Browse > Article
http://dx.doi.org/10.12989/anr.2019.7.3.191

Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT  

Boutaleb, Sabrina (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Benrahou, Kouider Halim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Bakora, Ahmed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Algarni, Ali (Statistics Department, Faculty of Science, King Abdulaziz University)
Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Tounsi, Abdeldjebbar (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
Advances in nano research / v.7, no.3, 2019 , pp. 191-208 More about this Journal
Abstract
In the present work the dynamic analysis of the functionally graded rectangular nanoplates is studied. The theory of nonlocal elasticity based on the quasi 3D high shear deformation theory (quasi 3D HSDT) has been employed to determine the natural frequencies of the nanosize FG plate. In HSDT a cubic function is employed in terms of thickness coordinate to introduce the influence of transverse shear deformation and stretching thickness. The theory of nonlocal elasticity is utilized to examine the impact of the small scale on the natural frequency of the FG rectangular nanoplate. The equations of motion are deduced by implementing Hamilton's principle. To demonstrate the accuracy of the proposed method, the calculated results in specific cases are compared and examined with available results in the literature and a good agreement is observed. Finally, the influence of the various parameters such as the nonlocal coefficient, the material indexes, the aspect ratio, and the thickness to length ratio on the dynamic properties of the FG nanoplates is illustrated and discussed in detail.
Keywords
nonlocal elasticity theory; FG nanoplate; free vibration; refined theory; elastic foundation;
Citations & Related Records
Times Cited By KSCI : 72  (Citation Analysis)
연도 인용수 순위
1 Pradyumna, S. and Bandyopadhyay, J. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finiteelement formulation", J. Sound Vib., 318, 176-192.   DOI
2 Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70.   DOI
3 Rafiee, M.A., Rafiee, J., Srivastava, I., Wang, Z., Song, H., Yu, Z.Z. and Koratkar, N. (2010), "Fracture and fatigue in graphene nanocomposites", small, 6, 179-183.   DOI
4 Reddy, J. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45, 288-307.   DOI
5 Reddy, J. (2011), "Microstructure-dependent couple stress theories of functionally graded beams", J. Mech. Phys. Solids, 59, 2382-2399.   DOI
6 Reddy, J. and Pang, S. (2008), "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103, 023511.   DOI
7 Sahoo, S.S., Panda, S.K. and Sen, D. (2016), "Effect of delamination on static and dynamic behavior of laminated composite plate", AIAA Journal, 54(8), 2530-2544.   DOI
8 Sahoo, S.S., Panda, S.K. and Singh, V.K. (2017), "Experimental and numerical investigation of static and free vibration responses of woven glass/epoxy laminated composite plate", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 231(5), 463-478.   DOI
9 Sakhaee-Pour, A., Ahmadian, M. and Vafai, A. (2008a), "Applications of single-layered graphene sheets as mass sensors and atomistic dust detectors", Solid State Commun., 145, 168-172.   DOI
10 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.
11 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
12 Bouazza, M., Lairedj, A., Benseddiq, N. and Khalki, S. (2016), "A refined hyperbolic shear deformation theory for thermal buckling analysis of cross-ply laminated plates", Mech. Res. Commun., 73, 117-126.   DOI
13 Bouazza, M., Zenkour, A.M. and Benseddiq, N. (2018), "Closed-from solutions for thermal buckling analyses of advanced nanoplates according to a hyperbolic four-variable refined theory with small-scale effects", Acta Mech., 229(5), 2251-2265.   DOI
14 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
15 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
16 Toupin, R.A. (1962), "Elastic materials with couple-stresses", Arch. Rational Mech. Anal., 11, 385-414.   DOI
17 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. Tech., 24, 209-220.   DOI
18 Ebrahimi, F. and Rastgo, A. (2008b), "An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory", Thin-Wall. Struct., 46(12), 1402-1408.   DOI
19 Ebrahimi, F. and Salari, E. (2015), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007.   DOI
20 Ebrahimi, F. and Rastgoo, A. (2008a), "Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers", Smart Mater. Struct., 17(1), 015044.   DOI
21 Ebrahimi, F., Rastgoo, A. and Atai, A.A. (2009a), "A theoretical analysis of smart moderately thick shear deformable annular functionally graded plate", Eur. J. Mech. -A/Solids, 28(5), 962-973.   DOI
22 Ebrahimi, F., Naei, M.H. and Rastgoo, A. (2009b), "Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation", J. Mech. Sci. Tech., 23(8), 2107-2124.   DOI
23 Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354, 56-58.   DOI
24 Hosseini-Hashemi, S., Zare, M. and Nazemnezhad, R. (2013b), "An exact analytical approach for free vibration of Mindlin rectangular nanoplates via nonlocal elasticity", Compos. Struct., 100, 290-299.   DOI
25 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
26 Huang, C., Yang, P. and Chang, M. (2012), "Threedimensional vibration analyses of functionally graded material rectangular plates with through internal cracks", Compos. Struct., 94, 2764-2776.   DOI
27 Janghorban, M. (2016), "Static analysis of functionally graded rectangular nanoplates based on nonlocal third order shear deformation theory", Int. J. Eng. Appl. Sci. (IJEAS), 8(2), 87-100.
