Edge stresses analysis in thick composite panels subjected to axial loading using layerwise formulation

DOI QR코드

DOI QR Code

Ahmadi, Isa

  • 투고 : 2015.10.06
  • 심사 : 2016.01.21
  • 발행 : 2016.02.25

초록

Based on a reduced displacement field, a layer-wise (LW) formulation is developed for analysis of thick shell panels which is subjected to axial tension. Employing the principle of minimum total potential energy, the local governing equations of thick panel which is subjected to axial extension are obtained. An analytical method is developed for solution of the governing equations for various edge conditions. The governing equations are solved for free and simply supported edge conditions. The interlaminar stresses in the panel are investigated by means of Hooke's law and also by means of integration of the equilibrium equations of elasticity. Dependency of the result upon the number of numerical layers in the layerwise theory (LWT) is studied. The accuracy of the numerical results is validated by comparison with the results of the finite element method and with other available results in the open literature and good agreement is seen between the results. Numerical results are then presented for the distribution of interlaminar normal and shear stresses within the symmetric and un-symmetric cross-ply thick panels with free and simply supported boundaries. The effects of the geometrical parameters such as radius to thickness and width to thickness ratio are investigated on the distribution of the interlaminar stresses in thick panels.

키워드

thick shell panel;interlaminar stresses;layerwise theory;cross-ply laminate;free edge;simply supported edge

