Deformation of Thin Elastic Rod Under Large Deflections

2018 ◽  
pp. 185-196
Author(s):  
V. S. Zhernakov ◽  
V. P. Pavlov ◽  
V. M. Kudoyarova
Keyword(s):  
Large Deflections ◽  
Elastic Rod ◽  
Thin Elastic Rod

Cantilever Rod in Cross Wind

1989 ◽  
Vol 56 (3) ◽  
pp. 639-643 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Numerical Integration ◽  
Large Deformation ◽  
Aerodynamic Drag ◽  
Flexural Rigidity ◽  
Relative Importance ◽  
Elastic Rod ◽  
Nondimensional Parameter ◽  
Cantilever Rod ◽  
Thin Elastic Rod

A thin elastic rod is held at one end in a strong cross wind. The nonlinear large deformation equations are formulated and solved by perturbation and numerical integration. The problem is governed by a nondimensional parameter K representing the relative importance of aerodynamic drag to flexural rigidity. For large K, phenomena such as nonuniqueness, instability, and hysteresis may occur.

The shape of a Möbius band

1993 ◽  
Vol 440 (1908) ◽  
pp. 149-162 ◽  
Keyword(s):  
Aspect Ratio ◽  
Asymptotic Solution ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Elastic Rods ◽  
Large Deflections ◽  
Mechanical Equilibrium ◽  
Elastic Rod ◽  
Flexible Material ◽  
Möbius Band

The shape of a Möbius band made of a flexible material, such as paper, is determined. The band is represented as a bent, twisted elastic rod with a rectangular cross-section. Its mechanical equilibrium is governed by the Kirchhoff–Love equations for the large deflections of elastic rods. These are solved numerically for various values of the aspect ratio of the cross-section, and an asymptotic solution is found for large values of this ratio. The resulting shape is shown to agree well with that of a band made from a strip of plastic.

PHYSICAL REALIZATION OF THE JIMBO-MIWA THEORY OF THE MODIFIED KORTEWEG-DE VRIES EQUATION ON A THIN ELASTIC ROD: FERMIONIC THEORY

1995 ◽  
Vol 10 (22) ◽  
pp. 3091-3107 ◽  
Author(s):  
SHIGEKI MATSUTANI
Keyword(s):  
Dimensional Space ◽  
Mkdv Equation ◽  
Dirac Field ◽  
Elastic Rod ◽  
Bilinear Method ◽  
Physical Relation ◽  
De Vries ◽  
Lax Operator ◽  
Thin Elastic Rod ◽  
Hirota Bilinear

Recently we found that the Dirac operator on a thin elastic rod is identical with the Lax operator of the modified Korteweg-de Vries (MKdV) equation while the thin elastic rod is governed by the MKdV equation. In this article, we will show the physical relation between the Hirota bilinear method and the Dirac field in a thin rod on two-dimensional space, along the lines of the Jimbo-Miwa construction of the MKdV soliton.

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