- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Advances in Mechanical Engineering
Volume 2012 (2012), Article ID 530132, 12 pages
Graph-Theoretic Approach for the Dynamic Simulation of Flexible Multibody Systems
1Département de Génie Mécanique, Université Laval, 1065 Avenue de la Médecine, Québec, QC, G1V 0A6, Canada
2Département de Génie Mécanique, Université du Québec à Chicoutimi, 555 de l'Université, Saguenay, QC, G7H 2B1, Canada
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.
- W. T. Tutte, Graph Theory, Cambridge University Press, New York, NY, USA, 2001.
- J. L. Gross and J. Yellen, Graph Theory and Its Applications, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2nd edition, 2005.
- S. Even, Graph Algorithms, Computer Science Press, 1979.
- H. E. Koenig and W. S. Blackwell, “Linear graph theory—a fundamental engineering discipline,” IRE Transaction on Education, vol. 3, pp. 42–62, 1960.
- G. C. Andrews, The vector-network model : a topological approach to mechanics, Ph.D. thesis, University of Waterloo, Waterloo, Ontario, Canada, 1971.
- H. E. Koenig, Y. Tokad, and H. K. Kesavan, Analysis of Discrete Physical Systems, McGraw-Hill, 1967.
- G. C. Andrews and H. K. Kesavan, “The vector-network model: a new approach to vector dynamics,” Mechanism and Machine Theory, vol. 10, no. 1, pp. 57–75, 1975.
- M. J. Richard, Dynamic simulation of constrained three dimensional multibody systems using vector network techniques, Ph.D. thesis, Queen's University, Kingston, Ontario, Canada, 1985.
- P. Shi and J. McPhee, “Dynamics of flexible multibody systems using virtual work and linear graph theory,” Multibody System Dynamics, vol. 4, no. 4, pp. 355–381, 2000.
- P. Shi, J. McPhee, and G. R. Heppler, “A deformation field for Euler-Bernoulli beams with applications to flexible multibody dynamics,” Multibody System Dynamics, vol. 5, no. 1, pp. 79–104, 2001.
- M. J. Richard, M. Bouazara, and J. N. Therien, “Analysis of multibody systems with flexible plates using variational graph-theoretic methods,” Multibody System Dynamics, vol. 25, no. 1, pp. 43–63, 2011.
- T. M. Wasfy and A. K. Noor, “Computational strategies for flexible multibody systems,” Applied Mechanics Reviews, vol. 56, no. 6, pp. 553–613, 2003.
- J. J. McPhee and S. M. Redmond, “Modelling multibody systems with indirect coordinates,” Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 50-51, pp. 6942–6957, 2006.
- M. J. Richard, M. Z. Huang, and M. Bouazara, “Computer aided analysis and optimal design of mechanical systems using vector-network techniques,” Applied Mathematics and Computation, vol. 157, no. 1, pp. 175–200, 2004.
- P. Shi and J. McPhee, “On the use of virtual work in a graph-theoretic formulation for multibody dynamics,” in Proceedings of the ASME Design Engineering Technical Conference, Sacramento, Caif, USA, 1997, DETC97/VIB-4199.
- J. J. McPhee, “Automatic generation of motion equations for planar mechanical systems using the new set of branch coordinates,” Mechanism and Machine Theory, vol. 33, no. 6, pp. 805–823, 1998.
- M. Behzad and G. Chartrand, Introduction to the Theory of Graphs, Allyn and Bacon, 1971.
- N. Christofides, Graph Theory, An Algorithmic Approach, Academic Press, New York, NY, USA, 1975.
- R. E. Roberson, “The path matrix of a graph, its construction and its use in evaluating certain products,” Computer Methods in Applied Mechanics and Engineering, vol. 42, no. 1, pp. 47–56, 1984.
- K. Arczewski, “Application of graph theory to the mathematical modelling of a class of rigid body systems,” Journal of the Franklin Institute, vol. 327, no. 2, pp. 209–223, 1990.
- G. Baciu, J. C. K. Chou, and H. K. Kesavan, “Constrained multibody systems: graph-theoretic Newton-Euler formulation,” IEEE Transactions on Systems, Man and Cybernetics, vol. 20, no. 5, pp. 1025–1048, 1990.
- K. Arczewski, “Application of graph theory to the determination of kinetic energy of rigid body systems,” Journal of the Franklin Institute, vol. 324, no. 3, pp. 351–367, 1987.
- J. C. K. Chou, H. K. Kesavan, and K. Singhal, “Dynamics of 3-D isolated rigid-body systems: graph-theoretic models,” Mechanism and Machine Theory, vol. 21, no. 3, pp. 261–272, 1986.
- A. M. Bos, Modelling Multibody Systems in Terms of Multibond Graphs with Application to a Motorcycle, Dissertation Twente University, Enschede, The Netherlands, 1986.
- Y. Hu, “Applications of bond graphs and vector bond graphs to rigid body dynamics,” Journal of China Textile University, vol. 5, no. 4, p. 67, 1988.
- D. L. Margolis, “Bond graphs for automated simulation and control of nonlinear vehicle systems,” in Proceedings of the Future Transportation Technology Conference and Exposition, p. 8, Seattle, Wash, USA, 1987, SAE paper no. 871558.
- G. C. Andrews, A General Re-statement of the Laws of Dynamics Based on Graph Theory, Problem Analysis in Science and Engineering, Academic Press, 1977.
- C. Schmitke and J. McPhee, “Using linear graph theory and the principle of orthogonality to model multibody, multi-domain systems,” Advanced Engineering Informatics, vol. 22, no. 2, pp. 147–160, 2008.
- A. A. Shabana, “Transient analysis of flexible multi-body systems. Part I: dynamics of flexible bodies,” Computer Methods in Applied Mechanics and Engineering, vol. 54, no. 1, pp. 75–91, 1986.
- M. Tennich, Dynamique de systèmes multi-corps exibles, une approche générale, Ph.D. dissertation, Laval University, Québec, Canda, 1994.
- J. Wittenburg, Dynamics of Systems of Rigid Bodies, Teubner, Stuttgart, Germany, 1977.
- W. Flugge, Viscoelasticity, Blaisdell, New York, NY, USA, 1967.
- R. M. Christensen, Theory of Viscoelasticity: An Introduction, Academic Press, New York, NY, USA, 1975.
- O. A. Bauchau, G. Damilano, and N. J. Theron, “Numerical integration of non-linear elastic multi-body systems,” International Journal for Numerical Methods in Engineering, vol. 38, no. 16, pp. 2727–2751, 1995.
- MapleSim5, High-Performance Multi-Domain Modeling and Simulation, 2011, http://www.maplesoft.com/products/maplesim/index.aspx.
- B. Jonker, “A finite element dynamic analysis of spatial mechanisms with flexible links,” Computer Methods in Applied Mechanics and Engineering, vol. 76, no. 1, pp. 17–40, 1989.
- ADAMS, MSC/Software Simulating Reality, Delivering Certainty, 2011, http://www.mscsoftware.com/Products/Modeling-Solutions/Default.aspx.