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Curved laminate analysis

  • Chiang., Yih-Cherng (Department of Mechanical Engineering, Chinese Culture University)
  • Received : 2009.08.25
  • Accepted : 2011.02.22
  • Published : 2011.07.25

Abstract

This paper is devoted to the development of the equations which describe the elastic response of a curved laminate subjected to in-plane loads and bending moments. Similar to the classic $6{\times}6$ ABD matrix constitutive relation of a flat laminate, a new $6{\times}6$ matrix constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures for a curved laminate is formulated. This curved lamination theory will provide the fundamental basis for the analyses of curved laminated structures. The stress predictions by the present curved lamination theory are compared to those by the curved laminate analysis that neglected the nonlinear terms in the derivation of the constitutive relation. The results show that the curved laminate analysis that neglected the nonlinear terms cannot reflect the effect of curvature and can no longer predict the stresses accurately as the curvature becomes noticeable. In this paper, a curved lamination theory that retains the nonlinear terms and, therefore, accounts for the effect of the non-flat geometry of the structure will be developed.

Keywords

References

  1. Alt nok, M., Burdurlu, E. and Özkaya, K. (2008), "Deformation analysis of curved laminated structural wood elements", Constr. Buil. Mater., 22(8), 1643-1647. https://doi.org/10.1016/j.conbuildmat.2007.06.007
  2. Ambartsumyan, S.A. (1964), Theory of Anisotropic Shells, NASA Report-TT-F-118.
  3. Bickford, W.B. (1998), Advanced Mechanics of Materials, Addison Wesley Longman Inc.
  4. Bozhevolnaya, E. and Frostig, Y. (1997), "Nonlinear closed-form high-order analysis of curved sandwich panels", Compos. Struct., 38(1), 383-394. https://doi.org/10.1016/S0263-8223(97)00073-1
  5. Chiang, Y.C. (2006), "On the theory of curved anisotropic plate", Struct. Eng. Mech., 22(6), 741-759. https://doi.org/10.12989/sem.2006.22.6.741
  6. Christensen, R.M. (1979), Mechanics of Composite Materials, John Wiley & Sons Inc., New York.
  7. Dong, S.B., Pister, K.S. and Taylor, R.L. (1962), "On the theory of laminated anisotropic shells and plates", J. Aerosp. Sci., 29, 969-975. https://doi.org/10.2514/8.9668
  8. Herakovich, C.T. (1998), Mechanics of Fibrous Composites, John Wiley & Sons Inc., New York.
  9. Hu, H.T. and Yang, J.S. (2007), "Buckling optimization of laminated cylindrical panels subjected to axial compressive load", Compos. Struct., 81, 374-385. https://doi.org/10.1016/j.compstruct.2006.08.025
  10. Kedward, K.T., Wilson, R.S. and McLean, S.K. (1989), "Flexure of simply curved composite shapes", Composites, 20(6), 527-536. https://doi.org/10.1016/0010-4361(89)90911-7
  11. Koiter, W.T. (1959), "A consistent first approximation in the general theory of thin elastic shells", Proceeding of the IUTAM Symposium on the Theory of Thin Elastic Shells, Delft, August.
  12. Kraus, H. (1967), Thin Elastic Shells, John Wiley& Sons Inc., New York.
  13. Kundu, C.K., Maiti, D.K. and Sinha, P.K. (2007), "Post buckling analysis of smart laminated doubly curved shells", Compos. Struct., 81(3), 314-322. https://doi.org/10.1016/j.compstruct.2006.08.023
  14. Lin, K.C. and Hsieh, C.M. (2007), "The closed form general solutions of 2-D curved laminated beams of variable curvatures", Compos. Struct., 79(4), 606-618. https://doi.org/10.1016/j.compstruct.2006.02.027
  15. Mangala, A., Jayasuriya, M., Dwivedi, S.N., Louisiana, L., Sivaneri, N.T. and Lyons, D.W. (2002), "Doubly curved laminated composite shells with hygrothermal conditioning and dynamic loads, Part 2: FEA and numerical results of shells of revolution", Mech. Adv. Mater. Struct., 9(1), 69-97. https://doi.org/10.1080/153764902317224888
  16. Nemeth, M.P. and Smeltzer, S.S. (2000), "Bending boundary layers in laminated-composites circular cylindrical shells", NASA Report-TP-2000-210549.
  17. Pister, K.S. and Dong, S.B. (1959), "Elastic bending of layered plates", J. Eng. Mech. Div., EM 4, October.
  18. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells Theory and Analysis, CRC Press.
  19. Reissner, E. and Stavsky, Y. (1961), "Bending and stretching of certain types of heterogeneneous aeolotropic elastic plates", J. Appl. Mech., 28, 402-408. https://doi.org/10.1115/1.3641719
  20. Ren, L., Parvizi-Majidi, A. and Li, Z. (2003), "Cured shape of cross-ply composite thin shells", J. Compos. Mater., 37(20), 1801-1820. https://doi.org/10.1177/002199803035184
  21. Sun, C.T. and Kelly, S.R. (1988), "Failure in composite angle structures, Part I: Initial failure", J. Reinf. Plast. Compos., 73, 220-232.
  22. Swanson, S.R. (1997), Introduction to Design and Analysis with Advanced Composite Materials, Prentice-Hall Inc.
  23. Ventsel, E., Krauthammer, T. and Ventsel, V. (2001), Thin Plates and Shells: Theory: Analysis, and Applications, Marcel Dekker Inc., New York.
  24. Vinson, J.R. and Chou, T.W. (1975), Composite Materials and Their Use in Structures, Applied Science Publishers, London.
  25. Vinson, J.R. and Sierakowski, R.L. (1987), The Behavior of Structures Composed of Composite Materials, Kluwer Adademic Publishers, Norwell.
  26. Volovoi, V.V. and Hodges, D.H. (2002), "Single- and multi-celled composite thin-walled beams", AIAA J., 40(5), 960-966. https://doi.org/10.2514/2.1733
  27. Whitney, J.M. (1987), Structure Analysis of Laminated Anisotropic Plates, Technomic Publishing Co. Inc., Lancaster.