An efficiency comparison of different ANCF implementations

For multibody dynamics simulation using the Absolute Nodal Coordinate Formulation, multiple strategies are reported in the linear elastic material literature for calculating the generalized internal force and its Jacobian matrix. When examining the presentation of these strategies, which are all sound, it is difficult to assess which method is more efficient. We seek to clarify this issue by reporting the results of a comprehensive study that included five different ANCF solution strategies discussed in the literature. To increase the relevance of the study, we first extended these methods to incorporate a linear viscoelastic material model to account for damping effects within the elements. A beam, a shell, and a hexahedral element are each examined to provide a broader comparison. Both simple hand calculations and actual timing comparisons on a multi-core CPU architecture are investigated. For the simple beam element, only small differences manifest among the methods studied. However, for the shell and hexahedral elements, we noticed pronounced performance and storage cost differences among the methods.