A Discrete Quasi-Coordinate Formulation for the Dynamics of Elastic Bodies

[+] Author and Article Information
G. M. T. D’Eleuterio

Institute for Aerospace Studies, University of Toronto, Toronto, ON, M3H 5T6, Canadagabriele.deleuterio@utoronto.ca

T. D. Barfoot

Institute for Aerospace Studies, University of Toronto, Toronto, ON, M3H 5T6, Canadatim.barfoot@utoronto.ca

There is potentially a confusion in using the word order for it may refer to differential order as well as algebraic order. To avoid this, we shall restrict the use of the term order to the former and cmploy degree, which is customarily used in reference to polynomials, for the latter.

J. Appl. Mech 74(2), 231-239 (Jan 30, 2006) (9 pages) doi:10.1115/1.2189873 History: Received July 12, 2004; Revised January 30, 2006

The discretized equations of motion for elastic systems are typically displayed in second-order form. That is, the elastic displacements are represented by a set of discretized (generalized) coordinates, such as those used in a finite-element method, and the elastic rates are simply taken to be the time-derivatives of these displacements. Unfortunately, this approach leads to unpleasant and computationally intensive inertial terms when rigid rotations of a body must be taken into account, as is so often the case in multibody dynamics. An alternative approach, presented here, assumes the elastic rates to be discretized independently of the elastic displacements. The resulting dynamical equations of motion are simplified in form, and the computational cost is correspondingly lessened. However, a slightly more complex kinematical relation between the rate coordinates and the displacement coordinates is required. This tack leads to what may be described as a discrete quasi-coordinate formulation.

Copyright © 2007 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 2

Transverse deflection (full model, Q=3)

Grahic Jump Location
Figure 3

Axial deflection (full model, Q=3)

Grahic Jump Location
Figure 4

Effect of higher-degree terms on transverse deflection (Ne=1)

Grahic Jump Location
Figure 5

Effect of higher-degree terms on axial deflection (Ne=1)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In