  The present work focuses on geometrically exact finite elements for highly
slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love
type, a detailed review of existing formulations of Kirchhoff-Love and
Simo-Reissner type as well as a careful evaluation and comparison of the
proposed and existing formulations. Two different rotation interpolation
schemes with strong or weak Kirchhoff constraint enforcement, respectively, as
well as two different choices of nodal triad parametrizations in terms of
rotation or tangent vectors are proposed. The combination of these schemes
leads to four novel finite element variants, all of them based on a
C1-continuous Hermite interpolation of the beam centerline. Essential
requirements such as representability of general 3D, large-deformation, dynamic
problems involving slender beams with arbitrary initial curvatures and
anisotropic cross-section shapes or preservation of objectivity and
path-independence will be investigated analytically and verified numerically
for the different formulations. It will be shown that the geometrically exact
Kirchhoff-Love beam elements proposed in this work are the first ones of this
type that fulfill all the considered requirements. On the contrary,
Simo-Reissner type formulations fulfilling these requirements can be found in
the literature very well. However, it will be argued that the shear-free
Kirchhoff-Love formulations can provide considerable numerical advantages when
applied to highly slender beams. Concretely, several representative numerical
test cases confirm that the proposed Kirchhoff-Love formulations exhibit a
lower discretization error level as well as a considerably improved nonlinear
solver performance in the range of high beam slenderness ratios as compared to
two representative Simo-Reissner element formulations from the literature.
