Kirchhoff’s Problem of Helical Equilibria of Uniform Rods

Autor: Nadia Chouaieb, John H. Maddocks
Rok vydání: 2004
Předmět:
Zdroj: Journal of Elasticity. 77:221-247
ISSN: 1573-2681
0374-3535
DOI: 10.1007/s10659-005-0931-z
Popis: It is demonstrated that a uniform and hyperelastic, but otherwise arbitrary, nonlinear Cosserat rod subject to appropriate end loadings has equilibria whose center lines form two-parameter families of helices. The absolute energy minimizer that arises in the absence of any end loading is a helical equilibrium by the assumption of uniformity, but more generally the helical equilibria arise for non-vanishing end loads. For inextensible, unshearable rods the two parameters correspond to arbitrary values of the curvature and torsion of the helix. For non-isotropic rods, each member of the two-dimensional family of helical center lines has at least two possible equilibrium orientations of the director frame. The possible orientations are characterized by a pair of finite-dimensional, dual variational principles involving pointwise values of the strain-energy density and its conjugate function. For isotropic rods, the characterization of possible equilibrium configurations degenerates, and in place of a discrete number of two-parameter families of helical equilibria, typically a single four-parameter family arises. The four continuous parameters correspond to the two of the helical center lines, a one-parameter family of possible angular phases, and a one-parameter family of imposed excess twists.
Databáze: OpenAIRE
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