Steel and Composite Structures

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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)
  • Received : 2017.07.13
  • Accepted : 2018.06.05
  • Published : 2018.08.25
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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

References

  1. Arya, H. (2003), "A new zig-zag model for laminated composite beams: free vibration analysis", J. Sound Vib., 264, 485-490. https://doi.org/10.1016/S0022-460X(02)01489-X
  2. 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. https://doi.org/10.1016/j.ijmecsci.2005.06.010
  3. Aydogdu, M. (2006), "Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method", Compos. Sci. Technol., 66(10), 1248-1255. https://doi.org/10.1016/j.compscitech.2005.10.029
  4. Banerjee, J.R. (1998), "Free vibration of axially loaded composite Timoshenko beams using the dynamic stiffness matrix method", Comput. Struct., 69(2), 197-208. https://doi.org/10.1016/S0045-7949(98)00114-X
  5. 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.
  6. 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. https://doi.org/10.1016/S0263-8223(01)00130-1
  7. 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. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:7(762)
  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. https://doi.org/10.1016/j.compositesb.2016.04.050
  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. https://doi.org/10.1016/j.finel.2006.11.011
  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. https://doi.org/10.1016/j.ijmecsci.2012.09.007
  11. Kahya, V. (2012), "Dynamic analysis of laminated composite beams under moving loads using finite element method", Nuclear Eng. Des., 243, 41-48. https://doi.org/10.1016/j.nucengdes.2011.12.015
  12. Kahya, V. (2016), "Buckling analysis of laminated composite and sandwich beams by the finite element method", Compos. Part B: Eng., 91, 126-134. https://doi.org/10.1016/j.compositesb.2016.01.031
  13. 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. https://doi.org/10.1016/S0263-8223(97)00133-5
  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. https://doi.org/10.1016/S1359-8368(97)00024-3
  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. https://doi.org/10.1016/j.engstruct.2014.12.028
  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. https://doi.org/10.1016/j.compstruct.2016.05.037
  17. Matsunaga, H. (2001), "Vibration and buckling of multilayered composite beams according to higher order deformation theories", J. Sound Vib., 246(1), 47-62. https://doi.org/10.1006/jsvi.2000.3627
  18. 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. https://doi.org/10.1016/j.compstruct.2016.10.033
  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. https://doi.org/10.1016/S0263-8223(00)00162-8
  20. Reddy, J.N. (1997), Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, Boca Raton, FL, USA.
  21. Teboub, Y. and Hajela, P. (1995), "Free vibration of generally layered composite beams using symbolic computations", Compos. Struct., 33, 123-134. https://doi.org/10.1016/0263-8223(95)00112-3
  22. 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. https://doi.org/10.1016/j.ijmecsci.2012.06.001
  23. 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. https://doi.org/10.1016/j.ijmecsci.2015.10.008
  24. Yuan, F.G. and Miller, R.E. (1989), "A new finite element for laminated composite beams", Comput. Struct., 31(5), 737-745. https://doi.org/10.1016/0045-7949(89)90207-1
  25. Yuan, F.G. and Miller, R.E. (1990), "A higher-order finite element for laminated beams", Compos. Struct., 14(2), 125-150. https://doi.org/10.1016/0263-8223(90)90027-C
  26. 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. https://doi.org/10.1016/j.compstruct.2007.10.005

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