Skip to main content
SpringerLink
Log in

On the stresses around an elliptic hole in a cylindrical shell

Die Spannungen in der Umgebung eines elliptischen Loches in einer Kreiszylinderschale

  • Contributed Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

A theoretical analysis is presented for the membrane and bending stresses around an elliptic hole in an infinitely long, thin circular cylindrical shell. The shell is loaded by a uniformly distributed bending moment around the elliptic cutout. The method of solution is a perturbation technique and the results obtained are valid, if the hole is small in size compared to the shell.

Zusammenfassung

Es wird eine theoretische Analyse der Membran- und Biegespannungen in der Nähe eines elliptischen Loches in einer unendlich langen dünnen Kreiszylinderschale angegeben. Die Schale wird durch ein gleichförmig verteiltes Biegemoment am Rande des elliptischen Ausschnittes belastet. Die Lösung wird mittels einer Störungsmethode erhalten. Sie gilt für Löcher die im Verhältnis zum Schalendurchmesser klein sind.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lur'e, A. I.: Statics of Thin-Walled Elastic Shells, Chapter 4, Art. 9. Moscow: State Publishing House of Technical and Theoretical Literature. 1947. (In Russian.)

    Google Scholar 

  2. Lur'e, A. I.: Concentration of Stresses in the Vicinity of an Aperture in the Surface of a Circular Cylinder. Prik. Mat. i Mekh.10, 397–406 (1946). (In Russian.)

    Google Scholar 

  3. Shevliakov, Ju. A., andF. S. Ziegel: Torsion of a Cylinder with a Hole in the Lateral Surface. Dopovidi Akademii Nauk Ukrainjskoi R.S.R. p. 41–44, 1954.

  4. Withum, D.: Die Kreiszylinderschale mit kreisförmigem Ausschnitt unter Schubbeanspruchung. Ing.-Arch.26, 435–446 (1958).

    Google Scholar 

  5. Kline, L. V., R. C. Dixon, N. F. Jordan, andA. C. Eringen: Stresses in Pressurized Cylindrical Shell with Circular Cutout. General Technology Corporation Technical Report No. 3-1, August 1961.

  6. Naghdi, A. K., andA. C. Eringen: Stress Analysis of a Circular Cylindrical Shell with Circular Cutout. General Technology Corporation Technical Report No. 3-2, January 1963.

  7. Koh, S. L., C. C. Thiel, andA. C. Eringen: Computations for Stress and Stress Concentration in a Circular Cylindrical Shell with Circular Cutout. General Technology Corporation Technical Report No. 3-3, April 1963.

  8. Thiel, C. C., andA. C. Eringen: Stress Concentration in a Capped Circular Cylindrical Shell with Circular Cutout. General Technology Corporation Technical Report 3-4, June 1963.

  9. Naghdi, A. K., andA. C. Eringen: Stress Concentration in a Capped Circular Cylindrical Shell with Circular Cutout. General Technology Corporation Technical Report No. 3-5, August 1964.

  10. Eringen, A. C., A. K. Naghdi, andC. C. Thiel: State of Stress in a Circular Cylindrical Shell. General Technology Corporation Technical Report No. 3-6, August 1964.

  11. Eringen, A. C., A. K. Naghdi, andC. C. Thiel: State of Stress in a Circular Cylindrical Shell with a Circular Hole. Welding Research Council Bulletin No. 102, January 1965.

  12. Van Dyke, P.: Stresses about a Circular Hole in a Cylindrical Shell. Harvard U. Div. of Eng. and Appl. Phy., Tech. Rep. No. 21, 1964.

  13. Lekkerkerker, J. G.: On the Stress Distribution in Cylindrical Shells Weakened by a Circular Hole. Ph.D. diss., Tech. Univ. of Delft (Netherlands). 1964.

  14. Lekkerkerker, J. G.: Stress Concentration Around Circular Holes in Cylindrical Shells. Proc. Eleventh Int. Cong. of Appl. Mech. 1964.

  15. Reidelbach, W.: Der Spannungszustand im Übergangsgebiet einer rechtwinkligen Rohrabzweigung. Ing.-Arch.30, 293–316 (1961).

    Google Scholar 

  16. Eringen, A. C., andE. S. Suhubi: Stress Distribution at Two Normally Intersecting Cylindrical Shells. General Technology Corporation Technical Report No. 3-7, April 1965.

  17. Eringen, A. C., A. K. Naghdi, S. S. Mahmood, C. C. Thiel, andT. Ariman: Analysis of Stress and Deformation in Two Normally Intersecting Cylindrical Shells Subject to Internal Pressure. Gen. Tech. Corp., Tech. Rep. No. 3-8, December 1965.

  18. Eringen, A. C., A. K. Naghdi, S. S. Mahmood, C. C. Thiel, andT. Ariman: Stress Concentrations in Two Normally Intersecting Cylindrical Shells Subject to Internal Pressure. Gen. Tech. Corp., Tech. Rep. No. 3-9, January 1967.

  19. Eringen, A. C., A. K. Naghdi, S. S. Mahmood, C. C. Thiel, andT. Ariman: Welding Research Council Bulletin No. 139, April 1969.

  20. Savin, G. N.: The Stress Distribution in a Thin Shell with an Arbitrary Hole. Problems of Continuum Mechanics, SIAM, Philadelphia, 1961.

    Google Scholar 

  21. Savin, G. N., andA. N. Guz: On the State of Stress Near Curvilinear Holes in Shells. NASA Technical Translation, NASA TTF-423, May 1966.

  22. Savin, G. N., andA. N. Guz: On the Stress State Near Curvilinear Reinforced Openings in Shells. Inz. Zhurnal5, 1 (1965).

    Google Scholar 

  23. Vainberg, D. V., andA. L. Siniavskii: Approximate Analysis of Shells with Holes by the Methods of Potential Theory. Problems of Continuum Mechanics, SIAM. Philadelphia: 1961.

    Google Scholar 

  24. Murthy, V. V. M.: Stresses Around an Elliptic Hole in a Cylindrical Shell. J. of App. Mech.36, 39–46 (1969).

    Google Scholar 

  25. Green, A. E. andW. Zerna: Theoretical Elasticity. Oxford: Clarendon Press. 1960.

    Google Scholar 

  26. Vlasov, V. Z.: General Theory of Shells and its Applications in Engineering. NASA Technical Translation, NASA TTF-99, April 1964.

  27. McLachlan, N. W.: Theory and Application of Mathieu Functions. Oxford University Press. 1951.

  28. Taylor, C. E., andN. C. Lind: Photoelastic Study of the Stresses Near Openings in Pressure Vessels. Welding Research Council Bulletin, No. 113, April 1966.

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Notre Dame, 46556, Notre Dame, IN, USA

    M. N. B. Rao &  T. Ariman

Authors
  1. M. N. B. Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Ariman
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

With 10 Figues

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rao, M.N.B., Ariman, T. On the stresses around an elliptic hole in a cylindrical shell. Acta Mechanica 12, 1–20 (1971). https://doi.org/10.1007/BF01178386

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01178386

Keywords

Search

Navigation