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http://dx.doi.org/10.12989/scs.2018.28.4.415

Vibration and buckling of laminated beams by a multi-layer finite element model  

Kahya, Volkan (Department of Civil Engineering, Faculty of Engineering, Karadeniz Technical University)
Turan, Muhittin (Department of Civil Engineering, Faculty of Engineering, Karadeniz Technical University)
Publication Information
Steel and Composite Structures / v.28, no.4, 2018 , pp. 415-426 More about this Journal
Abstract
This paper presents a multi-layer finite element for buckling and free vibration analyses of laminated beams based on a higher-order layer-wise theory. An N-layer beam element with (9N + 7) degrees-of-freedom is proposed for analyses. Delamination and slip between the layers are not allowed. Element matrices for the single- and multi-layer beam elements are derived by Lagrange's equations. Buckling loads and natural frequencies are calculated for different end conditions and lamina stacking. Comparisons are made to show the accuracy of proposed element.
Keywords
laminated beams; finite element method; free vibration; buckling; higher-order shear deformation theory;
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  • Reference
1 Banerjee, J.R. (1998), "Free vibration of axially loaded composite Timoshenko beams using the dynamic stiffness matrix method", Comput. Struct., 69(2), 197-208.   DOI
2 Chakrabarti, A., Chalak, H.D., Iqbal, M.A. and Sheikh, A.H. (2012), "Buckling analysis of laminated sandwich beam with soft core", Latin Am. J. Solids Struct., 9(3), 1-15.
3 Chakraborty, A., Mahapatra, R.D. and Gopalakrishan, S. (2002), "Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities", Compos. Struct., 55(1), 23-36.   DOI
4 Dafedar, J.B. and Desai, Y.M. (2004), "Stability of composite and sandwich struts by mixed formulation", ASCE J. Eng. Mech., 130(7), 762-770.   DOI
5 Arya, H. (2003), "A new zig-zag model for laminated composite beams: free vibration analysis", J. Sound Vib., 264, 485-490.   DOI
6 Aydogdu, M. (2006), "Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method", Compos. Sci. Technol., 66(10), 1248-1255.   DOI
7 Kahya, V. (2012), "Dynamic analysis of laminated composite beams under moving loads using finite element method", Nuclear Eng. Des., 243, 41-48.   DOI
8 Filippi, M. and Carrera, E. (2016), "Bending and vibrations analyses of laminated beams by using a zig-zag-layer-wise theory", Compos. Part B: Eng., 98, 269-280.   DOI
9 Goyal, V.K. and Kapania, R.K. (2007), "A shear-deformable beam element for the analysis of laminated composites", Finite Elem. Anal. Des., 43(6-7), 463-477.   DOI
10 Jafari-Talookolaei, R.A., Abedi, M., Kargarnovin, M.H. and Ahmadian M.T. (2012), "An analytical approach for the free vibration analysis of generally laminated composite beams with shear effect and rotary inertia", Int. J. Mech. Sci., 65(1), 97-104.   DOI
11 Kahya, V. (2016), "Buckling analysis of laminated composite and sandwich beams by the finite element method", Compos. Part B: Eng., 91, 126-134.   DOI
12 Kant, T., Marur, S.R. and Rao, G.S. (1998), "Analytical solution to the dynamic analysis of laminated beams using higher order refined theory", Compos. Struct., 40(1), 1-9.   DOI
13 Matsunaga, H. (2001), "Vibration and buckling of multilayered composite beams according to higher order deformation theories", J. Sound Vib., 246(1), 47-62.   DOI
14 Karama, M., Abou Harb, B., Mistou, S. and Caperaa, S. (1998), "Bending, buckling and free vibration of laminated composite with a transverse shear stress continuity model", Compos. Part B: Eng., 29(3), 223-234.   DOI
15 Li, Z.M. and Qiao, P. (2015), "Buckling and postbuckling behavior of shear deformable anisotropic laminated beams with initial geometric imperfections subjected to axial compression", Eng. Struct., 85, 277-292.   DOI
16 Mantari, J.L. and Canales, F.G. (2016), "Free vibration and buckling of laminated beams via hybrid Ritz solution for various penalized boundary conditions", Compos. Struct., 152, 306-315.   DOI
17 Nguyen, T.K., Nguyen, N.D., Vo, T.P. and Thai, H.T. (2017), "Trigonometric-series solution for analysis of laminated composite beams", Compos. Struct., 160, 142-151.   DOI
18 Teboub, Y. and Hajela, P. (1995), "Free vibration of generally layered composite beams using symbolic computations", Compos. Struct., 33, 123-134.   DOI
19 Rao, K.M., Desai, Y.M. and Chitnis, M.R. (2001), "Free vibrations of laminated beams using mixed theory", Compos. Struct., 52(2), 149-160.   DOI
20 Reddy, J.N. (1997), Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, Boca Raton, FL, USA.
21 Vo, T.P. and Thai, H.T. (2012), "Vibration and buckling of composite beams using refined shear deformation theory", Int. J. Mech. Sci., 62(1), 67-76.   DOI
22 Yuan, F.G. and Miller, R.E. (1989), "A new finite element for laminated composite beams", Comput. Struct., 31(5), 737-745.   DOI
23 Yuan, F.G. and Miller, R.E. (1990), "A higher-order finite element for laminated beams", Compos. Struct., 14(2), 125-150.   DOI
24 Zhen, W. and Wanji, C. (2008), "An assessment of several displacement theories for the vibration and stability analysis of laminated composite and sandwich beams", Compos. Struct., 84(4), 337-349.   DOI
25 Aydogdu, M. (2005), "Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method", Int. J. Mech. Sci., 47(11), 1740-1755.   DOI
26 Wang, X., Zhu, X. and Hu, P. (2015), "Isogeometric finite element method for buckling analysis of generally laminated composite beams with different boundary conditions", Int. J. Mech. Sci., 104, 190-199.   DOI