Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Neal, B. G. and Symonds, P. S., The calculation of collapse loads for framed structures, J. Inst. Civil Engineers, 35 (1950) 21.
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.
Baker, J. F., Home, M. R. and Heyman, J., The Steel Skeleton, vol. 2, Cambridge University Press 1956.
Neal, B. G., The Plastic Methods of Structural Analysis, 2nd Edition, Chapman and Hall 1963.
Maier, G. and Munro, J., Mathematical programming applications to engineering plastic analysis, Applied Mech. Rev., 35 (1982) 1631–1643.
Maier, G., Linear flow-laws of elastoplasticity: a unified general approach, Rendic. Acad. Naz. Lincei, Series 8, 47 (1969) 266.
Teixeira de Freitas, J. A., An efficient Simplex method for the limit analysis of structures, Computers & Structures, 21 (1985) 1255–1265.
Salençon, J., Applications of the Theory of Plasticity in Soil Mechanics, Wiley 1977.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Wien
About this chapter
Cite this chapter
Smith, D.L. (1990). Plastic Limit Analysis. In: Smith, D.L. (eds) Mathematical Programming Methods in Structural Plasticity. International Centre for Mechanical Sciences, vol 299. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2618-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2618-9_5
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82191-6
Online ISBN: 978-3-7091-2618-9
eBook Packages: Springer Book Archive