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- Title
Geometric effects of cross sections on equilibrium of helical and twisted ribbon.
- Authors
Xiao, Ye; Huang, Zaixing
- Abstract
In the framework of elastic rod model, the Euler-Lagrange equations characterizing the equilibrium configuration of the polymer chain are derived from a free energy functional associated with the curvature, torsion, twisting angle, and its derivative with respect to the arc-length. The configurations of the helical ribbons with different cross-sectional shapes are given. The effects of the elastic properties, the cross-sectional shapes, and the intrinsic twisting on the helical ribbons are discussed. The results show that the pitch angle of the helical ribbon decreases with the increase in the ratio of the twisting rigidity to the bending rigidity and approaches the intrinsic twisting. If the bending rigidity is much greater than the twisting rigidity, the bending and twisting of the helical ribbon always appear simultaneously.
- Subjects
NUCLEAR cross sections; ELASTIC rods &; wires; EULER-Lagrange equations; RIBBONS; EQUILIBRIUM; FREE energy (Thermodynamics)
- Publication
Applied Mathematics & Mechanics, 2017, Vol 38, Issue 4, p495
- ISSN
0253-4827
- Publication type
Article
- DOI
10.1007/s10483-017-2182-6