Abstract
The paper deals with the shakedown of systems with kinematic hardening materials. Analytical, numerical and experimental methods to solve shakedown problems will be introduced and discussed. Some examples are treated with these methods. Comparison shows that the results of these methods are in good agreement.
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References
1924 Masing, G., ”Zur Heyn'schen Theorie der Vestigung der Metalle durch verborgen elastische Spannungen”, Wissenschaftliche Veröffentlichungen aus dem Siemens-Konzern, 3, pp. 231–239.
1932 Bleich, H., ”Über die Bemessung statisch unbestimmter Stahltragwerke unter Berücksichtigung des elastisch-plastischen Verhalten des Baustoffes”, Der Bauingenieur 19/20, pp. 261–267.
1938a Melan, E., ”Der Spannungszustand eines Mises-Henckyschen Kontinuums bei veränderlicher Belastung”, Sitzber. Akad. Wiss. Wien, IIa147, pp. 73–78.
1938b Melan, E., ”Zur Plastizität des räumlichen Kontinuums”, Ing.-Arch. 8, pp. 116–126.
1950 Neal, B.G., ”Plastic collapse and shake-down theorems for structures of strain-hardening material”, J. Aero. Sci., 17, pp. 297–306.
1953 Besseling, J. F., ”A theory of plastic flow for anisotropic hardening in plastic deformation of an initially isotropic material”. National aeronautical research institute, Amsterdam, Report pp. 410.
1956 Koiter, W.T., ”A new general theorem on shake-down of elastic-plastic structures”, Proc. Koninkl. Akad. Wet. B 59, pp. 24–34.
1956a Prager, W., ”A new method of analyzing stresses and strains in work-hardening plastic solids”, Journal of Applied Mechanics, pp. 493–496.
1956b Prager, W., ”Shakedown in elastic-plastic media subjected to cycles of load and temperature”, Proc. Symp. Plasticita nella Scienza delle Costruzioni, Bologna, pp. 239–244.
1957 Rozenblum, V.I., ”On shakedown of uneven heated elastic-plastic bodies” (in Russian), Izw. Akad. Nauk SSSR. OTN, Mekh. Mash., 7, pp. 136–138.
1959 Coffin, L. F.O and Tavernelli, J. F., ”The cycle strain and fatigue of metals”, Transactions of society of AIME. 215, pp. 794–807.
1959 Ziegler, H., ”A modification of Prager's hardening rule”. Quart. Appl. Math., 17, pp. 55–65 (1959).
1965 Paris, P. C. and Sih, G. C., ”Fracture toughness testing and its applications”, ASTM STP 381, American Society for testing and materials, pp. 30–83.
1966 Frederick, C.O. and Armstrong, P. J., ”Convergent internal stresses and steady cyclic states of stress”, J. Srain Anal., 2, pp. 154–160.
1967 Iwan, W. D., ”On a class of models for the yielding behavior of continuous and composite systems”, Journal of Applied Mechanics, pp. 612–617.
1967 MrÓZ, Z., ”On the description of anisotropic workhardening”, J. Mech. Phys. Solids 15, pp. 163–175.
1969 Ceradini, G., ”Sull' adattamento dei corpi elasto-plastici soggetti ad azioni dinamiche”, Giorn. Genio Civile 106, No. 4/5, pp. 239–250.
1969 KÖNig, J.A., ”A shakedown theorem for temperature dependent elastic moduli”, Bull. Acad. Polon. Sci. Sér. Sci. Tech. 17, pp. 161–165.
1972 Maier, G., ”A shakedown matrix theory allowing for workhardening and second-order geometric effects”, Proc. Foundations of Plasticity, Warsaw.
1972 Zienkiewicz, O. C, Najak, G. C. and Owen, D. R. J., ”Composite and ‘overlay’ models in numerical analysis of elasto-plastic continua”, Pro. of Int. Symp. on Foundations of plasticity, ed. A. Sawczuk, Noorhoff Publishing Leyden.
1973 Corradi, L. and Maier, G., ”Inadaption theorems in the dynamics of elastic-workhardening structures”, Ing.-Arch. 43, pp. 44–57.
1975 Dafalias, Y.F. and Popov, E.P., ”A model of nonlinearly hardening materials for complex loading”, Acta Mechanica 21, pp. 173–192.
1981 Schittkowski, K., ”The nonlinear programming method of Wilson, Han and Powell with an augmented Lagrangian type line search function”, Numer. Math., 38, pp. 83–127.
1986 Weichert, D., ”On the influence of geometrical nonlinearities on the shakedown of elastic-plastic structlures”, Int. J. Plasticity, 2, pp. 135–148.
1990 Scheer, J., Scheibe, H. J. and Ruch, D., ”Untersuchung von Trägerschwäschungen unter wiederholter Belastung bis in den plastischen Bereich”, Bericht Nr. 6099, Institut für Stahlbau, TU Braunschweig.
1990 Scheibe, H. J., ”Zum zyklischen Materialverhalten von Baustahl und dessen Berücksichtigung in Konstruktionsberechnung”, Ph.D. thesis, Institut für Stahlbau, Universität Braunschweig.
1992 Mahnken, R., ”Duale Methoden für nichtlineare Optimierungsprobleme in der Strukturmechanik”, Ph.D. thesis, Institut für Baumechanik und Numerische Mechanik, Universität Hannover.
1992a Stein, E., Zhang G. and KÖNIG, J.A., ”Shakedown with nonlinear hardening including structural computation using finite element method”, Int. J. Plasticity, 8, pp. 1–31.
1992b Stein, E. and Zhang, G., ”Theoretical and numerical shakedown analysis for kinematic hardening materials”, in Proc. 3rd Conf. on Computational Plasticity, Barcelona, pp. 1–25.
1992 Zhang, G., ”Einspielen und dessen numerische Behandlung von Flächentragwerken aus ideal plastischem bzw. kinematisch verfestigendem Material”, Ph.D. thesis, Institut für Baumechanik und Numerische Mechanik, Universität Hannover.
1993a Stein, E., Zhang, G. and Huang, Y., ”Modeling and computation of shakedown problems for nonlinear hardening materials”, Computer Methods in Mechanics and Engineering, 1-2, pp. 247–272.
1993b Stein, E., Zhang, G. and Mahnken, R., ”Shake-down analysis for perfectly plastic and kinematic hardening materials, in Stein, E. (ed.) Progress in computational analysis of inelastic structures”, Springer-Verlag, Wien-New York, CISM courses and lecture, 321, pp. 175–244.
1994 Stein, E. and Huang, Y., ”An analytical method to solve shakedown problems with linear kinematic hardening materials”, Int. J. of solids and structures, 31, No. 18, pp. 2433–2444.
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Stein, E., Huang, Y.J. (1995). Shakedown for systems of kinematic hardening materials. 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_3
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DOI: https://doi.org/10.1007/978-94-011-0271-1_3
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