Browse > Article
http://dx.doi.org/10.12989/scs.2018.27.1.109

A novel four variable refined plate theory for wave propagation in functionally graded material plates  

Fourn, Hocine (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Atmane, Hassen Ait (Advanced Materials and Structures Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Bourada, Mohamed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
Publication Information
Steel and Composite Structures / v.27, no.1, 2018 , pp. 109-122 More about this Journal
Abstract
In This work an analysis of the propagation of waves of functionally graduated plates is presented by using a high order hyperbolic (HSDT) shear deformation theory. This theory has only four variables, which is less than the theory of first order shear deformation (FSDT). Therefore, a shear correction coefficient is not required. Unlike other conventional shear deformation theories, the present work includes a new field of displacement which introduces indeterminate integral variables. The properties of materials are supposed classified in the direction of the thickness according to two simple distributions of a power law in terms of volume fractions of constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.
Keywords
wave propagation; phase velocity; vibration; functionally graded plate; plate theory; porosity;
Citations & Related Records
Times Cited By KSCI : 51  (Citation Analysis)
연도 인용수 순위
1 Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., Int. J., 18(1), 187-212.   DOI
2 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.
3 Bakhadda, B., Bachir Bouiadjra, M., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., Int. J. [In Press]
4 Barati, R.M. (2017), "On wave propagation in nanoporous materials", Int. J. Eng. Sci., 116, 1-11.   DOI
5 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
6 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.
7 Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo-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.   DOI
8 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
9 Hachemi, H., Kaci, A., Houari, M.S.A., Bourada, A., Tounsi, A. and Mahmoud, S.R. (2017), "A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations", Steel Compos. Struct., Int. J., 25(6), 717-726.
10 Benachour, A., Daouadji, H.T., 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
11 Benadouda, M., Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2017), "An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities", Earthq. Struct., Int. J., 13(3), 255-265.
12 Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., Int. J., 65(1), 19-31.
13 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
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 vibrationanalysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15, 671-703.   DOI
15 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.
16 Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, Int. J., 18(5), 1053-1063.   DOI
17 Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017b), "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.
18 Belkorissat, I., Houari, M.S.A., Tounsi, A., AddaBedia, 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
19 Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Brazil. Soc. Mech. Sci. Eng., 38(1), 265-275.   DOI
20 Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017a), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., Int. J., 62(6), 695-702.
21 Abo-Dahab, S.M., Abd-Alla, A.M. and Khan, A. (2016), "Rotational effect on Rayleigh, Love and Stoneley waves in non-homogeneous fibre-reinforced anisotropic general viscoelastic media of higher order", Struct. Eng. Mech., Int. J., 58(1), 181-197.   DOI
22 Afaq, K.S., Karama, M. and Mistou, S. (2003), "Un nouveau modele raffine pour les structures multicouches", In : Comptesrendus des 13 emes Journees Nationales sur les Composite s. Strasbourg, March, pp. 289-292.
23 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
24 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.
25 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.
26 Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with SiO2 nano-particles", Wind Struct., Int. J., 24(1), 43-57.   DOI
27 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
28 Ahmed, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civil Struct. Environ., 4(2), 59-64.
29 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.
30 Abualnour, M., Houari, M.S.A., Tounsi, A., AddaBedia, E.A., 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
31 Han, X., Liu, G.R., Xi, Z.C. and Lam, K.Y. (2001), "Transient responses in a functionally graded cylinder", Int. J. Solids Struct., 38, 3021-3037.   DOI
32 Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, SR. (2018), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 1099636217698443.
33 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.
34 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.
35 Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally gradedcarbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., p. 1099636217720373.
36 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
37 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, 374-383.   DOI
38 Ait Atmane, H., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mater. Des., 6(2), 113-121.   DOI
39 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
40 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
41 Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., Int. J., 19(2), 369-384.   DOI
42 Kar, V.R. and Panda, S.K. (2016a), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chinese J. Aeronaut., 29(1), 173-183.   DOI
43 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
44 Kar, V.R. and Panda, S.K. (2015a), "Thermoelastic analysis of functionally graded doubly curved shell panels using nonlinear finite element method", Compos. Struct., 129, 202-212.   DOI
45 Kar, V.R. and Panda, S.K. (2015b), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Latin Am. J. Solids Struct., 12(11), 2006-2024.   DOI
46 Ambartsumyan, S.A. (1969), Theory of Anisotropic Plate, Technomic Publishing Co.
47 Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165.   DOI
48 Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447.   DOI
49 Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630.   DOI
50 Sharma, N., Mahapatra, T.R. and Panda, S.K. (2017), "Vibroacoustic behaviour of shear deformable laminated composite flat panel using BEM and the higher order shear deformation theory", Compos. Struct., 180, 116-129.   DOI
51 Panda, S.K. and Singh, B.N. (2009), "Thermal post-buckling behaviour of laminated composite cylindrical/hyperboloid shallow shell panel using nonlinear finite element method", Compos. Struct., 91(3), 366-374.   DOI
52 Panda, S.K. and Singh, B.N. (2013), "Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre", Aerosp. Sci. Technol., 29(1), 47-57.   DOI
53 Reddy, J.N. (1987), "A generalization of two-dimensional theories of laminated composite plates", Commun. Appl. Numer. Methods, 3, 173-180.   DOI
54 Panda, S.K. and Mahapatra, T.R. (2014), "Nonlinear finite element analysis of laminated composite spherical shell vibration under uniform thermal loading", Meccanica, 49(1), 191-213.   DOI
55 Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Methods Eng., 47, 663-684.   DOI
56 Reddy, J.N. and Cheng, Z.Q. (2002), "Frequency correspondence between membranes and functionally graded spherical shallow shells of polygonal planform", Int. J. Mech. Sci., 44(5), 967-985.   DOI
57 Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12, 69-77.
