Abstract
Bounds to functions of the plastic strains produced during the elastic-plastic stage of a dynamic loading process leading to shakedown can be constructed on the basis of the solution of a single, static, holonomic elastic-plastic problem. This bounding procedure is described in detail with respect to the case of periodic external loading, and the generalization to an arbitrary dynamic loading condition is provided. Simple examples illustrate the bounding effectiveness of the proposed technique.
sommario
Si mostra come sia possibile produrre delimitazioni di funzioni delle deformazioni plastiche che avvengono durante la fase iniziale di un processo dinamico che si concluda con l'adattamento in regime elastico (shakedown). Si illustra in dettaglio la procedure di delimitazione con riferimento al caso di carichi esterni periodici, e si fornisce l'estensione concettuale al caso di una condizione di carico generica. Due esempi numerici mostrano l'accuratezza e l'efficienza numerica della tecnica proposta.
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References
Polizzotto, C., ‘A unified treatment of shakedown theory and related bounding techniques’, SM Archives, 7(1) (1982) 19–75.
Corradi, L. and Poggi, C., ‘Estimates of the post-shakedown response of hardening structures by means of simplified computations’, Meccanica, 22 (1987) 193–202.
Genna, F., ‘A nonlinear inequality, finite element approach to the direct computation of shakedown load safety factors’, Int. J. Mech. Sci., 30(10) (1988) 769–789.
Maier, G., ‘A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes’, Meccanica, 5 (1970) 54–66.
Maier, G., ‘“Linear” flow-laws of elastoplasticity: a unified general approach’, Rend. Acc. Naz. Lincei, Serie VIII, XLVII(5) (1969), 266–276.
Ceradini, G., ‘Sull'adattamento dei corpi elasto-plastici soggetti ad azioni dinamiche’, Giornale del Genio Civile, 107 (1969) 239–250.
Corradi, L. and Maier, G., ‘Inadaptation theorems in the dynamics of elastic-work hardening structures’, Ingenieur-Archiv, 43 (1973) 44–57.
Maier, G., ‘Upper bounds on deformations of elastic-workhardening structures in the presence of dynamic and second-order geometric effects’, J. Struct. Mech., 2(4) (1973) 265–280.
Franchi, A. and Genna, F., STRUPL-2 User's Manual, Technical Report, Dept. Structural Engineering, Politecnico di Milano, 1984.
Gavarini, C., ‘Sul rientro in fase elastica delle vibrazioni forzate elasto-plastiche’, Giornale del Genio Civile, 107 (1969) 251–261.
Cottle, R. W., ‘Fundamentals of quadratic programming and linear complementarity’, In Cohn, M. Z. and Maier, G. (Eds.) Engineering Plasticity by Mathematical Programming, Chapter 12, Pergamon Press, 1979, pp. 292–323.
Martin, J. B., ‘Bounding principles and discrete time integration for statically loaded elastic plastic bodies’, Laboratoire de Mécanique des Solides, Ecole Politechnique, Palaiseau, Paris (7–10 October, 1985).
Ponter, A. R. S., ‘Shakedown and ratchetting below the creep range’, Commission of the European Communities, Nuclear Science and Technology, Report EUR 8702 EN, 1983.
Ponter, A. R. S. and Karadeniz, S., ‘An extended shakedown theory for structures that suffer cyclic thermal loading, Parts 1 and 2’, Trans. ASME, J. Appl. Mech., 52 (1985) 877–889.
Corradi, L. and Nova, R., ‘A comparative study of bounding techniques in dynamic shakedown of elastoplastic structures’, Earthquake Eng. and Struct. Dynamics, 3 (1974) 139–155.
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Genna, F. Bilateral bounds for structures under dynamic shakedown conditions. Meccanica 26, 37–46 (1991). https://doi.org/10.1007/BF00517724
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DOI: https://doi.org/10.1007/BF00517724