References
- Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2
- Batou, B., Nebab, M., Bennai, R., AitAtmane, H., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs ", Steel Compos. Struct., Int. J., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699
- Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., Int. J., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761
- 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. https://doi.org/10.12989/cac.2016.18.5.1053
- Bodaghi, M. and Saidi, A.R. (2010), "Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory", Appl. Math. Model., 34, 3659-3673. https://doi.org/10.1016/j.apm.2010.03.016
- Bouazza, M., Zenkour, A.M. and Benseddiq, N. (2018), "Effect of material composition on bending analysis of FG plates via a twovariable refined hyperbolic theory", Arch. Mech., 70(2), 107-129.
- Chen, W.R. and Chang, H. (2018), "Vibration analysis of functionally graded timoshenko beams", Int. J. Struct. Stab. Dyn., 18, 1850007. https://doi.org/10.1142/S0219455418500074
- Eltaher, M.A., Khairy, A., Sadoun, A.M. and Omar, F.A. (2014), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Mathe. Computat., 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072
- Eltaher, M.A., Attia, M.A., Soliman, A.E. and Alshorbagy, A.E. (2018a), "Analysis of crack occurs under unsteady pressure and temperature in a natural gas facility by applying FGM", Struct. Eng. Mech., Int. J., 66(1), 97-111. https://doi.org/10.12989/sem.2018.66.1.097
- Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018b), "Modified porosity model in analysis of functionally gradedporous nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40(3), 141. https://doi.org/10.1007/s40430-018-1065-0
- Eltaher, M.A., Mohamed, N., Mohamed, S.A. and Seddek, L.F. (2019a), "Periodic and nonperiodic modes of postbuckling and nonlinear vibration of beams attached to nonlinear foundations", Appl. Mathe. Model., 75, 414-445. https://doi.org/10.1016/j.apm.2019.05.026
- Eltaher, M.A., Mohamed, N., Mohamed, S. and Seddek, L.F. (2019b), "Postbuckling of curved carbon nanotubes using energy equivalent model", J. Nano Res., 57, 136-157. https://doi.org/10.4028/www.scientific.net/JNanoR.57.136
- Emam, S. and Eltaher, M.A. (2016), "Buckling and postbuckling of composite beams in hygrothermal environments", Compos. Struct., 152, 665-675. https://doi.org/10.1016/j.compstruct.2016.05.029
- Emam, S., Eltaher, M.A., Khater, M. and Abdalla, W. (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Sci., 8(11), 2238. https://doi.org/10.3390/app8112238
- Hadji, L., Hassaine Daouadji, T., Ait Amar Meziane, M., Tlidji, Y. and Adda Bedia, E.A. (2016), "Analysis of functionally graded beam using a new first-order shear deformation theory", Struct. Eng. Mech., Int. J., 57(2), 315-325. https://doi.org/10.12989/sem.2016.57.2.315
- Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., Int. J., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231
- Hamed, M.A., Eltaher, M.A., Sadoun, A.M. and Almitani, K.H. (2016), "Free vibration of symmetric and sigmoid functionally graded nanobeams", Appl. Phys. A, 122(9), 829. https://doi.org/10.1007/s00339-016-0324-0
- Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", Int. J. Mech. Sci., 53, 11-22. https://doi.org/10.1016/j.ijmecsci.2010.10.002
- Jha, D.K., Kant, T. and Singh, R.K. (2013), "A critical review of recent research on functionally graded plates", Compos. Struct., 96, 833-849. https://doi.org/10.1016/j.compstruct.2012.09.001
- 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. https://doi.org/10.1016/j.compstruct.2015.04.006
- 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), 20062024. https://doi.org/10.1590/1679-78251691
- Kar, V.R. and Panda, S.K. (2015c), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., Int. J., 53(4), 661-679. https://doi.org/10.12989/sem.2015.53.4.661
- Kar, V.R. and Panda, S.K. (2015d), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
- Kar, V.R. and Panda, S.K. (2017), "Large-amplitude vibration of functionally graded doubly-curved panels under heat conduction", AIAA J., 55(12), 4376-4386. https://doi.org/10.2514/1.J055878
- 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. https://doi.org/10.12989/amr.2016.5.4.205
- Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2017), "Effect of different temperature load on thermal postbuckling behaviour of functionally graded shallow curved shell panels", Compos. Struct., 160, 1236-1247. https://doi.org/10.1016/j.compstruct.2016.10.125
- Mahdavian, M. (2009), "Buckling analysis of simply-supported functionally graded rectangular plates under non-uniform inplane compressive loading", J. Solid Mech., 1, 213-225.
