Co-Simulation Methods with Variable Communication Step Size and Alternative Approaches for Solving Constrained Mechanical Systems

This dissertation has two parts. The first part deals with co-simulation schemes for mechanical systems, concretely for multibody systems. Applying a co-simulation approach, a large differential-algebraic system is decomposed into several subsystems, which are also multibody systems. Coupling variables are defined to describe the connection between adjacent subsystems. Moreover, a communication time grid has to be introduced. The coupling variables are exchanged only at the communication time points. Within two communication time points, the coupling variables are approximated, so that the subsystems can be computed independently with classical integration schemes to solve initial value problems. Each subsystem can be computed with an appropriate integration scheme and individual integration step sizes. The efficiency of classical time integration schemes is improved by using a step size control algorithm. This doctoral thesis is focused on the development and error analysis for controlling a variable communication step size. The analysis is carried out for coupling techniques with constitutive laws as well as for constraint coupling. Error estimators are derived for several co-simulation methods. With the help of classical methods for step size control, co-simulation can be implemented with variable communication step sizes. Numerical results are presented with convergence plots confirming the results of the error analysis. Furthermore, plots to compare the estimated local errors with the real local errors are depicted. Also, results of co-simulations with variable communication time grids are shown. In the second part of this thesis, alternative approaches for solving constrained mechanical systems are developed. The general idea of the methods are based on the usage of intermediate time points. The approaches are discussed for implicit Runge-Kutta methods, backward differentiation formulas, and the generalized-α method. The approach can also be applied for non-mechanical higher-index systems of differential-algebraic equations