A geometrically exact Kirchhoff beam finite element with torsion warping

Abstract

In this paper, a geometrically exact beam model is presented that includes the Kirchhoff constraint and torsion-related warping, aiming at capturing accurately the flexural-torsional behaviour of slender thin-walled beams undergoing large displacements. The cross-section rotation tensor is obtained from two successive rotations: a torsional rotation and a smallest rotation to the tangent vector of the beam axis. Noteworthy aspects of the proposed formulation are the following: (i) the equilibrium equations and their linearization are completely written in terms of the independent kinematic parameters, (ii) torsion-warping is allowed, as well as Wagner effects, and (iii) arbitrary cross-sections are considered, namely cross-sections where the shear centre and centroid do not coincide. The accuracy and computational efficiency of the finite element implementation of the proposed model is demonstrated in several numerical examples involving large displacements.