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http://dx.doi.org/10.12989/anr.2018.6.4.339

Critical buckling loads of carbon nanotube embedded in Kerr's medium  

Bensattalah, Tayeb (Universite Ibn Khaldoun)
Bouakkaz, Khaled (Laboratory of Materials et Hydrology, University of Sidi Bel Abbes)
Zidour, Mohamed (Universite Ibn Khaldoun)
Daouadji, Tahar Hassaine (Universite Ibn Khaldoun)
Publication Information
Advances in nano research / v.6, no.4, 2018 , pp. 339-356 More about this Journal
Abstract
In this article, the critical buckling of a single-walled carbon nanotube (SWCNT) embedded in Kerr's medium is studied. Based on the nonlocal continuum theory and the Euler-Bernoulli beam model. The governing equilibrium equations are acquired and solved for CNTs subjected to mechanical loads and embedded in Kerr's medium. Kerr-type model is employed to simulate the interaction of the (SWNT) with a surrounding elastic medium. A first time, a comparison with the available results is made, and another comparison between various models Winkler-type, Pasternak-type and Kerr-type is studied. Effects of nonlocal parameter and aspect ratio of length to diameter of nanobeam, as well as the foundation parameters on buckling of CNT are investigated. These results are important in the mechanical design considerations of nanocomposites based on carbon nanotubes.
Keywords
Kerr's medium; Euler-Bernoulli; buckling; carbon nanotubes; nanobeam;
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1 Bouderba, B., Houari, M.S.A. and Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., Int. J., 58(3), 397-422.   DOI
2 Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., Int. J., 66(1), 61-73.
3 Boukhari, A., AitAtmane, H., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., Int. J., 57(5), 837-859.   DOI
4 Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249.   DOI
5 Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423.   DOI
6 Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., Int. J., 18(4), 1063-1081.   DOI
7 Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017a), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., Int. J., 25(3), 257-270.
8 Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017b), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., Int. J., 62(6), 695-702.
9 Belmahi, S., Zidour, M., Meradjah, M., Bensattalah, T. and Dihaj, A. (2018), "Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix", Struct. Eng. Mech., Int. J., 67(5), 517-525.
10 Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431.   DOI
11 Chemi, A., Zidour, M., Heireche, H., Rakrak, K. and Bousahla, A.A. (2018), "Critical Buckling Load of Chiral Double-Walled Carbon Nanotubes Embedded in an Elastic Medium", Mech. Compos. Mater., 53(6), 827-836.   DOI
12 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. Meth., 11(6), 1350082.   DOI
13 Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., Int. J., 60(2), 313-335.
14 Chemi, A., Heireche, H., Zidour, M., Rakrak, K. and Bousahla, A.A. (2015), "Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity", Adv. Nano Res., Int. J., 3(4), 193-206.
15 Cherif, R.H., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, H. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14.   DOI
16 Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., Int. J., 19(3), 289-297.   DOI
17 Dihaj, A., Zidour, M., Meradjah, M., Rakrak, K., Heireche, H. and Chemi, A. (2018), "Free vibration analysis of chiral double-walled carbon nanotube embedded in an elastic medium using non-local elasticity theory and Euler Bernoulli beam model", Struct. Eng. Mech., Int. J., 65(3), 335-342.
18 Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., Int. J., 11(5), 671-690.   DOI
19 Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., Int. J., 19(6), 601-614.
20 Bensattalah, T., Daouadji, T.H., Zidour, M., Tounsi, A. and Bedia, E.A. (2016), "Investigation of thermal and chirality effects on vibration of single-walled carbon nanotubes embedded in a polymeric matrix using nonlocal elasticity theories", Mech. Compos. Mater., 52(4), 555-568.   DOI
21 Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., Int. J., 6(2), 147-162.
22 Fakhar, A. and Kolahchi, R. (2018), "Dynamic buckling of magnetorheological fluid integrated by viscopiezo- GPL reinforced plates", Int. J. Mech. Sci., 144, 788-799.   DOI
23 Ebrahimi, F. and Fardshad, R.E. (2018), "Modeling the size effect on vibration characteristics of functionally graded piezoelectric nanobeams based on Reddy's shear deformation beam theory", Adv. Nano Res., Int. J., 6(2), 113-133.
