Nonuniform Torsion Without Shear Deformation Effect Using FEM

Abstract

This paper presents the use of a finite element method (FEM) to analyze nonuniform torsion with an arbitrary cross-section with homogeneous elastic material without shear deformation effect. Beams are constrained by the most common types of supports, such as fixed, pinned, and roller, and are subjected to any applied torsional load, concentrated, and distributed. The presented FEM transforms the 3D analysis of nonuniform torsion beams into separated 2D cross-sectional and 1D modeling. The geometric constants of the cross-section are firstly derived from 2D FEM, which uses a 9-node isoparametric element. Then, a 1D FEM, which uses the Hermitian shape function, is developed for computing the twist angle, the derivative of twist angle, and stress resultants. Finally, the stress field is obtained from the local analysis on the 2D-cross section. A MATLAB program is executed to validate the numerical method through examples. The validation examples have proven the reliability of the author's numerical method for analyzing problems defined above.