristics of higher-order inhomogeneous nanosize beams embedded in elastic medium / 4 (3) , 229
6	Seref D. Akbas. (2016) Smart Structures and Systems Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium / 18 (6) , 1125
1	Majid Azimi. (2017) Applied Physics A Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam / 123 (1)
10	Farzad Ebrahimi. (2016) Smart Materials and Structures Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory / 25 (10) , 105014
4	Boumediene Kheroubi. (2016) Advances in nano research A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams / 4 (4) , 251
15	Farzad Ebrahimi. (2017) Journal of Intelligent Material Systems and Structures Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams / 28 (15) , 2007
	M. Kamali. (2017) Microsystem Technologies Parametric excitation analysis of a piezoelectric-nanotube conveying fluid under multi-physics field /
5	M. Arefi. (2017) Applied Physics A Application of nonlocal strain gradient theory and various shear deformation theories to nonlinear vibration analysis of sandwich nano-beam with FG-CNTRCs face-sheets in electro-thermal environment / 123 (5)
3	Mustapha Meradjah. (2015) Steel and Composite Structures A new higher order shear and normal deformation theory for functionally graded beams / 18 (3) , 793
	M. Mohammadimehr. (2017) International Journal of Smart and Nano Materials Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM / , 1
3	L. Hadji. (2015) Wind and Structures Influence of the porosities on the free vibration of FGM beams / 21 (3) , 273
2	O. Rahmani. (2018) The European Physical Journal Plus Dynamic response of a single-walled carbon nanotube under a moving harmonic load by considering modified nonlocal elasticity theory / 133 (2)
2	Aicha Bessaim. (2015) Structural Engineering and Mechanics A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates / 56 (2) , 223
3	Misagh Zarepour. (2017) Applied Physics A Free vibration investigation of nano mass sensor using differential transformation method / 123 (3)
12	Majid Ghadiri. (2016) Applied Physics A Thermo-mechanical analysis of FG nanobeam with attached tip mass: an exact solution / 122 (12)
2	Mohammed Sid Ahmed Houari. (2016) Steel and Composite Structures A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates / 22 (2) , 257
4	Benoumrane Sallai. (2015) Steel and Composite Structures Analytical solution for bending analysis of functionally graded beam / 19 (4) , 829
	Farzad Ebrahimi. (2017) Composite Structures Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory / 159 , 433
3	Ali Jamalpoor. (2017) Applied Physics A Vibration analysis of bonded double-FGM viscoelastic nanoplate systems based on a modified strain gradient theory incorporating surface effects / 123 (3)
3	Salima Abdelbari. (2016) Wind and Structures An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations / 22 (3) , 329
6	D.P. Zhang. (2017) Brazilian Journal of Physics Effect of Longitudinal Magnetic Field on Vibration Characteristics of Single-Walled Carbon Nanotubes in a Viscoelastic Medium / 47 (6) , 640
10	Farzad Ebrahimy. (2016) Applied Physics A Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates / 122 (10)
4	Amine Zemri. (2015) Structural Engineering and Mechanics A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory / 54 (4) , 693
6	Fouad Bourada. (2016) Steel and Composite Structures Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory / 21 (6) , 1287
11	Farzad Ebrahimi. (2017) Journal of Intelligent Material Systems and Structures Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field / 28 (11) , 1472
2	Hayat Saidi. (2016) Geomechanics and Engineering A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations / 11 (2) , 289
6	A. Chemi. (2018) Mechanics of Composite Materials Critical Buckling Load of Chiral Double-Walled Carbon Nanotubes Embedded in an Elastic Medium / 53 (6) , 827
11	Farzad Ebrahimi. (2016) The European Physical Journal Plus Nonlocal thermo-elastic wave propagation in temperature-dependent embedded small-scaled nonhomogeneous beams / 131 (11)
	Farzad Ebrahimi. (2017) Mechanics of Advanced Materials and Structures A modified nonlocal couple stress-based beam model for vibration analysis of higher-order FG nanobeams / , 1
5	Seyed Sajad Mirjavadi. (2017) Applied Physics A On size-dependent free vibration and thermal buckling of axially functionally graded nanobeams in thermal environment / 123 (5)
5-6	M.A. Eltaher. (2016) Applied Mathematical Modelling A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams / 40 (5-6) , 4109
9	M. A. Hamed. (2016) Applied Physics A Free vibration of symmetric and sigmoid functionally graded nanobeams / 122 (9)
	Navvab Shafiei. (2017) Aerospace Science and Technology Buckling analysis on the bi-dimensional functionally graded porous tapered nano-/micro-scale beams / 66 , 1
5	Elyas Shivanian. (2017) Applied Physics A Influence of size effect on flapwise vibration behavior of rotary microbeam and its analysis through spectral meshless radial point interpolation / 123 (5)