24 Ebrahimi, F. and Mahmoodi, F. (2018), "Vibration analysis of carbon nanotubes with multiple cracks in thermal environment", Adv. Nano Res., Int. J., 6(1), 57-80.
25 Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16.   DOI
26 Filonenko-Borodich, M.M. (1940), "Some approximate theories of elastic foundation", Uchenyie Zapiski Moskovkogo Gosudarstuennogo Universiteta Mekhanika, Moscow, Russia, 46, 3-18.
27 Fourn, H., Ait Atmane, H., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., Int. J., 27(1), 109-122.
28 Golabchi, H., Kolahchi, R. and Bidgoli, M.R. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concrete, Int. J., 21(4), 431-440.
29 Guessas, H., Zidour, M., Meradjah, M. and Tounsi, A. (2018), "The critical buckling load of reinforced nanocomposite porous plates", Struct. Eng. Mech., Int. J., 67(2), 115-123.
30 Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally graded-carbon nanotube-reinforced laminated plates/actuator based on sinusoidalvisco- piezoelasticity theories", J. Sandw. Struct. Mater., 1099636217720373.
31 Limkatanyu, S., Prachasaree, W., Damrongwiriyanupap, N., Kwon, M. and Jung, W. (2013), "Exact stiffness for beams on Kerr-Type foundation: the virtual force approach", J. Appl. Math.
32 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017d), "Wave propagation of embedded viscoelastic FG-CNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545.   DOI
33 Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel. Compos. Struct., Int. J., 18(2), 425-442.
34 Kitipornchai, S., He, X.Q. and Liew, K.M. (2006), "Continuum model for the vibration of multilayered graphene sheets", Acta Mater., 54, 4229.
35 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
36 Ehyaei, J., Akbarshahi, A. and Shafiei, N. (2017), "Influence of porosity and axial preload on vibration behavior of rotating FG nanobeam", Adv. Nano Res., Int. J., 5(2), 141-169.
37 El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., Int. J., 63(5), 585-595.
38 Eringen, A.C. (1976), Nonlocal Polar Field Models, Academic Press, New York, NY, USA.
39 Bouazza, M., Amara, K., Zidour, M., Abedlouahed, T. and El Abbas, A.B. (2014), "Thermal effect on buckling of multiwalled carbon nanotubes using different gradient elasticity theories", Nanosci. Nanotechnol., 4(2), 27-33.
40 Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., Int. J., 19(2), 115-126.
41 Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and Adda-Bedia, E.A. (2015a), "Postbuckling Analysis of Functionally Graded Beams Using Hyperbolic Shear Deformation Theory", Rev. Info. Eng. Appl., 2(1), 1-14.   DOI
42 Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and Bedia, E.A. (2015b), "Postbuckling analysis of nanobeams using trigonometric Shear deformation theory", Appl. Sci. Reports, 10, 112-121.
43 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
44 Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., Int. J., 21(4), 397-405.
45 Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNT-reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel. Compos. Struct., Int. J., 22(4), 889-913.   DOI
46 Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39, 2489-2508.   DOI
47 Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel. Compos. Struct., Int. J., 25(2), 157-175.
48 Hajmohammad, M.H., Maleki, M. and Kolahchi, R. (2018c), "Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer", Soil Dyn. Earthq. Eng., 110, 18-27.
49 Hajmohammad, M.H., Farrokhian, A. and Kolahchi, R. (2018a), "Smart control and vibration of viscoelastic actuator-multiphase nanocomposite conical shells-sensor considering hygrothermal load based on layerwise theory", Aerosp. Sci. Technol., 78, 260-270.   DOI
50 Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Maleki, M. (2018b), "Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects", Compos. Struct., 187, 498-508.   DOI
51 Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 235-253.   DOI
52 Hamidi, A., Zidour, M., Bouakkaz, K. and Bensattalah, T. (2018), "Thermal and Small-Scale Effects on Vibration of Embedded Armchair Single-Walled Carbon Nanotubes", J. Nano Res., 51, 24-38.
