Energy method for solving the stability problem of an elastic rod with variable stiffness taking into account its dead weight

Abstract

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 Iz(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.