Jump to ContentJump to Main Navigation
Show Summary Details
More options …

International Journal of Applied Mechanics and Engineering

The Journal of University of Zielona Góra

Editor-in-Chief: Walicki, Edward

4 Issues per year

CiteScore 2016: 0.12

SCImago Journal Rank (SJR) 2016: 0.127
Source Normalized Impact per Paper (SNIP) 2016: 0.063

Open Access
See all formats and pricing
More options …

Plastic limit load of ellipsoidal pressure vessel head with nozzle under internal pressure loading

V.N. Skopinsky / N.A. Berkov / A.B. Smetankin
Published Online: 2014-03-07 | DOI: https://doi.org/10.2478/ijame-2013-0077


A new method and numerical procedure for determining the plastic limit load in an ellipsoid-cylinder intersection using the elastic-plastic finite element analysis are presented. The proposed method is based on the maximum criterion of the rate of change of the relative plastic work. For the elastic-plastic analysis of the nozzle connections the 2D finite element method and plasticity theory with strain hardening are used. The results of the comparison of the plastic limit pressure obtained on the basis of different known criteria and the proposed criterion are presented. A parametric study of ellipsoidal heads with a nozzle under internal pressure loading was performed. The effects of nondimensional geometric parameters of shell intersection on the plastic limit pressure are discussed.

Keywords : shell intersection; elastic-plastic finite element analysis; plastic limit load; ellipsoidal head; nozzle connection


  • ASME (2004): Boiler and Pressure Vessel Code. Sections II and VIII. - New York.Google Scholar

  • BSI. PD 5500 (2006): Specification for Unfired Fusion Welded Pressure Vessels. -London: British Standards Institution.Google Scholar

  • Camilleri D., Mackenzie D. and Hamilton R. (2006): Evaluating plastic loads in torispherical heads using a new criterion of collapse. - ASME PVP Conference, Vancouver, Canada, vol.3, pp.701-708. EN 13445 (2002): Unfired Pressure Vessels. Part 3: Design. European Committee for Standardisation (CEN), Brussels.Google Scholar

  • Gerdeen J.C. (1979): A critical evaluation of plastic behavior data and a unified definition of plastic loads for pressure components. - Welding Research Council Bulletin, No.254, pp.1-64.Google Scholar

  • Hsieh M.F., Moffat D.G. and Mistry J. (2000): Nozzles in the knuckle region of a torispherical head: limit load interaction under combined pressure and piping loads. - Int. J. Pressure Vessels and Piping, vol.77, No.13, pp.807-815.Google Scholar

  • Hsieh M.F., Moreton D.N., Mistry J. and Moffat D.G. (2002): Limit loads for knuckle-encroaching nozzles in torispherical heads: experimental verification of finite element predictions. - J. Strain Analysis, vol.37, No.4, pp.313-326.Google Scholar

  • Iliushin A.A. (1948): Plastisity. - Мoscow: GITTL.Google Scholar

  • Li H. and Mackenzie D. (2005): Characterising gross plastic deformation in design by analysis. - Int. J. Pressure Vessels and Piping, vol.82, No.10, pp.777-786.Google Scholar

  • Mackenzie D. and Li H. (2006): A plastic load criterion for inelastic design by analysis. - Trans. ASME, J. Pressure Vessel Technology, vol.128, No.1, pp.39-45.Google Scholar

  • Muscat M., Mackenzie D. and Hamilton R. (2003): A work criterion for plastic collapse. - Int. J. Pressure Vessels and Piping, vol.80, No.1, pp.49-58.Google Scholar

  • Nayak G.G. and Zienkiewicz O.С. (1973): Elasto-plastic stress analysis. A generalization for various constitutive relations including strain softening. - Int. J. Numer. Meth. Engn., vol.5, No.1, pp.113-135.Google Scholar

  • Skopinsky V.N. (2000): Stresses in ellipsoidal pressure vessel heads with noncentral nozzle. - Nuclear Engineering and Design, vol.198, pp.317-323.Google Scholar

  • Skopinsky V.N. (2008): Stresses in Intersecting Shells. - Moscow: Fizmatlit.Google Scholar

  • Skopinsky V.N. and Berkov N.A. (1994): Stress analysis of ellipsoidal shell with nozzle under internal pressure loading. - Trans. ASME, J. Pressure Vessel Technology, vol.116, No.3, pp.431-436.Google Scholar

  • Skopinsky V.N. and Berkov N.A. New criterion for the definition of plastic limit load in nozzle connections of pressure vessels. - Trans. ASME, J. Pressure Vessel Technology (in press).Web of ScienceGoogle Scholar

  • Skopinsky V.N. and Smetankin A.B. (2003): Parametric study of reinforcement of pressure vessel head with offset nozzle. - Int. J. Pressure Vessels and Piping, vol.80, No.5, pp.333-343.Google Scholar

  • Skopinsky V.N. and Smetankin A.B. (2006): Modelling and stress analysis of nozzle connections in ellipsoidal heads of pressure vessels under external loading. - Int. J. Applied Mechanics and Engineering, vol.4, No.11, pp.965-979. Google Scholar

About the article

Published Online: 2014-03-07

Published in Print: 2013-12-01

Citation Information: International Journal of Applied Mechanics and Engineering, Volume 18, Issue 4, Pages 1263–1274, ISSN (Print) 1734-4492, DOI: https://doi.org/10.2478/ijame-2013-0077.

Export Citation

This content is open access.

Comments (0)

Please log in or register to comment.
Log in