Sommario
Si propone un procedimento semplificato per la valutazione della risposta ad adattamento avvenuto di strutture elasto plastiche soggette ad azioni esterne variabili e ripetute. Il procedimento richiede una singola soluzione olonoma della struttura sotto carichi fittizi, ottenuta sostituendo l'effettiva risposta elastica in termini di sforzi, variabile nel tempo, con il suo inviluppo. Si ottiene in tal modo una stima, spesso ragionevole, della soluzione. Inoltre, su questa base si possono costruire delimitazioni, comparativamente buone, sia inferiori che superiori, su alcune funzioni delle deformazioni plastiche effettivamente sviluppate. Queste funzioni sono spesso correlate ad informazioni ingegneristicamente significative, il che conferisce interesse pratico al procedimento.
Summary
A simplified procedure, aiming at the estimate of the post-shakedown response of elastic-plastic structures under varying external actions, is proposed in the paper. A single step, holonomic elastic-plastic analysis is performed under fictitious loads obtained by replacing the actual, variable, elastic stress response with its envelope. Such a solution is usually a reasonable estimate of the actual response and permits a comparatively stringent bracketing from below and above of some particular functions of the plastic strains actually developed. Often these functions are closely related to quantities of direct engineering relevance, thus stressing the practical interest of the proposed procedure.
This is a preview of subscription content, log in via an institution to check access.
References
Koiter W.T., General Theorems for Elastic-Plastic Solids, inProgress in Solid Mechanics (Hill and Sneddon Eds.), North Holland, (1960), 167–221.
Neal B.G.,The Plastic Method of Structural Analysis, Chapman Hall, London, U.K., 1963.
Ponter A.R.S., A General Shakedown Theorem for Elastic-Plastic Bodies with Work Hardening,3rd SMiRT Conference, Proc. Paper L 5/2, London, 1975.
Maier G., A Shakedown Matrix Theory Allowing for Work-Hardening and Second Order Geometric Effects,Proc. Symposium on Foundation of Plasticity, Warsaw, September 1972.
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).
Vitiello E., Upper Bounds to Plastic Strains in Shakedown of Structures Subjected to Cyclic Loads,Meccanica, 7, (1972) 205–231.
Ponter A.R.S., An upper Bound to Small Displacements of Elastic, Perfectly Plastic Structures,Proc. ASME, J. Appl. Mech, 39, (1972) 959–963.
Capurso M., A Displacement Bounding Principle on Shakedown of Structures Subjected to Cyclic Loads,Int. J. Solids and Structures, 10, (1974) 77–92.
Capurso M., Some Upper Bound Principles to Plastic Strains in Dynamic Shakedown of Elastic-Plastic Structures,J. Struc. Mech., 7, (1979) 1–20.
Polizzotto C., A Unified treatment of Shakedown Theory and Related Bounding Techniques,S.M. Archives, 7, (1982) 19–75.
Capurso M.,Corradi L.,Maier G., Bounds on Deformations and Displacements in Shakedown Theory,Materiaux et Structures sous Chargement Cyclique, 231–244, Palaiseau (Paris), 28–29 sept. 1978.
Martin J.B., Bounding Principles and Discrete Time Integration for Statically Loaded Elastic Plastic Bodies, Laboratoire de Mécanique des Solides, Ecole Polytechnique, Palaiseau (Paris), 7–10 oct. 1985.
Polizzotto C., Bounding Principles for Elastic-Plastic-Creeping Solids Loaded Below and Above the Shakedown Limit,Meccanica, 17 (1982) 143–148.
Polizzotto C., A Bounding Technique for Dynamic Plastic Deformations of Damped Structures,Nuclear Engineering and Design, 79, (1984) 363–376.
Maier G., Quadratic Programming and Theory of Elastic, Perfectly Plastic Structures,Meccanica, 3, (1968) 265–273.
Corradi L., A Displacement Formulation for the Finite Element Elastic-Plastic Problem,Meccanica, 18, (1983) 77–91.
Boot J.C.G.,Quadratic Programming, North Holland, Amsterdam, 1964.
Maier G., A Matrix Structural Theory of Piecewiselinear Elasto-plasticity with Interacting Yield Places,Meccanica, 5, (1970) 54–66.
Corradi L., Poggi C., A Refined Finite Element Model for the Analysis of Elastic-Plastic Frames,Int. J. Num. Methods Eng., 20, (1984) 2155–2174.
Bree J., Elastic-Plastic Behaviour of Thin Tubes Subjected to Inward Pressure and Intermittent Heat Fluxes, with Application to Fast-Nuclear-Reactor Fuel Elements,J, Strain Analysis, 2, (1962) 226–238.
Ponter A.R.S., Karadeniz S., An Extended Shakedown Theory for Structures that Suffer Cyclic Thermal Loading, part 1 and 2.Trans. ASME, J. Appl. Mech., 52, (1985) 877–889.
Sawczuk A., Shakedown Analysis of Elastic-Plastic Structures,Nuclear Engineering and Design, 28, (1974) 121–136.
Webster J.J., Hardy S.J., Hyde T.H., Inelastic Behaviour of Rectangular Beams Subjected to Steady Axial Load and Cyclic Bending,Int. J. Mech. Sct., 27, (1985) 257–271.
Hyde T.H., Sahari B.B., Webster J.J., The Effect of ≪Material Ratchetting≫ on the Incremental Growth of Beams Subjected to Steady Axial Loads and Cyclic Bending,Int. J. Mech Sct., 27, (1985) 207–223.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Corradi, L., Poggi, C. Estimates of the post-shakedown response of hardening structures by means of simplified computations. Meccanica 22, 193–202 (1987). https://doi.org/10.1007/BF01573812
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01573812