Inverse design of a suspended Kirchhoff rod: From theory to practice - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2019

Inverse design of a suspended Kirchhoff rod: From theory to practice

Abstract

Our study focuses on finding the natural shape of a given hanging deformed isotropic rod, made of a known material, the input shape is described as a mere geometric curve that we subsequently frame to compute a material curvature field and feed our inverse problem. We prove that the natural shape of the rod satisfying equilibrium exists and is unique, regardless of the infinity compatible frames for the input curve. The natural shape is computed efficiently by solving in sequence three linear initial value problems. We illustrate our theoretical results trough numerical examples of well known curves to which we apply our inverse procedure. By direct simulation we show that indeed those natural shapes fall, under the effect of gravity, onto the expected equilibrium. We stress on the fact that the obtained rest shapes are complex and far from intuitive. Finally, we complement this study with experimental corroborations. By means of a standard array of cameras, we spatially reconstruct real elastic hanging rods with well-defined geometrical features. We find some good agreements with model prediction despite the experimental limitations on the estimation of the curvature fields of the rod’s center line.
Fichier principal
Vignette du fichier
APS_2019_abstract.pdf (41.89 Ko) Télécharger le fichier
Vignette du fichier
APS2019.png (261.77 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Format : Figure, Image
Licence : CC BY - Attribution

Dates and versions

hal-01981923 , version 1 (07-04-2021)

Identifiers

  • HAL Id : hal-01981923 , version 1

Cite

Victor Romero, Florence Bertails-Descoubes, Alexandre Derouet-Jourdan, Arnaud Lazarus. Inverse design of a suspended Kirchhoff rod: From theory to practice. APS 2019 - American Physical Society March Meeting, Mar 2019, Boston, United States. ⟨hal-01981923⟩
322 View
107 Download

Share

Gmail Facebook X LinkedIn More