ANCF Consistent Rotation-Based Finite Element Formulation

In this technical brief, a consistent rotation-based formulation is proposed using the absolute nodal coordinate formulation (ANCF) kinematic description. The proposed formulation defines a unique rotation field, employs one interpolation, captures shear deformations, does not suffer from the redundancy problem encountered when using large rotation vector formulations, allows for systematically describing curved geometry, and leads to elastic force definitions that eliminate high-frequency modes associated with the deformation of the cross section. The drawback of this formulation, as it is the case with the large rotation vector formulations, is the nonlinearity of the inertia forces including nonzero Coriolis and centrifugal forces. Furthermore, the formulation does not capture deformation modes that can be captured using the more general ANCF finite elements. Nonetheless, the proposed method is consistent with the continuum mechanics general description, can be related to computational geometry methods, and can be used to develop beam, plate, and shell models without violation of basic mechanics principles.