Torsion of bars with regular polygonal sections

Abstract

In this article, the study of the torsion of cylindrical bars using large singular finite elements method leads to the resolution of the system of linear equations using MATLAB software. Particularly, the numerical solution of the problem of beams with regular section shows clearly the precision of the method depending upon the choice of different collocation points and gives in many cases, the exact solution with a relatively short computation time. The
case of bars with regular polygonal section treated numerically, illustrates the precision of the method. If the number of sides is more than five, we always observe an exponential decrease in the total error with the number of coefficients preserved under field, this one reaching a minimal value for each polygon and starts increasing beyond this value. When the number of sides becomes larger, the solution tends towards the one of the circle that is known.