0
RESEARCH PAPERS

Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor

[+] Author and Article Information
D. A. Danielson

Department of Mathematics, Naval Postgraduate School, Monterey, CA 93943

D. H. Hodges

Rotorcraft Dynamics Division, Aeroflightdynamics Directorate, US Army Aviation Research & Technology Activity (AVSCOM), Ames Research Center, Moffett Field, CA 94035

J. Appl. Mech 54(2), 258-262 (Jun 01, 1987) (5 pages) doi:10.1115/1.3173004 History: Received May 03, 1986; Revised September 02, 1986; Online July 21, 2009

Abstract

A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion, extension, shear deformation, and warping of an initially curved and twisted beam.

Copyright © 1987 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

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