참고문헌

  1. Ahmadi, I. (2005), "Analysis of interlaminar stresses in thin composite shells", MSc. Thesis, Sharif University of Technology, Tehran, Iran.
  2. Ahn, J.S. and Woo, K.S. (2014), "Interlaminar stress distribution of laminated composites using the mixeddimensional transition element", J. Compos. Mater., 48(1), 3-20. https://doi.org/10.1177/0021998312467551
  3. Bheskar, K. and Varadan, T.K. (1993), "Interlaminar stresses in composite cylindrical shells under transient loads", J. Sound Vib., 168(3), 469-477. https://doi.org/10.1006/jsvi.1993.1386
  4. Chaudhuri, R.A. (1990), "On the prediction of interlaminar stresses in a thick laminated general shell", Int. J. Solid. Struct., 26(5-6), 499-510. https://doi.org/10.1016/0020-7683(90)90024-P
  5. Cho, M. and Kim, H.S. (2000), "Iterative free-edge stress analysis of composite laminates under extension, bending, twisting and thermal loadings", Int. J. Solid. Struct., 37(3), 435-459. https://doi.org/10.1016/S0020-7683(99)00014-1
  6. Ding, S., Tong, J.W., Shen, M. and Huo, Y. (2010), "Three-Dimensional elastic-plastic analysis of the interlaminar stresses for the AS4/PEEK composite laminate with a circular hole", Mech. Adv. Mater. Struct., 17(6), 406-418. https://doi.org/10.1080/15376494.2010.483322
  7. Fagiano, C., Abdalla, M.M. and Gurdal, Z. (2010), "Interlaminar stress recovery of multilayer composite shell structures for three-dimensional finite elements", Finite Elem. Anal. Des., 46(12), 1122-1130. https://doi.org/10.1016/j.finel.2010.08.004
  8. Franklin, H.G. and Kicher, T.P. (1968), "Stresses in laminated composite cylinders", AIAA J., 6(11), 2208-2209. https://doi.org/10.2514/3.4966
  9. Fung, Y.C. and Tong, P. (2001), Classical and Computational Solid Mechanics, World Scientific, New Jersey.
  10. Herakovich, C.T. (1998), Mechanics of Fibrous Composite, John Wiley & Sons, New York.
  11. Hsu, P.W, and Herakovich, C.T. (1977), "Edge effects in angle-ply composite laminate", J. Compos. Mater., 11(4), 422-428. https://doi.org/10.1177/002199837701100405
  12. Huang, B. and Kim, H.S. (2015), "Interlaminar stress analysis of piezo-bonded composite laminates using the extended Kantorovich method", Int. J. Mech. Sci., 90(1), 16-24. https://doi.org/10.1016/j.ijmecsci.2014.11.003
  13. Isavand, S., Bodaghi, M., Shakeri M. and Mohandesi J.A. (2015), "Dynamic response of functionally gradient austenitic-ferritic steel composite panels under thermo-mechanical loadings", Steel Compos. Struct., 18(1), 1-28. https://doi.org/10.12989/scs.2015.18.1.001
  14. Kant, T. and Menon, M.P. (1991), "Estimation of Interlaminar Stresses in Fiber Reinforced Composite Cylindrical Shells", Comput. Struct., 38(2), 131-147. https://doi.org/10.1016/0045-7949(91)90092-Z
  15. Kant, T. and Swaminathan, K. (2000), "Estimation of transverse/interlaminar stresses in laminated composites-a selective review and survey of current developments", Compos. Struct., 49(1), 65-75. https://doi.org/10.1016/S0263-8223(99)00126-9
  16. Kapoor, H., Kapania, R.K. and Soni, S.R. (2013), "Interlaminar stress calculation in composite and sandwich plates in NURBS isogeometric finite element analysis", Compos. Struct., 106(1), 537-548. https://doi.org/10.1016/j.compstruct.2013.05.028
  17. Kar, V.R., Mahapatra, T.R. and Subrata, K.P. (2015), "Nonlinear flexural analysis of laminated Composite flat Panel under hygro-thermo-mechanical loading", Steel Compos. Struct., 19(4), 1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011
  18. Kim, H.S., Zhou, X. and Chattopadhyay, A. (2002), "Interlaminar stress analysis of shell structures with piezoelectric patch including thermal loading", AIAA J., 40(12), 2517-2525. https://doi.org/10.2514/2.1596
  19. Li, S., Wang, R. and Luo, Z. (1985), "An analytic solution for interlaminar stresses in a fiber reinforced double-layer cylindrical shell", Acta Mech., 1 (2), 159-170. https://doi.org/10.1007/BF02487872
  20. Miri, A.K. and Nosier, A. (2011), "Interlaminar stresses in antisymmetric angle-ply cylindrical shell panels", Compos. Struct., 93(2), 419-429. https://doi.org/10.1016/j.compstruct.2010.08.038
  21. Most, J., Stegmair, D. and Petry, D. (2015), "Error estimation between simple, closed-form analytical formulae and full-scale FEM for interlaminar stress prediction in curved laminates", Compos. Struct., 131(1), 72-81. https://doi.org/10.1016/j.compstruct.2015.03.075
  22. Murthy, P.L.N. and Chamis, C.C. (1989), "Free-edge delamination: laminate width and loading conditions effects", J. Comp. Technol. Res., 11(1), 15-22. https://doi.org/10.1520/CTR10144J