28 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.
29 Kadari, B., Bessaim, A., Tounsi, A., Heireche, H., Bousahla, A.A. and Houari, M.S.A. (2018), "Buckling analysis of orthotropic nanoscale plates resting on elastic foundations", J. Nano Res., 55, 42-56.   DOI
30 Kar, V.R. and Panda, S.K. (2016a), "Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties", J. Thermal Stress., 39(8), 942-959.   DOI
31 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., 27(5), 311-324.
32 Sakhaee-Pour, A., Ahmadian, M. and Vafai, A. (2008b), "Potential application of single-layered graphene sheet as strain sensor", Solid State Commun., 147, 336-340.   DOI
33 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
34 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.
35 Becheri, T., Amara, K., Bouazza, M. and Benseddiq, N. (2016), "Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects", Steel Compos. Struct., Int. J., 21(6), 1347-1368.   DOI
36 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.
37 Ungbhakorn, V. and Wattanasakulpong, N. (2013), "Thermo-elastic vibration analysis of third order shear deformable functionally graded plates with distributed patch mass under thermal environment", Appl. Acoust., 74, 1045-1059.   DOI
38 Vel, S.S. and Batra, R. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272, 703-730.   DOI
39 Wang, L. (2009), "Dynamical behaviors of double walled carbon nanotubes conveying fluidaccounting for the role of small length scale", Comput. Mater. Sci., 45, 584-588.   DOI
40 Yahia, S.A., 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
41 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.
42 Ye, C., Bando, Y., Shen, G. and Golberg, D. (2006), "Thickness-dependent photocatalytic performance of ZnO nanoplatelets", J. Phys. Chem. B, 110, 15146-15151.   DOI
43 Ellali, M., Amara, K., Bouazza, M. and Bourada, F. (2018), "The buckling of piezoelectric plates on Pasternak elastic foundation using higher order shear deformation plate theories", Smart Struct. Syst., Int. J., 21(1), 113-122.
44 Ebrahimi, F., Mahmoodi, F. and Barati, M.R. (2017), "Thermo-mechanical vibration analysis of functionally graded micro/nanoscale beams with porosities based on modified couple stress theory", Adv. Mater. Res., Int. J., 6(3), 279-301.
45 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.
46 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.
47 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.
48 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.
49 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.   DOI
50 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
51 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.   DOI
52 Mehar, K. and Panda, S.K. (2018), "Nonlinear finite element solutions of thermoelastic flexural strength and stress values of temperature dependent graded CNT-reinforced sandwich shallow shell structure", Struct. Eng. Mech., Int. J., 67(6), 565-578.
53 Mehar, K., Panda, S.K. and Patle, B.K. (2017), "Thermoelastic vibration and flexural behavior of FG-CNT reinforced composite curved panel", Int. J. Appl. Mech., 9(4), 1750046.   DOI
54 Mehar, K., Panda, S.K. and Patle, B.K. (2018a), "Stress, deflection, and frequency analysis of CNT reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach", Polym. Compos., 39(10), 3792-3809.   DOI
55 Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Beg, O.A. (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
56 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.
