Many works deal with possible approaches to develop an efficient beam element
for large displacement analysis of frame structures. In this work an original non linear FEM
approach applied to elastic beams is presented. It is based on the use of rotations only as
generalised coordinates. Euler-Rodrigues quaternion approach is used in the case of large
displacements. A simplified non-linear theory is presented if the hypothesis of small displacements
holds and therefore additive properties of rotations are still valid. Equilibrium
equations are written in the deformed configuration, thus permitting a non-incremental approach
to be applied. Some cases related to buckling are analyzed from a theoretical point of
view and a numerical validation has been finally performed.
