A FEW GOOD REASONS TO CONSIDER A BEAM FINITE ELEMENT FORMULATION ON THE LIE GROUP SE(3)

Based on an original interpolation method we develop a
beam finite element formulation on the Lie group SE(3) which relies
on a mathematically rigorous framework and provides compact
and generic 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 differs from classical Timoshenko/Cosserat formulations.
We highlight several important properties such as
a constant deformation measure over the element, an invariant
tangent stiffness matrix under of rigid motions or the absence of
shear locking.