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Acta Mechanica

, Volume 230, Issue 11, pp 4061–4075 | Cite as

A rod model for large bending and torsion of an elastic strip with a geometrical imperfection

  • Yu. VetyukovEmail author
  • C. Schmidrathner
Open Access
Original Paper

Abstract

We consider an initially horizontal curved elastic strip, which bends and twists under the action of the varying length of the span between the clamped ends and of the gravity force. Equations of the theory of rods, linearized in the vicinity of a largely pre-deformed state, allow for semi-analytical (or sometimes closed-form) solutions. A nonlinear boundary value problem determines the vertical bending of a perfect beam, while the small natural curvature additionally leads to torsion and out-of-plane deflections described by the linear equations of the incremental theory. Numerical experiments demonstrate perfect correspondence to the finite element rod model of the strip. Comparisons to the predictions of the shell model allow estimating the range of applicability of the three-dimensional theory of rods. Practically relevant conclusions follow for the case of high pre-tension of the strip.

Keywords

Elastic rods Incremental equations Spatial Kirchhoff rods Shell finite elements Asymptotics 

Notes

Acknowledgements

Open access funding provided by TU Wien (TUW). This research was supported by the Austrian Research Promotion Agency (FFG), project number: 861493.

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© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Vienna University of TechnologyViennaAustria

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