57 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
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 Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., Int. J., 7(2), 89-98.
61 Shahadat, M.R.B., Alam, M.F., Mandal, M.N.A. and Ali, M.M. (2018), "Thermal transportation behaviour prediction of defective graphene sheet at various temperature: A Molecular Dynamics Study", Am. J. Nanomater., 6(1), 34-40.
62 Karami, B., Janghorban, M. and Tounsi, A. (2018a), "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
63 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.
64 Zhao, X., Lee, Y. and Liew, K.M. (2009), "Free vibration analysis of functionally graded plates using the element-free kp-Ritz method", J. Sound Vib., 319, 918-939.   DOI
65 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
66 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.
67 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.
68 Kar, V.R. and Panda, S.K. (2016b), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chinese J. Aeronaut., 29(1), 173-183.   DOI
69 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.
70 Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018b), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., Int. J., 28(1), 99-110.
71 Karami, B., Janghorban, M. and Tounsi, A. (2018c), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., Int. J., 27(2), 201-216.
72 Karami, B., Janghorban, M. and Tounsi, A. (2018d), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput. [In press]
73 Karami, B., Shahsavari, D., Janghorban, M. and Tounsi, A. (2019a), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", Int. J. Mech. Sci., 156, 94-105.   DOI
74 Karami, B., Janghorban, M. and Tounsi, A. (2019b), "On exact wave propagation analysis of triclinic material using three dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., 69(5), 487-497.   DOI
75 Karami, B., Janghorban, M. and Tounsi, A. (2019c), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., Int. J., 7(1), 55-66.
76 Meziane, M.A.A., 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
77 Mehar, K., Mahapatra, T.R, Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018b), "Finite-element solution to nonlocal elasticity and scale effect on frequency behavior of shear deformable nanoplate structure", J. Eng. Mech., 144(9), 04018094.   DOI
78 Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 21(2), 727-757.   DOI
79 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.
80 Miller, R.E. and Shenoy, V.B. (2000), "Size-dependent elastic properties of nanosized structural elements", Nanotechnology, 11, 139.   DOI
81 Mindlin, R. and Tiersten, H. (1962), "Effects of couple-stresses in linear elasticity", Arch. Rational Mech. Anal., 11, 415-448.   DOI
82 Tang, Y. and Liu, Y. (2018), "Effect of van der Waals force on wave propagation in viscoelastic double-walled carbon nanotubes", Modern Phys. Lett. B, 32(24), 1850291.   DOI
83 Shahsavari, D., Karami, B. and Li, L. (2018), "A high-order gradient model for wavepropagation analysis of porous FG nanoplates", Steel Compos. Struct., Int. J., 29(1), 53-66.
84 Shen, H.S. and Zhang, C.L. (2010), "Torsional buckling and postbuckling of double-walled carbon nanotubes by nonlocal shear deformable shell model", Compos. Struct., 92, 1073-1084.   DOI
85 Singh, V.K. and Panda, S.K. (2017), "Geometrical nonlinear free vibration analysis of laminated composite doubly curved shell panels embedded with piezoelectric layers", J. Vib. Control, 23(13), 2078-2093.   DOI
86 Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., Int. J., 69(6), 637-649.
87 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
88 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
89 Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., Int. J. [To be published]
90 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
91 Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., Int. J., 68(6), 661-675.
92 Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., Int. J., 28(1), 19-30.
93 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
94 Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., Int. J., 4(1), 51-64.
95 Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Computat., 218, 7406-7420.   DOI
96 Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013a), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201.   DOI
97 Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2013b), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88.   DOI
98 Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16.   DOI
99 Abdelaziz, H.H., Meziane, M.A.A, 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.
100 Aagesen, M. and Sorensen, C. (2008), "Nanoplates and their suitability for use as solar cells", Proceedings of Clean Technol., 109-112.
101 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
102 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.
103 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.
104 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. Braz. Soc. Mech. Sci. Eng., 38, 265-275.   DOI
105 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.
106 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.
