A comparison of nonlinear beam finite element formulations

Two alternative nonlinear finite element formulations emanating from the Simo‐Reissner beam theory are considered. The orientation of the beam cross section is characterised by a director frame which can be either represented by means of rotational parameters or the direction cosine matrix. In the planar case the use of a single angle can be considered as the canonical formulation. The corresponding finite element approximation relies on the interpolation of the nodal angles. However, the extension of this approach to the three‐dimensional case is nontrivial and often leads to element formulations beeing not frame‐indifferent. On the other hand, the interpolation of the nodal direction cosines in general yields frame‐indifferent element formulations [1, 2]. The present talk focuses on a comparison of the two aforementioned finite element beam formulations for planar problems. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)