Lock-on to tape-like behaviour in the torsional buckling of anisotropic rods
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Cited by (33)
A discrete differential geometry-based numerical framework for extensible ribbons
2022, International Journal of Solids and StructuresShear induced supercritical pitchfork bifurcation of pre-buckled bands, from narrow strips to wide plates
2020, Journal of the Mechanics and Physics of SolidsBifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations
2019, Journal of the Mechanics and Physics of SolidsCitation Excerpt :Theory, numerics, and experiment show that circular cross section rods, an integrable system, when subject to such boundary conditions will buckle, hockle into a loop, or snarl into a self-contacting twisted structure (Coleman et al., 1995; Coyne, 1990; Goss et al., 2005; Goyal et al., 2005; van der Heijden et al., 2003; van der Heijden and Thompson, 2000; Miyazaki and Kondo, 1997; Thompson and Champneys, 1996; Yabuta et al., 1982). Anisotropic rods, those with preferred bending directions, display even more complicated and potentially non-integrable behavior due to non-conserved twist (Béda et al., 1992; Buzano, 1986; Champneys and Thompson, 1996; Goriely et al., 2001; van der Heijden and Thompson, 1998; Mielke and Holmes, 1988). van der Heijden and Thompson (1998) distinguish between weakly anisotropic and strongly anisotropic “tape-like” behavior such as that we will discuss in this paper.
Deformation and vibration of a spatial clamped elastica with noncircular cross section
2014, European Journal of Mechanics, A/SolidsCitation Excerpt :This implies the existence of a smooth manifold of localized buckling solutions. In the case of noncircular cross section, the integrability is lost and the manifold splits; see Champneys and Thompson (1996), van der Heijden et al. (1998), and van der Heijden and Thompson (1998). Compared to static analysis, the studies on the vibration of spatial elastica are relatively rare.
Homoclinic complexity in the localised buckling of an extensible conducting rod in a uniform magnetic field
2014, Physica D: Nonlinear PhenomenaCitation Excerpt :Concluding remarks are made in Section 5. The Hamiltonian–Hopf bifurcation is known to mark buckling in the classical anisotropic rod [10,14]. From normal-form analysis of this bifurcation one generically expects homoclinic orbits to exist near the Hamiltonian–Hopf curve, on the side where the complex quadruple of eigenvalues occurs if the bifurcation is subcritical [14,15].
Instability and self-contact phenomena in the writhing of clamped rods
2003, International Journal of Mechanical Sciences