On the Precisely Uniform and Uniaxial Tensioning of a Film Sheet via Integrated Catenary

Abstract

The conditions for and practicability of the stretching of a £lm sheet in a precisely uniaxial and uniform manner by tension cords (“catenaries”) integrated with the sheet edges is investigated. It is shown that kinematic incompatibility between membrane and cord renders such suspension impossible for shallow catenary sections where the edge curve is suf£ciently close to the direction of £lm Poisson contraction. This region of incompatibility is de£ned by the cord geometry and the membrane Poisson’s ratio. A design solution to permit uniformly uniaxial suspension despite this limitation, whereby the shallow cord (section) is replaced with a compressive arch, is investigated. Arch stability is considered and is placed in the context of a speci£c hardware con£guration. Scope is limited to material isotropy and linear elasticity in two dimensions. Nomenclature