A geometrically exact curved thin-walled beam finite element accounting for cross-section deformation

This paper proposes a new geometrically exact beam formulation and ensuing finite element implementation that can handle naturally curved thin-walled members susceptible to global-distortional-local cross-section deformation. The configuration of each cross-section is described by a position vector, a rotation tensor (parameterized using the so-called rotation vector) and arbitrary cross-section deformation modes complying with Kirchhoff's thin plate assumption, meaning that the deformation modes of Generalized Beam Theory can be straightforwardly incorporated. The finite element is obtained by interpolating the independent kinematic parameters using Hermite cubic polynomials. Besides handling large displacements and finite rotations, combined with cross-section deformation, the element is also capable of performing linear stability analyses (of curved members). The accuracy and efficiency of the proposed finite element is demonstrated through several illustrative numerical examples. For validation and comparison purposes, shell finite element model results are provided.