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Title:Thermomechanics of helical strands and helical-fiber-reinforced rods
Author(s):Zhang, Dansong
Director of Research:Ostoja-Starzewski, Martin
Doctoral Committee Chair(s):Ostoja-Starzewski, Martin
Doctoral Committee Member(s):Masud, Arif; Gazzola, Mattia; Sinha, Sanjiv
Department / Program:Mechanical Sci & Engineering
Discipline:Mechanical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
bending stiffness
Timoshenko rod
finite element analysis
thermomechanical constitutive relation
bending-shearing coupling
thermal-torsional coupling
thermoelastic wave
adiabatic-isothermal transition
telegraph equation
phase velocity
group velocity
spectral finite element
Maxwell-Cattaneo heat conduction
dispersion relation
thermal relaxation time
Abstract:Helical strands, or helically wound cables, are made of layers of individual wires wrapped around a common central axis. They are seen in ropes and power transmission cables. Similar structures are also present in biological tissues in the form of helical fiber reinforced composites. Regardless of the distinct applications, the helical wrapping in all such structures introduces mirror asymmetry, i.e. chirality, resulting in effective properties not present in the base material. One most prominent effect of the presence of helices is the coupling between tension and torsion, which is widely modeled and studied in the literature. However, complex issues arise when there is bending. First, the effective bending stiffness is difficult to estimate and existing analytical models require careful validation. We conduct a full-fledged finite element analysis of the bending of a single layered helical strand, with internal friction and pretension. The effects of the pretension level, bending amplitude, and the friction coefficient on the effective bending stiffness are elucidated. Second, in the no-slip regime, the existing Euler-Bernoulli framework for helical strands is extended. A Timoshenko rod model is established for helical strands, with a 6 by 6 stiffness matrix governed by five independent elastic moduli. The model is capable of capturing the bending-shearing coupling in helical strands due to the underlying chirality, and correctly predicting the cross section forces and moments under several boundary value problems when compared with finite element results, whereas the existing Euler-Bernoulli model wrongly predicts particular forces or moments to be zero. The bending-shearing coupling is also demonstrated by the non-planar bending of helical strands under a single transverse force, or a single bending moment. The equations of vibration are then derived, with the eigenfrequencies and mode shapes identified. Due to chirality, the longitudinal and torsional modes are coupled, as are the bending-shearing modes in the two principal directions of the cross section. The Timoshenko rod model for helical strands is further extended by considering thermal expansion. The finite element analysis demonstrates a coupling between thermal expansion and torsion, due to the structural chirality, which is also incorporated into the final form of the thermomechanical constitutive relation of helical strands. With the thermomechanical constitutive relation, the thermoelastic waves in a helical strand are solved. With Fourier-type heat conduction, the thermelastic wave solutions are governed by four non-dimensional parameters: two thermoelastic coupling constants (in the longitudinal and torsional directions), a chirality parameter, and the Fourier number. The longitudinal and the torsional waves are dispersive and damped, and are dependent on the temperature. The adiabatic-isothermal transition of the wave propagation is dictated by the Fourier number. With Maxwell-Cattaneo-type heat conduction, the heat propagation follows a hyperbolic differential equation, with the heat wave celerity depending on the thermal relaxation $\tau$. The full thermoelastic wave solutions for helical strands are governed by a sixth-order algebraic equation. An additional non-dimensional parameter comes into play; it characterizes the speed of heat propagation compared with that of mechanical perturbations. The solutions show distinct behaviors for fast heat propagation v.s. slow heat propagation.
Issue Date:2018-12-07
Rights Information:Copyright 2018 Dansong Zhang
Date Available in IDEALS:2019-02-08
Date Deposited:2018-12

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