International Journal of Fracture

, Volume 19, Issue 4, pp 257–275 | Cite as

On an analytical-numerical procedure for the analysis of cylindrical shells with arbitrarily oriented cracks

  • H. V. Lakshminarayana
  • M. V. V. Murthy
  • L. S. Srinath


An analytical-numerical procedure for obtaining stress intensity factor solutions for an arbitrarily oriented crack in a long, thin circular cylindrical shell is presented. The method of analysis involves obtaining a series solution to the governing shell equation in terms of Mathieu and modified Mathieu functions by the method of separation of variables and satisfying the crack surface boundary conditions numerically using collocation. The solution is then transformed from elliptic coordinates to polar coordinates with crack tip as the origin through a Taylor series expansion and membrane and bending stress intensity factors are computed. Numerical results are presented and discussed for the pressure loading case.


Stress Intensity Factor Cylindrical Shell Crack Surface Series Solution Taylor Series Expansion 
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  1. [1]
    H.V. Lakshminarayana and M.V.V. Murthy, International Journal of Fracture 12 (1976) 547–566.Google Scholar
  2. [2]
    M.V.V. Murthy, A.K. Rao and K.P. Rao, International Journal of Solids and Structures 10 (1974) 1243–1269.Google Scholar
  3. [3]
    Mechanics of Fracture, Vol. 3, ed. G.C. Sih, Noordhoff International Publishing, Leyden (1977).Google Scholar
  4. [4]
    E.S. Folias, International Journal of Fracture Mechanics 5 (1969) 327–346.Google Scholar
  5. [5]
    J.G. Simmonds, M.R. Bradley and J.W. Nicholson, Journal of Applied Mechanics 45 (1978) 135–141.Google Scholar
  6. [6]
    P.D. Ewing and J.G. Williams, International Journal of Fracture 10 (1974) 537–544.Google Scholar
  7. [7]
    V.Z. Vlasov, General Theory of Shells and its Applications in Engineering, NASA Technical Translation, NASA TT F-99, April 1964.Google Scholar
  8. [8]
    H.V. Lakshminarayana, Ph.D. Thesis, Indian Institute of Science, Bangalore, India (1980).Google Scholar
  9. [9]
    N.W. McLachlan, Theory and Application of Mathieu Functions, Oxford University Press (1951).Google Scholar
  10. [10]
    M.L. Williams, Journal of Applied Mechanics 24 (1957) 109–114.Google Scholar
  11. [11]
    M.L. Williams, Journal of Applied Mechanics 28 (1961) 78–82.Google Scholar
  12. [12]
    S. Krenk, International Journal of Fracture 14 (1978) 123–143.Google Scholar
  13. [13]
    F. Delale and F. Erdogan, Quarterly of Applied Mathematics 37 (1979) 239–258.Google Scholar

Copyright information

© Martinus Nijhoff Publishers 1982

Authors and Affiliations

  • H. V. Lakshminarayana
    • 1
  • M. V. V. Murthy
    • 1
  • L. S. Srinath
    • 2
  1. 1.Structures DivisionNational Aeronautical LaboratoryBangaloreIndia
  2. 2.Department of Mechanical EngineeringIndian Institute of ScienceBangaloreIndia

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