Influence of Cyclic Creep on the Upper Bound to Shakedown Inelastic Deflections

  • Stanisław Dorosz
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 36)


for structures of linear elastic, perfectly plastic and creeping materials subjected to cyclic loading, a bounding principle for the maximum residual deflection at a given point is presented. The bound is valid for a simple non-interactive creep.


Plastic Strain Creep Strain Plastic Strain Rate Plastic Structure Residual Displacement 
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  1. 1960 Koiter, W.T.: General theorems for elastic-plastic solids, In: Progress in Solid Mechanics, North Holland, Amsterdam, p. 165.Google Scholar
  2. 1960 Boley, B.A., Weiner, J.H.: Theory of Thermal Stress, John Wiley & Sons.Google Scholar
  3. 1972 MrÓZ, Z.: On the theory of steady plastic cycles in structures, Proc. of SMiRT 1, 6 part L, p. 489.Google Scholar
  4. 1972 Ponter, A.R.S.: Deformation, displacement, and work bounds for structures in a state of creep and subjected to variable loading, J. Appl. Mech. Trans. of the ASME, 39, p. 953.Google Scholar
  5. 1972 Vitiello, E.: Upper bounds to plastic strains in shakedown of structures subjected to cyclic loads. Meccanica, Vol. 7, pp. 205–213.Google Scholar
  6. 1972 BrzeziŃSki, R. and KÖnig, J.A.: Evaluation of shakedown deflections of framed structures by linear programming. In: Symp. Plastic Analysis of Structures, Jassy, pp. 101–116.Google Scholar
  7. 1972 Ponter, A.R.S.: An upper bound on the small displacements of elastic, perfectly plastic structures, J.Appl. Mech., Vol. 39, pp. 959–963.Google Scholar
  8. 1973 Maier, G.: A shakedown matrix theory allowing for work-hardening and second-order geometric effects, Foundations of Plasticity, ed. A. Sawczuk, Nordhoff, Ley den, pp.417–43Google Scholar
  9. 1973 BrzeziŃSki, R. and KÖnig, J.A.: Deflection analysis of elastic-plastic frames at shakedown, J. Struct. Mech., vol. 2, pp. 211–228.Google Scholar
  10. 1974 Capurso, M.: A displacement bounding principle in shakedown of structures subjected to cyclic loads. Int. J. Solids Structures, Vol. 10, pp. 77–92.Google Scholar
  11. 1974 Leckie, F. A.: A review of bounding techniques in shake down and ratchetting at elevated temperature, Welding Research Council Bull., No. 195, p. 1.Google Scholar
  12. 1974 Maier, G. and Vitiello E.: Bounds on plastic strains and displacements in dynamic shakedown of workhardening structures, J. Appl. Mech., Vol. 41, pp. 434–440.Google Scholar
  13. 1976 Dorosz, S.: An upper bound to maximum residual deflections of elastic-plastic structures at shakedown. Bull. de l'Acad. Pol. Sci., Ser. Sci. Techn., Vol 24, pp. 167–174.Google Scholar
  14. 1978 Dorosz, S.: An improved upper bound to maximum deflections of elastic-plastic structures at shakedown, J. Struct. Mech., 76, 3, p. 267.Google Scholar
  15. 1978 Polizzotto, C: A unified approach to quasi-elastic shakedown problems for elastic-plastic solids with piecewise linear yield surface. Meccanica, vol. 13, pp. 109–120Google Scholar
  16. 1978 Loi, F.T. and Grundy, P.: Deflection stability of workhardening structures, J. Struct. Mech., vol.6, pp. 331–347.Google Scholar
  17. 1980 Loi, F.T.: Deflection bounding at shakedown, J. Struct. Div., Proc. ASCE, vol. 106, pp. 1209–1215.Google Scholar
  18. 1981 Dorosz, S. and Sawczuk, A: Deflections of elastic-plastic beams at finite spread of plastic zones. In: Physical Non-linearities in Structural Analysis. Eds.: J. Hult and J. Lemaitre, Berlin, Springer, pp. 64–73.Google Scholar
  19. 1981 KÖnig, J.A., Maier, G.: Shakedown analysis of elastoplastic structures: A review of recent developments, Nuclear Engineering and Design, 66, 81–95.Google Scholar
  20. 1981 Ainsworth, R.A.: Bounding structural deformation due to combined creep and plasticity. IUTAM Symposium Creep in Structures, Springer Verlag.Google Scholar
  21. 1981 Ponter, A.R.S.: On the creep modified shakedown limit, IUTAM Symposium, Leicester 1980, Creep in Structures ed. A.R.S. Ponter, D.P. Hayhurst, Springer Verlag, p. 264,.Google Scholar
  22. 1982 Anderberg, Y.: Behaviour of steel at high temperatures, RILEM-COMMITTEE 44-PHT, Nov. 1982.Google Scholar
  23. 1982 Polizzotto, C: Bounding principles for elastic-plastic-creeping solids loaded below and above the shakedown limit, Meccanica, 17, p. 143.Google Scholar
  24. 1986 KÖNig J.A.: Shakedown of Elastic-Plastic Structures, Elsevier & Polish Scientific Publishers, Warsaw.Google Scholar
  25. 1994 Dorosz, S.: Method of calculation for elastic-plastic-creeping structures subjected to variable loading, (in preparation).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Stanisław Dorosz
    • 1
  1. 1.Institute of Fundamental Technological ResearchPolish Academy of SciencesWarsawPoland

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