Numerical calculation of rectangular cross-section beams on the stability of a flat bending shape

Abstract

Numerical calculation of rectangular cross-section beams on the stability of a flat bending shape

Chepurnenko A.S., Ulianskaya V.V., Vysokovsky D.A., Zotov I.M.

Incoming article date: 12.04.2018

Flat bending stability problem of constant rectangular transverse section wooden beam, loaded by a concentrated force in the middle of the span is considered. Differential equation is provided for the cases when force is located not in the center of gravity. The solution of the equation is generated numerically by the method of finite differences. For the case of applying a load at the center of gravity, the problem reduces to a generalized secular equation. In other cases, the iterative algorithm developed by the authors is implemented, in the package Matlab. A relationship is obtained between the value of the critical force and the position of the load application point. For this dependence, a linear approximating function is chosen. A comparison of the results obtained by the authors with an analytical solution using the Bessel functions is performed.

Keywords: flat bending stability, secular equation, finite difference method, iteration process