Open AccessAn analytical solution to the problem of stability loss of the rod under the combined action of concentrated force and dead weight
Author(s) -
Yurii Krutii,
S. Bekshaev,
Vladimir Osadchiy
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1164/1/012010
Subject(s) - action (physics) , buckling , mathematics , ideal (ethics) , differential equation , boundary value problem , stability (learning theory) , column (typography) , mechanics , mathematical analysis , differential (mechanical device) , classical mechanics , physics , geometry , thermodynamics , computer science , law , quantum mechanics , machine learning , political science , connection (principal bundle)
The exact solution of the differential equation of buckling of the prismatic column under the combined action of a longitudinal concentrated end force and its own weight is constructed. Formulas are written for the state parameters of the rod, expressed in terms of the initial parameters. For six cases of ideal boundary conditions, finite analytical formulas are obtained that establish the dependence of the critical force on the weight of the rod.