Efficient and robust co-simulation of geometrically exact Cosserat rod model and multibody system
In modern system simulation, the increasing complexity and level of detail in the formulation of single subsystems is a challenging task for the numerical integration. To achieve efficient simulation, often co-simulation is used, i.e. the subsystems are solved with especially suited numerical methods and data is only exchanged at discrete points in time. Moreover, this allows to perform the numerical integration of subsystems in parallel and, thus, additionally saves computation time. Unfortunately, co-simulation may result in unstable numerical simulation. This is the case, if algebraic loops arise due to the data exchange [1, 2]. One way out are, e.g., implicit co-simulation schemes, which, however, are computationally expensive. Our main focus is the fast simulation of slender components, like cables and hoses, in vehicle dynamics. Thus, we kinematically couple a very efficient and geometrically exact Cosserat rod model  with classical rigid multibody systems. In order to do so, we describe the kinematic coupling by an algebraic constraint, which enables a simple formulation of different coupling joints. From this constraint coupling, an efficient force-displacement co-simulation scheme is developed , which performs explicitly and in parallel. We want to remark, that our coupling strategy could also be applied to arbitrary kinematically coupled mechanical subsystems, and especially to kinematic couplings in flexible multibody dynamics. It turns out, that the mass ratio of the coupled masses of the subsystems is decisive for stable cosimulation. Modifying the masses of the multibody system to improve the mass ratio would also change the system dynamics. In contrast, the coupled mass of the flexible structure can be changed by modifying the spatial discretization of the cable model, without varying the physical properties. In particular, a refined discretization leads to stable co-simulation. For equidistant spatial discretization, this might lead to a drastically increasing number of degrees of freedom. Thus, only a local refinement close to the coupling interface would be preferable. How this behaves for the complex cable model is part of our current research.