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http://dx.doi.org/10.12989/scs.2019.31.5.503

A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation  

Boukhlif, Zoulikha (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Faculte de Technologie, Departement de Genie Civil, Universite de Sidi Bel Abbes)
Bouremana, Mohammed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Faculte de Technologie, Departement de Genie Civil, Universite de Sidi Bel Abbes)
Bourada, Fouad (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, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes)
Bourada, Mohamed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Al-Osta, Mohammed A. (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
Publication Information
Steel and Composite Structures / v.31, no.5, 2019 , pp. 503-516 More about this Journal
Abstract
This work presents a dynamic investigation of functionally graded (FG) plates resting on elastic foundation using a simple quasi-3D higher shear deformation theory (quasi-3D HSDT) in which the stretching effect is considered. The culmination of this theory is that in addition to taking into account the effect of thickness extension (${\varepsilon}_z{\neq}0$), the kinematic is defined with only 4 unknowns, which is even lower than the first order shear deformation theory (FSDT). The elastic foundation is included in the formulation using the Pasternak mathematical model. The governing equations are deduced through the Hamilton's principle. These equations are then solved via closed-type solutions of the Navier type. The fundamental frequencies are predicted by solving the eigenvalue problem. The degree of accuracy of present solutions can be shown by comparing it to the 3D solution and other closed-form solutions available in the literature.
Keywords
vibration; FG plate; Quasi-3D HSDT;
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Times Cited By KSCI : 75  (Citation Analysis)
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88 Yu, T., Zhang, J., Hu, H. and Bui, T.Q. (2019), "A novel sizedependent quasi-3D isogeometric beam model for twodirectional FG microbeams analysis", Compos. Struct., 211, 76-88.   DOI
89 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. http://dx.doi.org/10.12989/anr.2018.6.2.147   DOI
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. http://dx.doi.org/10.12989/sss.2017.19.2.115   DOI
91 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. http://dx.doi.org/10.12989/sem.2016.58.3.397   DOI
92 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. http://dx.doi.org/10.12989/sem.2018.66.1.061   DOI
93 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. http://dx.doi.org/10.12989/sem.2016.57.5.837   DOI
94 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. http://dx.doi.org/10.12989/scs.2016.20.2.227   DOI
95 Sayyad, A.S., Shinde, B.M. and Ghugal, Y.M. (2016), "Bending, vibration and buckling of laminated composite plates using a simple four variable plate theory", Lat. Am. J. Solids Struct., 13(3), 516-535.   DOI
96 Hasani Baferani, A., Saidi, A.R. and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93, 1842-1853.   DOI
97 Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Maleki, M. (2018c), "Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects", Compos. Struct., 187, 498-508.   DOI
98 Hajmohammad, M.H., Zarei, M.S., Farrokhian, A. and Kolahchi, R. (2018d), "A layerwise theory for buckling analysis of truncated conical shells reinforced by CNTs and carbon fibers integrated with piezoelectric layers in hygrothermal environment", Adv. Nano Res., Int. J., 6(4), 299-321. http://dx.doi.org/10.12989/anr.2018.6.4.299   DOI
99 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. http://dx.doi.org/10.12989/scs.2015.18.1.235   DOI
100 Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140(2), 374-383.   DOI
101 Hosseini-Hashemi, Sh., Rokni Damavandi Taher, H., Akhavan, H. and Omidi, M. (2010), "Free vibration of functionally graded rectangular platesusing first-order shear deformation plate theory", Appl. Math. Model., 34, 1276-1291.   DOI
102 Hosseini-Hashemi, Sh., Fadaee, M. and Rokni Damavandi Taher, H. (2011), "Exact solutions for free flexural vibration of Levytype rectangular thick plates via third-order shear deformation plate theory", Appl. Math. Model., 35, 708-727.   DOI
103 Akavci, S.S. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667676.   DOI
104 Shokravi, M. (2017c), "Dynamic pull-in and pull-out analysis of viscoelastic nanoplates under electrostatic and Casimir forces via sinusoidal shear deformation theory", Microelectro. Reliabil., 71, 17-28.   DOI
105 Shokravi, M. (2017d), "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. http://dx.doi.org/10.12989/scs.2017.23.6.623   DOI
106 Shufrin, I. and Eisenberger, M. (2005), "Stability and vibration of shear deformable plates - first order and higher order analyses", Int. J. Solids Struct., 42, 1225-1251.   DOI
107 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.
