A few good reasons to consider a beam nite element formulation on the Lie group SEp3q

Based on an original interpolation method we develop a beam nite element formulation on the Lie group SEp3q which relies on a mathematically rigorous framework and provides compact notations. We work out the beam kinematics in the SE(3) context, the beam deformation measure and obtain the expression of the internal forces using the virtual work principle. The proposed formulation exhibits important features from both the theoretical and numerical points of view. The approach leads to a natural coupling of position and rotation variables and thus di ers from classical Timoshenko/Cosserat formulations. We highlight several important properties such as a constant deformation measure over the element, an invariant tangent sti ness matrix under of rigid motions or the absence of shear locking.