1435-5663	(2019) Engineering with Computers On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell / (1435-5663)
2008-6695	(2019) International Journal of Advanced Structural Engineering Modal participation of fixed–fixed single-walled carbon nanotube with vacancies / (2008-6695)
2041-2983	Behrouz Karami. (2019) Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory / (2041-2983) , 095440621875645
1432-1858	(2018) Microsystem Technologies Buckling of magneto-electro-hygro-thermal piezoelectric nanoplates system embedded in a visco-Pasternak medium based on nonlocal theory / (1432-1858)
1661-9897	(2018) Journal of Nano Research Vibration Analysis of Nano Beam Using Differential Transform Method Including Thermal Effect / 54 (1661-9897) , 1
8	(2018) Journal of the Brazilian Society of Mechanical Sciences and Engineering Forced vibration analysis of cracked nanobeams / 40 (8)
5	(2018) The European Physical Journal Plus Free vibration analysis of a piezoelectric curved sandwich nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal elasticity theories / 133 (5)
1661-9897	(2018) Journal of Nano Research Thermal and Small-Scale Effects on Vibration of Embedded Armchair Single-Walled Carbon Nanotubes / 51 (1661-9897) , 24
10	(2018) Journal of Vibration and Control Nonlocal strain gradient theory for damping vibration analysis of viscoelastic inhomogeneous nano-scale beams embedded in visco-Pasternak foundation / 24 (10) , 2080
1539-7742	(2019) Mechanics Based Design of Structures and Machines A novel approach for nonlinear bending response of macro- and nanoplates with irregular variable thickness under nonuniform loading in thermal environment / (1539-7742) , 1
2	(2017) Smart structures and systems A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams / 19 (2) , 115
5	(2015) Steel & Composite structures : an international journal A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates / 22 (5) , 975
1	(2017) Steel & Composite structures : an international journal Buckling analysis of functionally graded truncated conical shells under external displacement-dependent pressure / 23 (1) , 1
1	(2015) Geomechanics & engineering A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation / 12 (1) , 9
3	(2015) Steel & Composite structures : an international journal A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation / 23 (3) , 317
1	(2017) Advances in materials research : AMR Bending and stability analysis of size-dependent compositionally graded Timoshenko nanobeams with porosities / 6 (1) , 45
2	(2015) Structural engineering and mechanics : An international journal Wave propagation in functionally graded beams using various higher-order shear deformation beams theories / 62 (2) , 143
4	(2017) Smart structures and systems Analysis of functionally graded plates using a sinusoidal shear deformation theory / 19 (4) , 441
4	(2017) Structural engineering and mechanics : An international journal A novel and simple HSDT for thermal buckling response of functionally graded sandwich plates / 62 (4) , 401
6	(2017) Structural engineering and mechanics : An international journal A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams / 62 (6) , 695
6	(2015) Smart structures and systems Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory / 19 (6) , 601
5	(2017) Steel & Composite structures : an international journal A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates / 24 (5) , 569
5	(2017) Steel & Composite structures : an international journal Free vibrations of laminated composite plates using a novel four variable refined plate theory / 24 (5) , 603
2	(2015) Computers & concrete Dynamic bending response of SWCNT reinforced composite plates subjected to hygro-thermo-mechanical loading / 20 (2) , 229
3	(2015) Smart structures and systems Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory / 20 (3) , 369
5	(2015) Structural engineering and mechanics : An international journal A simple analytical approach for thermal buckling of thick functionally graded sandwich plates / 63 (5) , 585
3	(2015) Earthquakes and structures An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities / 13 (3) , 255
3	(2015) Geomechanics & engineering A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates / 13 (3) , 385
2	(2015) Steel & Composite structures : an international journal A new and simple HSDT for thermal stability analysis of FG sandwich plates / 25 (2) , 157
2	(2015) Structural engineering and mechanics : An international journal A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams / 64 (2) , 145
4	(2017) Smart structures and systems Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory / 20 (4) , 509
3	(2015) Steel & Composite structures : an international journal An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates / 25 (3) , 257
3	(2017) Steel & Composite structures : an international journal Effects of triaxial magnetic field on the anisotropic nanoplates / 25 (3) , 361
