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http://dx.doi.org/10.12989/sem.2015.53.6.1215

A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations  

Meksi, Abdeljalil (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil)
Benyoucef, Samir (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil)
Houari, Mohammed Sid Ahmed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil)
Tounsi, Abdelouahed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil)
Publication Information
Structural Engineering and Mechanics / v.53, no.6, 2015 , pp. 1215-1240 More about this Journal
Abstract
In this work, a novel simple first-order shear deformation plate theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded plates and supported by either Winkler or Pasternak elastic foundations. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Numerical results of present theory are compared with results of the traditional first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.
Keywords
vibration; bending; FGM; plate theory; elastic foundation; neutral surface position;
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Times Cited By KSCI : 11  (Citation Analysis)
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1 Cheng, Z.Q. and Kitipornchai, S. (1999), "Membrane analogy of buckling and vibration of inhomogeneous plates", J. Eng. Mech., ASCE, 125, 1293-1297.   DOI
2 Croce, L.D. and Venini, P. (2004), "Finite elements for functionally graded Reissner-Mindlin plates", Comput. Meth. Appl. Mech. Eng., 193, 705-725.   DOI
3 Curiel Sosa, J.L., Anwar Beg, O. and Liebana Murillo, J.M. (2013), "Finite element analysis of structural instability using a switching implicit-explicit technique", Int. J. Comp. Meth. Eng. Sci. Mech., 14, 452- 464.   DOI
4 Curiel Sosa, J.L., Munoz, J.J., Pinho, S.T. and Anwar Beg, O. (2012), "(XFEM) Simulation of damage in laminates", Applied Sciences and Engineering (ECCOMAS 2012), Eds. Eberhardsteiner, J. et al., Vienna, Austria, September.
5 Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., 17(1), 69-81.   DOI
6 El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53, 237-247.   DOI   ScienceOn
7 Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49, 795-810.   DOI
8 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., 18(1), 235-253.   DOI
9 Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., ASCE, 140, 374-383.   DOI
10 Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Adda Bedia, E.A. (2008), "Sound Wave Propagation in Single- Walled Carbon Nanotubes using Nonlocal Elasticity", Physica E, 40, 2791-2799.   DOI
11 Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011a), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", Int. J. Mech. Sci., 53(1), 11-22.   DOI   ScienceOn
12 Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011b), "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.   DOI   ScienceOn
13 Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111.   DOI
14 Huang, Z.Y., Lü, C.F. and Chen, W.Q. (2008), "Benchmark solutions for functionally graded thick plates resting on Winkler-Pasternak elastic foundations", Compos. Struct., 85, 95-104.   DOI
15 Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Comput. Meth., 11(5), 135007.
16 Koizumi, M. (1993), "Concept of FGM", Ceramic Tran., 34, 3-10.
17 Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B, 28, 1-4.
18 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. (in Press)
19 Lam, K.Y., Wang, C.M. and He, X.Q. (2000), "Canonical exact solutions for Levy-plates on two-parameter foundation using Green's functions", Eng. Struct., 22, 364-378.   DOI
20 Lu, C.F., Lim, C.W. and Chen, W.Q. (2009), "Exact solutions for free vibrations of functionally graded thick plates on elastic foundations", Mech. Adv. Mater. Struct., 16, 576-584.   DOI
21 Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", ASME J. Appl. Mech., 18, 31-38.
22 Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 641-650.   DOI
23 Ould Larbi, L., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Base. Des. Struct. Mach., 41, 421-433.   DOI   ScienceOn
24 Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation", J. Sound. Vib, 318, 176-192.   DOI
25 Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solid. Struct., 35, 4457-4476.   DOI
26 Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47, 663-684.   DOI
27 Qian, L.F., Batra, R.C. and Chen, L.M. (2004), "Static and dynamic deformations of thick functionally graded elastic plate by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method", Compos. Part B, 35, 685-697.   DOI
28 Rashidi, M.M., Shooshtari, A. and Anwar Beg, O. (2012), "Homotopy perturbation study of nonlinear vibration of Von Kármán rectangular plates", Comput. Struct., 106/107, 46-55.   DOI   ScienceOn
29 Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons Inc.
30 Reissner, E. (1950), "On a variational theorem in elasticity", J. Math. Phys. (Cambridge, Mass.), 29, 90-95.   DOI
31 Semmah, A., Tounsi, A., Zidour, M., Heireche, H. and Naceri, M. (2014), "Effect of chirality on critical buckling temperature of a zigzag single-walled carbon nanotubes using nonlocal continuum theory", Full., Nanotub. Carb. Nanostr., 23, 518-522.
32 Sadoune, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2014), "A novel first-order shear deformation theory for laminated composite plates", Steel Compos. Struct., 17(3), 321-338   DOI
33 Thai, H.T. and Choi, D.H. (2013a), "A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates", Compos. Struct., 101, 332-340.   DOI
34 Thai, H.T. and Choi, D.H., (2013b), "A simple first-order shear deformation theory for laminated composite plates", Compos. Struct., 106, 754-763.   DOI
35 Vel, S.S. and Batra, R.C. (2002), "Three-dimensional analysis of transient thermal stresses in functionally graded plates", Int. J. Solid. Struct., 40, 7181-7196.
