Systematic mesh and nodal descriptions of the laws of statics and kinematics for the limiting state of plastic collapse in a structural system are set out. Then the constitutive relations appropriate to this condition are presented in such a way as to emphasise their inherent complementarity. The mixing together of these three independent ingredients — statics, kinematics and material constitution — gives rise to the vectorial formulation which governs plastic collapse: it is identified as a linear complementarity problem. From it are derived the dual linear programs which give expression to the variational principles associated with upper and lower bounds on the collapse load factor.


Yield Surface Plastic Hinge Linear Complementarity Problem Critical Section Admissible Solution 
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.
    Neal, B. G. and Symonds, P. S., The calculation of collapse loads for framed structures, J. Inst. Civil Engineers, 35 (1950) 21.CrossRefGoogle Scholar
  2. 2.
    Neal, B. G. and Symonds, P. S., The rapid calculation of the plastic collapse load for a framed structure, Proc. Inst. Civil Engineers, 1 (1952) 58.Google Scholar
  3. 3.
    Baker, J. F., Home, M. R. and Heyman, J., The Steel Skeleton, vol. 2, Cambridge University Press 1956.Google Scholar
  4. 4.
    Neal, B. G., The Plastic Methods of Structural Analysis, 2nd Edition, Chapman and Hall 1963.Google Scholar
  5. 5.
    Maier, G. and Munro, J., Mathematical programming applications to engineering plastic analysis, Applied Mech. Rev., 35 (1982) 1631–1643.Google Scholar
  6. 6.
    Maier, G., Linear flow-laws of elastoplasticity: a unified general approach, Rendic. Acad. Naz. Lincei, Series 8, 47 (1969) 266.Google Scholar
  7. 7.
    Teixeira de Freitas, J. A., An efficient Simplex method for the limit analysis of structures, Computers & Structures, 21 (1985) 1255–1265.CrossRefMATHGoogle Scholar
  8. 8.
    Salençon, J., Applications of the Theory of Plasticity in Soil Mechanics, Wiley 1977.Google Scholar

Copyright information

© Springer-Verlag Wien 1990

Authors and Affiliations

  • D. Lloyd Smith
    • 1
  1. 1.Imperial CollegeLondonUK

Personalised recommendations