108 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. http://dx.doi.org/10.12989/scs.2016.20.5.963   DOI
109 Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B: Eng., 96, 136-152.   DOI
110 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
111 Aldousari, S.M. (2017), "Bending analysis of different material distributions of functionally graded beam", Appl. Phys. A, 123, 296.   DOI
112 Sheikholeslami, S.A. and Saidi, A.R. (2013), "Vibration analysis of functionally graded rectangular plates resting on elastic foundation using higher-order shear and normal deformable plate theory", Compos. Struct., 106, 350-361.   DOI
113 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. http://dx.doi.org/10.12989/scs.2017.25.4.389   DOI
114 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. http://dx.doi.org/10.12989/.2017.64.6.737
115 Selmi, A. and Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vibroeng., 20(5), 2151-2164.   DOI
116 Shi, P., Dong, C., Sun, F., Liu, W. and Hu, Q. (2018), "A new higher order shear deformation theory for static, vibration and buckling responses of laminated plates with the isogeometric analysis", Compos. Struct., 204, 342-358.   DOI
117 Shokravi, M. (2017a), "Vibration analysis of silica nanoparticlesreinforced concrete beams considering agglomeration effects", Comput. Concrete, Int. J., 19(3), 333-338. http://dx.doi.org/10.12989/cac.2017.19.3.333   DOI
118 Shokravi, M. (2017b), "Buckling analysis of embedded laminated plates with agglomerated CNT-reinforced composite layers using FSDT and DQM", Geomech. Eng., Int. J., 12(2), 327-346. http://dx.doi.org/10.12989/gae.2017.12.2.327   DOI
119 Thai, H.T. and Choi, D.H. (2012), "A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation", Compos. Part B: Eng., 43(5), 2335-2347.   DOI
120 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. http://dx.doi.org/10.12989/sem.2018.66.1.085   DOI
121 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. http://dx.doi.org/10.12989/sem.2019.69.6.637   DOI
122 Tounsi, A, Houari, M.S.A. and Benyoucef, S. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220.   DOI
123 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
124 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. http://dx.doi.org/10.12989/sem.2016.60.2.313   DOI
125 Amnieh, H.B., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by SiO2 nanoparticles subjected to blast load experimentally and theoretically", Constr. Build. Mater., 174, 633-644.   DOI
126 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. http://dx.doi.org/10.12989/cac.2016.17.5.567   DOI
127 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. http://dx.doi.org/10.12989/scs.2015.18.2.409   DOI
128 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. http://dx.doi.org/10.12989/sem.2018.68.6.661   DOI
129 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. http://dx.doi.org/10.12989/was.2019.28.1.019   DOI
130 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
131 Chen, C.S., Hsu, C.Y. and Tzou, G.J. (2009),"Vibration and stability of functionally graded platesbased on a higher-order deformation theory", J. Reinf. Plast Compos., 28(10), 1215-1234.   DOI
132 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
133 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. http://dx.doi.org/10.12989/scs.2018.26.2.125   DOI
134 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
135 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. http://dx.doi.org/10.12989/scs.2016.22.2.257   DOI
136 Jin, G., Su, Z., Shi, S., Ye, T. and Gao, S. (2014), "Threedimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions", Compos. Struct., 108, 565-577.   DOI
137 Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of sheardeformable composite beams using a novel simple twounknown beam theory", Struct. Eng. Mech., Int. J., 65(5), 621-631. http://dx.doi.org/10.12989/sem.2018.65.5.621   DOI
138 Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. http://dx.doi.org/10.12989/scs.2015.18.3.693   DOI
139 Karamanli, A. (2017), "Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory", Compos. Struct., 174, 70-86.   DOI
140 Karami, B. and Karami, S. (2019), "Buckling analysis of nanoplate-type temperature-dependent heterogeneous materials", Adv. Nano Res., Int. J., 7(1), 51-61. http://dx.doi.org/10.12989/anr.2019.7.1.051   DOI
141 Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11, 232.   DOI
142 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. http://dx.doi.org/10.12989/scs.2015.18.1.187   DOI
143 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. http://dx.doi.org/10.12989/sem.2018.65.4.453   DOI
144 Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. http://dx.doi.org/10.12989/scs.2019.30.6.603   DOI