107 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
108 Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10, 233-248.   DOI
109 Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018a), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14.   DOI
110 Faleh, N.M., Fenjan, R.M. and Ahmed, R.A. (2018b), "Dynamic analysis of graded small-scale shells with porosity distributions under transverse dynamic loads", Eur. Phys. J. Plus, 133, 348.   DOI
111 Katariya, P.V., Panda, S.K, Hirwani, C.K., Mehar, K. and Thakare, O. (2017b), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., Int. J., 20(5), 595-605.
112 Katariya, P.V. and Panda, S.K. (2018), "Numerical evaluation of transient deflection and frequency responses of sandwich shell structure using higher order theory and different mechanical loadings", Eng. Comput. [In press]
113 Katariya, P.V. and Panda, S.K. (2019), "Frequency and deflection responses of shear deformable skew sandwich curved shell panel: A Finite Element Approach", Arab. J. Sci. Eng., 44(2), 1631-1648.   DOI
114 Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017a), "Prediction of nonlinear eigenfrequency of laminated curved sandwich structure using higher-order equivalent single-layer theory", J. Sandw. Struct. Mater. [In press]
115 Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017c), "Nonlinear thermal buckling behaviour of laminated composite panel structure including the stretching effect and higher-order finite element", Adv. Mater. Res., Int. J., 6(4), 349-361.
116 Katariya, P.V., Das, A. and Panda, S.K. (2018a), "Buckling analysis of SMA bonded sandwich structure - using FEM", IOP Conf. Series: Materials Science and Engineering, 338, 012035.   DOI
117 Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2018b) "Bending and vibration analysis of skew sandwich plate", Aircraft Eng. Aerosp. Technol., 90(6), 885-895.   DOI
118 Murmu, T. and Pradhan, S. (2009b), "Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Comput. Mater. Sci., 46, 854-859.   DOI
119 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.
120 Murmu, T. and Pradhan, S. (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", Phys. E, 41, 1232-1239.   DOI
121 Narendar, S. (2011), "Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects", Compos. Struct., 93, 3093-3103.   DOI
122 Nie, G. and Zhong, Z. (2007), "Semi-analytical solution for three-dimensional vibration of functionally graded circular plates", Comput. Method Appl. M, 196, 4901-4910.   DOI
123 Nix, W.D. and Gao, H. (1998), "Indentation size effects in crystalline materials: a law for strain gradient plasticity", J. Mech. Phys. Solids, 46, 411-425.   DOI
124 Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41, 305-312.   DOI
125 Pradhan, S. and Phadikar, J. (2009), "Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models", Phys. Lett. A, 373, 1062-1069.   DOI
126 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
127 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.
128 Benahmed, A., Houari, M.S.A., Benyoucef, S., Belakhdar, K. and Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomech. Eng., Int. J., 12(1), 9-34.   DOI
129 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.
130 Bensaid, I. (2017), "A refined nonlocal hyperbolic shear deformation beam model for bending and dynamic analysis of nanoscale beams", Adv. Nano Res., Int. J., 5(2), 113-126.   DOI
131 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.
132 Katariya, P.V., Hirwani, C.K. and Panda, S.K. (2019), "Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory", Eng. Comput., 35(2), 467-485.   DOI
133 Ke, L.L., Yang, J., Kitipornchai, S. and Bradford, M.A. (2012), "Bending, buckling and vibration of size-dependent functionally graded annular microplates", Compos. Struct., 94, 3250-3257.   DOI
134 Ke, L.L., Yang, J., Kitipornchai, S., Bradford, M.A. and Wang, Y.S. (2013), "Axisymmetric nonlinear free vibration of sizedependent functionally graded annular microplates", Compos. Part B: Eng., 53, 207-217.   DOI
135 Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput. [In press]
136 Khorshidi, K., Asgari, T. and Fallah, A. (2015), "Free vibrations analysis of functionally graded rectangular nano-plates based on nonlocal exponential shear deformation theory", Mech. Adv. Compos. Struct., 2, 79-93.
137 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.
