Advanced Composite Materials

The Korean Society for Composite Materials (한국복합재료학회)
권호 표지
DOI QR코드

DOI QR Code

Vibration and Post-buckling Behavior of Laminated Composite Doubly Curved Shell Structures

  • Kundu, Chinmay Kumar (Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology) ;
  • Han, Jae-Hung (Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology)
  • Received : 2007.11.08
  • Accepted : 2008.01.19
  • Published : 2009.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

The vibration characteristics of post-buckled laminated composite doubly curved shells are investigated. The finite element method is used for the analysis of post-buckling and free vibration of post-buckled laminated shells. The geometric non-linear finite element model includes the general non-linear terms in the strain-displacement relationships. The shell geometry used in the present formulation is derived using an orthogonal curvilinear coordinate system. Based on the principle of virtual work the non-linear finite element equations are derived. Arc-length method is implemented to capture the load-displacement equilibrium curve. The vibration characteristics of post-buckled shell are performed using tangent stiffness obtained from the converged deflection. The code is first validated and then employed to generate numerical results. Parametric studies are performed to analyze the snapping and vibration characteristics. The relationship between loads and fundamental frequencies and between loads and the corresponding displacements are determined for various parameters such as thickness ratio and shallowness.

Keywords

References

  1. R. D. Wood and O. C. Zienkiewicz, Geometrically nonlinear finite element analysis of beams, frames, arches and axisymmetric shells, Computers and Structures 7, 725–735 (1977) https://doi.org/10.1016/0045-7949(77)90027-X
  2. K. J. Bathe, E. Ramm and E. L. Wilson, Finite element formulations for large deformation dynamic analysis, Intl. J. Numer. Methods Engng 9, 353–386 (1975) https://doi.org/10.1002/nme.1620090207
  3. S. Ilanko and S.M. Dickinson, The vibration and post-buckling of geometrically imperfect, simply supported, rectangular plates under uni-axial loading, Part I: Theoretical approach, J. Sound Vibr. 118, 313–336 (1987) https://doi.org/10.1016/0022-460X(87)90529-3
  4. A. N. Palazotto and P. E. Linnemann, Vibration and buckling characteristics of composite cylindrical panels incorporating the effects of a higher order shear theory, Intl. J. Solids Struct. 28, 341–361 (1991) https://doi.org/10.1016/0020-7683(91)90198-O
  5. M. A. Souza, Vibration of thin-walled structures with asymmetric post-buckling characteristics, Thin-Walled Structures 14, 45–57 (1992) https://doi.org/10.1016/0263-8231(92)90054-Z
  6. D. Lee and I. Lee, Vibration behaviors of thermally post-buckled anisotropic plates using firstorder shear deformable plate theory, Compos. Struct. 63, 371–378 (1997) https://doi.org/10.1016/S0045-7949(96)00378-1
  7. I. K. Oh, J. H. Han and I. Lee, Post-buckling and vibration characteristics of piezolaminated composite plate subject to thermopiezoelectric loads, J. Sound Vibr. 233, 19–40 (2000)
  8. H. Chen and W. Yu, Post-buckling and mode jumping analysis of composite laminates using an asymptotically correct, geometrically non-linear theory, Intl. J. Non-Linear Mech. 41, 1143–1160 (2006) https://doi.org/10.1016/j.ijnonlinmec.2006.11.004
  9. J. G. Teng and T. Hong, Nonlinear thin shell theories for numerical buckling predictions, Thin-Walled Structures 31, 89–115 (1998) https://doi.org/10.1016/S0263-8231(98)00014-7
  10. C. K. Kundu and P. K. Sinha, Post-buckling analysis of laminated composite shells, Compos. Struct. 78, 316–324 (2007) https://doi.org/10.1016/j.compstruct.2005.10.005
  11. A. K. Jha and D. J. Inman, Importance of geometric nonlinearity and follower pressure load in the dynamic analysis of a gossamer structure, J. Sound Vibr. 278, 207–231 (2004) https://doi.org/10.1016/j.jsv.2003.10.026
  12. M. A. Crisfield, A fast incremental iterative solution procedure that handles snap through, Computers and Structures 13, 55–62 (1981) https://doi.org/10.1016/0045-7949(81)90108-5
  13. H. Kraus, Thin Elastic Shells. John Wiley and Sons, New York, USA (1967)
  14. A. S. Saada, Elasticity: Theory and Applications. Pergamon Press, New York, USA (1974)
  15. R. Jones, Mechanics of Composite Materials. Taylor and Francis, Philadelphia, USA (1999)
  16. O. C. Zienkiewicz and R. L. Taylor, The Finite ElementMethod, Vol. 1.McGraw Hill International Edition, Singapore (1989)
  17. A. B. Sabir and M. S. Djoudi, Shallow shell finite element for the large deformation geometrically nonlinear analysis of shells and plates, Thin-Walled Structures 21, 253–267 (1995)
  18. K. Kim and G. Z. Voyiadjis, Nonlinear finite element analysis of composite panels, Composites:Part B 30, 365–381 (1999) https://doi.org/10.1016/S1359-8368(99)00007-4
  19. S. Saigal, R. K. Kapania and T. Y. Yang, Geometrically nonlinear finite element analysis of imperfect laminated shells, J. Compos. Mater. 20, 197–214 (1986) https://doi.org/10.1177/002199838602000206
  20. A. K. Noor, Free vibrations of multilayered composite plates, AIAA Journal 7, 1038–1039 (1973)
  21. K. Chandrashekhara, Free vibration of anisotropic laminated doubly curved shells, Computers and Structures 33, 435–440 (1989) https://doi.org/10.1016/0045-7949(89)90015-1