Abstract
The Simplified Theory of Plastic Zones (STPZ) is primarily intended to estimate stresses and strains at variable load. However, the basic idea of the STPZ, based on Zarka’s method, is easier to present initially for monotonic loading. A bilinear stress–strain curve, that is, linear kinematic hardening, is initially assumed as well as constant material data that do not change with temperature during thermal loading. After introducing a transformed internal variable, the yield criterion is reformulated. A modified elastic material law is obtained, and its modified elastic material parameters are identified. Furthermore, the transformed internal variable is used to define initial strains, which are estimated in a suitable manner and can be applied as a modified loading in a modified elastic analysis. The results in terms of residual quantities can be superimposed on the results of a fictitious elastic analysis to get an approximation of the elastic-plastic solution, which in turn is the starting point for an iterative improvement. Examples illustrate the calculation process and the quality of the approximate solution obtained, along with the computational burden involved. Chapter 4 then presents an extension to cyclic loading, Chap. 5 to temperature-dependent material data, and Chap. 7 to multilinear stress–strain behavior.
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Zarka, J., Frelat, J., Inglebert, G., Kasmai Navidi, P.: A new Approach to Inelastic Analyses of Structures. Martinus Nijhoff Publishers, Dordrecht/Boston/Lancaster (1988) and (greatly expanded) 1990
Zarka, J., Inglebert, G., Engel, J.J.: On a Simplified Inelastic Analysis of Structures. Nucl. Eng. Des. 57, 333–368 (1980)
Zarka, J.: On Simplified Mathematical Modelling of Cyclic Behaviour. Res Mechanica 4, 203–223 (1982)
Zarka, J., Casier, J.: Elastic-Plastic Response of a Structure to Cyclic Loading: Practical Rules. In: Nemet-Nasser, S. (ed.) Mechanics Today, vol. 6, pp. 93–198. Pergamon Press, New York (1981)
Zarka, J.: Direct Analysis of Elastic-Plastic Structures with ‘Overlay’ Materials during Cyclic Loading. Int. J. Numerical Methods in Engineering 15, 225–235 (1980)
Zarka, J.: Sur l’étude du comportement global des matériaux soumis à un chargement cyclique. Journal de Mécanique appliquée 3(3), 291–326 (1979)
Hübel, H.: Ermittlung realistischer Ke-Faktoren (Plastifizierungsfaktoren) als Grundlage für die Präzisierung des kerntechnischen Regelwerkes hinsichtlich der Ermüdungsanalyse. Project SR2221 for the Federal Ministry for environment, nature conservation and nuclear safety (BMU-1997-481). ISSN 0724-3316 (1997)
ANSYS Release 14.5, ANSYS Inc. Canonsburg, USA (2012)
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Hübel, H. (2017). STPZ at Monotonic Loading. In: Simplified Theory of Plastic Zones. Springer, Cham. https://doi.org/10.1007/978-3-319-29875-7_3
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DOI: https://doi.org/10.1007/978-3-319-29875-7_3
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