Graph-Theoretic Approach for the Dynamic Simulation of Flexible Multibody Systems

Abstract

This paper provides a general description of a variational graph-theoretic formulation for simulation of flexible multibody systems (FMSs) which includes a brief review of linear graph principles required to formulate this algorithm. The system is represented by a linear graph, in which nodes represent reference frames on flexible bodies, and edges represent components that connect these frames. The method is based on a simplistic topological approach which casts the dynamic equations of motion into a symmetrical format. To generate the equations of motion with elastic deformations, the flexible bodies are discretized using two types of finite elements. The first is a 2 node 3D beam element based on Mindlin kinematics with quadratic rotation. This element is used to discretize unidirectional bodies such as links of flexible systems. The second consists of a triangular thin shell element based on the discrete Kirchhoff criterion and can be used to discretize bidirectional bodies such as high-speed lightweight manipulators, large high precision deployable space structures, and micro/nano-electromechanical systems (MEMSs). Two flexible systems are analyzed to illustrate the performance of this new variational graph-theoretic formulation and its ability to generate directly a set of motion equations for FMS without additional user input.

Graph Models of Automobile Gears - Kinematics

“…The simplicity of analysis of consecutive drives and comparisons of results are interesting features. Versatile analyses and simulations are possible (Luo Yutao and Tan Di, 2011;Kurth, 2012;Rajasri et al, 2014;Richard and Bouazara, 2012;Zanasi and Grossi, 2009). Further considerations on the dynamics will be presented in a separate paper.…”

“…Bond graphs can also be used for modeling of gears (Brown, 2001;Merzouki et al, 2013;Richard and Bouazara, 2012). The bond graph or power flow graph consists of elements (vertices) and bonds (arcs).…”

“…In Deur et al (2006), the purpose of modeling was an analysis of power flow through a planetary gear. Moreover, in Deur et al (2006), Luo Yutao and Tan Di (2011), Richard and Bouazara (2012) the dynamics of automotive gears was analyzed by means of bond-graphs. In Drewniak and Zawiślak (2010) the authors analyzed kinematics of planetary gears using contour graphs introduced by Marghitu (2005).…”