4	(2017) Steel & Composite structures : an international journal A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate / 25 (4) , 389
5	(2015) Earthquakes and structures A simple quasi-3D sinusoidal shear deformation theory with stretching effect for carbon nanotube-reinforced composite beams resting on elastic foundation / 13 (5) , 509
4	(2015) Structural engineering and mechanics : An international journal A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates / 64 (4) , 391
6	(2015) Structural engineering and mechanics : An international journal Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory / 64 (6) , 683
6	(2015) Structural engineering and mechanics : An international journal A new quasi-3D HSDT for buckling and vibration of FG plate / 64 (6) , 737
6	(2015) Steel & Composite structures : an international journal An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions / 25 (6) , 693
6	(2015) Steel & Composite structures : an international journal A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations / 25 (6) , 717
6	(2015) Steel & Composite structures : an international journal An original HSDT for free vibration analysis of functionally graded plates / 25 (6) , 735
2	(2015) Geomechanics & engineering Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory / 16 (2) , 141
1	(2018) Structural engineering and mechanics : An international journal A nonlocal strain gradient theory for nonlinear free and forced vibration of embedded thick FG double layered nanoplates / 68 (1) , 103
5	(2015) Structural engineering and mechanics : An international journal Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory / 65 (5) , 621
1	(2015) Advances in materials research : AMR Thermal stability analysis of temperature dependent inhomogeneous size-dependent nano-scale beams / 7 (1) , 1
1	(2015) Advances in nano research Forced vibration analysis of cracked functionally graded microbeams / 6 (1) , 39
6	(2015) Steel & Composite structures : an international journal Post-buckling responses of a laminated composite beam / 26 (6) , 733
1	(2018) Steel & Composite structures : an international journal A novel four variable refined plate theory for wave propagation in functionally graded material plates / 27 (1) , 109
1	(2015) Structural engineering and mechanics : An international journal Improved HSDT accounting for effect of thickness stretching in advanced composite plates / 66 (1) , 61
4	(2018) Computers & concrete Vibration and instability analysis of pipes reinforced by SiO<SUB>2</SUB> nanoparticles considering agglomeration effects / 21 (4) , 431
2	(2015) Steel & Composite structures : an international journal Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles / 27 (2) , 201
2	(2015) Structural engineering and mechanics : An international journal Three dimensional dynamic response of functionally graded nanoplates under a moving load / 66 (2) , 249
4	(2015) Smart structures and systems A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory / 21 (4) , 397
6	(2015) Geomechanics & engineering Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates / 14 (6) , 519
3	(2018) Steel & Composite structures : an international journal Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory / 27 (3) , 311
3	(2018) Steel & Composite structures : an international journal Size dependent bending analysis of micro/nano sandwich structures based on a nonlocal high order theory / 27 (3) , 371
3	(2015) Structural engineering and mechanics : An international journal Free vibration of FGM plates with porosity by a shear deformation theory with four variables / 66 (3) , 353
1	(2015) Geomechanics & engineering Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory / 15 (1) , 711
5	(2018) Computers & concrete Vibration and instability of nanocomposite pipes conveying fluid mixed by nanoparticles resting on viscoelastic foundation / 21 (5) , 569
4	(2015) Steel & Composite structures : an international journal Mathematical modeling of smart nanoparticles-reinforced concrete foundations: Vibration analysis / 27 (4) , 465
4	(2018) Steel & Composite structures : an international journal Nonlocal free vibration analysis of a doubly curved piezoelectric nano shell / 27 (4) , 479
4	(2018) Structural engineering and mechanics : An international journal Three dimensional finite elements modeling of FGM plate bending using UMAT / 66 (4) , 487
5	(2015) Steel & Composite structures : an international journal A novel four-unknown quasi-3D shear deformation theory for functionally graded plates / 27 (5) , 599
2	(2015) Advances in nano research A new nonlocal HSDT for analysis of stability of single layer graphene sheet / 6 (2) , 147
6	(2018) Structural engineering and mechanics : An international journal Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions / 66 (6) , 761
6	(2018) Structural engineering and mechanics : An international journal A new quasi-3D higher shear deformation theory for vibration of functionally graded carbon nanotube-reinforced composite beams resting on elastic foundation / 66 (6) , 771
