Partial constraint singularities in elastic rods

Abstract

We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions. Our approach encompasses both sleeve and adhesion problems, and provides simple and unambiguous derivations of counterintuitive results in the literature. Relationships between reaction forces and moments, geometry, and adhesion energies follow from the balance of energy during quasistatic motion. We also relate our approach to the balance of material momentum and the concept of a driving traction. The theory is generalizable and can be applied to a wide array of contact, adhesion, gripping, and locomotion problems.

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Cited by in corpus (8)

• Configurational forces and nonlinear structural dynamics
• Energy based methods applied in mechanics by using the extended Noether's formalism
• Nested Bloch waves in elastic structures with configurational forces
• Stabilization against gravity and self-tuning of an elastic variable-length rod through an oscillating sliding sleeve
• Planar equilibria of an elastic rod wrapped around a circular capstan
• Avoiding localization instabilities in rotary pleating
• Adhesive tape loops
• Self-contact in a buckled elastica