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http://dx.doi.org/10.12989/amr.2019.8.3.155

Static analysis of functionally graded sandwich plates with porosities  

Keddouri, Ahemd (Department of Earth Sciences and Universe, Ziane Achour University)
Hadji, Lazreg (Department of Mechanical Engineering, Ibn Khaldoun University)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes 22000)
Publication Information
Advances in materials Research / v.8, no.3, 2019 , pp. 155-177 More about this Journal
Abstract
In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate with new definition of porosity distribution taking into account composition and the scheme of the sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Material properties of FGM layers are assumed to vary continuously across the plate thickness according to either power-law or sigmoid function in terms of the volume fractions of the constituents. The face layers are considered to be FG across each face thickness while the core is made of a ceramic homogeneous layer. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinusoidal loading has been obtained by using the Navier method. Numerical results are presented to show the effect of the material distribution, the sandwich plate geometry and the porosity on the deflections and stresses of FG sandwich plates. The validity of the present theory is investigated by comparing some of the present results with other published results.
Keywords
functionally graded materials; sandwich plates; refined plate theory; bending; Navier solution; porosity;
Citations & Related Records
Times Cited By KSCI : 10  (Citation Analysis)
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1 Akbas, S.D. (2015a), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421   DOI
2 Akbas, S.D. (2015b), "Post-buckling analysis of axially functionally graded three-dimensional beams", Int. J. Appl. Mech., 7(3), 1550047. https://doi.org/10.1142/S1758825115500477   DOI
3 Menaa, R., Tounsi, A., Mouaici, F., Mechab, I., Zidi, M. and Adda Bedia, E.A. (2012), "Analytical solutions for static shear correction factor of functionally graded rectangular beams", Mech. Adv. Mater. Struct., 19, 641-652. https://doi.org/10.1080/15376494.2011.581409   DOI
4 Safa, A., Hadji, L. and Bourada, M. (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
5 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
6 Shashank, P. and Pradyumna, S. (2018), "Analysis of functionally graded sandwich plates using a higherorder layerwise theory", Compos. Part B, 153, 325-336. https://doi.org/10.1016/j.compositesb.2018.08.121   DOI
7 Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nuc. Eng. Des., 240, 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013   DOI
8 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., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143   DOI
9 Simsek, M. and Al-shujairi, M. (2017), "Static, free and forced vibration of functionally graded (FG) sandwich beams excited by two successive moving harmonic loads", Compos. Part B, 108, 18-34. https://doi.org/10.1016/j.compositesb.2016.09.098   DOI
10 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, 209-220. https://doi.org/10.1016/j.ast.2011.11.009   DOI
11 Xuan, H.N., Thai, C.H. and Thoi, T.N. (2013), "Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory", Compos.: Part B, 55, 558-574. https://doi.org/10.1016/j.compositesb.2013.06.044   DOI
12 Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015), "Static behaviour of functionally graded sandwich beams using a quasi-3D theory", Compos.: Part B, 68, 59-74. https://doi.org/10.1016/j.compositesb.2014.08.030   DOI
13 Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002   DOI
14 Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190. https://doi.org/10.1016/j.matdes.2011.10.049   DOI
15 Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., Int. J., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389
16 Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 1-Deflection and stresses", Int. J. Solids Struct., 42, 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015   DOI
17 Zenkour, A.M. and Alghamdi, N. (2010), "Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads", Mech. Adv. Mater. Struct., 17, 419-432. https://doi.org/10.1080/15376494.2010.483323   DOI
18 Zouatnia, N. and Hadji, L. (2019), "Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory", Earthq. Struct., Int. J., 16(2), 177-183. https://doi.org/10.12989/eas.2019.16.2.177
19 Akbas, S.D. (2017a), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stabil. Dyn., 17(3), 1750033. https://doi.org/10.1142/S021945541750033X   DOI
20 Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of $ZrO_2$-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68, 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2   DOI
21 Akbas, S.D. (2017b), "Thermal effects on the vibration of functionally graded deep beams with porosity", Int. J. Appl. Mech., 9(5), 1750076. https://doi.org/10.1142/S1758825117500764   DOI
22 Akbas, S.D. (2017c), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(7), 1750100. https://doi.org/10.1142/S1758825117501009   DOI
23 Benhenni, M.A., Hassaine Daouadji, T., Abbes, B., Adim, B., Li, Y. and Abbes, F. (2018), "Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates", Adv. Mater. Res., Int. J., 7(2), 119-136. https://doi.org/10.12989/amr.2018.7.2.119
24 Akbas, S.D. (2018a), "Nonlinear thermal displacements of laminated composite beams", Coupl. Syst. Mech., Int. J., 7(6), 691-705. https://doi.org/10.12989/csm.2018.7.6.691
25 Akbas, S.D. (2018b), "Forced vibration analysis of cracked nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40(8), 392. https://doi.org/10.1007/s40430-018-1315-1   DOI
26 Akbas, S.D. (2018c), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., Int. J., 6(1), 39-55. https://doi.org/10.12989/anr.2018.6.1.039
27 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. https://doi.org/10.12989/was.2019.28.1.019
28 Daikh, A.A. and Zenkour, A.M. (2019), "Effect of porosity on the bending analysis of various functionally graded sandwich plates", Mater. Res. Express, 6(6), 065703. https://doi.org/10.1088/2053-1591/ab0971   DOI
29 Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A.A. and 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. Sandw. Struct. Mater. https://doi.org/10.1177/1099636219845841
30 Kadoli, R., Akhtar, K. and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Model., 32(12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015   DOI
31 Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (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
32 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. https://doi.org/10.1016/j.compstruct.2017.04.046   DOI