Finite element stress analysis of elastic beams under non-uniform torsion

Abstract

This paper presents a two-dimensional finite element formulation for the stress analysis of elastic beams subjected to non-uniform torsion. The element stiffness matrix and load vectors are derived using the primary and secondary warping functions. The primary function corresponds to that occurring with uniform torsion problems. The secondary function is introduced to take into account effects caused by the restrained warping. Thus, shear stresses are divided into the primary and secondary ones, keeping the same meaning as the warping functions. The proposed finite element model enables the stress analysis to be carried out regardless of crosssectional shapes. The material is assumed to obey Hooke's law. The effectiveness of the presented finite element algorithm is validated through two benchmark examples.