58 Sekkal, M., Fahsi, B., Tounsi, A., and Mahmoud, S.R. (2017a), "A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate", Steel Compos. Struct., Int. J., 25(4), 389-401.
59 Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017b), "A new quasi-3D HSDT for buckling and vibration of FG plate", Struct. Eng. Mech., Int. J., 64(6), 737-749.
60 Kar, V.R. and Panda, S.K. (2016b), "Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties", J. Thermal Stresses, 39(8), 942-959.   DOI
61 Kar, V.R., Panda, S.K. and Mahapatra, T.R. (2016), "Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties", Adv. Mater. Res., Int. J., 5(4), 205-221.
62 Khetir, H., Bachir Bouiadjra, M., Houari, M.S.A., Tounsi, A. and S.R. Mahmoud, (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.
63 Klouche, F., Darcherif, L., Sekkal, M., Tounsi, A. and Mahmoud, S.R. (2017), "An original single variable shear deformation theory for buckling analysis of thick isotropic plates", Struct. Eng. Mech., Int. J., 63(4), 439-446.
64 Cheng, Z.Q. and Batra, B.C. (2000), "Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plate", J. Sound Vib., 229(4), 879-895.   DOI
65 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
66 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.   DOI
67 Bresse, J.A.C. (1859), "Cours de Mecanique Applique", Mallet-Bachelier, Paris, France.
68 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
69 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
70 Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84.   DOI
71 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.
72 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.
73 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
74 Sahoo, S.S., Hirwani, C.K., Panda, S.K. and Sen, D. (2017), "Numerical analysis of vibration and transient behaviour of laminated composite curved shallow shell structure: an experimental validation", Scientia Iranica.
75 Shokravi, M. (2017a), "Dynamic pull-in and pull-out analysis of viscoelastic nanoplates under electrostatic and Casimir forces via sinusoidal shear deformation theory", Microelectronics Reliability, 71, 17-28.   DOI
76 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
77 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
78 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.   DOI
79 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017b), "Wave propagation of embedded viscoelastic FG-CNTreinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545.   DOI
80 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
81 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.
82 Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "Anew simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423.   DOI
83 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.
84 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.
85 Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates", Geomech. Eng., Int. J., 13(3), 385-410.
86 Farzad, E. and Reza Barati, M. (2016a), "Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory", Appl. Phys. A, 122(9), 843. DOI: doi.org/10.1007/s0033   DOI
87 Farzad, E., Barati, R.M. and Dabbagh, A. (2016b), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", Int. J. Eng. Sci., 107, 169-182.   DOI
88 Bourada, F., Amara, K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., Int. J., 21(6), 1287-1306.   DOI
89 Cranch, E.T. and Adler, A.A. (1956), "Bending vibration of variable section beams", J. Appl. Mech., 23(1), 103-108.
90 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.   DOI
91 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
92 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
93 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., (Accepted).
94 Boukhari, A., Ait Atmane, 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
95 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
96 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
97 Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., Int. J., 18(3), 659-672.   DOI
98 Shokravi, M. (2017d), "Buckling analysis of embedded laminated plates with agglomerated CNT-reinforced composite layers using FSDT and DQM", Geomech. Eng., Int. J., 12(2), 327-346.   DOI
99 Shokravi, M. (2017b), "Buckling of sandwich plates with FGCNT-reinforced layers resting on orthotropic elastic medium using Reddy plate theory", Steel Compos. Struct., Int. J., 23(6), 623-631.
100 Shokravi, M. (2017c), "Vibration analysis of silica nanoparticlesreinforced concrete beams considering agglomeration effects", Comput. Concrete, Int. J., 19(3), 333-338.   DOI
101 Sobhy, M. (2017), "Hygro-thermo-mechanical vibration and buckling of exponentially graded nanoplates resting on elastic foundations via nonlocal elasticity theory", Struct. Eng. Mech., Int. J., 63(3), 401-415.
102 Sun, D. and Luo, S.N. (2011a), "The wave propagation and dynamic response of rectangular functionally graded material plates with completed clamped supports under impulse load", Eur. J. Mech. - A/Solids, 30, 396-408.   DOI
103 Sun, D. and Luo, S.N. (2011b), "Wave propagation of functionally graded material plates in thermal environments", Ultrasonics, 51, 940-952.   DOI
104 Taibi, F.Z., Benyoucef, S., Tounsi, A., Bachir Bouiadjra, R., AddaBedia, E.A. and Mahmoud, S.R. (2015), "A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 17(2), 99-129   DOI
105 Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220.   DOI
106 Malekzadeh, P. (2009), "Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations", Compos. Struct., 89, 367-373.   DOI
107 Vel, S.S. and Batra, R.C. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272, 703-730.   DOI
108 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.   DOI
109 Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNTreinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., Int. J., 22(4), 889-913.   DOI
110 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(9), 2489-2508.   DOI
111 Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017), "Thermoelastic deflection responses of CNT reinforced sandwich shell structure using finite element method", Scientia Iranica.
112 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
113 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, 795-810.   DOI