A new approach for force-displacement co-simulation using kinematic coupling constraints

The separate numerical simulation of interacting subsystems, i.e. the co-simulation of subsystems, is widespread in advanced system simulation. Classically, mechanical subsystems are coupled by artificial stiffnesses, which often are unknown. In this paper, we present a coupling approach that uses no artificial stiffness, but a kinematic coupling constraint for the co-simulation of different subsystems. The algebraic constraint leads to corresponding constraint forces that only act in one direction of the coupling to avoid drift-off problems, while displacements are given in the opposite direction. Moreover, a strategy for an efficient computation of approximated constraint forces is provided. For the stability of the approach, we consider zero-stability as well as stability for finite time steps. Convergence is analyzed with a 2-mass spring-damper model, where the analytical solution is known. As application, we use our approach to simulate the more complex problem of a cable model, that is embedded in a multibody system.