Browse > Article
http://dx.doi.org/10.12989/sem.2017.63.5.683

A refined hyperbolic shear deformation theory for bending of functionally graded beams based on neutral surface position  

Zouatnia, Nafissa (Department of Civil Engineering, Laboratory of Structures, Geotechnics and Risks (LSGR), Hassiba Benbouali University of Chlef)
Hadji, Lazreg (Department of Civil Engineering, Ibn Khaldoun University)
Kassoul, Amar (Department of Civil Engineering, Laboratory of Structures, Geotechnics and Risks (LSGR), Hassiba Benbouali University of Chlef)
Publication Information
Structural Engineering and Mechanics / v.63, no.5, 2017 , pp. 683-689 More about this Journal
Abstract
In this paper, a hyperbolic shear deformation theory is presented for bending analysis of functionally graded beams. This theory used in displacement field in terms of thickness co-ordinate to represent the shear deformation effects and 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. The governing equations are derived by employing the virtual work principle and the physical neutral surface concept. A simply supported functionally graded beam subjected to uniformly distributed loads and sinusoidal loads are consider for detail numerical study. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.
Keywords
functionally graded; Navier's solution; physical neutral surface; virtual work; sinusoidal loads;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
1 Bouremana, M., Houari, M.S.A., Tounsi, A., Kaci, A., Adda Bedia, E.A. (2013), "A new first shear deformation beam theory based on neutral surface position for functionally graded beams", Steel and Composite Structures, 15(5), 467- 479.   DOI
2 Euler, L. (1744), Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Lausanne and Geneva.
3 Hadji, L., Daouadji, T.H., Tounsi, A. and Adda bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., 16(5), 507-519.   DOI
4 Hadji, L., Zouatnia, N. and Kassoul, A. (2016), "Bending analysis of FGM plates using a sinusoidal shear deformation theory", Wind Struct., 23(6), 543-558.   DOI
5 Hadji, L. (2017), "Analysis of functionally graded plates using a sinusoidal shear deformation theory", Smart Struct. Syst., 19(4), 441-448.   DOI
6 Klouche Djedid, I., Benachour, A., Houari, M.S.A., Tounsi, A. and Ameur, M. (2014), "A n-order four variable refined theory for bending and free vibration of functionally graded plates", Steel Compos. Struct., 17(1), 21-46.   DOI
7 Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib., 318, 1210-1229.   DOI
8 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. Bas. Des. Struct. Mach., 41, 421-433.   DOI
9 Reddy, J.N. (1984), "A Simple higher order theory for laminated composites plates", ASME J. Appl. Mech., 51, 745-752.   DOI
10 Simsek, M. and Kocaturk, T. (2009), "Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load", Compos. Struct., 90(4), 465-473.   DOI
11 Simsek, M. (2010a), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nucl. Eng. Des., 240(4), 697-705.   DOI
12 Simsek, M. (2010b), "Vibration analysis of a functionally graded beam under a moving mass by using different beam theories", Compos. Struct., 92(4), 904-917.   DOI
13 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, 57-66.   DOI
14 Timoshenko, S.P. (1921), "On the correction for shear of the differential equation for transverse vibration of prismatic bars", Phil. Mag. Ser. 6, 46, 744-746.
15 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, 2019-2039.   DOI