SUCCESSIVE APPROXIMATION METHOD FOR THE CALCULATION OF BENT-COMPRESSED BEAMS OF CONSTANT STIFFNESS

Abstract

The finite difference equations of the successive approximation method (SAM) which substitute the differential equations of
bending-compressed of constant stiffness are obtained. Difference equations of SAM, which approximate the limit conditions of
the hand ends of the beam, are also obtained: simply supported hand end; rigidly fixed hand end and freehand end. On the basis
of the obtained equations, a numerical algorithm was developed for calculating beams of constant thickness under the action of
various static loads. According to this algorithm, a program for calculating beams on a computer was performed. The examples
presented here show the accuracy of the results and the simplicity of the algorithm. Checks for integral equilibrium conditions of
beams were performed to validate the newly obtained results.