Features of mathematical modelling in the analysis of console-type structures

Abstract

The article deals with the mathematical model of console-type structural elements. The dynamic load is presented as quasi-static one. The differential equation of bending of an object is nonlinear and has movable singular points in which the solution has discontinuity. From a physical point of view, the object will break (collapse) in this place. The application of the majorant method to the solution of the problem allows, in contrast to the classical approach, establishing the boundaries of the solution area and to construct an analytical approximate solution to the problem with a given accuracy. As a result, it’s possible to calculate the displacement at any point of the cantilever structure and estimate the stress-strain state of the object.