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

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 t...

Full description

Saved in:
Bibliographic Details
Main Authors: G. M. Murtazaliev, M. M. Paizulaev
Format: Article
Language:Russian
Published: Dagestan State Technical University 2022-02-01
Series:Вестник Дагестанского государственного технического университета: Технические науки
Subjects:
Online Access:https://vestnik.dgtu.ru/jour/article/view/1010
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849691401768402944
author G. M. Murtazaliev
M. M. Paizulaev
author_facet G. M. Murtazaliev
M. M. Paizulaev
author_sort G. M. Murtazaliev
collection DOAJ
description 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.
format Article
id doaj-art-96b4f987c0d54d178a7f1284aff0f73e
institution DOAJ
issn 2073-6185
2542-095X
language Russian
publishDate 2022-02-01
publisher Dagestan State Technical University
record_format Article
series Вестник Дагестанского государственного технического университета: Технические науки
spelling doaj-art-96b4f987c0d54d178a7f1284aff0f73e2025-08-20T03:21:02ZrusDagestan State Technical UniversityВестник Дагестанского государственного технического университета: Технические науки2073-61852542-095X2022-02-0148417117710.21822/2073-6185-2021-48-4-171-177673Limit state according to the condition of loss of stability of equilibrium formsG. M. Murtazaliev0M. M. Paizulaev1Daghestan State Technical UniversityDaghestan State Technical UniversityObjective. 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.https://vestnik.dgtu.ru/jour/article/view/1010limit statesequilibrium formsbucklingbifurcation (branching)post-critical behaviorlimit loadscatastrophe theory
spellingShingle G. M. Murtazaliev
M. M. Paizulaev
Limit state according to the condition of loss of stability of equilibrium forms
Вестник Дагестанского государственного технического университета: Технические науки
limit states
equilibrium forms
buckling
bifurcation (branching)
post-critical behavior
limit loads
catastrophe theory
title Limit state according to the condition of loss of stability of equilibrium forms
title_full Limit state according to the condition of loss of stability of equilibrium forms
title_fullStr Limit state according to the condition of loss of stability of equilibrium forms
title_full_unstemmed Limit state according to the condition of loss of stability of equilibrium forms
title_short Limit state according to the condition of loss of stability of equilibrium forms
title_sort limit state according to the condition of loss of stability of equilibrium forms
topic limit states
equilibrium forms
buckling
bifurcation (branching)
post-critical behavior
limit loads
catastrophe theory
url https://vestnik.dgtu.ru/jour/article/view/1010
work_keys_str_mv AT gmmurtazaliev limitstateaccordingtotheconditionoflossofstabilityofequilibriumforms
AT mmpaizulaev limitstateaccordingtotheconditionoflossofstabilityofequilibriumforms