Limit state according to the condition of loss of stability of equilibrium forms

Abstract

Objective. The purpose of the study is to determine the group of the limiting state according to the condition of loss of stability of the equilibrium form of structures. Method. The study is based on the provisions of the theory of stability of equilibrium states of building structures; branching theory of solutions of nonlinear equations; perturbation method; methods of catastrophe theory.Result. The results of the analysis of the post-critical behavior of structures based on the solution of the problem in higher approximations and from the fundamental provisions of the theory of catastrophes are generalized. It is proved that the study of the stability of equilibrium forms of structures using algebraic means and geometric images of the theory of catastrophes makes it possible to unambiguously determine the type of critical bifurcation points, predict the nature of the behavior of the structure, and determine the limit state group to which the state reached by the structure should be attributed. Conclusion. It seems necessary to rename the ordinal numbers of the types of critical points of bifurcations so that they coincide with the numbers of the groups of limit states corresponding to them.