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Snap-through buckling of single-layer squarely-reticulated shallow spherical shells continuously supported on springs

  • Nie, G.H. (Key Laboratory of Solid and Failure Mechanics of MOE, Department of Engineering Mechanics, Tongji University)
  • Published : 2000.08.25

Abstract

An asymptotic solution for snap-through buckling of single-layer squarely-reticulated shallow spherical shells continuously supported on springs is developed in this paper. Based on the fundamental governing equations and boundary conditions, a nondimensional analytical expression associated with the external load, stiffness of spring and central transverse displacement (deflection) is derived with the aid of asymptotic iteration method. The effects of stiffness of spring and characteristic geometrical parameter on buckling of the structures are given by the analyses of numerical examples. In a special case, for reticulated circular plates, the influence of stiffness of spring on the characteristic relation between load and deflection is also demonstrated.

Keywords

References

  1. Chia, C.Y. (1980), Non-linear Analysis of Plates, McGraw-Hill, New York.
  2. Chia, C.Y. (1988), "Nonlinear analysis of doubly curved symmetrically laminated shallow shells with rectangular planform", Ingenieur-archiv, 58, 252-264. https://doi.org/10.1007/BF00535935
  3. Chia, C.Y. (1990), "Nonlinear analysis of imperfect cylindrical angle-ply panels", Advances in the Theory of Plates and Shells, Eds., G.Z. Voyiadjis and D. Karamanlidis, Elsevier Science Publishers B.V., Amsterdam, 197-212.
  4. Dumir, P.C. (1985), "Nonlinear axisymmetric response of orthotropic thin spherical caps on elastic foundation", Int. J. Mech Sci., 27, 751. https://doi.org/10.1016/0020-7403(85)90007-4
  5. Librescu, L. and Lin, W. (1997), "Postbuckling and vibration of shear detormable flat and curved panels on a non-linear elastic toundation", Int. J. Non-linear Mechanics, 32, 211-225. https://doi.org/10.1016/S0020-7462(96)00057-1
  6. Liu, R.H., Li, D., Nie, G.H. and Cheng, Z.Q. (1991), "Non-Iinear buckling of squarely-latticed shallow spherical shells", Int. J. Non-linear Mechanics, 26, 547-565. https://doi.org/10.1016/0020-7462(91)90009-I
  7. Massalas, C. and Katousias, N. (1979), "Non-linear vibrations of a shallow cylindrical panel on a non-Iinear elastic foundation", Journal of Sound and Vibration, 66, 507-512. https://doi.org/10.1016/0022-460X(79)90694-1
  8. Nath, Y. and Jain, R.K. (1983), "Non-linear dynamic analysis of shallow spherical shells on elastic foundations", Int. J. Mech Sci., 25, 409-419. https://doi.org/10.1016/0020-7403(83)90055-3
  9. Nath, Y. and Mahrenholtz, O. (1987), "Non-linear dynamic response of a doubly curved shallow shell on an elastic foundation", Journal of Sound and Vibration, 112, 53-61. https://doi.org/10.1016/S0022-460X(87)80093-7
  10. Nie, G.H. (1991), "A non-linear theory of reticulated shallow shells", Proceedings of the 22nd Midwestern Mechanics Conference, Rolla, Missouri, USA.
  11. Nie, G.H. and Liu, R.H. (1994), "Non-linear elastic theory of rectangular reticulated shallow shell structures", Appl. Math. Mech, 15, 413-423. https://doi.org/10.1007/BF02451491
  12. Nie, G.H. (1994), "Non-linear analysis of reticulated shallow shells on elastic foundation", Engineering Mechanics and Its Application, Eds., D,P, Yang et al., Jiangxi Gaoxiao Press, Nanchang, Jiangxi, China, 234-237 (in Chinese).
  13. Nie, G.H. and Cheung, Y.K. (1995), "A non-linear model tor stability analysis of reticulated shallow shells with imperfections", Int. J. of Space Structures, 10, 215-230. https://doi.org/10.1177/026635119501000404
  14. Nie, G.H. and Liu, R.H. (1995), "Non-linear characteristic relations of rectangular reticulated shallow shells", China Civil Engineering journal, 28, 12-21 (in Chinese).
  15. Nie, G.H. (1999), "An asymptotic analysis on non-Iinear free vibration of rectangular squarely-reticulated circular plates", Structural Engineering and Mechanics, 8(6), 547-560. https://doi.org/10.12989/sem.1999.8.6.547
  16. Paliwal, D.N., Sinha, S.N. and Choudhary, Jr., B.K. (1986), "Shallow spherical shells on pasternak foundation", ASCE Journal of Engineering Mechanics, 112,175-182. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:2(175)
  17. Ramachandran, J. and Murthy, P.A.X. (1976), "Non-Iinear vibrations of a shallow cylindrical panel on an elastic foundation", Journal of Sound and Vibration, 47,495-500. https://doi.org/10.1016/0022-460X(76)90876-2

Cited by

  1. On the buckling of imperfect squarely-reticulated shallow spherical shells supported by elastic media vol.41, pp.1, 2003, https://doi.org/10.1016/S0263-8231(02)00069-1
  2. Nonlinear analysis of imperfect squarely-reticulated shallow spherical shells vol.50, pp.1, 2007, https://doi.org/10.1007/s11433-007-0001-6