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http://dx.doi.org/10.12989/scs.2021.41.4.487

Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model  

Bouafia, Khadidja (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Selim, Mahmoud M. (Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University)
Bourada, Fouad (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes)
Bourada, Mohamed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Tounsi, Abdeldjebbar (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Adda Bedia, E.A. (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Publication Information
Steel and Composite Structures / v.41, no.4, 2021 , pp. 487-503 More about this Journal
Abstract
In this investigation, a novel analytical model based on combined (cubic, sinusoidal and exponential) higher order quasi-3D formulation is developed to examine flexural and free vibrational response on the various FG-plate resting on elastic foundation. The presented model is simple and contains a variable number less than others quasi-three dimensional theories. The effective properties of the structure are computed using linear, cubic, quadratic and inverse quadratic formulations which represent the volume fraction of the ceramic. The elastic foundation is structured by the constant parameter of Winkler which represents the reaction of the elastic springs and Pasternak one's in the form of a shear layer of subgrade. The analytical solution of the problem is obtained on the basis of the both Hamilton's principle and Navier's technique. The exactness of the current combined quasi-3D HSDT which takes into account the thickness stretching effect are checked and compared with others existing analytical models. Parametric studies are performed to shows the effects of the material distribution, inhomogeneity index, elastic foundation parameters, geometry and dimension ratios on displacements, stresses and naturel frequencies of the simply supported FG-plates.
Keywords
flexural analysis; functionally graded plate; Quasi 3D HSDT; vibrational analysis;
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1 Karami, B. and Janghorban, M. (2019), "A new size-dependent shear deformation theory for free vibration analysis of functionally graded/anisotropic nanobeams", Thin-Wall. Struct., 143, 106227. https://doi.org/10.1016/j.tws.2019.106227.   DOI
2 Khalaf, B.K., Fenjan, RM. and Faleh, N.M. (2019), "Analyzing nonlinear mechanical-thermal buckling of imperfect micro-scale beam made of graded graphene reinforced composites", Adv. Mater. Res., 8(3). 219-235. https://doi.org/10.12989/amr.2019.8.3.219.   DOI
3 Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of fgm beams", Struct. Eng. Mech., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427.   DOI
4 Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., 7(3), 181-190. https://doi.org/10.12989/anr.2019.7.3.181.   DOI
5 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. (2012), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B, 43, 711-725.https://doi.org/10.1016/j.compositesb.2011.08.009.   DOI
6 Vaishali, Mukhopadhyay, T., Karsh, P.K., Basu, B. and Dey, S. (2020), "Machine learning based stochastic dynamic analysis of functionally graded shells", Compos. Struct., 111870. https://doi.org/10.1016/j.compstruct.2020.111870.   DOI
7 Vinyas, M. (2020), "On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT", Compos. Struct., 240, 112044. https://doi.org/10.1016/j.compstruct.2020.112044.   DOI
8 Yaylaci, M. and Avcar, M. (2020), "Finite element modeling of contact between an elastic layer and two elastic quarter planes", Comput. Concrete, 26(2), 107-114. https://doi.org/10.12989/cac.2020.26.2.107.   DOI
9 Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018b), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149.   DOI
10 Zenkour, A.M. (2007), "Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate", Arch. Appl. Mech., 77(4), 197-214. https://doi.org/10.1007/s00419-006-0084-y.   DOI
11 Akgun, G. and Kurtaran, H. (2019), "Large displacement transient analysis of FGM super-elliptic shells using GDQ method", Thin-Wall. Struct., 141, 133-152. https://doi.org/1010.1016/j.tws.2019.03.049.   DOI
