Abstract
The aim of the present exposition is to summarize the main algebraic properties of classics plasticity, and thus help the understanding of the mathematical context of shakedown studies Hence nothing new must be expected, except some few improvements concerning presenta tion and hypothesis enlargement ; for instance the new concept of “elastic sanctuary” ha recently been introduced by the author and D. Weichert [1993] in order to give a maximal extension to the assumptions which ensure the classical proofs. We shall stay within th linear framework generated by the hypothesis that displacements and strains remain small in the vicinity of some strained configuration.
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References
1964 Koiter, W.T,. “General theorems for elastic-plastic solids “, Progress in Solid Mechanics, 1, Sneddon & Hill, North Holland P. C.
1969 Ceradini, G,. “Sull'adattamento dei corpi elasto-plastici sogetti ad azioni dinamiche”, Giornale del Genio Civile, 415.
1973 Moreau, J.J., “On Unilateral Constraints, Friction and Plasticity” Lecture Notes, CIME June, Edizione Cremonese.
1976 Debordes, O., et Nayroles, B., “Sur la théorie et le calcul à l'adaptation des structures élastoplastiques”,. J. de Mécanique, 15, N° 1.
1976 Johnson, C., “Existence theorems for plasticity problems”, J. Math. Pures et Appl., 55, pp. 431–444.
1978 Strang, G,. “A family of model problems in plasticity”, Proc. Symp. Comp. Meth. in AppL Sci. Ed. R. Glowinski an J.L. Lions, Lecture Notes in Math., 704. pp. 292–308.
1979 Suquet, P., “Un espace fonctionnel pour les équations de la plasticité”, Ann. Fac. Sci. Toulouse, 1. pp. 77–87.
1981 Debordes, O., “Przystosowanie ukladow sprezysto-idealnie plastycznych”, Metody analizy funkcjonalnej w plastycznosci, Ossolineum.
1981 Nayroles, B,. “Elementy analizy wypuklejw mechanice ciala stalego”, Metody analizy funkcjonalnej w plastycznosci, Ossolineum.
1987 KÖnig, J.A., “Shakedown of Elastic-Plastic Structures”, Elsevier, Amsterdam.
1988 Suquet, P., “Discontinuities and Plasticity”, Non Smooth Mechanics and Applications, Ed. J.J. Moreauand P.D. Panagiotopoulos, Int. Centre for Mech. Sci. Courses and Lectures, 302, pp. 280–340.
1993 Nayroles, B., and Weichert, D., “La notion de sanctuaire d'élasticité et l'adaptation des structures “, C. R. Acad.Sci. Paris, 316, Série II, pp. 1493–1498.
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Nayroles, B. (1995). Some Basic Elements of the Shakedown Theory. In: Mróz, Z., Weichert, D., Dorosz, S. (eds) Inelastic Behaviour of Structures under Variable Loads. Solid Mechanics and Its Applications, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0271-1_7
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