Shakedown of Shells Undergoing Moderate Rotations

  • Johannes Gross-Weege
  • Dieter Weichert
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 36)


A shakedown theorem for elasto-plastic shells undergoing moderate rotations is presented, particularly adapted to situations where perturbations of a permanent mechanical load may induce progressive deterioration. The numerical examples illustrate the importance of the effects of change of geometry during the process.


Moderate Rotation Middle Surface Undeformed Configuration Covariant Base Vector Plastic Material Behaviour 
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  1. 1938 Melan, E., “Theorie statisch bestimmter Tragwerke aus ideal-plastischem Baustoff”,.Sitzungsbericht der Akademie der Wissenschaften (Wien) Abt. IIA, 145,195.Google Scholar
  2. 1960 Koiter, W.T., “General theorems for elastic-plastic solids”, In: Progress in Solid Mechanics (Eds.: I. N. Sneddon and R. Hill), pp. 165–221, North-Holland, Amsterdam.Google Scholar
  3. 1973 Maier, G., “A Shakedown matrix theory allowing for workhardening and second-order geometric effects”, In: Foundations of Plasticity (Eds.: A. SAWCZUK), pp. 417–433. North-Holland, Amsterdam.Google Scholar
  4. 1975 Pointer, A.R.S., “A general shakedown theorem for elastic/plastic bodies with work hardening”, Proc. SMiRT-3, London, Paper L5/2.Google Scholar
  5. 1976 Mandel, J., “Adaptation d'une structure plastique écrouissable et approximation”, Mech. Res. Commun. 3, 483.Google Scholar
  6. 1976 Bieniek, Mp, Funaro, Jr., “Elastic-plastic theory of plates and shells”, Report NO. DNA 3954 T, Weidlinger Associate, New York.Google Scholar
  7. 1982 Sawczuk, A., “On plastic shell theories at large strains and displacements, Int. J. Mech. Sci, 24, 231.Google Scholar
  8. 1984 Weichert, D., “Shakedown at finite displacements; a note on Melan's theorem”, Mech. Res. Comm. 11 121.Google Scholar
  9. 1985 Basar, Y, KrÄTzig, W.B, “Mechanik der Flächentragwerke”, Vieweg, Braunschweig.Google Scholar
  10. 1986 Weichert, D, “On the Influence of geometrical nonlinearities on the shakedown of elastic-plastic structures”, Int. J. Plasticity, 2, 135.Google Scholar
  11. 1988 Gross-Weege, J. “Zum Einspielverhalten von Flächentragwerken”, Report 58, Institute of Mechanics, Ruhr-University Bochum.Google Scholar
  12. 1988 KÖnig, J.A., Siemaszko, A., “Strainhardening effects in shakedown processes”, Ing. Arch. 58, 58.Google Scholar
  13. 1988 Weichert, D., Gross-Weege, J., “The numerical assessment of elasticplastic sheets under variable mechanical and thermal loads using a simplified two surface yield-condition”, Int. J. Mech. Sci. 30, 757.Google Scholar
  14. 1989 Weichert, D., “Shakedown of shell-like structures allowing for certain geometrical nonlinearities”, Arch. Mech. 41(1), 61.Google Scholar
  15. 1990 Stein, E, Zhang, G., KÖNig, Ja., “Micromechanical modelling and computation of shakedown with nonlinear kinematic hardening including examples for 2D-problems”, In: Recent Developments of Micromechanics (Eds.: D. R. Axelrad and W. Muschik). Springer, Berlin.Google Scholar
  16. 1990 Gross-Weege, J., “A unified formulation of statical shakedown criteria for geometrically nonlinear problems”. Int. J. Plasticity 6, 433.Google Scholar
  17. 1992 Gross-Weege, J., Weichert, D., “Elastic-plastic shells under variable mechanical and thermal loads”, Int. J. Mech. Sci., 34, 863.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Johannes Gross-Weege
    • 1
  • Dieter Weichert
    • 2
  1. 1.KrefeldGermany
  2. 2.LML (EUDIL), CNRS URA 1441Université de Lille 1Villeneuve d’Ascq CedexFrance

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