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2008 Exact Curvature Elastica of a Thin Cantilever Under Terminal Loads
Giovanni Mingari Scarpello, Daniele Ritelli
J. Geom. Symmetry Phys. 12: 75-92 (2008). DOI: 10.7546/jgsp-12-2008-75-92


A thin, flexible, one side-built-in rod under a concentrated terminal force is studied in its elastic equilibrium configuration. In order to make the problem more tractable, a proper set of state variables is chosen, facing with a second order, nonlinear, but autonomous boundary value problem, in the rotation $\varphi (s)$ pertaining to each $s$-section. The search of the free end rotation $\varphi _{0}$, following the isoperimetric assumption, leads to a numerical sub-problem inside the main BVP. Furthermore, if $x(s)$ and $y(s)$ mean the elastica coordinates parametrized on the arclength $s$, one obtains $x^{\prime }(s)$ and $y^{\prime }(s)$ as elliptic functions of $s$. Finally, some minor changes have been shown in order to pass from a loading force to a more general free-end load combination, consisting of a force and a couple.


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Giovanni Mingari Scarpello. Daniele Ritelli. "Exact Curvature Elastica of a Thin Cantilever Under Terminal Loads." J. Geom. Symmetry Phys. 12 75 - 92, 2008.


Published: 2008
First available in Project Euclid: 24 May 2017

zbMATH: 1157.74024
MathSciNet: MR2498781
Digital Object Identifier: 10.7546/jgsp-12-2008-75-92

Rights: Copyright © 2008 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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