Limit Analysis of Geometrically Hardening Rod Systems using Bilevel Programming

The paper considers some new results of creating load-carrying systems that have uprated strength, rigidity and safety, and therefore are called geometrically hardening systems. Indicated structural features are found exactly with allowance for geometrical nonlinearity. Material deforming diagrams can be non-monotonic and non-smooth, and constraints can be unilateral, with gaps. The optimization mathematic models of structures as discrete mechanical systems withstanding dead load, monotonic or cyclic static and kinematic actions are proposed. To find limit parameters of these actions the extreme energetic principle is suggested what result in the bilevel mathematic programming problem statement. Here is given a set of criteria for plastic yielding stability of structures, including for non-smooth and non-convex problems of optimization. In the paper an example of using the proposed methods is presented and geometrically hardening system is taken into account.