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Non-axisymmetric instability of polar orthotropic annular plates

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Abstract

The non-axisymmetric instability of polar orthotropic annular plates under inplane uniform radial pressure is studied by use of the shooting method. The characteristic equations and eigenvalues under a variety of edge conditions are given. Under two appropriate hypotheses, we prove that all eigenvalues are bifurcation points. Hence, it is possible that non-axisymmetric buckled and post-buckled states branch from axisymmetric unbuckled states of an annular plate. Asymptotic formulae for buckled states are obtained and curves for the deflection and stress are shown.

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References

  1. G.K. Ramaiah: Buckling of polar orthotropic annular plates under uniform inplane compressive forces, J. Appl. Mech. 48 (3) (1981) 643–653.

    Google Scholar 

  2. B. Sckhar Raddy and R.S. Alwar: Post-buckling analysis of orthotropic annular plates, Acta Mech. 39 (1981) 289–296.

    Google Scholar 

  3. C.L. Huang: Post-buckling of an annular plate, AIAA J. 11 (1973) 1608–1612.

    Google Scholar 

  4. G.K. Ramaiah and K. Vuayakumar: Buckling of polar orthotropic annular plates under uniform internal pressure, AIAA J. 12(8) (1974) 1045–1050.

    Google Scholar 

  5. Cheng Chang-jun, Lu Xiao-an and Li Shi-rong: Buckling of polar orthotropic annular plates, Conference of Solid Mechanics in East China (Oct. 1986).

  6. Zhu Zheng-you and Cheng Chang-jun: General mathematical theory of large deflection of thin plates with some holes, Acta Mechanica Sinica 2(3) (1986) 278–288; Proc. ICNM (Shanghai, Oct. 1985) 428–432.

    Google Scholar 

  7. Cheng Chang-jun and Lu Xiao-an: General mathematical theory of large deflection of thin plates with some holes (continued), to appear.

  8. Shui-Nee Chow and Jack K. Hale: Methods of Bifurcation Theory. Springer-Verlag, New York/Berlin/Heidelberg (1982).

    Google Scholar 

  9. S.M. Roberts and J.S. Shipman: Two-point Boundary Value Problems: Shooting Methods, American Elsevier Publishing Company, Inc. (1972).

  10. Cheng Chang-jun and Zhu Zheng-you: The buckled states of annular plates, Scientia Sinica (Series A), XXIX (9) (1986) 954–965; Proc. ICNM (Shanghai, Oct. 1985) 990–996.

    Google Scholar 

  11. E.A. Coddington and N. Levinson: Theory of Ordinary Differential Equations. McGraw-Hill (1955).

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Authors and Affiliations

  1. Department of Mechanics, Lanzhou University, Lanzhou, China

    Cheng Chang-Jun

  2. Department of Theoretical Mechanics, University of Nottingham, NG7 2RD, Nottingham, England

    A. J. M. Spencer

Authors
  1. Cheng Chang-Jun
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  2. A. J. M. Spencer
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Chang-Jun, C., Spencer, A.J.M. Non-axisymmetric instability of polar orthotropic annular plates. J Eng Math 23, 29–51 (1989). https://doi.org/10.1007/BF00058432

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  • DOI: https://doi.org/10.1007/BF00058432

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