Study on sub-cycling algorithm for a flexible multi-body system

Great developments have been made in the field offlexible multi-body system (FMS) with modeling, computational andexperimental studies for nearly 30 years. The subcycling algorithms, whichwere firstly presented by Belytschko T. et al. in 1979, havebeen successfully applied in the structural dynamic analysis of FMS. However,subcycling algorithms for the FMS are still not presented up to now. Thispaper introduces a central difference method based sub-cycling algorithm forthe FMS. First, common update formulae and sub-step update formulae forquickly changing variables and slowly changing variables of the FMS areestablished. Second, the nonlinear differential-algebraic equations arecontracted to the original differential equations. Third, algorithmstability is validated with an energy balance computation during theintegration procedure. Numerical results indicate that the sub-cyclingalgorithm is available to enhance the computational efficiency withappropriate computational accuracy. Furthermore, the algorithm stability canbe determined by means of modifying the integral step sizes with theperturbation method.