Implicit co-simulation method for constraint coupling with improved stability behavior

This paper deals with a novel co-simulation approach for coupling mechanical subsystems in time domain. The submodels are assumed to be coupled by algebraic constraint equations. In contrast to well-known coupling techniques from the literature, the here presented index-1 approach uses a special technique for approximating the coupling variables so that the constraint equations together with the hidden constraints on velocity and acceleration level can be enforced simultaneously at the communication time points. The method discussed here uses second- and third-order approximation polynomials. Because of the high approximation order, the numerical errors are very small, and a good convergence behavior is achieved. A stability analysis is carried out, and it is shown that—despite the fact that higher-order approximation polynomials are applied—also a good numerical stability behavior is observed. Different numerical examples are presented, which illustrate the practical application of the approach.