138 Kocaturk, T. and Akbas, S.D. (2012), "Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading", Struct. Eng. Mech., Int. J., 41(6), 775-789.   DOI
139 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
140 Adda Bedia, W., Houari, M.S.A., Bessaim, A., Bousahla, A.A., Tounsi, A., Saeed, T. and Alhodaly, M.S. (2019), "A new hyperbolic two-unknown beam model for bending and buckling analysis of a nonlocal strain gradient nanobeams", J. Nano Res., 57, 175-191.   DOI
141 Aifantis, E. (1999), "Strain gradient interpretation of size effects", Int. J. Fract., 95, 299-314.   DOI
142 Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., Int. J., 18(6), 1125-1143.   DOI
143 Akbas, S.D. (2018), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., Int. J., 6(1), 39-55.
144 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
145 Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425.   DOI
146 Asghari, M. and Taati, E. (2013), "A size-dependent model for functionally graded micro-plates for mechanical analyses", J. Vib. Cont., 19, 1614-1632.   DOI
147 Atmane, H.A., Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84.   DOI
148 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
149 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
150 Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech. [To be published]
151 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
152 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.   DOI
153 Chen, Y., Lee, J.D. and Eskandarian, A. (2004), "Atomistic viewpoint of the applicability of microcontinuum theories", Int. J. Sol. Struct., 41, 2085-2097.   DOI
154 Dash, S., Sharma, N., Mahapatra, T.R., Panda, S.K. and Sahu, P. (2018), "Free vibration analysis of functionally graded sandwich flat panel", IOP Conf. Series: Materials Science and Engineering, 377, 012140.   DOI
155 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
156 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.
157 Ghorbanpour Arani, A., Kolahchi, R. and Vossough, H. (2012), "Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory", Physica B: Condensed Matter, 407(22), 4458-4465.   DOI
158 Koiter, W.T. (1969), "Couple-stresses in the theory of elasticity, I & II", J. Philosoph. Transact. Royal Soc. London B, 67, 17-44.
159 Kumar, Y. and Lal, R. (2013), "Prediction of frequencies of free axisymmetric vibration of twodirectional functionally graded annular plates on Winkler foundation", Eur. J. Mech. A Solid, 42, 219-228.   DOI
160 Lam, D.C.C., Yang, F., Chong, A.C.M. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51, 1477-1508.   DOI
161 Li, L, Li, X. and Hu, Y. (2016), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92.   DOI
162 Ma, M., Tu, J.P., Yuan, Y.F., Wang, X.L., Li, K.F., Mao, F. and Zeng, Z.Y. (2008), "Electrochemical performance of ZnO nanoplates as anode materials for Ni/Zn secondary batteries", J. Power Sources, 179, 395-400.   DOI
163 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
164 Malekzadeh, P. and Beni, A.A. (2010), "Free vibration of functionally graded arbitrary straight-sided quadrilateral plates in thermal environment", Compos. Struct., 92, 2758-2767.   DOI
165 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
166 Bensaid, I., Bekhadda, A. and Kerboua, B. (2018), "Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory", Adv. Nano Res., Int. J., 6(3), 279-298.
167 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.
168 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
169 Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135.   DOI
170 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.
171 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
172 Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Bedia, E.A. (2008), "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity", Phys. E, 40, 2791-2799.   DOI
173 Hirwani, C.K., Panda, S.K., Mahapatra, T.R. and Mahapatra, S.S. (2017), "Numerical study and experimental validation of dynamic characteristics of delaminated composite flat and curved shallow shell structure", J. Aerosp. Eng., 30(5), 04017045.   DOI
174 Hosseini-Hashemi, S., Taher, H.R.D., Akhavan, H. and Omidi, M. (2010), "Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory", Appl. Math. Model, 34, 1276-1291.   DOI
175 Hosseini-Hashemi, S., Bedroud, M. and Nazemnezhad, R. (2013a), "An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity", Compos. Struct., 103, 108-118.   DOI
176 Malekzadeh, P. and Heydarpour, Y. (2012), "Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment", Compos. Struct., 94, 2971-2981.   DOI
177 Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82, 499-512.   DOI
178 Mehar, K. and Panda, S.K. (2016), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346.   DOI