Method of fundamental solutions and random numbers for the torsion of bars with multiply connected cross sections

Abstract

The torsion of bars with multiply connected cross section by means of the method of fundamental solutions (MFS) is considered. Random numbers were used to determine the minimal errors for MFS. Five cases of cross sections are examined. The numerical results for different cross sectional shapes are presented to demonstrate the efficiency and accuracy of the method. Non-dimensional torsional stiffness was calculated by means of numerical integration of stress function for one of the cases. This stiffness was compared with the exact stiffness for the first case and with the stiffness resulting from Bredt's formulae for thin-walled cross sections.