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International Journal of Differential Equations
Volume 2012 (2012), Article ID 718308, 15 pages
An Energy Conserving Numerical Scheme for the Dynamics of Hyperelastic Rods
1Fraunhofer Institut für Techno- und Wirtschaftsmathematk, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany
2Fachbereich Mathematik, Technische Universität Kaiserslautern, 67653 Kaiserslautern, Germany
Received 12 January 2012; Revised 21 June 2012; Accepted 5 July 2012
Academic Editor: Mapundi Banda
Copyright © 2012 Thorsten Fütterer et al. 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.
- D. K. Pai, “Interactive simulation of thin solids using Cosserat models,” Computer Graphics Forum, vol. 21, no. 3, pp. 347–352, 2002.
- J. Barbic and D. James, “Real-time subspace integration for St. Venant-Kirchhoff deformable models,” ACM Transactions on Graphics, vol. 24, no. 3, pp. 982–990, 2005.
- A. Weber, T. Lay, and G. Sobottka, “Stable integration of the dynamic Cosserat equations with application to hair modeling,” Journal of WSCG, vol. 16, pp. 73–80, 2008.
- J. C. Simo, “A finite beam formulation. The three dimensional dynamic problem. Part I,” Computer Methods in Applied Mechanics and Engineering, vol. 49, pp. 55–70, 1985.
- J. C. Simo and L. Vu-Quoc, “A three dimensional finite-strain rod model. Part II: computational aspects,” Computer Methods in Applied Mechanics and Engineering, vol. 58, pp. 79–116, 1986.
- J. C. Simo and L. Vu-Quoc, “On the dynamics in space of rods undergoing large motions—a geometrically exact approach,” Computer Methods in Applied Mechanics and Engineering, vol. 66, no. 2, pp. 125–161, 1988.
- J. C. Simo, J. E. Marsden, and P. S. Krishnaprasad, “The Hamiltonian structure of nonlinear elasticity: the material and convective representations of solids, rods, and plates,” Archive for Rational Mechanics and Analysis, vol. 104, no. 2, pp. 125–183, 1988.
- L. Vu-Quoc and X. Tan, “Optimal solid shells for nonlinear analyses of multilayer composites. part ii: dynamics,” Computer Methods in Applied Mechanics and Engineering, vol. 192, no. 9-10, pp. 1017–1059, 2003.
- E. Wittbrodt, I. Adamiec-Wojcik, and S. Wojciech, Dynamic of Flexible Multibody Systems, Springer, 2006.
- S. S. Antman, Nonlinear Problems of Elasticity, Springer, New York, NY, USA, 2005.
- J. C. Simo, N. Tarnow, and K. K. Wong, “Exact energymomentum conserving algorithms and symplectic schemes for nonlinear dynamics,” Computer Methods in Applied Mechanics and Engineering, vol. 100, no. 1, pp. 63–116, 1992.
- S. Li and L. Vu-Quoc, “Finite difference calculus invariant structure of a class of algorithms for the nonlinear Klein-Gordon equation,” SIAM Journal on Numerical Analysis, vol. 32, no. 6, pp. 1839–1875, 1995.
- L. Vu-Quoc and J. Simo, “On the dynamics of earth-orbiting flexible satellites with multibody components,” AIAA Journal of Guidance, Control, and Dynamics, vol. 10, no. 6, pp. 549–558, 1987.
- L. Vu-Quoc, Dynamics of flexible structures performing large overall motions: a geometrically-nonlinear approach, technical report no. UCB/ERL M86/36 [Ph.D. thesis], University of California at Berkeley, 1986.
- F. A. McRobie and J. Lasenby, “Simo-Vu Quoc rods using Clifford algebra,” International Journal for Numerical Methods in Engineering, vol. 45, no. 4, pp. 377–398, 1999.
- L. Mahadevan and J. B. Keller, “Coiling of flexible ropes,” Proceedings of the Royal Society A, vol. 452, no. 1950, pp. 1679–1694, 1996.
- S. P. Timoshenko, “On the correction for shear of differential equations for transverse vibrations of prismatic bars,” Philosophical Magazine, vol. 6, no. 41, pp. 744–746, 1921.
- L. Vu-Quoc and S. Li, “Invariant-conserving finite difference algorithms for the nonlinear Klein-Gordon equation,” Computer Methods in Applied Mechanics and Engineering, vol. 107, no. 3, pp. 341–391, 1993.
- C. Peterson, Dynamik der Baukonstruktionen, Vieweg, 1996.
- S. P. Timoshenko, Schwingungsproblem der Technik, Springer, 1932.