Limit Design: Formulations and Properties

  • C. Cinquini
Part of the International Centre for Mechanical Sciences book series (CISM, volume 332)


In the present paper a general formulation of optimal design problems is firstly proposed, and the variational method founded on Lagrangian multiplier technique is shown. As an application a simple example for optimal plastic design of beams is solved.

The variational formulation is discussed in detail for the case of plastic design of circular plates: optimality criterion is shown and special features of optimal solutions are discussed.

Then the same problem is proposed in a discretized form, which makes use of a finite different technique and leads to a linear programming formulation. The features of such an approach are discussed and numerical solutions are shown as well.


Circular Plate Limit Design Sandwich Plate Optimal Design Problem Collapse Mechanism 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Drucker, D.C. and R.T.Shield, Design for minimum weight, Proc. 9th Int. Congr. of Applied Mechanics, Brussels, 5, 1956, 212–222Google Scholar
  2. 2.
    Gross, O. and W.Prager, Minimum-Weight Design for Moving Loads, Proc.4th U.S. Nat. Congr. Appl.Mech.ASME, New York, 2, 1962, 1047Google Scholar
  3. 3.
    Prager, W. and R.T.Shield, A General Tehory of Optimal Plastic Design, J.Appl. Mech. Trans. A.S.M.E., 34, 1, 1967CrossRefGoogle Scholar
  4. 4.
    Chern, J.M. and W.Prager, Optimum Design for Prescribed Compliance Under Alternative Loads, J. Opt.Th.Appl., 5 (1970), 424–431CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Save, M., A Unified Formulation of the Theory of Optimal plastic Design with Convex Cost Function, J.Struct. Mech., 1(1972), 267276Google Scholar
  6. 6.
    Rozvany, G.I.N., Optimal Design of Flexural Systems, Pergamon Press, Sydney, 1976Google Scholar
  7. 7.
    Prager, W. and J.E.Taylor, Problems of Optimal Structural Design, J.Appl. Mech., 35, (1968), 102–106CrossRefMATHGoogle Scholar
  8. 8.
    Prager, W. Conditions for Structural Optimality, Computers and Structures, 2, (1972), 833–840CrossRefGoogle Scholar
  9. 9.
    Save, M., A general criterion for Optimal Structural Design, J.Opt. Tehory Appl., 15, (1975), 119–129CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Rozvany, G.I.N., Optimal design of Flexural Systems, Oxford, Pergamon Press (1976)Google Scholar
  11. 11.
    Hemp, W.S., Optimum Structures, Claredon Press, Oxford, 1973Google Scholar
  12. 12.
    Cinquini, C. and B.Mercier, Minimal Cost in Elastoplastic Structures, Meccanica, 11, 4, 1976, 219–226CrossRefMATHGoogle Scholar
  13. 13.
    Huang, N.C., Optimal Design of Elastic Beams for Minimum-Maximum Deflection, J. Appl. Mech.Trans. A.S.M.E., Dec., 1971, 1078–1081Google Scholar
  14. 14.
    Cinquini. C. Optimal Elastic Design for Prescribed Maxium Deflection, J. Struct. Mech., Vol. 7, 1, 1979, 21–34CrossRefMathSciNetGoogle Scholar
  15. 15.
    Cohn, M.Z., Analysis and Design of Inelastic Structures, Univ. of Waterloo Press, Waterloo, 1972Google Scholar
  16. 16.
    Sawczuk A. and Z.Mroz, Optimization in Structural Design, Proc. IUTAM Symp., Warsaw 1973, Springer Verlag, Berlin, 1975Google Scholar
  17. 17.
    Haug, E.J. and J. Cea, Optimization of Distributed Parameter Structures, Proc. NATO ASI, Iowa City, Iowa, 1980, Noordhoff, The Netherlands, 1981Google Scholar
  18. 18.
    Gallager, R.H., Proceedings International Symposium on Optimum Structural Design, Univ. of Arizona, Tucson, Arizona, 1981Google Scholar
  19. 19.
    Morris, A.J., Foundations of Structural Optimization: A Unified Approach, Proc. NATO ASI, Liege, Belgium, 1980, Chichester, 1982Google Scholar
  20. 20.
    Ekeland, I. and R.Temam, Analyse convexe et problemes variationnels, Dunod, Paris, 1973Google Scholar
  21. 21.
    Cinquini, C. and G.Sacchi, Problems of optimal design for elastic and plastic structures, J. de Mecanique Appl., 4, (1980), 31–59MATHMathSciNetGoogle Scholar
  22. 22.
    Guerlement, G., Lamblin, D. and C. Cinquini, Dimensionnement plastique de cout minimal avec contraintes technologiques de poutres soumines a plusieurs ensembles de charges, J. de Mec. Appl., 1, 1, 1977, 1–25MathSciNetGoogle Scholar
  23. 23.
    Guerlement, G., Lamblin, D. and C. Cinquini, Variational formulation of the optimal plastic design of circular plates, Comput. Meth. Appl. Mech. Eng. 11, 1977, 19–30CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    Guerlement, G., Lamblin, D. and C. Cinquini, Application of linear programming to the optimal plastic design of circular plates subject to technological constrains, Coput. Meth. Appl. Mech. Eng., 13, 2, 1978, 233–243CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    Sheu,C.Y. and W. Prager, Optimal Plastic Design of circular and annular sandwich plates with piecewise constant cross section, J. Mech.Phys. Solids, 17. 1969„ 11–16Google Scholar
  26. 26.
    Hadley, G., Nonlinear and dynamic programming, Addinson Wesley, Chicago, 1965Google Scholar
  27. 27.
    Hopkins, H. and W.Prager, Limits of economy of material in plates, J. Appl. Mech., 22, 1955, 372–374MATHGoogle Scholar
  28. 28.
    Hopkins, H. and W.Prager, The load carrying capacity of circular plates, J. Mech. Phys. Solids, 2, 1953, 372–374CrossRefMathSciNetGoogle Scholar
  29. 29.
    Guerlement, G. and D. Lamblin, Dimensionnement plastique de volume minimal sous contraintes de plaques sandwhich circulaires soumises a des charges fixes ou mobiles, J.Mec., 15, 1 1976, 55–84Google Scholar
  30. 30.
    Lamblin, D. Analyse et dimensionnement plastique de cout minimum de plaques circulaires, These de Doctorat en Sciences Appl., Faculte Polytechnique de Mons, 1975Google Scholar
  31. 31.
    Mgarefs, G.J., Method for minimal design of axisymmetric plates, Asce J. Eng.Mech. Div., 92, 1966, 79–99Google Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • C. Cinquini
    • 1
  1. 1.University of PaviaPaviaItaly

Personalised recommendations