Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Stable analysis of long duration motions of FE‐discretized structures in central force fields

Stable analysis of long duration motions of FE‐discretized structures in central force fields The computation of structures moving in central force fields generally requires long‐time integration including geometrically nonlinear behavior (large rotations) as such, e.g. satellite structures move for a long time. To achieve a numerically stable computation the energy momentum method which fulfills linear and angular momentum as well as energy conservation within the time step is chosen for the time integration. The focus in the contribution is on Hamiltonian systems. A formulation for the gravitational force in a central force field as external force on a rigid or flexible satellite is given. The presented formulation enables the computation of the exact spatial distribution of the gravitational forces acting on a structure using the FE‐discretization which is necessary to analyze, e.g. the orientation of a satellite in a gravitational field. The fulfillment of the conservation laws within the time step is proved. The necessity for considering the spatial distribution of the gravitational forces is discussed based on numerical examples. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations Emerald Publishing

Stable analysis of long duration motions of FE‐discretized structures in central force fields

Burkhard Göttlicher; Karl Schweizerhof
Engineering Computations , Volume 21 (7): 10 – Oct 1, 2004
Download PDF
10 pages

Loading next page...
 
/lp/emerald-publishing/stable-analysis-of-long-duration-motions-of-fe-discretized-structures-G97fyAhzX0
Publisher
Emerald Publishing
Copyright
Copyright © 2004 Emerald Group Publishing Limited. All rights reserved.
ISSN
0264-4401
DOI
10.1108/02644400410548350
Publisher site
See Article on Publisher Site

Abstract

The computation of structures moving in central force fields generally requires long‐time integration including geometrically nonlinear behavior (large rotations) as such, e.g. satellite structures move for a long time. To achieve a numerically stable computation the energy momentum method which fulfills linear and angular momentum as well as energy conservation within the time step is chosen for the time integration. The focus in the contribution is on Hamiltonian systems. A formulation for the gravitational force in a central force field as external force on a rigid or flexible satellite is given. The presented formulation enables the computation of the exact spatial distribution of the gravitational forces acting on a structure using the FE‐discretization which is necessary to analyze, e.g. the orientation of a satellite in a gravitational field. The fulfillment of the conservation laws within the time step is proved. The necessity for considering the spatial distribution of the gravitational forces is discussed based on numerical examples.

Journal

Engineering Computations – Emerald Publishing

Published: Oct 1, 2004

Keywords: Finite element analysis; Force; Motion

References

  • Conservation properties of a time FE method. Part I: time‐stepping schemes for n‐body problems
    Betsch, P.; Steinmann, P.
  • Inherently energy conserving time finite elements for classical mechanics
    Betsch, P.; Steinmann, P.
  • Pressure loaded structures under large deformations
    Bufler, H.
  • Energy‐momentum conserving methods for three dimensional dynamic nonlinear multibody systems”,
    Chen, A.
  • Mechanical systems subject to holonomic constraints: differential‐algebraic formulations and conservative integration
    Gonzalez, O.
  • Exact energy and momentum conserving algorithms for general models in nonlinear elasticity
    Gonzalez, O.
  • On the stability of symplectic and energy‐momentum algorithms for non‐linear hamiltonian systems with symmetry
    Gonzalez, O.; Simo, J.
  • Completely conservative, covariant numerical methodology
    Greenspan, D.
  • On rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3d geometrically exact beam model
    Ibrahimbegovic, A.; Mamouri, S.
  • Finite element method in dynamics of flexible multibody systems: modeling of holonomic constraints and energy conserving integration schemes
    Ibrahimbegovic, A.; Mamouri, S.; Taylor, R.; Chen, A.
  • Energy‐conserving and decaying algorithms in non‐linear structural dynamics
    Kuhl, D.; Crisfield, M.
  • Constraint energy momentum algorithm and its application to non‐linear dynamics of shells
    Kuhl, D.; Ramm, E.
  • Displacement dependent pressure loads in nonlinear finite element analysis
    Schweizerhof, K.; Ramm, E.
  • The discrete energy‐momentum method. Conserving algorithms for nonlinear elastodynamics
    Simo, J.; Tarnow, N.
  • Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum
    Simo, J.; Wong, K.