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The effect of non-homogeneity on the stability of laminated orthotropic conical shells subjected to hydrostatic pressure

  • Zerin, Zihni (Department of Civil Engineering, Ondokuz Mayis University)
  • Received : 2011.08.15
  • Accepted : 2012.05.31
  • Published : 2012.07.10

Abstract

In this study, the stability of laminated homogeneous and non-homogeneous orthotropic truncated conical shells with freely supported edges under a uniform hydrostatic pressure is investigated. It is assumed that the composite material is orthotropic and the material properties depend only on the thickness coordinate. The basic relations, the modified Donnell type stability and compatibility equations have been obtained for laminated non-homogeneous orthotropic truncated conical shells. Applying Galerkin method to the foregoing equations, the expression for the critical hydrostatic pressure is obtained. The appropriate formulas for the single-layer and laminated, cylindrical and complete conical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, effects of non-homogeneity, number and ordering of layers and variations of shell characteristics on the critical hydrostatic pressure are investigated.

Keywords

References

  1. Aganesov, L.G. and Sachenkov, A.V. (1964), "The stability and vibration of circular conical and cylindrical shells at different boundary conditions", Res. Theo. Plates Shells, Kazan State University, Kazan, 2, 111-126. (in Russian)
  2. Babich, D.V. and Khoroshun, L.P. (2001), "Stability and natural vibrations of shells with variable geometric and mechanical parameters", Int. Appl. Mech., 37, 837-869. https://doi.org/10.1023/A:1012503024244
  3. Civalek, O. (2005), "Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of HDQ-FD methods", Int. J. Press. Ves. Pip., 82, 470-479. https://doi.org/10.1016/j.ijpvp.2004.12.003
  4. Civalek, O. (2007), "Linear vibration analysis of isotropic conical shells by discrete singular convolution (DSC)", Struct. Eng. Mech., 25, 127-130. https://doi.org/10.12989/sem.2007.25.1.127
  5. Ding, H.J, Wang, H.M. and Chen, W.Q. (2003), "A solution of a non-homogeneous orthotropic cylindrical shell for axisymmetric plane strain dynamic thermo-elastic problems", J. Sound Vib., 263, 815-829. https://doi.org/10.1016/S0022-460X(02)01075-1
  6. Elishakoff, I. (2001), "Inverse buckling problem for inhomogeneous columns", Int. J. Solid Struct., 38, 457-464. https://doi.org/10.1016/S0020-7683(00)00049-4
  7. Goldfeld, Y. and Arbocz, J. (2004), "Buckling of laminated conical shells given the variations of the stiffness coefficients", AIAA J., 42, 642-649. https://doi.org/10.2514/1.2765
  8. Gupta, A.K., Johri, T. and Vats, R.P. (2010), "Study of thermal gradient effect on vibrations of a nonhomogeneous orthotropic rectangular plate having bi-direction linearly thickness variations", Meccanica, 45, 393-400. https://doi.org/10.1007/s11012-009-9258-3
  9. Han, B. and Simitses, G.J. (1991), "Analysis of anisotropic laminated cylindrical shells subjected to destabilizing loads. Part II: Numerical results", Compos. Struct., 19, 183-205. https://doi.org/10.1016/0263-8223(91)90022-Q
  10. Li, J., Xiang, Z.H. and Xue, M.D. (2005), "Buckling analysis of rotationally periodic laminated composite shells by a new multilayered shell element", Compos. Struct., 70, 24-32. https://doi.org/10.1016/j.compstruct.2004.08.009
  11. Li, S.R. and Batra, R.C. (2005), "Buckling of a laminated cylindrical shell with functionally graded middle layer under axial compressive load", Proc. Int. Conf. Mech. Eng. Mech., Nanjing, China, 1-2, 796-800.
  12. Massalas, C., Dalamanagas, D. and Tzivanidis, G. (1981), "Dynamic instability of truncated conical shells with variable modulus of elasticity under periodic compressive forces", J. Sound Vib., 79, 519-528. https://doi.org/10.1016/0022-460X(81)90463-6
