Geometric effects of cross sections on equilibrium of helical and twisted ribbon

doi:10.1007/s10483-017-2182-6

Abstract

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 crosssectional 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.

Key words: closed-cell foam, plate vibration, natural frequency, cell volume distribu-tion, effective Young’s modulus, scale factor, pitch angle, Euler-Lagrange equation, twisting angle, elastic rod model, helical and twisted ribbon

2010 MSC Number:

Ye XIAO, Zaixing HUANG. Geometric effects of cross sections on equilibrium of helical and twisted ribbon. Applied Mathematics and Mechanics (English Edition), 2017, 38(4): 495-504.

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