Deformations of a clamped–clamped elastica inside a circular channel with clearance

In this paper, we study the planar deformations of an elastica inside a circular channel with clearance. One end of the elastica is fully clamped, while the other end is partially clamped in the lateral direction and is subject to a pushing force longitudinally. In the experiment we first observe various deformation patterns after pushing the elastica through the partial clamp. Both symmetric and asymmetric deformations are recorded. Special attention is focused on the contact conditions between the elastica and the circular channel. In order to analyze the elastica deformation theoretically, we first divide the elastica into several elementary sub-domains depending on the contact condition between the elastica and the circular channel. In each sub-domain the elastica is either loaded only at the ends or in full contact with the outer wall. Armed with these basic equilibrium analyses, we proceed to calculate and classify the loaded elastica into several deformation patterns. Finally, we present the load-deflection curves, both theoretically and experimentally, which relate the longitudinal forces at both ends to the elastica length increase inside the channel. The branching phenomena predicted theoretically agree fairly well quantitatively with the experimental measurements.