Study on sub-cycling algorithm for flexible multi-body system—integral theory and implementation flow chart

Abstract

A sub-cycling integration algorithm (or named multi-time-steps integration algorithm), which has been successfully applied to FEM dynamical analysis, was firstly presented by Belytschko et al. (Comput Methods Appl Mech Eng 17/18:259-275, 1979). However, the problem of how to apply this type of algorithm to flexible multi-body dynamics (FMD) problems still lacks investigation up to now. Similar to the region-partitioning method used in FEM, this paper presents a central-difference-based sub-cycling integral method by decomposing the variables of an FMD equation into several groups and adopting different integral step sizes to each group of the variables. Based on the condensed form of an FMD equation, a group of common update formulae and a sub-step update formula, which constitute the sub-cycling together, are established in the paper. Furthermore, an implementation flowchart of the sub-cycling is presented. Stability of the sub-cycling will be analyzed and numerical examples will be performed to verify availability and precision of the sub-cycling in part II of the paper.

Discrete time transfer matrix method for dynamics analysis of complex weapon systems

“…Substituting eqs. (10) and (11) into eq. (9), the deformation vector of arbitrary point P on the element e k of a flexible body can be expressed as…”

“…The ship body, revolving mechanism, elevating mechanism and gun breech are regarded as rigid bodies (2,4,6,8), respectively. The gun tube is regarded as a flexible body (10). The effect of seawater on the ship body is equivalent to the distributing basic elastic damping hinge (1).…”

“…In order to improve the computational efficiency of complex mechanical dynamics and structure dynamics, many researchers attempted a lot of methods in theory and numerical simulation, such as recursive solution procedures [5,6], parallel computational strategies [7,8], object-oriented strategies, computerized symbolic manipulation, adaptive approximation strategies [1], multirate algorithms [9,10]. Rui et al developed the discrete time transfer matrix method of multibody system (MS-DT-TMM) [11][12][13] for highly efficient dynamic modelling and computation of MBS by combining and expanding the classical transfer matrix method [14] and the numerical integration procedure.…”

Discrete Time Transfer Matrix Method for Launch Dynamics Modeling and Cosimulation of Self-Propelled Artillery System

“…Many researchers, such as Neal [8], Daniel [9], Prakash [10], Cavin [11], Zheng [12], and so on, improved and modified these algorithms for application to different engineering problems. Arnold [1] and Miao [13] introduced the multirate algorithm into mechanical dynamics form a theoretical and practical standpoint. Rui [14] and Rong [15,16] developed the discrete time transfer matrix method of multibody system (MS-DT-TMM) for highly efficient dynamic computation of MBS by combining and expanding the classical transfer matrix method [17] and the numerical integration procedure.…”

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

“…Otherwise, the perturbation error will be linear increase as max|λ i | = 1, or exponential increase as max|λ i | > 1. We will apply this method to analyze the stability of the sub-cycling algorithm, which was presented in part I [2] of the paper, in the following sections.…”