1	(2015) Steel & Composite structures : an international journal Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter / 28 (1) , 13
1	(2015) Steel & Composite structures : an international journal A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates / 28 (1) , 99
1	(2015) Structural engineering and mechanics : An international journal Dynamic stability of nanocomposite Mindlin pipes conveying pulsating fluid flow subjected to magnetic field / 67 (1) , 21
1	(2018) Computers & concrete Technical and economical assessment of applying silica nanoparticles for construction of concrete structures / 22 (1) , 117
1	(2015) Smart structures and systems Size-dependent free vibration and dynamic analyses of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory / 22 (1) , 27
1	(2015) Smart structures and systems Size-dependent free vibration and dynamic analyses of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory / 22 (1) , 27
3	(2015) Steel & Composite structures : an international journal Forced vibration response in nanocomposite cylindrical shells - Based on strain gradient beam theory / 28 (3) , 381
3	(2015) Structural engineering and mechanics : An international journal Single variable shear deformation model for bending analysis of thick beams / 67 (3) , 291
3	(2015) Earthquakes and structures Seismic analysis of AL<SUB>2</SUB>O<SUB>3</SUB> nanoparticles-reinforced concrete plates based on sinusoidal shear deformation theory / 15 (3) , 285
3	(2018) Structural engineering and mechanics : An international journal Numerical study for vibration response of concrete beams reinforced by nanoparticles / 67 (3) , 311
5	(2015) Structural engineering and mechanics : An international journal Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix / 67 (5) , 517
5	(2018) Structural engineering and mechanics : An international journal Effect of homogenization models on stress analysis of functionally graded plates / 67 (5) , 527
6	(2015) Steel & Composite structures : an international journal Free vibration analysis of functionally graded cylindrical shells with different shell theories using semi-analytical method / 28 (6) , 735
3	(2015) Smart structures and systems A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates / 22 (3) , 303
3	(2015) Smart structures and systems Dynamic buckling of smart sandwich beam subjected to electric field based on hyperbolic piezoelasticity theory / 22 (3) , 327
4	(2015) Earthquakes and structures Dynamic analysis of immersion concrete pipes in water subjected to earthquake load using mathematical methods / 15 (4) , 361
4	(2018) Earthquakes and structures Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory / 15 (4) , 369
4	(2015) Wind & structures An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory / 27 (4) , 247
4	(2015) Wind & structures A refined quasi-3D hybrid-type higher order shear deformation theory for bending and Free vibration analysis of advanced composites beams / 27 (4) , 269
5	(2015) Smart structures and systems Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory / 22 (5) , 527
5	(2018) Wind & structures Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation / 27 (5) , 311
4	(2018) Advances in nano research A layerwise theory for buckling analysis of truncated conical shells reinforced by CNTs and carbon fibers integrated with piezoelectric layers in hygrothermal environment / 6 (4) , 299
4	(2018) Advances in nano research Finite strain nonlinear longitudinal vibration of nanorods / 6 (4) , 323
1	(2015) Steel & Composite structures : an international journal A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations / 30 (1) , 13
1	(2015) Earthquakes and structures Finite element solution of stress and flexural strength of functionally graded doubly curved sandwich shell panel / 16 (1) , 55
2	(2015) Structural engineering and mechanics : An international journal Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method / 69 (2) , 205
1	(2015) Wind & structures Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory / 28 (1) , 19
1	(2015) Wind & structures Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory / 28 (1) , 49
3	(2019) Structural engineering and mechanics : An international journal A novel refined shear deformation theory for the buckling analysis of thick isotropic plates / 69 (3) , 335
1	(2015) Advances in concrete construction Dynamic analysis of concrete column reinforced with Sio<SUB>2</SUB> nanoparticles subjected to blast load / 7 (1) , 51
2	(2015) Smart structures and systems Application of nonlocal elasticity theory on the wave propagation of flexoelectric functionally graded (FG) timoshenko nano-beams considering surface effects and residual surface stress / 23 (2) , 141
5	(2015) Structural engineering and mechanics : An international journal Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT / 69 (5) , 511
2	(2015) Advances in nano research Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT / 7 (2) , 89
