A geometrically exact beam finite element for curved thin-walled bars with deformable cross-section

This paper presents a geometrically exact beam finite element for curved and twisted thin-walled bars undergoing large displacements and finite rotations, combined with cross-section in-plane and out-of-plane (warping) deformation. The underlying formulation is based on a previous work by the authors Gonçalves et al. (2010), which is now improved and extended for the pre-curved/twisted case. Cross-section deformation is allowed for by adding kinematic DOFs, the so-called “cross-section deformation modes”, which are obtained using Generalised Beam Theory. All expressions required to implement the proposed finite element are derived. For validation purposes, several numerical examples are presented and discussed. In each case, the results obtained with the proposed element and refined shell finite element models are compared, and an excellent agreement is found. In particular, it is demonstrated that the proposed element predicts very accurately the spatial behaviour of curved beams undergoing complex coupling between large displacements, finite rotations and cross-section deformation.