Section Shear Between Straight Ribs in Spirally Stowed Sheets

摘要

Since, a quarter of a century ago, Temple proposed a spirally tessellated pattern to fold a thin sheet and Guest studied how to apply this concept to sheets of finite thickness, the idea to wrap a deployable surface on a hub for stowage has attracted ever increasing interest in the space industry. The applications proposed include solar sail membranes, photovoltaic arrays, photon sieves, and even doubly curved reflector dishes. Derivatives of the concept have been developed and ribs for the lateral stiffening of the deployed disk have also been proposed. However, the engineering understanding of this concept is still lacking: despite many examples of its use, simple tools to aid quantitative design are hard to find. In order to contribute to bridging this gap, the present paper offers a method to estimate the shear that develops during roll-up in the sheet if the latter is divided into sections by straight ribs that are embedded in the stowage roll when packaged.