0

Full Content is available to subscribers

Subscribe/Learn More  >

Integrability Conditions in Nonlinear Beam Kinematics

[+] Author Affiliations
Hidenori Murakami

University of California, San Diego, La Jolla, CA

Paper No. IMECE2016-65293, pp. V04BT05A068; 17 pages
doi:10.1115/IMECE2016-65293
From:
  • ASME 2016 International Mechanical Engineering Congress and Exposition
  • Volume 4B: Dynamics, Vibration, and Control
  • Phoenix, Arizona, USA, November 11–17, 2016
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5055-8
  • Copyright © 2016 by ASME

abstract

In order to develop an active nonlinear beam model, the beam’s kinematics is examined by employing the kinematic assumption of a rigid cross section during deformation. As a mathematical tool, the moving frame method, developed by Élie Cartan (1869–1951) on differentiable manifolds, is utilized by treating a beam as a frame bundle on a deforming centroidal curve. As a result, three new integrability conditions are obtained, which play critical roles in the derivation of beam equations of motion. They also serve a role in a geometrically-exact finite-element implementation of beam models. These integrability conditions enable the derivation of beam models starting from the three-dimensional Hamilton’s principle and the d’Alembert principle of virtual work. Finally, the reconstruction scheme for rotation matrices for given angular velocity at each time is presented.

Copyright © 2016 by ASME
Topics: Kinematics

Figures

Tables

Interactive Graphics

Video

Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature

Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

NOTE:
Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

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 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