6	(2015) Structural engineering and mechanics : An international journal Vibration analysis of different material distributions of functionally graded microbeam / 69 (6) , 637
3	(2015) Smart structures and systems Nonlocal strain gradient model for thermal stability of FG nanoplates integrated with piezoelectric layers / 23 (3) , 215
None	(2015) Journal of nano research Static and Dynamic Behavior of Nanotubes-Reinforced Sandwich Plates Using (FSDT) / 57 (None) , 117
None	(2015) Journal of nano research Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model / 57 (None) , 136
None	(2015) Journal of nano research Participation Factor and Vibration of Carbon Nanotube with Vacancies / 57 (None) , 158
5	(2015) European physical journal Plus Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency / 134 (5) , 214
3	(2019) Structural engineering and mechanics : An international journal Theoretical analysis of chirality and scale effects on critical buckling load of zigzag triple walled carbon nanotubes under axial compression embedded in polymeric matrix / 70 (3) , 269
3	(2019) Structural engineering and mechanics : An international journal A simple HSDT for bending, buckling and dynamic behavior of laminated composite plates / 70 (3) , 325
3	(2019) Advances in aircraft and spacecraft science Improvement of thermal buckling response of FG-CNT reinforced composite beams with temperature-dependent material properties resting on elastic foundations / 6 (3) , 207
3	(2015) Advances in nano research Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT / 7 (3) , 191
4	(2015) Structural engineering and mechanics : An international journal Influence of shear preload on wave propagation in small-scale plates with nanofibers / 70 (4) , 407
2	(2015) Geomechanics & engineering The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate / 18 (2) , 161
5	(2015) Steel & Composite structures : an international journal A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation / 31 (5) , 503
7	(2019) European physical journal Plus Stability analysis of embedded graphene platelets reinforced composite plates in thermal environment / 134 (7) , 349
7	(2015) European physical journal Plus Dynamic analysis of multi-layered composite beams reinforced with graphene platelets resting on two-parameter viscoelastic foundation / 134 (7) , 339
16	(2015) Proceedings of the Institution of Mechanical Engineers. Part C : Journal of mechanical engineering science Vibration characteristics of zigzag and chiral functionally graded material rotating carbon nanotubes sandwich with ring supports / 233 (16) , 5763
5	(2019) Advances in nano research Vibration analysis of nonlocal porous nanobeams made of functionally graded material / 7 (5) , 351
10	(2019) European physical journal Plus Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets / 134 (10) , 508
1	(2015) Structural engineering and mechanics : An international journal Frequency response of initially deflected nanotubes conveying fluid via a nonlinear NSGT model / 72 (1) , 71
4	(2015) Computers & concrete Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT / 24 (4) , 347
None	(2015) Journal of nano research A Non-Linear Spring Model for Predicting Modal Behavior of Oscillators Built from Double Walled Carbon Nanotubes / 60 (None) , 21
6	(2015) Advances in nano research The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory / 7 (6) , 443
5	(2019) Structural engineering and mechanics : An international journal A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates / 72 (5) , 653
6	(2015) Wind & structures On the modeling of dynamic behavior of composite plates using a simple nth-HSDT / 29 (6) , 371
None	(2015) Procedia structural integrity A refined of trigonometric shear deformation plate theory based on neutral surface position is proposed for static analysis of FGM plate. / 26 (None) , 129
1	(2020) Advances in nano research Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle / 8 (1) , 37
2	(2015) Advances in aircraft and spacecraft science Mechanical-hygro-thermal vibrations of functionally graded porous plates with nonlocal and strain gradient effects / 7 (2) , 169
1	(2015) Advances in nano research On transient hygrothermal vibration of embedded viscoelastic flexoelectric/piezoelectric nanobeams under magnetic loading / 8 (1) , 49
2	(2015) European physical journal Plus Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells / 135 (2) , 242
2	(2020) Smart structures and systems A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates / 25 (2) , 197
1	(2015) Advances in materials research : AMR A review of effects of partial dynamic loading on dynamic response of nonlocal functionally graded material beams / 9 (1) , 33
1	(2020) Structural monitoring and maintenance A numerical method for dynamic characteristics of nonlocal porous metal-ceramic plates under periodic dynamic loads / 7 (1) , 27
4	(2015) Microsystem technologies : sensors, actuators, systems integration Parametrically excited nonlinear dynamics and instability of double-walled nanobeams under thermo-magneto-mechanical loads / 26 (4) , 1121
