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Plastic Shakedown Analysis

  • Nguyen Dang Hung
  • P. Morelle
Part of the International Centre for Mechanical Sciences book series (CISM, volume 299)

Abstract

Structures of mechanical engineering for instance power plants, reactors, pressure vessels, etc. or civil engineering for instance, frames, grids, bridge decks etc. are exposed to variable loading particularly cyclic or repeated loading. In these situations, classical limit analysis which assumes proportional loading are out of question because the results deduced present no security step-by-step elastic-plastic calculation is somewhat very costly in computing times. The most efficient way to handle the problem is to apply the shakedown theory. This theory is based on experimental facts obtained from realistic structures or laboratory specimen [1–4]. It offers a direct method as like as limit analysis to perform the analysis of the problem.

Keywords

Residual Stress Finite Element Formulation Plastic Strain Rate Residual Stress Field Repeated Loading 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    GRUNING, M.: Die Tragfähigkeit con Balken aus Stahl mit Berücksichtigung des plastischen Verformungsvermögens, Bautechnik, (1930).Google Scholar
  2. [2]
    GURALNICK, S.A., SURANDA SINGH, ERBER T.: Plastic collapse, shakedown and hysteresis, J1. Struct. Eng., 110, n° 9, pp. 2103–2119, (1984).CrossRefGoogle Scholar
  3. [3]
    MASSONNET, Ch.: Essais d’adaptation et de stabilisation plastiques sur des poutrelles laminées (Mémoires de l’AIPC, vol. 13, p. 239 (1953).Google Scholar
  4. [4]
    MASSONNET, Ch. et SAVE, M.: Plastic Analysis and Design. Vol. 1: Beams and Frames. Blaisdell, Publ. Co, (1965), éd. francaise, Cenrri. Belgo-Luxembourgeois d’Information de l’Acier, Bruxelles, (1961).Google Scholar
  5. [5]
    BLEICH, H.: Uber die Bemessung statisch unbestimmter stahltragwerke unter Berücksichtigung des elastisch-plastischen Verhaltens des Baustoffes, Bauingenieur, 19 /20, (1932), p. 261Google Scholar
  6. [6]
    MELAN, E.: Theorie statisch unbestimmter Systeme. Prelim. Publ., 2nd Cong. Int. Assoc. Bridge and Struct. Eng., Berlin, 43 (1936).Google Scholar
  7. [7]
    SYMONDS, P.S.: Shakedown in Continuous Media, J. Appl. Mech., 18 (1951), p. 85.MathSciNetMATHGoogle Scholar
  8. [8]
    KOITER, W.T.: Some Remarks on Plastic Shakedown Theorems, Prei, Rrh Int. Cong. Appl. Mech., 1, 220, Istanbul (1952).Google Scholar
  9. [9]
    NEAL, B.G.: The Plastic Method of Structural Analysis, London, Chapman and Hall, 1956.Google Scholar
  10. [10]
    PRAGER, W.: Shakedown in Elastic-Plastic Media Subjected to Cycles of Load and Temperature, Symp. sulla plasticita nella scienza delle costruzioni, Bologna (1957).Google Scholar
  11. [11] ROSENBLUM, V.I.: Adaptation des corps élasto-plastiques soumis à une température non uniforme (en russe).
    Izv. Ak. N., URSS, OTN n° 7 (1957).Google Scholar
  12. [12]
    GOKHFELD, D.A.. Carrying Capacity of Structures under Variable Thermal Condition (en russe). Mashinostroyeniye, Moscou (1970).Google Scholar
  13. [13]
    KONIG, J.A.: Engineering Applications of Shakedown Theory, Lecture Notes, CISM, Udine (1977).Google Scholar
  14. [14]
    HO HWA-SHAN: Shakedown in Elastic-Plastic Systems under Dynamic Loading, J. Appl. Mech. 39 (1972), pp. 416–421.CrossRefGoogle Scholar
  15. [15]
    CORRADI, L. and MAIER, G.: Inadaptation Theorems in the Dynamics of Elastic-Work Hardening Structures. Ing. Arch., 43 (1973), pp. 44–57.MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    CORRADI, L. and MAIER, G.: Dynamic Non-Shakedown Theorem for Elastic Perfectly Plastic Continua. J. Mech. Phys. Solids, 22 (1974), pp. 401–413.CrossRefMATHGoogle Scholar
  17. [17]
    POLIZZOTTO, C.: Adaptation of Rigid-Plastic Continua Under Dynamic Loadings. Tech. Rep. SISTA-77-OMS-2, Facolta di Architettura di Palermo, Palermo (1977).Google Scholar
  18. [18]
    NGUYEN DANG HUNG and KONIG, J.A.: A Finite Element Formulation for Shakedown Problems Using a Yield Criterion of the Mean. Comp. Meth. Appl. Mech. Eng., vol. 8, n° 2, pp. 179–192 (1976).CrossRefMATHGoogle Scholar
  19. [19]
    NGUYEN DANG HUNG and PALGEN, L.: Shakedown Analysis by Displacement Method and Equilibrium Finite Element. Trans. of the CSME, vol. 6, n° 1, pp. 34–40, (1980–81).Google Scholar
  20. [20]
    NGUYEN DANG HUNG and MORELLE, P.: Numerical Shakedown Analysis of Plates and Shells of Revolution. New and Future Developments in Commercial Finite Element Methods, édité par J. Robinson, pp. 422–435 (1980).Google Scholar
  21. [21]
    MORELLE, P. and NGUYEN DANG HUNG: Etude numérique de l’adaptation plastique des plaques et des coques de révolution par les éléments finis d’équilibre. J. de Méc. Théorique et appliquée, vol. 2, n° 4, pp. 567–599 (1983).MATHGoogle Scholar
  22. [22]
    NGUYEN DANG HUNG: Sur la plasticité et le calcul des états limites par éléments finis. Thèse de doctorat spéciale, University of Liége, (1984).Google Scholar
  23. [23]
    DE SAXCE, G.: Sur quelques problèmes de mécanique des solides considérés comme matériaux à potentiels convexes. Ph. D. Thesis, University of Liège (1986).Google Scholar
  24. [24]
    MORELLE, P.: Analyse duale de l’adaptation plastique des structures par la méthode des éléments et la programmation mathématique, Ph. D. Thesis, University of Liége (1989).Google Scholar
  25. [25]
    SAVE, M. DE SAXCE, G. BORKOWSKI, A.: Computation of Shakedown Loads Feasibility Study. Final Report, Contract FA 1–0100-B ( GDF/DSF ), Commission of the European Communities, (1987).Google Scholar
  26. [26]
    MAIER, G. Shakedown Theory in Perfect Elastoplasticity with Associated and Non-Associated Flow-Laws, A Finite Element Linear Programming Approach, Meccanica, 4 (1969), p. 250.CrossRefMATHGoogle Scholar
  27. [27]
    MAIER, G.: Shakedown of Plastic Structures with Unstable Parts. ASCE, J. Eng. Mech. Div. vol. 98 (1972), pp. 1322.Google Scholar

Copyright information

© Springer-Verlag Wien 1990

Authors and Affiliations

  • Nguyen Dang Hung
    • 1
  • P. Morelle
  1. 1.University of LiègeLiègeBelgium

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