Study on sub-cycling algorithm for flexible multi-body system: stability analysis and numerical examples

Abstract

Numerical stability is an important issue for any integral procedure. Since sub-cycling algorithm has been presented by Belytschko et al. (Comput Methods Appl Mech Eng 17/18: 259–275, 1979), various kinds of these integral procedures were developed in later 20 years and their stability were widely studied. However, on how to apply the sub-cycling to flexible multi-body dynamics (FMD) is still a lack of investigation up to now. A particular sub-cycling algorithm for the FMD based on the central difference method was introduced in detail in part I (Miao et al. in Comp Mech doi: 10.1007/s00466-007-0183-9) of this paper. Adopting an integral approximation operator method, stability of the presented algorithm is transformed to a generalized eigenvalue problem in the paper and is discussed by solving the problem later. Numerical examples are performed to verify the availability and efficiency of the algorithm further.