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Advances in Mechanical Engineering
Volume 2012 (2012), Article ID 530132, 12 pages
Research Article

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

1Département de Génie Mécanique, Université Laval, 1065 Avenue de la Médecine, Québec, QC, Canada G1V 0A6
2Département de Génie Mécanique, Université du Québec à Chicoutimi, 555 de l'Université, Saguenay, QC, Canada G7H 2B1

Received 30 August 2011; Accepted 10 November 2011

Academic Editor: Moran Wang

Copyright © 2012 M. J. Richard and M. Bouazara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.