International Applied Mechanics

, Volume 46, Issue 1, pp 69–77 | Cite as

Stability of shallow anisotropic shells of revolution

  • N. P. Semenyuk
  • V. M. Trach

The paper outlines a method of analyzing layered anisotropic shells of revolution for stability using complex Fourier series. This simplifies the derivation of the basic equations compared with complete trigonometric Fourier series. Anisotropic shells in the form of a torus segment are analyzed for stability. This method allows optimizing the structure of the material and the geometry of the shell


stability torus-like shells of revolution Fourier series complex numbers anisotropy of material external pressure axial compression torsion 


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  1. 1.
    S. A. Ambartsumyan, General Theory of Anisotropic Shells [in Russian], Nauka, Moscow (1974).Google Scholar
  2. 2.
    I. Ya. Amiro, “Stability of thin cylindrical shells,” Prikl. Mekh., 9, No. 3, 264–269 (1963).Google Scholar
  3. 3.
    A. T. Vasilenko, “An investigation into the stress state of thin anisotropic shells of revolution under antisymmetric loading,” Int. Appl. Mech., 3, No. 11, 77–79 (1967).Google Scholar
  4. 4.
    F. R. Gantmakher, Matrix Theory [in Russian], Nauka, Moscow (1974).Google Scholar
  5. 5.
    S. S. Kan, “Stability of shells of revolution with curvilinear generators in axial compression,” Prikl. Mekh., 2, No. 1, 35–39 (1966).Google Scholar
  6. 6.
    B. Budiansky and J. W. Hatchinson, “A survey of some buckling problems,” AIAA J., 4, No. 9, 1505–1510 (1966).CrossRefADSGoogle Scholar
  7. 7.
    N. P. Semenyuk and N. B. Zhukova, “Initial postbuckling behavior of cylindrical shells under axisymmetric deformation,” Int. Appl. Mech., 42, No. 4, 461–470 (2006).CrossRefGoogle Scholar
  8. 8.
    N. P. Semenyuk and V. M. Trach, “Stability of axially compressed cylindrical shells made of reinforced materials with specific fiber orientation within each layer,” Int. Appl. Mech., 42, No. 3, 318–324 (2006).CrossRefGoogle Scholar
  9. 9.
    N. P. Semenyuk and V. M. Trach, “Stability and postbuckling behavior of cylindrical shells under external pressure,” Int. Appl. Mech., 43, No. 3, 314–328 (2007).CrossRefGoogle Scholar
  10. 10.
    N. P. Semenyuk, V. M. Trach, and N. B. Zhukova, “Stability and initial postbuckling behavior of anisotropic cylindrical shells subject to torsion,” Int. Appl. Mech., 44, No. 1, 41–60 (2008).CrossRefGoogle Scholar
  11. 11.
    V. M. Trach, “Stability of cylindrical shells with one plane of elastic symmetry under axial compression and torsion,” Int. Appl. Mech., 42, No. 8, 943–948 (2006).CrossRefGoogle Scholar
  12. 12.
    V. M. Trach, “Stability of composite shells of revolution,” Int. Appl. Mech., 44, No. 3, 109–124 (2008).zbMATHCrossRefGoogle Scholar
  13. 13.
    P. M. Weaver, “The effect of extension/twist anisotropy on compression buckling in cylindrical shells,” Composites, Part B, 34, 251–260 (2003).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.National University of Water Management and Natural ResourcesRivneUkraine

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