Description of Elastic Forces in Absolute Nodal Coordinate Formulation

The objective of this paper is to investigate the accuracy of the elastic force models that can be used in the absolute nodal coordinate finite element formulation. This study focuses on the description of the elastic forces in three-dimensional beams. The elastic forces of the absolute nodal coordinate formulation can be derived using a continuum mechanics approach. This study investigates the accuracy and usability of such an approach for a three-dimensional absolute nodal coordinate beam element. This study also presents an improvement proposal for the use of a continuum mechanics approach in deriving the expression of the elastic forces in the beam element. The improvement proposal is verified using several numerical examples that show that the proposed elastic force model of the beam element agrees with the analytical results as well as with the solutions obtained using existing finite element formulation. In the beam element under investigation, global displacements and slopes are used as the nodal coordinates, which resulted in a large number of nodal degrees of freedom. This study provides a physical interpretation of the nodal coordinates used in the absolute nodal coordinate beam element. It is shown that a beam element based on the absolute nodal coordinate formulation relaxes the assumption of a rigid cross-section and is capable of representing a distortional deformation of the cross-section. The numerical results also imply that the beam element does not suffer from the phenomenon called shear locking.