Bilevel limit analysis of self-hardening rod systems under moving load

  • Piotr Alawdin University of Zielona Góra
  • Krystyna Urbańska University of Zielona Góra


This paper considers results of an analysis of self-hardening systems (SHS), i.e. load-carrying systems with improved strength and rigidity. The indicated structural features can be only found if geometrical nonlinearity is taken into consideration. Material deforming diagrams can be non-monotonic and non-smooth, and constraints can be unilateral, with gaps. Furthermore, optimisation of a mathematical model of a rod structure as a discrete mechanical system withstanding dead (constant) and/or moving loads is proposed. This model is formulated using bilevel mathematical programming. The limit parameters of standard loads and actions are found in the low-level optimisation. An extreme energy principle is proposed to obtain the limit parameters of these actions. On the upper level, the parameters of moving load are maximized. A positive influence of equilibrium or quasi-equilibrium constant load with the possible preloading of SHS is shown. A set of criteria for the stability of plastic yielding of structures, including non-smooth and non-convex problems of optimisation is given. The paper presents an exemplary application of the proposed method which takes into account the self-hardening effect.


self-hardening systems, bilevel programming, limit analysis, constant equilibrium and moving load,


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Jun 11, 2018
How to Cite
ALAWDIN, Piotr; URBAŃSKA, Krystyna. Bilevel limit analysis of self-hardening rod systems under moving load. Computer Assisted Methods in Engineering and Science, [S.l.], v. 24, n. 4, p. 225–238, june 2018. ISSN 2299-3649. Available at: <>. Date accessed: 26 jan. 2022. doi: