Sommario
Facendo riferimento a un solido elastico perfettamente plastico soggetto a carichi ciclici, si considera il problema del moltiplicatore dei carichi ad adattamento e si studiano le equazioni di Eulero-Lagrange ad esso associate. Si trova che la soluzione di queste equazioni descrive il gradiente, rispetto al moltiplicatore dei carichi, della risposta stazionaria del solido ai carichi ciclici al limite di adattamento, e che quindi essa consente di predire la natura del collasso incipiente, Questi risultati vengono quindi estesi al caso più generale di carichi variabili in un dato dominio.
Summary
Making reference to elastic perfectly plastic solids subjected to cyclic loads, the problem of the shakedown load factor is considered and the relevant Euler-Lagrange equations are discussed. It is proved that the solution to these equations describes the gradient, with respect to the load multiplier, of the steady-state response of the solid body to the cyclic loads at the shakedown limit, and that it thus enables one to predict the nature of the impending collapse. These results are then extended to the more general case of loads varying within a given load domain.
References
Martin J.B.,Plasticity: Fundamentals and General Results, The MIT Press, Cambridge, Ma., 1975.
Gokhfeld D.A. andCherniavsky O.F.,Limit Analysis of Structures at Thermal Cycling, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlans, 1980.
König J.A.,Shakedown of Elastic-Plastic Structures, PWN-Polish Scientific Publishers, Warsaw, and Elsevier, Amsterdam, 1987.
Koiter W.T.,General theorems for elastic-plastic solids, In J.N. Sneddon and R. Hill (eds.), Progress in Solid Mechanics, North Holland, 1964, Vol. 1, pp. 167–221.
Capurso M., Corradi L. andMaier G.,Bounds on deformations and displacements in shakedown theory, in Matériaux et Structures sous Chargement Cyclique, Ass. Amicale des Ingénieurs Anciens Elèves de l'E.N.P.C., Paris, 1979.
König J. andMaier G.,Shakedown analysis of elastoplastic structures: a review of recent developments, Nuclear Engng. Design, Vol. 66, 1981, pp. 81–95.
Polizzotto C.,A unified treatment of shakedown theory and related bounding techniques, S.M. Archives, Vol. 7, 1982, pp. 19–75.
Frederick C.O. andArmstrong P.J.,Convergent internal stresses and steady cyclic states of stress, J. Strain Analysis, Vol. 1, 1966, p. 154.
König J.A.,On upper bounds to shakedown loads, Z. Angew. Math., Vol. 59, 1979, pp. 349–354.
Leers K., Klie W., König J.A. andMahrenholtz O.,Experimental investigations of shakedown of tubes, in A. Sawczuk and G. Bianchi, (eds.), Plasticity Today, Elsevier Appl. Sci. Pubs., London-New York, 1985, pp. 259–275.
Ponter A.R.S.,Shakedown and Ratchetting Below the Creep Range, Report EUR 8702 EN, Commission of the European Communities, 1983.
Author information
Authors and Affiliations
Additional information
This paper is part of a research project sponsored by the National Research Council (CNR) of Italy.
Rights and permissions
About this article
Cite this article
Panzeca, T., Polizzotto, C. On shakedown of elastic plastic solids. Meccanica 23, 94–101 (1988). https://doi.org/10.1007/BF01556707
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01556707