12 Shokouhifard, V., Mohebpour, S., Malekzadeh, P. and Alighanbari, H. (2020), "An inclined FGM beam under a moving mass considering Coriolis and centrifugal accelerations", Steel Compos. Struct., 35(1), 61-76. https://doi.org/10.12989/scs.2020.35.1.061.   DOI
13 Zhang, H., Jiang, J.K. and Zhang, Z.C. (2014), "Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates", Appl. Math. Mech., 35(11), 1467-1478. https://doi.org/10.1007/s10483-014-1871-7.   DOI
14 Abdelrahman, W.G. (2020), "Effect of material transverse distribution profile on buckling of thick functionally graded material plates according to TSDT", Struct. Eng. Mech., 74(1), 83-90. https://doi.org/10.12989/sem.2020.74.1.083.   DOI
15 Abdulrazzaq, M.A. Fenjan, R.M Ahmed, R.A. and Faleh, N.M. (2020), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", Steel Compos. Struct., 35(1), 147-157. https://doi.org/10.12989/scs.2020.35.1.147.   DOI
16 Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.   DOI
17 Liu, W., Liu, S., Fan, M., Tian, W., Wang, J. and Tahouneh, V. (2020), "Influence of internal pores and graphene platelets on vibration of non-uniform functionally graded columns", Steel Compos. Struct., 35(2), 295-303. https://doi.org/10.12989/scs.2020.35.2.295.   DOI
18 Fenjan, R.M., Faleh, N.M. and Ahmed, R.A. (2020b), "Geometrical imperfection and thermal effects on nonlinear stability of microbeams made of graphene-reinforced nano-composites", Adv. Nano Res., 9(3). 147-156.: https://doi.org/10.12989/anr.2020.9.3.147.   DOI
19 Ahmed, R.A., Moustafa, N.M., Faleh, N.M. and Fenjan, R.M. (2020), "Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method", Struct. Eng. Mech., 76(3), 413-420. https://doi.org/10.12989/sem.2020.76.3.413.   DOI
20 Akavci, S.S. and Tanrikulu, A.H. (2015), "Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories", Compos. Part B, 83, 203-215. https://doi.org/10.1016/j.compositesb.2015.08.043.   DOI
21 Asiri, S.A., Akbas, S.D. and Eltaher, M.A. (2020), "Damped dynamic responses of a layered functionally graded thick beam under a pulse load", Struct. Eng. Mech., 75(6), 713-722. https://doi.org/10.12989/sem.2020.75.6.713.   DOI
22 Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421.   DOI
23 Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", Int. J. Eng. Sci., 115, 73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011.   DOI
24 Bharath, H.S., Waddar, S., Bekinal, S.I., Jeyaraj, P. and Doddamani, M. (2020), "Effect of axial compression on dynamic response of concurrently printed sandwich", Compos. Struct., 113223. https://doi.org/10.1016/j.compstruct.2020.113223.   DOI
25 Bouazza, M., Antar, K., Amara, K., Benyoucef, S. and Adda Bedia, E.A. (2019), "Influence of temperature on the beams behavior strengthened by bonded composite plates",Geomech. Eng., 18(5), 555-566. https://doi.org/10.12989/gae.2019.18.5.555.   DOI
26 Farzam-Rad, S.A., Hassani, B. and Karamodin, A. (2017), "Isogeometric analysis of functionally graded plates using a new quasi-3D shear deformation theory based on physical neutral surface", Compos. Part B, Eng., 108, 174-189. https://doi.org/10.1016/j.compositesb.2016.09.029.   DOI
27 Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B, 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005.   DOI
28 Daouadji, T.H. and Hadji, L. (2015), "Analytical solution of nonlinear cylindrical bending for functionally graded plates", Geomech. Eng., 9(5), 631-644. https://doi.org/10.12989/gae.2015.9.5.631.   DOI
29 Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates", Adv. Nano Res., 8(2), 115-134. https://doi.org/10.12989/anr.2020.8.2.115.   DOI
30 Eldeeb, A.M., Shabana, Y. M. and Elsawaf, A. (2020a), "Influences of angular deceleration on the thermoelastoplastic behaviors of nonuniform thickness multilayer FGM discs", Compos. Struct., 113092. https://doi.org/10.1016/j.compstruct.2020.113092.   DOI
31 Fenjan, R.M., Moustafa, N.M. and Faleh, N.M. (2020a), "Scale-dependent thermal vibration analysis of FG beams having porosities based on DQM", Adv. Nano Res., 8(4), 283-292. https://doi.org/10.12989/anr.2020.8.4.283.   DOI
