A geometrically exact Kirchhoff beam model including torsion warping. (December 2016) - Manta, David; Gonçalves, Rodrigo
Highlights: A geometrically exact Kirchhoff beam model is presented, including torsion-warping and Wagner effects. Arbitrary cross-sections can be considered. Closed-form expressions for the strain measure variations are presented. The equilibrium equations and their linearization are written in terms of the independent kinematic parameters. Abstract: This paper presents a geometrically exact beam model that includes the Kirchhoff constraint (null shear deformation), torsion-related warping and Wagner effects, and aims at capturing the flexural-torsional behaviour of thin-walled beams undergoing large displacements. The parametrization of the cross-section rotation tensor is based on the composition of a torsional rotation and the so-called smallest rotation to the tangent vector of the beam axis, as proposed in Boyer and Primault (2004). The novel aspects of the proposed model are the following: (i) closed-form expressions for the variations of the strain measures are presented and 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. Moreover, several fundamental aspects related to the cross-section rotation parametrization are discussed. The accuracy and the computational efficiency of the finite element implementation of the proposed model is demonstrated in several numerical examples.