  13. Mecitoglu, Z. (1996), "Governing equations of a stiffened laminated inhomogeneous conical shell", AIAA J., 34, 2118-2125. https://doi.org/10.2514/3.13360
  14. Ootao, Y. and Tanigawa, Y. (2007), "Three-dimensional solution for transient thermal stresses of an orthotropic functionally graded rectangular plate", Compos. Struct., 80, 10-20. https://doi.org/10.1016/j.compstruct.2006.02.028
  15. Patel, S.N., Bisagni, C. and Datta, P.K. (2011), "Dynamic buckling analysis of a composite stiffened cylindrical shell", Struct. Eng. Mech., 37, 509-527. https://doi.org/10.12989/sem.2011.37.5.509
  16. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition, CRC Press.
  17. Shen, H.S. and Noda, N. (2007), "Post-buckling of pressure-loaded FGM hybrid cylindrical shell in thermal environments", Compos. Struct., 77, 546-560. https://doi.org/10.1016/j.compstruct.2005.08.006
  18. Sofiyev, A.H. (2002), "The buckling of a cross-ply laminated non-homogeneous orthotropic composite cylindrical thin shell under time dependent external pressure", Struct. Eng. Mech., 14, 661-677. https://doi.org/10.12989/sem.2002.14.6.661
  19. Sofiyev, A.H. and Aksogan, O. (2002), "The dynamic stability of a non-homogeneous orthotropic elastic truncated conical shell under a time dependent external pressure", Struct. Eng. Mech., 13, 329-343. https://doi.org/10.12989/sem.2002.13.3.329
  20. Sofiyev, A.H. and Schnack, E. (2003), "The buckling of cross-ply laminated non-homogeneous orthotropic composite conical thin shells under a dynamic external pressure", Acta Mech., 162, 29-40. https://doi.org/10.1007/s00707-002-1001-2
  21. Sofiyev, A.H., Zerin, Z., Yucel, K. and Avcar, M. (2006), "The dynamic stability of orthotropic cylindrical shells with non-homogenous material properties under axial compressive load varying as a parabolic function of time", J. Reinf. Plast. Compos., 25(18), 1877-1886. https://doi.org/10.1177/0731684406069914
  22. Sofiyev, A.H. (2009), "The vibration and stability behaviors of freely supported FGM conical shells subjected to external pressure", Compos. Struct., 89, 356-366. https://doi.org/10.1016/j.compstruct.2008.08.010
  23. Tong, L. (1999), "Buckling of filament-wound laminated conical shells under axial compression", AIAA J., 37, 778-781. https://doi.org/10.2514/2.792
  24. Volmir, A.S. (1967), Stability of Elastic Systems, Nauka, Moscow, English Translation: Foreign Tech. Division, Air Force Systems Command, Wright-Patterson Air Force Base, Ohio, AD628508.
  25. Wang, H. and Wang, T.K. (1991), "Stability of laminated composite circular conical shells under external pressure", Appl. Math. Mech., (Eng. Ed.) 12, 1153-1161. https://doi.org/10.1007/BF02456054
  26. Wu, C.P. and Chen, C.W. (2001), "Elastic buckling of multi-layered anisotropic conical shells", J. Aero. Eng., 1, 29-36.
  27. Yakushev, A.N. (1991), The Stability of Orthotropic Conical Shells Under Dynamic Pressure, Res. Theo. Plates Shells, Kazan State University, Kazan 21, 186-191. (in Russian)
  28. Yas, M.H. and Garmsiri, K. (2010), "Three-dimensional free vibration analysis of cylindrical shells with continuous grading reinforcement", Steel Compos. Struct., 10, 349-360. https://doi.org/10.1007/BF03215843
  29. Zenkour, A.M. and Fares, M.E. (2001), "Bending, buckling and free vibration of non-homogeneous composite laminated cylindrical shells using a refined first-order theory", Compos. B. Eng., 32, 237-247. https://doi.org/10.1016/S1359-8368(00)00060-3
  30. Zhang, X. and Hasebe, N. (1999), "Elasticity solution for a radially non-homogeneous hollow circular cylinder", J. Appl. Mech., 66, 598-606. https://doi.org/10.1115/1.2791477

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