Dual-rate integration using partitioned Runge-Kutta methods for mechanical systems with interacting subsystems

A framework is presented that allows dual-rate numerical integration of the equations of mechanical system dynamics to be considered as a form of Partitioned Runge-Kutta (PRK) integration. Certain coefficients of a PRK integrator are made equal to zero, so that two Runge-Kutta integrators that constitute the PRK integrator can be made to have different numbers of stages. As a result, one Runge-Kutta integrator requires fewer function evaluations than the other, which is a form of dual-rate integration. Well-established order of accuracy theory of PRK integrators is used to develop a rigorous methodology for designing PRK dual-rate integrators. All integrators considered in the research are explicit integrators.; Using methodologies presented in this thesis, integrators are designed specifically for dual-rate integration. The main thrust of this research is to develop PRK dual-rate integrators that have enhanced stability. There does not exist a comprehensive stability theory that can be directly used to design PRK dual-rate integrators, while accounting for the effect of coupling on stability. However, using existing theory, a number of approaches are developed for designing enhanced stability PRK dual-rate integrators.; Numerical experiments, first with simple and then more complex models, are carried out to evaluate different methodologies for designing PRK dual-rate integrators. From these numerical experiments, it is determined that the stabilized Runge-Kutta approach is the most promising for the intended application of vehicle system simulation. In this approach, stabilized Runge-Kutta theory is combined with PRK integrator theory to design PRK dual-rate integrators with the largest possible stability regions.; PRK dual-rate integrators are used to simulate models of vehicle systems that contain subsystems with high frequency response characteristics. A vehicle model with a spatial rigid ring tire model is simulated 2.4 times faster than is possible using a comparable single-rate integrator. Results also indicate that if methodologies presented in this thesis are used to design PRK dual-rate integrators with higher orders of accuracy than those designed in this research, further improvements in computational performance are expected.