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http://dx.doi.org/10.12989/sem.2019.72.5.653

A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates  

Chikr, Sara Chelahi (Universite Dr Tahar Moulay, Faculte de Technologie, Departement de Genie Civil et Hydraulique)
Kaci, Abdelhakim (Universite Dr Tahar Moulay, Faculte de Technologie, Departement de Genie Civil et Hydraulique)
Yeghnem, Redha (Universite Dr Tahar Moulay, Faculte de Technologie, Departement de Genie Civil et Hydraulique)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Publication Information
Structural Engineering and Mechanics / v.72, no.5, 2019 , pp. 653-673 More about this Journal
Abstract
This work investigates a novel quasi-3D hyperbolic shear deformation theory is presented to discuss the buckling of new type of sandwich plates. This theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements through the thickness. The enhancement of this formulation is due to the use of only five unknowns by including undetermined integral terms, contrary to other theories where we find six or more unknowns. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. A new type of FGM sandwich plates, namely, both FGM face sheets and FGM hard core are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Analytical solutions are obtained for a simply supported plate. The accuracy of the present theory is verified by comparing the obtained results with quasi-3D solutions and those predicted by higher-order shear deformation theories. The comparison studies show that the obtained results are not only more accurate than those obtained by higher-order shear deformation theories, but also comparable with those predicted by quasi-3D theories with a greater number of unknowns.
Keywords
buckling analysis; functionally graded plate; new type of sandwich plate; refined plate theory; novel quasi-3D theory;
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Times Cited By KSCI : 74  (Citation Analysis)
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88 Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A., Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.   DOI
89 Cherif, R.H., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, H., Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res.,54, 1-14. https://doi.org/10.4028/www.scientific.net/JNanoR.54.1   DOI
90 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., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289.   DOI
91 Chih-Ping, W, Hao-Yuan, L. (2010), "An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates", Compos. Struct., 92(10), 2591-2605. https://doi.org/10.1016/j.compstruct.2010.01.022.   DOI
92 Shen, H.S., Li, S.R. (2008), "Postbuckling of sandwich plates with FGM face sheets and temperature-dependent properties", Compos Pt B-Eng, 39(2), 332-344. https://doi.org/10.1016/j.compositesb.2007.01.004.   DOI
93 Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A.A., Mahmoud, S.R. (2019), "Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandwich Struct. Mater., https://doi.org/10.1177/1099636219845841.
94 Avcar, M and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11, 232. https://doi.org/10.1007/s12517-018-3579-2.   DOI
95 Ayat, H., Kellouche, Y., Ghrici, M., Boukhatem, B. (2018), "Compressive strength prediction of limestone filler concrete using artificial neural networks", Adv. Comput. Design, 3(3), 289-302. https://doi.org/10.12989/acd.2018.3.3.289.   DOI
96 Bakhadda, B., Bachir Bouiadjra, M., Bourada, F., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., 27(5), 311-324. https://doi.org/10.12989/was.2018.27.5.311.   DOI
97 Behera, S., Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Design, 3(3), 213-232. https://doi.org/10.12989/acd.2018.3.3.213.   DOI
98 Bendaho, B., Belabed, Z., Bourada, M., Benatta, M.A., Bourada, F. and Tounsi, A. (2019), "Assessment of new 2D and quasi-3D Nonlocal theories for free vibration analysis of size-dependent functionally graded (FG) nanoplates", Adv. Nano Res., 7(4), 279-294. https://doi.org/10.12989/anr.2019.7.4.277.