32 Hadji, L. (2020), "Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model", Smart Struct. Syst., 26(2), 253-262. https://doi.org/10.12989/sss.2020.26.2.253.   DOI
33 Jalaei, M.H. and Civalek, O. (2019), "On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam", Int. J. Eng. Sci., 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013.   DOI
34 Civalek, O., Dastjerdi, S., Akbas, S.D. and Akgoz, B. (2021), "Vibration analysis of carbon nanotube-reinforced composite microbeams", Math. Method. Appl. Sci., Special issue, https://doi.org/10.1002/mma.7069.   DOI
35 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. https://doi.org/10.1016/j.compstruct.2007.01.030.   DOI
36 Karsh, P.K., Mukhopadhyay, T., Chakraborty, S., Naskar, S. and Dey, S. (2019), "A hybrid stochastic sensitivity analysis for low-frequency vibration and low-velocity impact of functionally graded plates", Compos. Part B: Eng., 107221. https://doi.org/10.1016/j.compositesb.2019.107221.   DOI
37 Kiani, Y. (2019), "NURBS-based thermal buckling analysis of graphene platelet reinforced composite laminated skew plates", J. Therm. Stresses, 1-19. https://doi.org/10.1080/01495739.2019.1673687.   DOI
38 Mantari, J.L. 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.   DOI
39 Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J, Mech, - A/Solids, 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005.   DOI
40 Merzoug, M., Bourada, M., Sekkal, M., Ali Chaibdra, A., Belmokhtar, C., Benyoucef, S. and Benachour, A. (2020), "2D and quasi 3D computational models for thermoelastic bending of FG beams on variable elastic foundation: Effect of the micromechanical models", Geomech. Eng., 22(4), 361-374. https://doi.org/10.12989/gae.2020.22.4.361.   DOI
41 Karsh, P.K., Mukhopadhyay, T. and Dey, S. (2018), "Stochastic dynamic analysis of twisted functionally graded plates", Compos. Part B: Eng., 147, 259-278. https://doi.org/10.1016/j.compositesb.2018.03.043.   DOI
42 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. https://doi.org/10.1016/j.compstruct.2013.06.016.   DOI
43 Shahmohammadi, M.A., Azhari, M. and Saadatpour, M.M. (2020), "Free vibration analysis of sandwich FGM shells using isogeometric B-spline finite strip method", Steel Compos. Struct., 34(3), 361-376. https://doi.org/10.12989/scs.2020.34.3.361.   DOI
44 Shabana, Y.M., Elsawaf, A., Khalaf, H. and Khalil, Y. (2017), "Stresses minimization in functionally graded cylinders using particle swarm optimization technique", Int. J. Press. Vess. Piping, 154, 1-10. https://doi.org/10.1016/j.ijpvp.2017.05.013.   DOI
45 Akgoz, B. and Civalek, O. (2013), "Buckling analysis of functionally graded microbeams based on the strain gradient theory", Acta Mechanica, 224(9), 2185-2201. https://doi.org/10.1007/s00707-013-0883-5.   DOI
46 Akbas, S.D., Fageehi, Y.A., Assie, A.E. and Eltaher, M.A. (2020), "Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load", Eng. with Comput., https://doi.org/10.1007/s00366-020-01070-3.   DOI
47 Alijani, F. and Amabili, M. (2014), "Effect of thickness deformation on large-amplitude vibrations of functionally graded rectangular plates", Compos. Struct., 113, 89-107. https://doi.org/10.1016/j.compstruct.2014.03.006.   DOI
48 Bouiadjra, R.B., Bachiri, A., Benyoucef, S., Fahsi, B. and Bernard, F. (2020), "An investigation of the thermodynamic effect on the response of FG beam on elastic foundation", Struct. Eng. Mech., 76(1), 115-127. https://doi.org/10.12989/sem.2020.76.1.115.   DOI
49 Sadoughifar, A., Farhatnia, F., Izadinia, M. and Talaeetaba, S.B. (2020), "Size-dependent buckling behaviour of FG annular/circular thick nanoplates with porosities resting on Kerr foundation based on new hyperbolic shear deformation theory", Struct. Eng. Mech., 73(3), 225-238. https://doi.org/10.12989/sem.2020.73.3.225.   DOI
50 Pham, Q.H., Pham, D.T., Trinh, Q.V. and Phan, D.H. (2020), "Geometrically nonlinear analysis of functionally graded shells using an edge-based smoothed MITC3 (ES-MITC3) fnite elements", Eng. with Computers., 36, 1069-1082. https://doi.org/10.1007/s00366-019-00750-z.   DOI
51 Srinivas, S, JogaRao, CV, Rao, AK.(1970), "An exact analysis for vibration of simply supported homogeneous and laminated thick rectangular plates", J Sound Vib, 12(2), 187-199. https://doi.org/10.1016/0022-460X(70)90089-1.   DOI
