Optimal Plastic Design and the Development of Practical Software

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


The purpose of this work is to present a simple, practical and automatic procedure for the rigid-plastic analysis and design of frame structures under both proportional and repeated loadings. The applicability of linear programming techniques to this kind of problem was pointed out some twenty years ago. The principle of the method is widely exposed in the literature1–17. In this paper we restrict ourselves to some particular aspects of the automatic calculations and practical implementations. These are:
  1. 1)

    the efficient choice between the statical and kinematical formulations leading to a minimum number of variables. This affects considerably the size of the problem:

  2. 2)

    the automatic construction of the characteristic matrices, mainly the independent equilibrium-compatibility matrix;

  3. 3)

    the direct calculations of dual variables which allows the necessary results to be obtained by a simple procedure;

  4. 4)

    the realistic verifications of the stability conditions imposed by European norms for steel structures.



Design Variable Critical Section Collapse Mechanism Plastic Analysis Shakedown Analysis 
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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  1. 1.
    Ch. Massonnet and M. Save, Calcul plastique des constructions. Vol. 1 Structures dépendent dun paramètre. Sème édition, Nélissen B., Liége. (1976).Google Scholar
  2. 2.
    B. G. Neal, The Plastic Methods of Structural Analysis. Chapman and Hall, London, (1956).MATHGoogle Scholar
  3. 3.
    P. G. Hodge, Jr.. Plastic Analysis of Structures. McGraw-Hill, (1959).Google Scholar
  4. 4.
    D. B. Martin: Plasticity, Fundamentals and General Results. MIT Press, Cambridge, Massachusetts. Londres, 1975.Google Scholar
  5. 5.
    K. I. Majid, Non-linear Structures. Butterworths, London, (1978).Google Scholar
  6. 6.
    M. Z. Cohn. S. K. Ghosh. and S. R. Parimi. “A Unified Approach to Theory of Plastic Structures.” Solid Mech. Division, University of Waterloo, Canada, Report nr 26, June (1973).Google Scholar
  7. 8.
    A. Charles, C. E. Lemke, and O. C. Zienkiewicz, “Virtual work. Linear Programming and Plastic Limit Analysis,” Proc. Royal Soc. A, 251, (1959).Google Scholar
  8. 9.
    W. S. Dorn, “On the Plastic Collapse of Structures and Linear Programming,” Ph.D. Thesis, Dept. of Mathematics, Carnegie Institute of Techn. Pittsburgh, Pa. May (1955).Google Scholar
  9. 10.
    W. S. Dorn and H. J. Greenberg, “Linear Programming and Plastic Limit Analysis of Structures.” Quart. J. Appl. Math., 15, (1957).Google Scholar
  10. 11.
    G. Ceradini and C. Gavarini, “Calcolo a rottura e programmazione lineare,” Giornale del Genio Civile, 3, (1965).Google Scholar
  11. 12.
    D. E. Grierson and G. M. L. Gladwell, “Collapse Load Analysis Using Linear Programming.” J. Str. Dit. ASCE.. 97. (ST 5), May, (1971).Google Scholar
  12. 13.
    R. K. Livesley. “The Automatic Design of Structural Frames,” Quart. J. Mec/n. and Appl. Matin.. 8. (3), September (1956).Google Scholar
  13. 14.
    W. Prager, “Linear Programming and Structural Design,” Rand Research Mennora ch nt KM-2021. ASTIA Document AP 150661. December (1957).Google Scholar
  14. 15.
    G. Maier, R. Srininavan, and M. Save, “On Limit Design of Frames using Linear Programming.” “Proc. int. Symp. on Computer-Aided Structural Design. University of Warwick, Coventry, (1972).Google Scholar
  15. 16.
    G. Sacchi, M. Maier, and M. Save, “Limit Design of Frames for Movable Loads by Linear Programming,” IUTAM Symposium on Optimization in Structural Design. Warsaw 1973, (ed. Sawczuk and Mroz ), Springer, (1975).Google Scholar
  16. 17.
    G. Maier, “Mathematical Programming Methods in Structural Analysis,” Proc. Int. Si’mp. on Variational Methods in Engineering, (ed. C. Brebbia and H. Tottenham ), Southampton University Press, (1973).Google Scholar
  17. 18.
    Nguyen Dang Hung and G. De Saxce, “Analyse et dimensionnement plastique des structures 6 barres dans des conditions de stabilité,” Construction métallique, (3), 15–28, (1981).Google Scholar
  18. 19.
    C. E. C. M., European Recommendations for Steel Constructions, ECCS-EG 77–2E, March (1978).Google Scholar
  19. 20.
    D. E. Grierson, “Elastic-Plastic Deformation Analysis usine Linear Programming,” Solid Mech. Div., University of Waterloo, Report No.. 88, July (1971).Google Scholar
  20. 21.
    M. Z. Cohn, Analysis and Design of Inelastic Structures. Vol. 2. Problems, University of Waterloo Press, (1972).Google Scholar

Copyright information

© Springer-Verlag Wien 1990

Authors and Affiliations

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

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