53 Hamza-Cherif, R., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, S. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14.   DOI
54 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
55 Pradhan, S.C. and Phadikar, J.K. (2009), "Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory", Struct. Eng. Mech., Int. J., 33(2), 193-213.   DOI
56 Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., Int. J., 20(3), 369-383.
57 Murmu, T. and Pradhan, S.C. (2010), "Thermal effects on the stability of embedded carbon nanotubes", Computat. Mater. Sci., 47(3), 721-726.   DOI
58 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(12), 124322.   DOI
59 Hosseini, H. and Kolahchi, R. (2018), "Seismic response of functionally graded-carbon nanotubes-reinforced submerged viscoelastic cylindrical shell in hygrothermal environment", Phys. E: Low-dimens. Syst. Nanostruct., 102, 101-109.   DOI
60 Ould Youcef, D., Kaci, A., Houari, M.S.A., Tounsi, A., Benzair, A. and Heireche, H. (2015), "On the bending and stability of nanowire using various HSDTs", Adv. Nano Res., Int. J., 3(4), 177-191.
61 Pradhan, S.C. and Reddy, G.K. (2011), "Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM", Comput. Mater. Sci., 50, 1052-1056.   DOI
62 Rakrak, K., Zidour, M., Heireche, H., Bousahla, A.A. and Chemi, A. (2016), "Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory", Adv. Nano Res., Int. J., 4(1), 31-44.
63 Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2017), "Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment", Mater. Res. Express, 4(8), 085013.   DOI
64 Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., Int. J., 25(3), 361-374.
65 Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., Int. J., 22(2), 257-276.   DOI
66 Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory", Struct. Eng. Mech., Int. J., 65(5), 621-631.
67 Karami, B. and Janghorban, M. (2016), "Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory", Modern Phys. Lett. B, 30(36), 1650421.   DOI
68 Karami, B., Shahsavari, D. and Li, L. (2018a), "Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory", Phys. E: Low-dimens. Syst. Nanostruct., 97, 317-327.
69 Karami, B., Shahsavari, D. and Li, L. (2018b), "Temperature-dependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field", J. Thermal Stress., 41(4), 483-499.   DOI
70 Shahsavari, D., Karami, B. and Mansouri, S. (2018a), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech.-A/Solids, 67, 200-214.   DOI
71 Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018b), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149.   DOI
72 She, G.L., Ren, Y.R., Yuan, F.G. and Xiao, W.S. (2018a), "On vibrations of porous nanotubes", Int. J. Eng. Sci., 125, 23-35.   DOI
73 Ahouel, M., Houari, M.S.A., Adda Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., Int. J., 20(5), 963-981.   DOI
74 Abdelaziz, H.H., Ait Amar Meziane, M., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., Int. J., 25(6), 693-704.
75 Abdelmalek, A., Bouazza, M., Zidour, M. and Benseddiq, N. (2017), "Hygrothermal Effects on the Free Vibration Behavior of Composite Plate Using nth-Order Shear Deformation Theory: a Micromechanical Approach", Iran. J. Sci. Technol. Transact. Mech. Eng., 1-13.
76 Abualnour, M., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697.   DOI
77 She, G.L., Ren, Y.R., Xiao, W.S. and Liu, H.B. (2018c), "Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations", Struct. Eng. Mech., Int. J., 66(6), 729-736.
78 Karami, B., Shahsavari, D. and Janghorban, M. (2018c), "A comprehensive analytical study on functionally graded carbon nanotube-reinforced composite plates", Aerosp. Sci. Technol., 82, 499-512.
79 Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2018d), "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 0954406218756451.
80 She, G.L., Yuan, F.G. and Ren, Y.R. (2018b), "On wave propagation of porous nanotubes", Int. J. Eng. Sci., 130, 62-74.   DOI
81 Shokravi, M. (2017a), "Buckling analysis of embedded laminated plates with agglomerated CNT-reinforced composite layers using FSDT and DQM", Geomech. Eng., Int. J., 12(2), 327-346.
82 Shokravi, M. (2017b), "Dynamic pull-in and pull-out analysis of viscoelastic nanoplates under electrostatic and Casimir forces via sinusoidal shear deformation theory", Microelectron. Reliabil., 71, 17-28.
