Origami and tensegrity: structures and metamaterials
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Multi-functional structural systems are ubiquitous in nature, with potential applications across scales: from deployable outer space structures, to transformable multi-role robots, and to microstructures of metamaterials. To achieve the desired functionality, the system has to be able to change its behavior on demand, which usually involves programmable physical states, such as geometry, and stress distribution. Compared to other reconfigurable and programmable structural systems, such as membranes and truss frames, the present understanding of origami and tensegrity is incipient and thus there is room for further investigation and great creativity – this is the focus of this thesis. Both origami and tensegrity are deeply rooted in art, and are found to abound in nature under various forms, implying their exclusive performance as multi-functional platforms. Thus, we study the mechanics and physics of origami and tensegrity while emphasizing their subtle artistic connection. We explore their potential applications to reconfigurable structures and programmable metamaterials by means of examples of informative and illuminative designs. For instance, we demonstrate that by harnessing rigid and non-rigid folding of origami, we can generate a globally smooth hyperbolic paraboloid surfaces by folding a flat sheet; we can design metamaterials with arbitrary Poisson's ratio; and we can obtain programmable multi-stable structures and metamaterials. We also show that the mechanical properties of origami assemblages can be very sensitive to geometric imperfections. Moreover, by taking advantage of the prestress within tensegrity systems, we can deploy a stable structural platform of desired geometry from an unstable and compact assembly; we can create metamaterials whose elastostatic and elastodynamic properties are responsively tunable to changing prestress level, which provides a new dimension of programmability beyond geometry. The aforementioned findings open new avenues enabling their exploration beyond the realm of this thesis, while laying the path to unanticipated interdisciplinary discoveries.