Modeling Origami-Like Structures with Near Zero Stiffness: Modal Analysis and Crease/Wrinkle Correlations
Antonio F. Avila1; Fernanda L.R. Lima1; Guilherme C. Arantes1; Matheus Norton1; Marina Georgia M. Martins1
1 Universidade Federal de Minas Gerais
doi:10.20906/CPS/CILAMCE2017-0469
Resumo
The usage of origami techniques into space-structures, e.g. antennas, telescopes and solar panels, is a traditional approach employed for decades. These ultra-light space structures, in special Gossamer structures, are made of thin membranes made of polymeric composites with near zero stiffness. During the deploying process, traction forces are applied to specific locations. These locations and the deployment speed are two critical issues, as they may cause unexpected wrinkles and vibrations. As discussed by Wang et al (2011), wrinkles and creases in solar sails, for example, may reduce the thrust forces and introduce instabilities on control. Wrinkles and creases may also get large influence on surface accuracy of deployable antenna reflector. Thus, the structural analysis of these membrane structures must deal with the wrinkles, the creases, their interactions and influence into vibration frequencies and modes. This paper investigates the natural frequencies and vibration modes of two different space structures, i.e. the first one is a two dimensional structure based on Miura-Ori folding pattern (largely employed for solar panel), while the second structure is a tube-like structure following the Kresling folding pattern (commonly employed for antennas and telescopes). According to Dutta and Graham (2017), a Miura-patterned foldable sheet (also called as Miura- Ori) is a two-dimensional tessellation of unit cells, each made up of four identical facets in the shape of parallelograms. The facets are assumed to be infinitely thin and rigid. When completely folded, all the facets of the sheet are co-planar, i.e. the sheet folds flat. As described by Wilson et al (2013), Kresling cylindrical polyhedron consisting of two pairs of ring structures, at various stages of deployment. As the ring structures are folded, they become strained. During the deploying process, compression stresses are gradually replaced by the traction stresses. To be able to investigate the wrinkle and crease effect into natural freq
Palavras-chave: Thin structures; origami-like structures; finite element analysis; near zero stiffness