- Mantari, J.L. and Granados, E.V. (2015), "A refined FSDT for the static analysis of functionally graded sandwich plates", Thin Wall. Struct., 90, 150-158. https://doi.org/10.1016/j.tws.2015.01.015
- Mantari, J. and Soares, C.G. (2013), "A novel higher-order shear deformation theory with stretching effect for functionally graded plates", Compos. Part B, 45(1), 268-281. https://doi.org/10.1016/j.compositesb.2012.05.036
- Mantari, J.L., Oktem, A.S. and Soares, O.G. (2012), "Bending response of functionally graded plates by using a new higher order shear deformation theory", Compos. Struct., 94, 714-723. https://doi.org/10.1016/j.compstruct.2011.09.007
- Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2D higher-order deformation theory", Compos. Struct., 82, 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
- 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. https://doi.org/10.12989/sem.2018.67.6.565
- Mohamed, N., Eltaher, M.A., Mohamed, S. and Seddek, L.F. (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., Int. J., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737
- Mohammadi, M., Saidi, A.R. and Jomehzadeh, E. (2010), "A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges", Proc. Inst. Mech. Eng. Part CProc. Inst. Mech. Eng. Part C, 224, 1834-1841. https://doi.org/10.1243/09544062JMES1804
- Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2012a), "A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94, 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005
- Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012b), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B, 42, 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009
- Nguyen, T.K. (2015), "A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials", Int. J. Mech. Mater. Des., 11(2), 203-219. https://doi.org/10.1007/s10999-014-9260-3
- Nguyen, D.K., Nguyen, Q.H., Tran, T.T. and Bui, V.T. (2017), "Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load", Acta Mech., 228, 141-155. https://doi.org/10.1007/s00707-016-1705-3
- Pitakthapanaphong, S. and Busso, E.P. (2002), "Self-consistent elasto-plastic stress solutions for functionally graded material systems subjected to thermal transients", J. Mech. Phys. Solids, 50, 695-715. https://doi.org/10.1016/S0022-5096(01)00105-3
- Pradhan, K.K. and Chakraverty, S. (2014), "Effects of different shear deformation theories on free vibration of functionally graded beams", Int. J. Mech. Sci., 82, 149-160. https://doi.org/10.1016/j.ijmecsci.2014.03.014
- Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higherorder finite element formulation", J. Sound Vib., 318, 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
- Reddy, J.N. (2011), "A general nonlinear third-order theory of functionally graded plates", Int. J. Aerosp. Lightweight Struct., 1, 1-21. https://doi.org/10.3850/S201042861100002X
- Safa, A., Hadji, L., Bourada, M. and Zouatnia, N. (2019), "Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory", Earthq. Struct., Int. J., 17(3), 329-336. https://doi.org/10.12989/eas.2019.17.3.329
- Sahouane, A., Hadji, L. and Bourada, M. (2019), "Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., Int. J., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031
- Salah, F., Boucham, B., Bourada, F., Benzair, A., Bousahla, A.A. and Tounsi, A. (2019), "Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model", Steel Compos. Struct., Int. J., 33(6), 805-822. https://doi.org/10.12989/scs.2019.33.6.805
- Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017), "A new quasi-3D HSDT for buckling and vibration of FG plate", Struct. Eng. Mech., Int. J., 64(6), 737-749. https://doi.org/10.12989/sem.2017.64.6.737
- Selmi, A. and Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vibroeng., 20(5), 2151-2164. https://doi.org/10.21595/jve.2018.19445
- Shahrjerdi, A., Mustapha, F., Bayat, M. and Majid, D.L.A. (2011), "Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory", J. Mech. Sci. Technol., 25(9), 2195-2209. https://doi.org/10.1007/s12206-011-0610-x
- Simsek, M. (2010), "Vibration analysis of a functionally graded beam under a moving mass by using different beam theories", Compos. Struct., 92, 904-917. https://doi.org/10.1016/j.compstruct.2009.09.030
- Sina, S.A., Navazi, H.M. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30, 741-747. https://doi.org/10.1016/j.matdes.2008.05.015
- Sofiyev, A.H., Deniz, A., Akcay, I.H. and Yusufogclu, E. (2006), "The vibration and stability of a three-layered conical shell containing an FGM layer subjected to axial compressive load", Acta Mechanica, 183, 129-144. https://doi.org/10.1007/s00707-006-0328-5
- Soliman, A.E., Eltaher, M.A., Attia, M.A. and Alshorbagy, A.E. (2018), "Nonlinear transient analysis of FG pipe subjected to internal pressure and unsteady temperature in a natural gas facility", Struct. Eng. Mech., Int. J., 66(1), 85-96. https://doi.org/10.12989/sem.2018.66.1.085
- Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34, 3391-4011. https://doi.org/10.1016/j.apm.2010.03.034
- Viswanathan, K.K., Javed, S. and Abdul Aziz, Z. (2013), "Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness under shear deformation theory", Struct. Eng. Mech., Int. J., 45(2), 259-275. https://doi.org/10.12989/sem.2013.45.2.259
- Zhao, X., Lee, Y.Y. and Liew, K.M. (2009a), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 60, 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005
- Zhao, X., Lee, Y.Y. and Liew, K.M. (2009b), "Free vibration analysis of functionally graded plates using the element-free kp-Ritz method", J. Sound Vib., 319, 918-939. https://doi.org/10.1016/j.jsv.2008.06.025