Structural Engineering and Mechanics

  • 제42권4호
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  • Pages.471-488
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  • 2012
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Efficient finite element model for dynamic analysis of laminated composite beam

  • Naushad Alam, M. (Department of Mechanical Engineering, Aligarh Muslim University) ;
  • Upadhyay, Nirbhay Kr. (Department of Mechanical Engineering, Aligarh Muslim University) ;
  • Anas, Mohd. (Department of Mechanical Engineering, Aligarh Muslim University)
  • 투고 : 2011.02.21
  • 심사 : 2012.04.11
  • 발행 : 2012.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

An efficient one dimensional finite element model has been presented for the dynamic analysis of composite laminated beams, using the efficient layerwise zigzag theory. To meet the convergence requirements for the weak integral formulation, cubic Hermite interpolation is used for the transverse displacement ($w_0$), and linear interpolation is used for the axial displacement ($u_0$) and shear rotation (${\psi}_0$). Each node of an element has four degrees of freedom. The expressions of variationally consistent inertia, stiffness matrices and the load vector are derived in closed form using exact integration. The formulation is validated by comparing the results with the 2D-FE results for composite symmetric and sandwich beams with various end conditions. The employed finite element model is free of shear locking. The present zigzag finite element results for natural frequencies, mode shapes of cantilever and clamped-clamped beams are obtained with a one-dimensional finite element codes developed in MATLAB. These 1D-FE results for cantilever and clamped beams are compared with the 2D-FE results obtained using ABAQUS to show the accuracy of the developed MATLAB code, for zigzag theory for these boundary conditions. This comparison establishes the accuracy of zigzag finite element analysis for dynamic response under given boundary conditions.

키워드

참고문헌

  1. ABAQUS Documentation (2007), Version 6.6.
  2. Akhras, G. and Li, W. (2007), "Spline finite strip analysis of composites plates based on higher-order zigzag composites plates", Compos. Struct., 78, 112-118. https://doi.org/10.1016/j.compstruct.2005.08.016
  3. Arya, H., Shimpi, R.P. and Naik. (2002), "A zigzag model for laminated composite beams", Compos. Struct., 56, 21-24. https://doi.org/10.1016/S0263-8223(01)00178-7
  4. Averill, R.C. (1994), "Static and dynamic response of moderately thick laminated beams with damage", Compos. Eng., 4, 381-395. https://doi.org/10.1016/S0961-9526(09)80013-0
  5. Averill, R.C. and Yip, Y.C. (1996), "Thick beam theory and finite element model with zigzag approximation", AIAA J., 34, 1626-1632.
  6. Benjeddou, A. (2000), "Advances in piezoelectric finite element modeling of adaptive structural elements: a survey", Comput. Struct., 76, 347-363. https://doi.org/10.1016/S0045-7949(99)00151-0
  7. Cho, M. and Parmerter, R.R. (1992), "Efficient higher order plate theory for laminated composites", Compos. Struct., 20(2), 113-123. https://doi.org/10.1016/0263-8223(92)90067-M
  8. Chopra, I. (2002), "Review of state of art of smart structures and integrated systems", AIAA J., 40, 2145-2187. https://doi.org/10.2514/2.1561
  9. Fares, M.E. and Elmarghamy, M. Kh. (2008), "A refined zigzag nonlinear first order shear deformation theory of composite laminated plates", Compos. Struct., 82, 71-83. https://doi.org/10.1016/j.compstruct.2006.12.007
  10. Kapuria S. and Alam, N. (2006), "Efficient layerwise finite element model for dynamic analysis of laminated piezoelectric beams", Comput. Meth. Appl. Mech. Eng., 195, 2742-2760. https://doi.org/10.1016/j.cma.2005.06.008
  11. Kapuria, S. and Achary, G.G.S. (2008), "Benchmark 3D solution and assessment of a zigzag theory for free vibration of hybrid plates under initial electrothermomechanical stress", Compos. Sci. Technol., 68, 297-311. https://doi.org/10.1016/j.compscitech.2007.01.017
  12. Kapuria, S., Ahmed, A. and Dumir, P.C. (2005),"An efficient coupled zigzag theory for dynamic analysis of piezoelectric composite and sandwich beams with damping", J. Sound Vib., 279, 345-371. https://doi.org/10.1016/j.jsv.2003.11.018
  13. Kapuria, S., Bhattacharya, M. and Kumar, A.N. (2008), "Bending and free vibration response of layered functionally graded beams: A theoretical model and its experimental validation", Compos. Struct., 82, 390- 402. https://doi.org/10.1016/j.compstruct.2007.01.019
  14. Kapuria, S., Dumir, P.C. and Jain, N.K. (2004), "Assessment of zigzag theory for static loading, buckling, free and forced response of composite and sandwich beams", Compos. Struct., 64, 317-327. https://doi.org/10.1016/j.compstruct.2003.08.013
  15. Kumari, P., Nath, J.K., Kapuria, S. and Dumir, P.C. (2008), "An improved third order theory and assessment of efficient zigzag theory for angle-ply flat hybrid panels", Compos. Struct., 83, 226-236. https://doi.org/10.1016/j.compstruct.2007.04.018
  16. Mackerle, J. (2003), "Smart materials and structures-a finite element approach-an addendum: a bibliography (1997-2002)", Model. Simul. Mater. Sci. Eng., 11, 704-744.
  17. Noor, A.K. and Burton, W.S. (1994)," Three-dimensional solutions for initially stressed structural sandwiches"., J. Eng. Mech.-ASCE, 120, 284-303. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:2(284)
  18. Robbins, D.H. and Reddy, J.N. (1991), "Analysis of piezoelectrically actuated beams using a layer-wise displacement theory", Comput. Struct., 41, 265-279. https://doi.org/10.1016/0045-7949(91)90430-T
  19. Tang Y.Y., Noor, A.K. and Xu, K. (1996), "Assessment of computational models for thermoelectroelastic multilayered plates", Comput. Struct., 61, 915-933. https://doi.org/10.1016/0045-7949(96)00037-5

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