Analysis of Cross Folding an Elastic Sheet

Abstract

Large antenna reflectors used in space have to be folded before launching. Silicone rubber is commonly used as antenna material due to its ability to maintain a shape without external supports upon deployment. However, localized vertices could appear during the folding process, which might lead to material yielding and unrecoverable deformation after deployment. In this paper, the cross folding process of a thin elastic sheet, a common folding method in packaging a reflective membrane, was studied numerically with the aim of eliminating material failure in the sheet. The deformation, stress distribution, and peak stress of the sheet and the dependency of those properties on geometrical parameters were systematically investigated. Based on these studies, two methods, i.e., central hole method and central slit method, were explored to reduce the peak stress caused by cross folding. The results showed that a central slit parallel to the first folding crease was the most effective in reducing the peak stress without causing significant damage to the antenna.

Design of Hinge-Line Geometry to Facilitate Non-Plastic Folding in Thin Metallic Origami-Inspired Devices

“…Compared with conventional, rotational hinges and other mechanical hinges, membrane hinges are easily manufactured and assembled (Crampton, Magleby, & Howell, 2017). Some work has been done to study the geometry of the crease (Nguyen, Terada, Tokura, & Hagiwara, 2015;Hou, Ma, Chen, & You, 2017) and…”

“…how the membrane material folds under a prescribed type of loading (displacement controlled or force controlled) (Nguyen et al, 2015;Hou et al, 2017), however, there has not been a study to compare hinge stress and deformation across different loading conditions. Even though elastic sheet bending theories and various compliant beam bending theories (Greenberg et al, 2011;Howell, Magleby, & Olsen, 2013) provides a basic idea as to how crease geometry should be designed, there are many questions to be answered to facilitate using any particular thin sheet as simple membrane hinges.…”

“…-3: stress distribution of a cross folded membrane (2) effects of thickness on folding(Hou et al, 2017) …”