Open AccessEnergy method for solving the stability problem of an elastic rod with variable stiffness taking into account its dead weight
Author(s) -
Batyr Yazyev,
Leysan Akhtyamova,
Вячеслав Чепурненко,
A. A. Reshetnikov,
A. D. Ziganshin
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/1083/1/012005
Subject(s) - moment of inertia , stiffness , inertia , cantilever , variable (mathematics) , moment (physics) , mathematics , mathematical analysis , energy (signal processing) , mechanics , classical mechanics , physics , structural engineering , engineering , thermodynamics , statistics
The article is devoted to solving the stability problem of an elastic rod with variable stiffness taking into account its dead weight. The variable stiffness parameter is the rod section, in particular, the moment of inertia I z (x) . The moment of the section inertia and the intensity of the distributed load (dead weight) vary according to the power law. As a result, the solution of the resolving integro-differential equation for this model (cantilever rod) by the energy method was obtained. It is shown that the obtained solution allows satisfying all boundary conditions and another approach to the energy method use is found. The energy method in this case made it possible to determine the exact values of the critical load with a particular change in the rod cross-section taking into account its dead weight.