2	(2020) International journal of applied and computational mathematics Computation of Non-isothermal Thermo-convective Micropolar Fluid Dynamics in a Hall MHD Generator System with Non-linear Distending Wall / 6 (2) , 42
1	(2020) Steel & Composite structures : an international journal An inclined FGM beam under a moving mass considering Coriolis and centrifugal accelerations / 35 (1) , 61
1	(2020) Structural engineering and mechanics : An international journal A refined HSDT for bending and dynamic analysis of FGM plates / 74 (1) , 105
3	(2015) Advances in nano research Investigation of microstructure and surface effects on vibrational characteristics of nanobeams based on nonlocal couple stress theory / 8 (3) , 191
3	(2015) Advances in nano research Bending analysis of magneto-electro piezoelectric nanobeams system under hygro-thermal loading / 8 (3) , 203
2	(2020) Structural engineering and mechanics : An international journal Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories / 74 (2) , 175
4	(2015) Smart structures and systems Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory / 25 (4) , 409
4	(2020) Steel & Composite structures : an international journal Stability of perforated nanobeams incorporating surface energy effects / 35 (4) , 555
6	(2015) Acta mechanica Buckling of carbon nanotube (CNT)-reinforced composite skew plates by the discrete singular convolution method / 231 (6) , 2565
5	(2015) Structural engineering and mechanics : An international journal A comprehensive review on the modeling of smart piezoelectric nanostructures / 74 (5) , 611
3	(2020) Coupled systems mechanics Vibration analysis of nonlocal strain gradient porous FG composite plates coupled by visco-elastic foundation based on DQM / 9 (3) , 201
3	(2015) Coupled systems mechanics Mixture rule for studding the environmental pollution reduction in concrete structures containing nanoparticles / 9 (3) , 281
3	(2015) Engineering with computers Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures / 36 (3) , 953
4	(2015) Mechanics based design of structures and machines Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory / 48 (4) , 480
18	(2015) Proceedings of the Institution of Mechanical Engineers. Part C : Journal of mechanical engineering science Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects / 234 (18) , 3667
6	(2015) Steel & Composite structures : an international journal Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes / 36 (6) , 643
4	(2015) Engineering with computers Wave dispersion characteristics of fluid-conveying magneto-electro-elastic nanotubes / 36 (4) , 1687
3	(2021) Steel & Composite structures : an international journal Buckling treatment of piezoelectric functionally graded graphene platelets micro plates / 38 (3) , 337
2	(2021) Waves in random and complex media A nonlocal strain gradient theory for vibration and flutter instability analysis in rotary SWCNT with conveying viscous fluid / 31 (2) , 305
1	(2015) International journal of computational materials science and engineering : IJCMSE Nonlinear free vibration analysis of a bi-directional functionally graded microbeam on nonlinear elastic foundation using modified couple stress theory / 10 (1) , 2150001
3	(2015) Advances in nano research Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory / 10 (3) , 281
7	(2015) Applied sciences Buckling Analysis of CNTRC Curved Sandwich Nanobeams in Thermal Environment / 11 (7) , 3250
2	(2015) International journal of computational materials science and engineering : IJCMSE Closed-form expressions for bending and buckling of functionally graded nanobeams by the Laplace transform / 10 (2) , 2150012
7	(2015) Archive of applied mechanics : Ingenieur-Archiv Applying Eringen’s nonlocal elasticity theory for analyzing the nonlinear free vibration of bidirectional functionally graded Euler-Bernoulli nanobeams / 91 (7) , 2957
4	(2015) Waves in random and complex media Wave dispersion of nanobeams incorporating stretching effect / 31 (4) , 639
1	(2015) Advances in nano research Mechanical analysis of bi-functionally graded sandwich nanobeams / 11 (1) , 55
2	(2021) Steel & Composite structures : an international journal Free vibration analysis of open-cell FG porous beams: analytical, numerical and ANN approaches / 40 (2) , 157
3	(2021) Steel & Composite structures : an international journal On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations / 40 (3) , 389
8	(2021) The journal of sandwich structures & materials Bending and buckling behaviors of heterogeneous temperature-dependent micro annular/circular porous sandwich plates integrated by FGPEM nano-Composite layers / 23 (8) , 3836
12	(2015) Journal of mechanical science and technology Nonlinear bending and free vibration analyses of metal-ceramic functionally graded plates by 2-D natural element method / 35 (12) , 5591
None	(2022) Thin-walled structures A review of size-dependent continuum mechanics models for micro- and nano-structures / 170 (None) , 108562