International Journal of Fracture

, Volume 19, Issue 4, pp 257–275

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


  • H. V. Lakshminarayana
    • Structures DivisionNational Aeronautical Laboratory
  • M. V. V. Murthy
    • Structures DivisionNational Aeronautical Laboratory
  • L. S. Srinath
    • Department of Mechanical EngineeringIndian Institute of Science

DOI: 10.1007/BF00012483

Cite this article as:
Lakshminarayana, H.V., Murthy, M.V.V. & Srinath, L.S. Int J Fract (1982) 19: 257. doi:10.1007/BF00012483


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.

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© Martinus Nijhoff Publishers 1982