Variational formulations, instabilities and critical loadings of space curved beams

Variational formulations, instabilities and critical loadings of space curved beams Beam theories have been extensively studied for applications in structural engineering. Space curved beams with large displacements, however, have been explored to a much less extent, not to mention explicit solutions concerning instabilities and critical loadings. In this paper, by carefully accounting for geometric nonlinearity and different scalings of kinematic variables, we present a variational framework for large-displacement space curved beams. We show that the variational formulation is consistent with the classic field equations, derive the appropriate boundary value problems for a variety of loading conditions and kinematic constraints, and generalize the Kirchhoff’s helical solutions. Explicit planar solutions for semi-circular arches are obtained upon linearization. Further, two nonlinear asymptotic theories are proposed to address ribbon-like and moderately deformed curved beams, respectively. Based on the method of trial solutions, we obtain explicit approximate solutions to critical loadings for semi-circular arches losing stabilities due to twisting and out-of-plane displacement. The variational framework, nonlinear asymptotic theories, stability analysis and explicit solutions are anticipated to have novel applications in stretchable electronics and biological macromolecules. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Solids and Structures Elsevier

Variational formulations, instabilities and critical loadings of space curved beams

Loading next page...
 
/lp/elsevier/variational-formulations-instabilities-and-critical-loadings-of-space-ooKXr08hxL
Publisher
Elsevier
Copyright
Copyright © 2016 Elsevier Ltd
ISSN
0020-7683
eISSN
1879-2146
D.O.I.
10.1016/j.ijsolstr.2016.02.032
Publisher site
See Article on Publisher Site

Abstract

Beam theories have been extensively studied for applications in structural engineering. Space curved beams with large displacements, however, have been explored to a much less extent, not to mention explicit solutions concerning instabilities and critical loadings. In this paper, by carefully accounting for geometric nonlinearity and different scalings of kinematic variables, we present a variational framework for large-displacement space curved beams. We show that the variational formulation is consistent with the classic field equations, derive the appropriate boundary value problems for a variety of loading conditions and kinematic constraints, and generalize the Kirchhoff’s helical solutions. Explicit planar solutions for semi-circular arches are obtained upon linearization. Further, two nonlinear asymptotic theories are proposed to address ribbon-like and moderately deformed curved beams, respectively. Based on the method of trial solutions, we obtain explicit approximate solutions to critical loadings for semi-circular arches losing stabilities due to twisting and out-of-plane displacement. The variational framework, nonlinear asymptotic theories, stability analysis and explicit solutions are anticipated to have novel applications in stretchable electronics and biological macromolecules.

Journal

International Journal of Solids and StructuresElsevier

Published: Jun 1, 2016

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial