Formulation of the Torsion Problem in Stresses and Solution by Boundary Element Method

Abstract

The paper presents a boundary element method approach to solving the torsion problem for rods based on a stress formulation. This approach has a key advantage over classical torsion formulations, as it enables direct evaluation of stresses in the cross-section without numerical differentiation of auxiliary functions. A second-kind boundary integral equation is derived for the stress-based formulation. The boundary element solution procedure is described, and the resulting system of governing equations is constructed. The applicability of the proposed formulation for stress evaluation in multiply connected cross-sections is demonstrated using test problems. Comparison with available analytical solutions confirms the accuracy and reliability of the proposed approach, showing that the results meet engineering requirements.