83 Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013a), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24, 209-220.   DOI
84 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.
85 Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., Int. J., 65(4), 453-464.
86 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
87 Amnieh, H.B., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by SiO2 nanoparticles subjected to blast load experimentally and theoretically", Constr. Build. Mater., 174, 633-644.   DOI
88 Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, Int. J., 17(5), 567-578.   DOI
89 Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018f), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., Int. J., 28(1), 99-110.
90 Karami, B., Janghorban, M. and Tounsi, A. (2018e), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., Int. J., 27(2), 201-216.
91 Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2018g), "Wave dispersion of mounted graphene with initial stress", Thin-Wall. Struct., 122, 102-111.
92 Karami, B., Janghorban, M. and Tounsi, A. (2018h), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264.   DOI
93 Khetir, H., Bachir Bouiadjra, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., Int. J., 64(4), 391-402.
94 Kerr, A.D. (1965), "A study of a new foundation model", Acta Mechanica, 1(2), 135-147.   DOI
95 Kitipornchai, S., He, X.Q. and Liew, K.M. (2005), "Continuum model for the vibration of multilayered graphene sheets", Phys. Rev. B, 72(7), p.075443.   DOI
96 Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786.
97 Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., Int. J., 60(4), 547-565.
98 Van Cauwelaert, F., Stet, M. and Jasienski, A. (2002), "The general solution for a slab subjected to centre and edge loads and resting on a Kerr foundation", Int. J. Pave. Eng., 3(1), 1-18.   DOI
99 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.
100 Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., Int. J., 14(2), 103-115.
101 Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., Int. J., 21(1), 65-74.
102 Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248.   DOI
103 Kolahchi, R. and Bidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech., 37(2), 265-274.   DOI
104 Wang, C.M., Zhang, Y.Y., Ramesh, S.S. and Kitipornchai, S. (2006), "Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory", J. Phys. D: Appl. Phys., 39, 3904.   DOI
105 Wu, C.P., Chen, Y.H., Hong, Z.L. and Lin, C.H. (2018), "Nonlinear vibration analysis of an embedded multi-walled carbon nanotube", Adv. Nano Res., Int. J., 6(2), 163-182.
106 Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., Int. J., 21(1), 15-25.
107 Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., Int. J., 14(6), 519-532.
108 Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with $SiO_2$ nano-particles", Wind Struct., Int. J., 24(1), 43-57.   DOI
109 Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247.
110 Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlinear Dyn., 90(1), 479-492.   DOI
111 Kolahchi, R. and Moniri, A.M. (2016), "BidgoliSize-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech., 37(2), 265-274.   DOI
112 Kolahchi, R., Bidgoli, M.R., Beygipoor, G. and Fakhar, M.H. (2015), "A nonlocal nonlinear analysis for buckling in embedded FG-SWCNT-reinforced microplates subjected to magnetic field", J. Mech. Sci. Technol., 29(9), 3669-3677.   DOI
113 Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186.   DOI
114 Kolahchi, R., Safari, M. and Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265.   DOI
115 Zidi, M., Tounsi, A., Houari, M.S.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Tech., 34, 24-34.   DOI
116 Zarei, M.S., Kolahchi, R., Hajmohammad, M.H. and Maleki, M. (2017), "Seismic response of underwater fluid-conveying concrete pipes reinforced with $SiO_2$ nanoparticles and fiber reinforced polymer (FRP) layer", Soil Dyn. Earthq. Eng., 103, 76-85.   DOI
117 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017a), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Wall. Struct., 113, 162-169.
118 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017b), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Wall. Struct., 113, 162-169.   DOI
119 Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2017c), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm", J. Sandw. Struct. Mater., 1099636217731071.
120 Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., Int. J., 54(4), 693-710.   DOI
121 Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., Int. J., 64(2), 145-153.
122 Zidour, M., Daouadji, T.H., Benrahou, K.H., Tounsi, A., Bedia, E.A.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
123 Zidour, M., Hadji, L., Bouazza, M., Tounsi, A. and Bedia, E.A. (2015), "The mechanical properties of Zigzag carbon nanotube using the energy-equivalent model", J. Chem. Mater. Res., 3, 9-14.
124 Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., Int. J., 26(2), 125-137.