Summary
Melan's classical shakedown theorem for continuous media considered as a problem of methematical programming with constraints is reformulated and reduced to a solution of a certain min-max problem. A similar approach is presented for the structural theory described in terms of generalized variables. A distinction is made between alternating plasticity and incremental collapse modes in the analysis of structures with nonsandwich cross-sections.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Hill, R.: The extremal stress-field concept. J. Mech. Phys. Solids6, 239–243 (1966).
Koiter, W.T.: General theorems for elastic plastic solids. In: Progress in solid mechanics (Sneddon, I. N., Hill, R., eds.), pp. 165–221. Amsterdam: North-Holland 1960.
Sawczuk, A.: Evaluation of upper bounds to shakedown loads of shells. J. Mech. Phys. Solids17, 291–301 (1969).
Maier, G.: A matrix structural theory of piecewise-linear plasticity with interacting yield planes. Meccanica7, 51–66 (1970).
Mróz, Z.: On the theory of steady plastic cycles in structures. Proc. of SMiRT 1, 6 part L, pp. 489–501, 1972.
König, J. A.: A new method of shakedown structural analysis. Symp. Franco-Polonais, Problémes Non-Lineares de Mécanique, pp. 343–347, Kraków 1977.
Gokhfeld, D. A., Cherniavsky, O. F.: Limit analysis of structures at thermal cycling. Sijthoff & Noordhoff 1980.
König, J. A.: On exactness of the kinematical approach in the structural shakedown and limit analysis. Ing.-Arch.52, 318–326 (1982).
König, J. A.: Shakedown of elastic-plastic structures. Warsaw: Elsevier & PWN-Polish Scientific Publishers 1987.
Zwoliński, J., Bielawski, G.: An optimal selection of residual stress for determination limit and shakedown multiplier. Proc. Conf. Comp. Meth. Struct. Mech., pp. 459–462, Jadwisin 1987.
Zarka, J., Frelat, J., Inglebert, G., Kasmai-Navidi, P.: A new approach to inelastic analysis of structures. Dordrecht: Martinus Nijhoff 1988.
Genna, F.: A nonlinear inequality, finite element approach to the direct computation of shakedown load safety factors. Int. J. Mech. Sci.30, 769–789 (1988).
Pycko, S.: Alternative solution of shakedown problem with nonlinear yield condition. Proc. 28th Polish Mechanics Conf., Kozubnik 1990.
Stein, E., Zhang, G., Mahnkem, R., König, J. A.: Micromechanical modelling and computation of shakedown with nonlinear kinematic hardening including examples for 2-d problems. Proc. CSME Mechanical Engineering Forum, Toronto 1990.
Orkisz, J., Orringer, O., Holowinski, M., Pazdanowski, M., Cecot, W.: Discrete analysis of actual residual stress resulting from cyclic loadings. Comp. Struct.35, 397–412 (1990).
Pycko, S., König, J. A.: Determination of shakedown load as a solution of min-max problem. Proc. GAMM Conf., Kraków 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pycko, S., Mróz, Z. Alternative approach to shakedown as a solution of a min-max problem. Acta Mechanica 93, 205–222 (1992). https://doi.org/10.1007/BF01182585
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01182585