Summary
The formulation of element elastic-plastic laws is considered in the framework of the displacement approach. The finite element model is regarded as an actually discrete system, composed of a finite number of parts whose individual behaviour is described in terms of generalized stresses and strains. A general procedure for formulating the element laws is proposed, and it is shown that some commonly used formulations of finite element elastic-plastic analysis can be recovered on the basis of particular assumptions. It is pointed out that these formulations may violate some “consistency” requirements, which are discussed in the paper; these violations may explain some of the inaccuracies experienced in computations. A fairly general method for restoring consistency is proposed. The implications of some of the approximations involved are also discussed, with particular reference to the limit analysis problem. Simple examples illustrate the effects of lack of consistency.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Nayak, G.C.; Zienkiewicz, O.C.: Elastic-plastic stress analysis. A Generalization for various constitutive relations including strain softening. Int. J. Num. Meth. Engrg., 5, (1972), 113–135.
Zienkiewicz, O.C.: The finite element method. McGraw-Hill, London, 1977.
Besseling, J.F.: The force method and its application in plasticity problems. Computers and Structures, 8, (1978) 323–330.
Besseling, J.F.: Finite element method. 53–78, in: Trends in Solid Mechanics, Besseling and van der Heijden edts., Sijthoff & Noordhoff, 1979.
Argyris, J.H.: Continua and discontinua. 11–189, in: Proc. 1st Conf. on Matrix Methods in Structural Mechanics, Dayton, Ohio, AFFDL TR. 66. 80, 1966.
Scharpf, D.W.: A new method of stress calculation in the matrix displacement analysis. Computers and Structures, 8, (1978) 465–477.
Maier, G.: A matrix structural theory of piecewiselinear plasticity with interacting yield planes. Meccanica, 5 (1970) 54–66.
Corradi, L.: On compatible finite element models for elastic plastic analysis. Meccanica, 13 (1978) 133–150.
Corradi, L.: On some “consistent” finite element approximations in non-linear structural analysis. Proc. 5th ALMETA Conference, Palermo, Italy, Oct. 1980.
Corradi, L.; Gioda, G.: On the finite element modelling of elastic-plastic behaviour with reference to geotechnical problems. 1st. Int. Conf. on Numerical Methods for Non-Linear Problems, Swansea, U.K. Sept.1980.
Martin, J.: Plasticity. MIT Press, 1975.
Dang Hung, N.; König, J.A.: A finite element formulation of the shakedown problem using a yield criterion of the mean. Corp. Meth. Appl. Mech. Engrg., 8 (1976) 179–192.
Hodge, P.G. Jr.: A Consistent finite element model for the two-dimensional continuum. Ingenieur Archiv, 39 (1970) 375–383.
Cohn, M.Z.; Maier, G. Eds.: Engineering Plasticity by Mathematical Programming. Pergamon Press, New York, 1979.
Dang Hung, N.; Trapletti, M.; Ransart, D.: Bornes quasi inférieures et bornes supérieures de la pression de ruine de coques de révolution par la méthode des éléments finis et par la prograuimiation nonlinéare Int. J. Nonlinear Mech., 13 (1979) 79–102.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Corradi, L., Maier, G. (1981). Finite Element Elastoplastic and Limit Analysis: Some Consistency Criteria and Their Implications. In: Wunderlich, W., Stein, E., Bathe, KJ. (eds) Nonlinear Finite Element Analysis in Structural Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81589-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-81589-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-81591-1
Online ISBN: 978-3-642-81589-8
eBook Packages: Springer Book Archive