Browse > Article
http://dx.doi.org/10.12989/gae.2015.9.5.631

Analytical solution of nonlinear cylindrical bending for functionally graded plates  

Daouadji, Tahar Hassaine (Universite Ibn Khaldoun)
Hadji, Lazreg (Universite Ibn Khaldoun)
Publication Information
Geomechanics and Engineering / v.9, no.5, 2015 , pp. 631-644 More about this Journal
Abstract
This article considers the problems of cylindrical bending of functionally graded plates in which material properties vary through the thickness. The variation of the material properties follows two power-law distributions in terms of the volume fractions of constituents. In addition, this paper considers orthotropic materials rather than isotropic materials. The traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. Numerical results are presented to show the effect of the material distribution on the deflections and stresses. Results show that, all other parameters remaining the same, the studied quantities (stress, deflection) of P-FGM and E-FGM plates are always proportional to those of homogeneous isotropic plates. Therefore, one can predict the behaviour of P-FGM and E-FGM plates knowing that of similar homogeneous plates.
Keywords
functionally graded plates; cylindrical bending; stress; elasticity solutions;
Citations & Related Records
Times Cited By KSCI : 9  (Citation Analysis)
연도 인용수 순위
1 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
2 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.   DOI
3 Bao, G. and Wang, L. (1995), "Multiple cracking in functionally graded ceramic/metal coatings", Int. J. Solid. Struct., 32(19), 2853-2871.   DOI
4 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
5 Benachour, A., Daouadji, H.T., 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(6), 1386-1394.   DOI
6 Benatta, M.A., Mechab, I., Tounsi, A. and Adda bedia, E.A. (2008), "Static analysis of functionally graded short beams including warping and shear deformation effects", Computat. Mater. Sci., 44(2), 765-773.   DOI
7 Bouchafa, A., Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515.   DOI
8 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., Int. J., 14(1), 85-104.   DOI
9 Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33.   DOI
10 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.   DOI
11 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. Computat. Method., 11(6), 1350082.   DOI
12 Chung, Y.L. and Chi, S.H. (2001), "The residual stress of functionally graded materials", J. Chinese Inst. Civil Hydraul. Eng., 13, 1-9.
13 Delale, F. and Erdogan, F. (1983), "The crack problem for a nonhomogeneous plane", ASME J. Appl. Mech., 50(3), 609-614.   DOI
14 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(4), 237-247.   DOI
15 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(4), 795-810.   DOI
16 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, 467-479.
17 Hadji, L., Daouadji, T.H., Tounsi, A. and Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., Int. J., 16(5), 507-519.   DOI
18 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.   DOI
19 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, 140(2), 374-383.   DOI
20 Junga, W.Y. and Han, S.C. (2015), "Static and eigenvalue problems of Sigmoid Functionally Graded Materials (S-FGM) micro-scale plates using the modified couple stress theory", Appl. Math. Model., 39(12), 3506-3524.   DOI
21 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.   DOI
22 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. Computat. Method., 11(5), 135007.
23 Lee, Y.D. and Erdogan, F. (1994), "Residual/thermal stress in FGM and laminated thermal barrier coatings", Int. J. Fract., 69(2), 145-165.   DOI
24 Merazi, M., Hadji, L., Daouadji, T.H., Tounsi, A. and Adda Bedia, E.A. (2015), "A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position", Geomech. Eng., Int. J., 8(3), 305-321.   DOI
25 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., 39(9), 2489-2508.   DOI
26 Mantari, J.L. and Guedes Soares, C. (2012), "Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory", Compos. Struct., 94(6), 1991-2000.   DOI
27 Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(3), 793-809.   DOI
28 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. Based Des. Struct. Mach., 41(4), 421-433.   DOI
29 Saidi, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory", Steel Compos. Struct., Int. J., 15, 221-245.   DOI
30 Sallai, B.-O., Tounsi, A., Mechab, I., Bachir Bouiadjra, M., Meradjah, M. and Adda Bedia, E.A. (2009), "A theoretical analysis of flexional bending of $Al/Al_2O_3$ S-FGM thick beams", Computat. Mater. Sci., 44(4), 1344-1350.
31 Tounsi, A., Houari, M.S.A., Benyoucef, S. and 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.   DOI
32 Taj, M.N.A.G., Chakrabarti, A. and Sheikh, A.H. (2013), "Analysis of functionally graded plates using higher order shear deformation theory", Appl. Math. Model., 37(18-19), 8484-8494.   DOI
33 Thai, H.T. and Choi, D.H. (2013), "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 Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., 62(1), 57-66.   DOI
35 Wetherhold, R.C., Seelman, S. and Wang, J. (1996), "The use of functionally graded materials to eliminate or control thermal deformation", Compos. Sci. Technol., 56(9), 1099-1104.   DOI
36 Zhang, D.G. (2013), " Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory", Compos. Struct., 100, 121-126.   DOI
37 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. Technol., 34, 24-34.   DOI