On the Accuracy and Computational Costs of the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation in Deformable Multibody Systems

In the present paper, a comparison of the absolute nodal coordinate formulation (ANCF) and the floating frame of reference formulation (FFRF) is performed for standard static and dynamic problems, both in the small and large deformation regime. Special emphasis is laid on the converged solutions and a comparison to analytical and numerical solutions from the literature. In addition to the work of previous authors, the computational performance of both formulations is studied for the dynamic case, where detailed information is provided concerning the different effects influencing the single parts of the computation time. In case of the ANCF finite element, a planar formulation based on the Bernoulli-Euler theory is utilized, consisting of two position and two slope coordinates in each node only. In the FFRF beam finite element, the displacements are described by the rigid body motion and a small superimposed transverse deflection. The latter is described by means of two static modes for the rotation at the boundary and a user-defined number of eigenmodes of the clamped-clamped beam. In numerical studies, the accuracy and computational costs of the two formulations are compared for a cantilever beam, a pendulum and a slider-crank mechanism. It turns out that both formulations have comparable performance and that the choice of the optimal formulation depends on the problem configuration. Recent claims in the literature that the ANCF would have deficiencies compared to the FFRF thus can be refuted.