99 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. https://doi.org/10.1080/15376494.2014.984088.   DOI
100 Shahsavari, D., Karami, B., Li, L. (2018), "A high-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., 29(1), 53-66. https://doi.org/10.12989/scs.2018.29.1.053.   DOI
101 Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos Struct, 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018.   DOI
102 Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech, 94, 195-200. https://doi.org/10.1007/BF01176650.   DOI
103 Soliman, A.E., Eltaher, M.A., Attia, M.A, 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., 66(1), 85-96. https://doi.org/10.12989/sem.2018.66.1.085.   DOI
104 Swaminathan, K., Naveenkumar, D.T., Zenkour, A.M., Carrera, E. (2015), "Stress, vibration and buckling analyses of FGM plates-A state-of-the-art review", Compos. Struct., 120, 10-31. https://doi.org/10.1016/j.compstruct.2014.09.070.   DOI
105 Talha, M., Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034.   DOI
106 Thai, H.T., Kim, S.E. (2015), "A review of theories for the modeling and analysis of functionally graded plates and shells", Compos. Struct., 128, 70-86. https://doi.org/10.1016/j.compstruct.2015.03.010.   DOI
107 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. https://doi.org/10.4028/www.scientific.net/JNanoR.55.42.   DOI
108 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., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257.   DOI
109 Jha, D.K., Kant, T., Singh, R.K. (2012), "Higher order shear and normal deformation theory for natural frequency of functionally graded rectangular plates", Nucl Eng Des, 250, 8-13. https://doi.org/10.1016/j.nucengdes.2012.05.001.   DOI
110 Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2018), "Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory", Struct. Eng. Mech., 65(5), 621-631. https://doi.org/10.12989/sem.2018.65.5.621.   DOI
111 Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693.   DOI
112 Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solids Struct., 40, 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9.   DOI
113 Mahi, A., Adda Bedia, E.A., 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. https://doi.org/10.1016/j.apm.2014.10.045.   DOI
114 Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. https://doi.org/10.12989/eas.2018.14.2.103.   DOI
115 Belabed, Z, Houari , MSA, Tounsi, A, Mahmoud, SR, Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. B Eng., 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057.   DOI
116 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., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755.   DOI
117 Mahmoudi, A., Benyoucef, A., Tounsi, A., Benachour, A., Adda Bedia, E.A., Mahmoud, S.R. (2017), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandwich Struct. Mater., https://doi.org/10.1177/1099636217727577.
118 Mantari, J.L., Guedes Soares, C. (2012), "Generalized hybrid quasi-3D shear deformation theory for the static analysis of advanced composite plates", Compos. Struct., 94(8), 2561-2575. https://doi.org/10.1016/j.compstruct.2012.02.019.   DOI
119 Mantari, J.L., Guedes Soares, C. (2013), "A novel higher-order shear deformation theory with stretching effect for functionally graded plates", Compos. Part B Eng., 45(1), 268-281. https://doi.org/10.1016/j.compositesb.2012.05.036.   DOI
120 Berghouti, H., Adda Bedia, E.A. Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.   DOI
121 Bensattalah, T., Zidour, M., Daouadji, T.S. (2019), "A new nonlocal beam model for free vibration analysis of chiral single-walled carbon nanotubes", Compos. Mater. Eng., 1(1), 21-31. https://doi.org/10.12989/cme.2019.1.1.021.
122 Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R, Adda Bedia, E.A. (2013), "A new higher order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandwich Struct. Mater., 15(6), 671-703. https://doi.org/10.1177/1099636213498888.   DOI
123 Besseghier, A, Houari, MSA, Tounsi, A, Mahmoud, SR. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., 19(6), 601-614. https://doi.org/10.12989/sss.2017.19.6.601.   DOI
124 Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H., Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147.   DOI
125 Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A., 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., 20(3), 369-383. https://doi.org/10.12989/sss.2017.20.3.369.   DOI
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127 Matsunaga, H. (2009), "Stress analysis of functionally graded plates subjected to thermal and mechanical loadings", Compos. Struct., 87(4), 344-357. https://doi.org/10.1016/j.compstruct.2008.02.002.   DOI
128 Meftah, A., Bakora, A., Zaoui, F.Z., Tounsi, A., Adda Bedia, E.A. (2017), "A non-polynomial fourvariable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Steel Compos Struct., 23(3), 317-330. https://doi.org/10.12989/scs.2017.23.3.317   DOI
129 Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, SR. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct.Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443.   DOI
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131 Neves, A.M. A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012c), "Buckling analysis of sandwich plates with functionally graded skins using a new quasi-3D hyperbolic sine shear deformation theory and collocation with radial basis functions", ZAMM - J. Appl. Math. Mech. 92 (9), 749-766. https://doi.org/10.1002/zamm.201100186.   DOI
