Rigid-Plastic Analysis and Design

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


The paper first states the basic theorems of rigid-perfectly plastic limit analysis, proofs and details being given in appendices 1 and 2. It then explains how to base the description of structures on the theorem of virtual powers. Application to beams in bending follows, again with appendices 3 and 4 for details. Plates, shells and disks are briefly considered, the general solutions process being illustrated on circular plates examples. Multiple loading, optimal design and post-yield behaviour are then examined very rapidly. Experimental verification of the theory is discussed and the paper ends with remarks on the development of the numerical approach.


Circular Plate Limit Load Yield Locus Generalize Displacement Collapse Mechanism 
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  1. [1]:
    SAVE, M.A. and MASSONNET, C.E., Plastic Analysis and Design of Plates, Shells and Disks, North-Holland Pub., 1972.zbMATHGoogle Scholar
  2. [2]:
    COLLINS, I.F., “The Upper Bound Theorem for Rigid-Plastic Solids Generelized to Include Coulomb Friction”, Jour. Mech. Phys. Solids, Vol. 17, 1969, p. 323.CrossRefGoogle Scholar
  3. [3]:
    MASSONNET, C.E. and SAVE, M.A., Plastic Analysis and Design of Beams and Frames, Blaisdell Pub., Waltham, Mass., U.S.A., 1965.Google Scholar
  4. [4]:
    SAVE, M.A., A Unified Fromulation of the Theory of Optimal Plastic Design with Convex Cost Function, Journ. Struct. Mech., Vol. 1, 1972, p. 267–276.CrossRefGoogle Scholar
  5. [5]:
    ROZVANY, G.I.N., Optimal Design of Flexural Systems, Pergamon Press, Oxford, England, 1976.Google Scholar
  6. [6]:
    GAVARINI, C., “Une Méthode Générale pour l’Etude du Comportement des Structures après la Ruine Rigide-Plastique”, Séminaire de Mécanique des Solides et des Structures, Faculté Polytechnique, Département d’Architecture, Mons, 1969.Google Scholar
  7. [7]:
    MASSONNET, C.A. and SAVE, M.A., Calcul Plastique des Constructions, Vol. 1, 3ème édition, Nelissen Pub., Liège, 1977.Google Scholar
  8. [8]:
    LAY, M.G. and SMITH, P.D., “The Role of Strain-Hardening in Plastic Design”, Journ. Struct. Div., A.S.C.E., Vol. 91, 1965, p. 25.Google Scholar
  9. [9]:
    STUSSI, F. and KOLLBRUNNER, C.F., “Beitrag zum Traglastverfahren”, Bautechnik, Vol. 13, 1935, p. 264.Google Scholar
  10. [10]:
    COOPER, R.M. and SHIFRIN, G.A., “An Experiment on Circular Plates in the Plastic Range”, Proc. 2nd U.S. Nat. Cong., Appl. Mech. A.S.M.E., Ann Arbor, Michigan, 1954.Google Scholar
  11. [11]:
    HOPKINS, H.G. and PRAGER, W., “The Load-Carrying Capacity of Circular Plates”, J. Mech. Phys. Solids, Vol. 2, 1953, p. 1.CrossRefMathSciNetGoogle Scholar
  12. [12]:
    LANCE, R.H. and ONAT, E.T., “A Comparison of Experiments and Theory in the Plastic Bending of Plates”, J. Mech. Phys. Solids, Vol. 10, 1962, p. 301.CrossRefGoogle Scholar
  13. [13]:
    SAVE, M.A., “Vérification Expérimentale de l’Analyse des Plaques et des Coques en Acier Doux” (Experimental Verification of Plastic Limit of Mild Steel Plates and Shells), C.R.I.F. Report, M.T. 21, February, Fabrimetal, Brussels, 1966.Google Scholar
  14. [14]:
    DEL RIO, L., “Analyse Limite des Plaques Rectangulaires” These de Maitrise en Sciences Appliquées, Faculté Polytechnique, Mons, Belgique, 1970.Google Scholar
  15. [15]:
    WOOD, R.H., Plastic and Elastic Analysis and Design of Slabs and Plates, Thames an Hudson, London, 1961.Google Scholar
  16. [16]:
    JANAS, M., “Large Plastic Deflections of Reinforced Concrete Slabs”, Int. J. Solids and Struct., Vol. 3, November, 1967, p. 4.Google Scholar
  17. [17]:
    BOUMA, A.L., RIEL, A.C., VAN KOTEN, H. and BERANEK, W.J., Investigations on Models of Eleven Cylindrical Shells made of Reinforced and Prestressed Concrete, Shells Research, North-Holland Publ., Amsterdam, 1961, p. 79–101.Google Scholar
  18. [18]:
    SAVE, M. and PRAGER, W., Editors: Structural Optimization, Vol. 1 Optinalily criteria, by SAVE, PRAGER and SACCHI, Plenum Press, New-york, 1985.zbMATHGoogle Scholar
  19. [19]:
    SAVE, M. and PRAGER, W., Editors: Structural Optimization, Vol. 2 Mathematical Programming, by BORKOWSKI, JENDO, and REITMAN, Plenum Press, New-york, 1990.Google Scholar
  20. [20]:
    SAVE, M. and PRAGER, W., Editors: Structural Optimization, Vol. 3 Applications to metal and concrete structures, by COHN, FRANGOLOL and ESCHENAUER, to appear at Plenum Press, New-york.Google Scholar
  21. [21]:
    ROZVANY, G.I.N., Optimal Design of Flexural Systems, Pergamon Press, Oxford, 1976.Google Scholar
  22. [22]:
    ROZVANY, G.I.N., Structural design via optimal criteria, Kluwer, Doordrecht, 1989.CrossRefGoogle Scholar
  23. [23]:
    BRANDT, A., Editor: Criteria and Methods of structural Optimization, PWN - Polish Scientific Publishers, Warszawa, and Martinus Nijhoff Pub, The Hague - Boston - Lancaster, 1984.Google Scholar
  24. [24]:
    COHN, M.Z. and MAIER, Editors: G., Engineering Plasticity by Mathematical Programming, Pergamon Press, 1979.Google Scholar
  25. [25]:
    CHEN, W.F. and LIU, X.L., Limit Analysis in Soil Sechanics, Developments in Geotechnical Engineering, Vol. 52, Elsevier, 1990.Google Scholar
  26. [26]:
    NGUYEN DANG, H., The Plasticity and the Limit State Analysis and design by finite element method, Birhauser-verlag, 1990.Google Scholar
  27. [27]:
    SAVE, M. Editor: Atlas of Limit Loads of Metal Plates, Shells and Disks, to be published by Elsevier Pub. Co.Google Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • M. Save
    • 1
  1. 1.Faculté PolytechniqueMonsBelgium

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