52 Timesli, A. (2020), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete, 26(1), 53-62. https://doi.org/10.12989/cac.2020.26.1.053.   DOI
53 Yuan, Y., Zhao, K., Zhao, Y. and Kiani, K. (2020), "Nonlocal-integro-vibro analysis of vertically aligned monolayered nonuniform FGM nanorods", Steel Compos. Struct., 37(5), 551-569. https://doi.org/10.12989/scs.2020.37.5.551.   DOI
54 Zhu, P. and Liew, K.M. (2011), "Free vibration analysis of moderately thick functionally graded plates by local Krigingmeshless method", Compos. Struct., 93(11), 2925-2944. https://doi.org/10.1016/j.compstruct.2011.05.011.   DOI
55 Hosseini-Hashemi, S.H., Fadaee, M. and Atashipour, S.R. (2011), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed form procedure", Compos. Struct., 93(2), 722-735. https://doi.org/10.1016/j.compstruct.2010.08.007.   DOI
56 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. https://doi.org/10.1016/S0022-460X(03)00412-7.   DOI
57 Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H, and Abdel-Wahab, M. (2020), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA", Compos. Struct., 113216. https://doi.org/10.1016/j.compstruct.2020.113216.   DOI
58 Demir, C. and Civalek, O. (2017), "On the analysis of microbeams", Int. J. Eng. Sci., 121, 14-33. https://doi.org/10.1016/j.ijengsci.2017.08.016.   DOI
59 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., 21(1), 113-122. https://doi.org/10.12989/sss.2018.21.1.113.   DOI
60 Fenjan, R.M., Faleh, N.M., and Ahmed R.A. (2020c), "Strain gradient based static stability analysis of composite crystalline shell structures having porosities", Steel and Composite Structures, 36(6), 631-642. http://dx.doi.org/10.12989/scs.2020.36.6.631.   DOI
61 Selmi, A. (2020), "Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam". Smart Struct. Syst., 26(3), 361-371. https://doi.org/10.12989/sss.2020.26.3.361.   DOI
62 Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.   DOI
63 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.   DOI
64 Eldeeb, A., Shabana, Y. and Elsawaf, A. (2020b), "Thermo-elastoplastic behavior of a rotating sandwich disc made of temperature-dependent functionally graded materials", J. Sandw. Struct. Mater., 109963622090497. https://doi.org/10.1177/1099636220904970.   DOI
65 Jha, D.K., Kant, T. and Singh, R.K. (2013), "Free vibration response of functionally graded thick plates with shear and normal deformations effects", Compos. Struct., 96, 799-823. https://doi.org/10.1016/j.compstruct.2012.09.034.   DOI
66 Noroozi, R., Barati, A., Kazemi, A., Norouzi, S. and Hadi, A. (2020), "Torsional vibration analysis of bi-directional FG nano-cone with arbitrary cross-section based on nonlocal strain gradient elasticity", Adv. Nano Res., 8(1), 13-24. https://doi.org/10.12989/anr.2020.8.1.013.   DOI
67 Peng, L., Ni, Z. and Huang, X. (2013), "Review on the fire safety of exterior wall claddings in high-rise buildings in China", Procedia Eng., 62, 663-670. https://doi.org/10.1016/j.proeng.2013.08.112.   DOI
68 Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bachir Bouiadjra, R., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065.   DOI
69 Saadatfar, M. and Zarandi, M.H. (2020), "Effect of angular acceleration on the mechanical behavior of an exponentially graded piezoelectric rotating annular plate with variable thickness", Mech. Based Des. Struct., https://doi.org/10.1080/15397734.2020.1751198.   DOI
70 Selmi, A. (2019), "Effectiveness of SWNT in reducing the crack effect on the dynamic behavior of aluminium alloy", Adv. Nano Res., 7(5), 365-377. https://doi.org/10.12989/anr.2019.7.5.365.   DOI
71 Thai, H.T. and Kim, S.E. (2013), "A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates", Compos. Struct., 99, 172-180. https://doi.org/10.1016/j.compstruct.2012.11.030.   DOI
72 Thanh, C.L., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. with Comput.. https://doi.org/10.1007/s00366-020-01154-0.   DOI
73 Vaghefi, R., Baradaran, G.H. and Koohkan, H. (2010), "Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrove-Galerkin (MLPG) method", Eng. Anal. Bound Elem., 34, 564-573. https://doi.org/10.1016/j.enganabound.2010.01.005.   DOI