Interpolation of finite rotations in flexible multi-body dynamics simulations

The representation and manipulation of finite rotations and the modelling of flexible bodies are at the heart of flexible multi-body systems dynamics simulations. When dealing with finite element formulations, the interpolation of finite-rotation fields becomes a critical issue. Objectivity, i.e. the invariance of interpolated strain fields to the addition of a rigid body motion, has been an important problem. Furthermore, the manipulation of finite rotations and the unavoidable associated singularities must be dealt in a rational manner. The various approaches to these two problems are reviewed in this article. Simple algorithms that achieve objectivity are proposed. Furthermore, these algorithms can deal with finite rotations of arbitrary large magnitude through a simple rescaling operation. The choice of unknowns, total versus incremental, is also discussed as it affects the performance of the computational process. Numerical examples are presented, which demonstrate the ability of the proposed approach to handle finite rotations of arbitrary magnitudes in complex, flexible multi-body systems.