An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy–momentum conserving scheme in dynamics
- 5 June 2002
- journal article
- research article
- Published by Wiley in International Journal for Numerical Methods in Engineering
- Vol. 54 (12) , 1683-1716
Abstract
We present in this paper a new finite element formulation of geometrically exact rod models in the three‐dimensional dynamic elastic range. The proposed formulation leads to an objective (or frame‐indifferent under superposed rigid body motions) approximation of the strain measures of the rod involving finite rotations of the director frame, in contrast with some existing formulations. This goal is accomplished through a direct finite element interpolation of the director fields defining the motion of the rod's cross‐section. Furthermore, the proposed framework allows the development of time‐stepping algorithms that preserve the conservation laws of the underlying continuum Hamiltonian system. The conservation laws of linear and angular momenta are inherited by construction, leading to an improved approximation of the rod's dynamics. Several numerical simulations are presented illustrating these properties. Copyright © 2002 John Wiley & Sons, Ltd.Keywords
This publication has 22 references indexed in Scilit:
- On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: low-order methods for two model problems and nonlinear elastodynamicsComputer Methods in Applied Mechanics and Engineering, 2001
- Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systemsInternational Journal for Numerical Methods in Engineering, 2000
- On finite element implementation of geometrically nonlinear Reissner's beam theory: three-dimensional curved beam elementsComputer Methods in Applied Mechanics and Engineering, 1995
- A Geometrically-exact rod model incorporating shear and torsion-warping deformationInternational Journal of Solids and Structures, 1991
- Time integration of the equations of motion in mechanism analysisComputers & Structures, 1989
- On the dynamics in space of rods undergoing large motions — A geometrically exact approachComputer Methods in Applied Mechanics and Engineering, 1988
- A three-dimensional finite-strain rod model. part II: Computational aspectsComputer Methods in Applied Mechanics and Engineering, 1986
- A finite strain beam formulation. The three-dimensional dynamic problem. Part IComputer Methods in Applied Mechanics and Engineering, 1985
- On one-dimensional finite-strain beam theory: The plane problemZeitschrift für angewandte Mathematik und Physik, 1972
- A general theory of rodsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1966