- Crossref DOI Prefix: 10.31695/IJASRE
- ISSN: 2454 - 8006
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International Journal of Advances in Scientific Research and Engineering-IJASRE
THE FINITE DIFFERENCE EQUATIONS OF SUCCESSIVE APPROXIMATION METHOD FOR THE CALCULATION OF BENDING BEAMS OF VARIABLE THICKNESS UNDER THE STATIC ACTION OF LOADS
Article Category: Civil Engineering
Author: Moussa Sali ,Amba Jean Chills
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.
Keyword: Successive Approximation Method, Beam of Variable Thickness, Numerical Algorithm, Equilibrium Conditions, validate.
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