A geometrically exact Kirchhoff beam model including torsion warping

David Manta, Rodrigo Gonçalves

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)192-203
Number of pages12
JournalComputers and Structures
Publication statusPublished - 1 Dec 2016


  • Beam finite elements
  • Geometrically exact beams
  • Kirchhoff beams
  • Torsion warping


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