36 Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013a), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Tech., 24, 209-220.   DOI
37 Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013b), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., 1(1), 1-11.   DOI
38 Tounsi, A., Semmah, A. and Bousahla, A.A. (2013c), "Thermal buckling behavior of nanobeam using an efficient higher-order nonlocal beam theory", J. Nanomech. Micromech., ASCE, 3, 37-42.   DOI
39 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
40 Wu, C.P., Chiu, K.H. and Wang, Y.M. (2011), "RMVT-based meshless collocation and element free Galerkin methods for the quasi-3D analysis of multilayered composite and FGM plates", Compos. Struct., 93, 923-943.   DOI
41 Wu, C.P. and Chiu, K.H. (2011), "RMVT-based meshless collocation and element-free Galerkin methods for the quasi-3D free vibration analysis of multilayered composite and FGM plates", Compos. Struct., 93, 1433-1448.   DOI
42 Wu, C.P. and Li, H.Y. (2010b), "An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates", Compos. Struct., 92, 2591-2605.   DOI
43 Wu, C.P. and Li, H.Y. (2010), "RMVT- and PVD-based finite layer methods for the quasi-3D free vibration analysis of multilayered composite and FGM plates", Comput. Mater. Contin., 19, 155-198.
44 Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48(8), 2019-2035.   DOI   ScienceOn
45 Xiang, Y., Wang, C.M. and Kitipornchai, S. (1994), "Exact vibration solution for initially stressed Mindlin plates on Pasternak foundation", Int. J. Mech. Sci., 36, 311-316.   DOI
46 Xiang, Y. (2003), "Vibration of rectangular Mindlin plates resting on non-homogenous elastic foundations", Int. J. Mech. Sci., 45, 1229-1244.   DOI
47 Yahoobi, H. and Feraidoon, A. (2010), "Influence of neutral surface position on deflection of functionally graded beam under uniformly distributed load", World Appl. Sci. J., 10(3), 337-341.   DOI
48 Yamanouchi, M., Koizumi, M., Hirai, T. and Shiota I. (1990), Proceedings of the 1st International Symposium Functionally Gradient Material, Japan.
49 Yang, J., Liew, K.M. and Kitipornchai, S. (2005), "Second-order statistics of the elastic buckling of functionally graded rectangular plates", Compos. Sci. Tech., 65, 1165-1175.   DOI
50 Yang, J. and Shen, H.S. (2001), "Dynamic response of initially stressed functionally graded rectangular thin plates", Compos. Struct., 54, 497-508.   DOI
51 Ying, J., Lu, C.F. and Chen, W.Q. (2008), "Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations", Compos. Struct., 84, 209-219.   DOI
52 Yin, S., Hale, J.S., Yu, T., Bui, T.Q. and Bordas, S.P.A. (2014), "Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates", Compos. Struct., 118, 121- 138.   DOI
53 Zhou, D., Cheung, Y.K., Lo, S.H. and Au, F.T.K. (2004), "Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation", Int. J. Numer. Meth. Eng., 59, 1313-1334.   DOI
54 Zenkour, A.M., Allam, M.N.M., Shaker, M.O. and Radwan, A.F. (2011), "On the simple and mixed firstorder theories for plates resting on elastic foundations", Acta Mechanica, 220, 33-46.   DOI
55 Zenkour, A.M. and Radwan, A.F. (2013), "On the simple and mixed first-order theories for functionally graded plates resting on elastic foundations", Meccanica, 48, 1501-1516.   DOI
56 Zhong, Z. and Yu, T. (2006), "Vibration of a simply supported functionally graded piezoelectric rectangular plate", Smart. Mater. Struct, 15, 1404-1412.   DOI
57 Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (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
58 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., 18(1), 187-212.   DOI
59 Ait Amar Meziane, M., 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
60 Ait Yahia, S., 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.   DOI
61 Benachour, A., Daouadji Tahar, H., Ait Atmane, H., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B, 42, 1386-1394.   DOI
62 Bachir Bouiadjra, R., Adda Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., 48, 547 - 567.   DOI
63 Baferani, AH, Saidi, AR and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93(7), 1842- 1853.   DOI
64 Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (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
65 Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale rffects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Compos. Part B, 57, 21-24.   DOI
66 Benyoucef, S., Mechab, I., Tounsi, A., Fekrar, A., Ait Atmane, H. and Adda Bedia, E.A. (2010), "Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations", Mech. Compos. Mater., 46(4), 425-434.   DOI
67 Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N. and Boumia, L. (2008), "The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", J. Phys. D: Appl. Phys., 41, 225404.   DOI
68 Berrabah, H.M., Tounsi, A., Semmah, A. and Adda Bedia, E.A. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., 48(3), 351-365.   DOI
69 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., 14, 85-104.   DOI   ScienceOn
70 Birman, V. and Byrd, LW. (2007), "Modeling and analysis of functionally graded materials and structures", ASME Appl. Mech. Rev., 60, 195-216.   DOI
71 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., 18(2), 409-423.   DOI
72 Bouremana, M., Houari, M.S.A., Tounsi, A., Kaci, A. and Adda Bedia, E.A. (2013), "A new first shear deformation beam theory based on neutral surface position for functionally graded beams", Steel Compos. Struct., 15(5), 467-479.   DOI   ScienceOn
73 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
74 Brischetto, S. (2013), "Exact elasticity solution for natural frequencies of functionally graded simplysupported structures", CMES: Comput. Model. Eng. Sci., 95(5), 361-400.
75 Chakraverty, S. and Pradhan, K.K. (2014), "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions", Aerosp. Sci. Tech., 36, 132-156.   DOI
76 Cheng, Z.Q. and Batra, R.C. (2000), "Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories", Arch. Mech., 52, 143-158.