  23. Pipes, R.B. and Daniel, I.M. (1971), "Moire analysis of the interlaminar shear edge effect in laminated composites", J. Compos. Mater., 5(2), 255-259. https://doi.org/10.1177/002199837100500211
  24. Pipes, R.B. and Pagano, N.J. (1974), "Interlaminar stresses in composite laminates-an approximate elasticity solution", J. Appl. Mech., 41(3), 668-672. https://doi.org/10.1115/1.3423368
  25. Pipes, R.B. and Pagano, N.J. (1970), "Interlaminar stresses in composite laminates under uniform axial extension", J. Compos. Mater., 4(4), 538-548. https://doi.org/10.1177/002199837000400409
  26. Ramalingeswara, R. and Ganesan, N. (1996), "Interlaminar stresses in shells of revolution", Mech. Comp. Mater. Struct., 3(4), 321-329. https://doi.org/10.1080/10759419608945870
  27. Ramalingeswara, R. and Ganesan, N. (1997), "Interlaminar stresses in spherical shell", Comput. Mater. Struct., 65(4), 575-583. https://doi.org/10.1016/S0045-7949(96)00397-5
  28. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, New York.
  29. Ren, J.G. (1987), "Exact solution for laminated cylindrical shell in cylindrical bending", Compos. Sci. Tech., 29(3), 168-187.
  30. Sarvestani, H.Y. and Sarvestani M.Y. (2011), "Interlaminar stress analysis of general composite laminates", Int. J. Mech. Sci., 53(11), 958-967. https://doi.org/10.1016/j.ijmecsci.2011.07.007
  31. Shim, D.J. and Lagace, P. A. (2005), "An analytical method for interlaminar stresses due to global effects of ply drop-offs", Mech. Adv. Mater. Struct., 12(1), 21-32. https://doi.org/10.1080/15376490490491927
  32. Tahani, M. and Nosier, A. (2003), "Free edge stress analysis of a general cross-ply composite laminates under extension and thermal loading", Compos. Struct., 60(1), 91-103. https://doi.org/10.1016/S0263-8223(02)00290-8
  33. Tang, S. and Levy, A. (1975), "A boundary layer theory-part II: extension of laminated finite strip", J. Compos. Mater., 9(1), 42-52. https://doi.org/10.1177/002199837500900105
  34. Tong, J.W., Xie, M.Y. and Shen, M., and Li, H.Q. (2001), "The Interlaminar Stresses of Symmetric Composite Laminates", J. Reinf. Plast. Compos., 20(13), 1171-1182. https://doi.org/10.1106/1VK0-1BK7-QA7D-0M9D
  35. Varadan, T.K. and Bheskar, K. (1991), "Bending of laminated orthotropic cylindrical shells- an elasticity approach", Compos. Struct., 17(2), 141-156. https://doi.org/10.1016/0263-8223(91)90067-9
  36. Waltz, T.L. and Vinson, J.R. (1976), "Interlaminar stresses in laminated cylindrical shells of composite material", AIAA J., 14(76), 1213-1218. https://doi.org/10.2514/3.61455
  37. Wang, A.S.D. and Crossman, F.W. (1977a), "Edge effects on thermally induced stresses in composite laminates", J. Compos. Mater., 11(3), 300-312. https://doi.org/10.1177/002199837701100305
  38. Wang, A.S.D. and Crossman F.W. (1977b), "Some new results on edge effect in symmetric composite laminates", J. Compos. Mater., 11(1), 92-106. https://doi.org/10.1177/002199837701100110
  39. Wang, S.S. and Choi, I. (1982a), "Boundary-layer effects in composite laminates. Part II: Free-edge stress solutions and basic characteristics", ASME J. Appl. Mech., 49(3), 549-560. https://doi.org/10.1115/1.3162521
  40. Wang, S.S. and Choi, I. (1982b), "Boundary-layer effects in composite laminates. Part I: Free-edge stress singularities", ASME J. Appl. Mech., 49(3), 541-548. https://doi.org/10.1115/1.3162514
  41. Wang, X. and Li, S.J. (1992), "Analytical solution for interlaminar stresses in a multilaminated cylindrical shell under thermal and mechanical loads", Int. J. Solid. Struct., 29(10), 1293-1302. https://doi.org/10.1016/0020-7683(92)90239-P
  42. Wang, X., Cai, W. and Yu, Z.Y. (2002), "An analytic method for interlaminar stress in a laminated cylindrical shell", Mech. Adv. Mater. Struct., 9(2), 119-131. https://doi.org/10.1080/153764902753510507
  43. Whitcomb, J.D., Raju, I.S. and Goree, J.G. (1982), "Reliability of the finite element method for calculating free edge stresses in composite laminates", Comput. Struct., 15(1), 23-37. https://doi.org/10.1016/0045-7949(82)90030-X
  44. Wu, H. and Yan, X. (2005), "Interlaminar stress modeling of composite laminates with finite element method", J. Reinf. Plast. Compos., 24(3), 235-258. https://doi.org/10.1177/0731684405043553
  45. Wu, Z. and Chen, W. (2010), "A global-local higher order theory including interlaminar stress continuity and $C^0$ plate bending element for cross-ply laminated composite plates", Comput. Mech., 45(5), 387-400. https://doi.org/10.1007/s00466-009-0460-x