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

摘要

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.