Stiff Elastic Tape Wrapped Onto a Drum

Abstract

A nonlinear analysis is presented to describe the static equilibrium of a long elastic tape wrapped onto a rigid drum. Closed-form results are obtained for the case when the tape can be modeled as an inextensional beam with finite bending rigidity. Strains are assumed to be small, but rotations of the beam may be arbitrarily large. The tape’s stiffness in bending requires the abandonment of a common modeling assumption—that the tape approaches the drum along a perfectly straight tangent. After calculating the actual shape of the elastica, a number of changes are seen to occur in the loading and geometry of the system. Among these are a lower tape tension at the point of tape/drum contact, an increased torque on the drum, and the introduction of an elastic compliance between the drum and distant locations in the tape.