132 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. (2013), "Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique", Compos. Part B Eng., 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.   DOI
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134 Draoui, A., Zidour, M., Tounsi, A., Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.   DOI
135 Dai, HL, Rao, YN, Dai, T. (2016), "A review of recent researches on FGM cylindrical structures under coupled physical interactions, 2000-2015", Compos. Struct., 152, 199-225. https://doi.org/10.1016/j.compstruct.2016.05.042.   DOI
136 Dean, J., Fallah, A.S., Brown, P.M., Louca, L.A., Clyne, T.W. (2011), "Energy absorption during projectile perforation of lightweight sandwich panels with metallic fibre cores", Compos. Struct., 93(3), 1089-1095. https://doi.org/10.1016/j.compstruct.2010.09.019.   DOI
137 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., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671.   DOI
138 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., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585.   DOI
139 Eltaher, M.A., Mohamed, N., Mohamed, S.A., Seddek, L.F. (2019a), "Periodic and nonperiodic modes of postbuckling and nonlinear vibration of beams attached to nonlinear foundations", Appl. Math. Model., 75, 414-445. https://doi.org/10.1016/j.apm.2019.05.026.   DOI
140 Eltaher, M.A., Mohamed, N., Mohamed, S., 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.   DOI
141 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. https://doi.org/10.1007/s40430-015-0354-0.   DOI
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143 Karami, B., Janghorban, M., Tounsi, A. (2019a), "On exact wave propagation analysis of triclinic material using three dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487.   DOI
144 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., 18(4), 1063-1081. http://dx.doi.org/10.12989/scs.2015.18.4.1063.   DOI
145 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., 25(3), 257-270. https://doi.org/10.12989/scs.2017.25.3.257.   DOI
146 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., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695.   DOI
147 Benadouda, M., Ait Atmane, H., Tounsi, A., Bernard, F., Mahmoud, S.R. (2017), "An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities", Earthq. Struct., 13(3), 255-265. https://doi.org/10.12989/eas.2017.13.3.255.   DOI
148 Benahmed, A, Houari, MSA, Benyoucef, S, Belakhdar, K, Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomechan Eng., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009.   DOI
149 Tounsi, A, Houari, MSA, Benyoucef, S., 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. https://doi.org/10.1016/j.ast.2011.11.009.   DOI
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151 Tounsi, A., Ait Atmane, H., Khiloun, M., Sekkal, M., Taleb, O., Bousahla, A.A. (2019), "On buckling behavior of thick advanced composite sandwich plates", Compos. Mater. Eng., 1(1), 1-19. https://doi.org/10.12989/cme.2019.1.1.001.
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158 Karami, B., Janghorban, M., Tounsi, A. (2019b), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 7(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
159 Karami, B., Shahsavari, D., Janghorban, M., Tounsi, A. (2019c), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.   DOI
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161 Karami, B., Janghorban, M., Tounsi, A. (2018c), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.   DOI
162 Karami, B., Janghorban, M., Tounsi, A. (2018d), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Walled Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025.   DOI
163 Karami, B., Janghorban, M., Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. https://doi.org/10.12989/scs.2017.25.3.361.   DOI
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166 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 Comp. Struct., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157.   DOI
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169 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., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737.   DOI
170 Mohammadimehr, M., Atifeh, S.J., Navi, B.R. (2018), "Stress and free vibration analysis of piezoelectric hollow circular FG-SWBNNTs reinforced nanocomposite plate based on modified couple stress theory subjected to thermo-mechanical loadings", J. Vib. Control, 24(15), 3471-3486. https://doi.org/10.1177%2F1077546317706887.   DOI
171 Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A., 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., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397.   DOI
172 Yaghoobi, H., Valipour, M.S., Fereidoon, A., Khoshnevisrad, P. (2014), "Analytical study on post-buckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loadings using VIM", Steel Compos. Struct., 17(5), 753-776. http://dx.doi.org/10.12989/scs.2014.17.5.753.   DOI
173 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., 53(6), 1143-1165. http://dx.doi.org/10.12989/sem.2015.53.6.1143.   DOI