Non-Uniform Torsion Behavior of Thin-Walled Beams According to the Finite Element Method

Abstract

This study is based on a theory for analyzing non-uniform torsion in thin-walled beams made of homogeneous elastic material with arbitrary cross-sections by incorporating the effect of the shear deformation of a cross-section. Utilizing the Finite Element Method (FEM), the proposed numerical approach addresses non-uniform torsion by breaking down a 3D analysis into 2D cross-sectional and 1D modeling components. Initially, the geometric constants of the cross-section were computed using a 9-node isoparametric element in 2D FEM. Subsequently, a 1D FEM employing a linear isoparametric element calculated the twist angle, torsion warping parameters, and stress results. The stress field was determined through a local analysis of the 2D cross-section. Notably, the 2D FEM component aligns with contemporary trends in commercial software, thereby bolstering the potential and practical applicability of the proposed numerical approach. Its verification and validation through numerical analyses using MATLAB underscore the efficacy and reliability of the method in analyzing non-uniform torsion behavior in structural design, particularly under diverse boundary conditions.

Keywords

• non-uniform torsion
• structural design
• shear deformation
• thin-walled structures
• vlasov’s theory
• warping