Computational Mechanics

, Volume 64, Issue 4, pp 1155–1175 | Cite as

A finite element formulation for a geometrically exact Kirchhoff–Love beam based on constrained translation

  • Matthias Schulz
  • Markus BölEmail author
Original Paper


In this contribution, a new finite-element formulation of a geometrically exact Kirchhoff–Love beam, which requires \({\hbox {C}}^0\)-continuity and is capable of handling large-deformation problems that involve initially curved structures with arbitrary cross-sections, is presented. The absence of shear deformation that characterizes the Kirchhoff–Love beam is enforced by restricting the translation of the centerline to an axial displacement. Consequently, the configuration space has one translational and three rotational degrees of freedom everywhere along the beam, except for an arbitrary material point on the centerline whose position in space is defined by a total of 6 degrees of freedom. In addition, two different orthogonal transformation interpolation strategies are introduced and implemented. One of the interpolation schemes results in a novel mixed two-field variational principle, where the rotations and the axial strain are interpolated. In the second approach, the tangent field itself and a local twist parameter are discretized. In appropriate numerical examples, objectivity, path-independence, locking phenomena, error convergence behavior, and general performance of the Kirchhoff–Love beam are investigated and compared to other beam formulations.


Geometrically exact beam Kirchhoff–Love beam Kirchhoff rod Finite element implementation Locking-free 



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Authors and Affiliations

  1. 1.Institute of Solid MechanicsTechnische Universität BraunschweigBraunschweigGermany

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