Mechanics of Systematically Creased Thin-Film Membrane Structures

Abstract

This paper presents a study of a square membrane with speciflc dimensions and creases arranged according to the Miura-ori folding pattern. The stress distribution and the loaddisplacement relationship for in-plane, diagonal loading of the corners is determined. An existing model for randomly-creased membranes (Murphey 2000), consisting of a network of creased beams, is shown to predict accurately the load-displacement relationship of the corners also in the present case. here is currently much interest in the use of thin-fllm membrane structures for a variety of future gossamer spacecraft missions. In some of the proposed structural architectures it is envisaged that the thin fllms will be packaged by means of a regular arrangement of creases, or fold lines, and hence the question arises of how such pre-creased foils behave when they are deployed in orbit. One method of packaging membranes for deployment in space is known as Miura-ori folding. An ideal Miura-ori surface is a mechanical linkage of ∞at plates that behaves like a single degree of freedom mechanism; a membrane folded such that the pattern of the resulting creases mimics the arrangement of the hinges in an ideal Miura-ori surface can be packaged and deployed e‐ciently (Horner and Elliott, 2002). Given these useful properties, the Miura-ori crease pattern was selected for the present research. This paper presents a detailed study |involving both detailed flnite-element simulations and experiments| of a square membrane with speciflc dimensions and creases arranged according to the Miura-ori folding pattern. The loading conflguration assumed was symmetric corner loading, with the magnitudes of the corner forces chosen such as to yield stress levels of the order of 0.01 N/mm 2 at the centre of a 25 „m thick membrane. Randomly-creased thin fllms have been extensively investigated by Murphey (2000), and the present study is an extension of that work to fllms where the creases are arranged systematically, according to a repeating pattern. The aim of our study is to determine the shape of the membrane and the loaddisplacement relationship for in-plane, diagonal loading of the corners, starting from a conflguration that might be considered as the unstressed deployed shape of the membrane. We show that Murphey’s model of randomly-creased membrane, consisting of a network of creased beams, predicts accurately the displacements of the corners also in the present case. The paper is laid out as follows. Section II describes the results from flnite element modelling of a systematically wrinkled membrane with Miura-ori creases. Section III presents a series of experimental results and compares them to flnite element results. Finally, Section IV presents a theoretical model for the membrane’s load-displacement behaviour. The theoretical results are then compared to the flnite element results.