Solving the euler problem for a flexible support rod base on the finite difference method

Abstract

The article focuses on the non-classical problem of the stability loss in a rectilinear rod with a flexible support. The mathematical model employed to study bifurcation consists of a basic differential equation of rod bending enhanced with boundary conditions. Through the finite difference method, they are reduced to a system of algebraic equations with a square matrix. There is a view offered at rods with constant and variable cross sections. Critical forces taken as unknown values are contained in the characteristic equation of the matrix, of which they are extracted numerically and graphically with the Matlab computing system. The identified critical forces were verified with tests on the well-known Euler problem as well as by comparing the results of two examples. There are conclusions offered, whichi are of practical value.