International Applied Mechanics

, Volume 43, Issue 10, pp 1142–1148 | Cite as

Stress-strain state of a flexible spherical shell with an eccentric circular hole

  • I. S. Chernyshenko
  • E. A. Storozhuk
  • I. B. Rudenko
Article
Received:

Abstract

The stress-strain state of thin flexible spherical shells weakened by an eccentric circular hole is analyzed. The shells are made of an isotropic homogeneous material and subjected to internal pressure. A problem formulation is given, and a method of numerical solution with allowance for geometrical nonlinearity is outlined. The distribution of displacements, strains, and stresses along the hole boundary and in the region of their concentration is examined. The data obtained are compared with numerical solutions of the linear problem. The stress-strain state around the eccentric circular hole is analyzed with allowance for geometrical nonlinearity

Keywords

nonlinear problem spherical shell eccentric hole stress concentration internal pressure finite deflections 
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References

  1. 1.
    L. I. Golub, V. A. Maksimyuk, and I. S. Chernyshenko, “Modeling nonlinear elastic deformation of orthotropic spherical shells with curvilinear holes,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauky, No. 5, 256–258 (2001).Google Scholar
  2. 2.
    L. I. Golub, V. A. Maksimyuk, and I. S. Chernyshenko, “Numerical nonlinear elastic analysis of orthotropic spherical shells with an elliptic cutout,” Int. Appl. Mech., 38, No. 2, 203–208 (2002).CrossRefGoogle Scholar
  3. 3.
    O. M. Guz, “Approximate solutions for plates and shallow shells in the case of some doubly connected domains,” Prikl. Mekh., 9, No. 1, 103–108 (1963).Google Scholar
  4. 4.
    A. N. Guz, “Solution of problems for a shallow spherical shell in the case of multiply connected domains,” Dokl. AN SSSR, 158, No. 16, 1281–1284 (1964).Google Scholar
  5. 5.
    A. N. Guz, A. G. Makarenkov, and I. S. Chernyshenko, Structural Strength of Solid Propellant Engines [in Russian], Mashinostroenie, Moscow (1980).Google Scholar
  6. 6.
    A. N. Guz, I. S. Chernyshenko, and K. I. Shnerenko, Spherical Bottoms Weakened by Holes [in Russian], Naukova Dumka, Kyiv (1970).Google Scholar
  7. 7.
    A. N. Guz, I. S. Chernyshenko, and K. I. Shnerenko, “Stress concentration near openings in composite shells,” Int. Appl. Mech., 37, No. 2, 139–181 (2001).CrossRefGoogle Scholar
  8. 8.
    V. T. Dmitriev and I. N. Preobrazhenskii, “Deformation of flexible shells with holes,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 1, 177–184 (1988).Google Scholar
  9. 9.
    V. A. Maksimyuk and I. S. Chernyshenko, “Mixed functionals in the theory of nonlinearly elastic shells,” Int. Appl. Mech., 40, No. 11, 1226–1262 (2004).CrossRefMathSciNetGoogle Scholar
  10. 10.
    A. N. Guz, I. S. Chernyshenko, V. N. Chekhov, et al., Theory of Thin Shells Weakened by Holes, Vol. 1 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kyiv (1980).MATHGoogle Scholar
  11. 11.
    A. N. Guz, A. S. Kosmodamianskii, V. P. Shevchenko, et al., Stress Concentration, Vol. 7 of the 12-volume series Mechanics of Composite Materials [in Russian], Naukova Dumka, Kyiv (2000).Google Scholar
  12. 12.
    E. A. Gotsulyak, V. I. Gulyaev, I. Kubor, and I. S. Chernyshenko, “Nonlinear deformation of doubly connected shells with complex outline,” in: Theory and Methods of Design of Nonlinear Plates and Shells [in Russian], Izd. Saratov. Univ., Saratov (1981), pp. 51–53.Google Scholar
  13. 13.
    E. A. Gotsulyak, V. I. Gulyaev, K. Pemsing, and I. S. Chernyshenko, “Numerical analysis of stressed state of thin shells with curvilinear holes,” Int. Appl. Mech., 18, No. 8, 734–740 (1982).Google Scholar
  14. 14.
    V. L. Yaskovets, E. A. Storozhuk, and I. S. Chernyshenko, “Elastoplastic equilibrium of a spherical shell in the form of an eccentric ring,” Int. Appl. Mech., 26, No. 1, 56–61 (1990).MATHGoogle Scholar
  15. 15.
    I. S. Chernyshenko and E. A. Storozhuk, “Inelastic deformation of flexible cylindrical shells with a curvilinear hole,” Int. Appl. Mech., 42, No. 12, 1414–1420 (2006).CrossRefGoogle Scholar
  16. 16.
    E. A. Storozhuk and I. S. Chernyshenko, “Physically and geometrically nonlinear deformation of spherical shells with an elliptic hole,” Int. Appl. Mech., 41, No. 6, 666–674 (2005).CrossRefGoogle Scholar
  17. 17.
    E. A. Storozhuk and I. S. Chernyshenko, “Elastoplastic deformation of flexible cylindrical shells with two circular holes under axial tension,” Int. Appl. Mech., 41, No. 5, 506–511 (2005).CrossRefGoogle Scholar
  18. 18.
    E. A. Storozhuk and I. S. Chernyshenko, “Stress distribution in physically and geometrically nonlinear thin cylindrical shells with two holes,” Int. Appl. Mech., 41, No. 11, 1280–1287 (2005).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • I. S. Chernyshenko
    • 1
  • E. A. Storozhuk
    • 1
  • I. B. Rudenko
    • 1
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyiv

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