THE FINITE DIFFERENCE EQUATIONS OF SUCCESSIVE APPROXIMATION METHOD FOR THE CALCULATION OF BENDING BEAMS OF VARIABLE THICKNESS UNDER THE STATIC ACTION OF LOADS

Abstract

The finite difference equations of the successive approximation method (SAM) which substitute the differential equations of
bending beam of a variable 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 free hand end. On the basis of
the obtained equations, a numerical algorithm was developed for calculating beams of constant and variable thickness under the
action of various static loads. According to this algorithm, a program for calculating beams on a computer was performed. Variable stiffness simple supported hand ends beams, rigidly fixed hand ends beams with uniformly distributed loads along their
lengths, with concentrated force, were calculated. A cantilever beam of variable thickness was also calculated under the action of
the uniformly distributed load over its entire length. 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