Total Lagrangian Reissner's geometrically exact beam element without singularities

In this paper, we introduce a new Reissner's geometrically exact beam element, which is based on a total Lagrangian updating procedure. The element has the rotation vector as the dependent variable and the singularity problems at the rotation angle 2π and its multiples are passed by the change of parametrization on the rotation manifold. The beam formulation has several benefits such as all the unknown vectors belong to the same tangential vector space, no need for secondary storage variables, the path‐independence in the static case, any standard time‐integration algorithm may be used, and the symmetric stiffness. Copyright © 2006 John Wiley & Sons, Ltd.