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This work presents innovative origami optimization methods for the design of unit cells for complex origami tessellations that can be utilized for the design of deployable structures. The design method used to create origami tiles utilizes the principles of discrete topology optimization for ground structures applied to origami crease patterns. The initial design space shows all possible creases and is given the desired input and output forces. Taking into account foldability constraints derived from Maekawa's and Kawasaki's theorems, the algorithm designates creases as active or passive. Geometric constraints are defined from the target 3D object. The periodic reproduction of this unit cell allows us to create tessellations that are used in the creation of deployable shelters. Design requirements for structurally sound tessellations are discussed and used to evaluate the effectiveness of our results. Future work includes the applications of unit cells and tessellation design for origami inspired mechanisms. Special focus will be given to self-deployable structures, including shelters for natural disasters.
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Topological kinematics of origami metamaterials
A variety of electronic phases in solid-state systems can be understood by abstracting away microscopic details and refocusing on how Fermi surface topology interacts with band structure to define available electron states1. In fact, topological concepts are broadly applicable to non-electronic materials and can be used to understand a variety of seemingly unrelated phenomena2,3,4,5,6. Here, we apply topological principles to origami-inspired mechanical metamaterials7,8,9,10,11,12, and demonstrate how to guide bulk kinematics by tailoring the crease configuration-space topology. Specifically, we show that by simply changing the crease angles, we modify the configuration-space topology, and drive origami structures to dramatically change their kinematics from being smoothly and continuously deformable to mechanically bistable and rigid. In addition, we examine how a topologically disjointed configuration space can be used to constrain the locally accessible deformations of a single folded sheet. While analyses of origami structures are typically dependent on the energetics of constitutive relations11,12,13,14, the topological abstractions introduced here are a separate and independent consideration that we use to analyse, understand and design these metamaterials.
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- Award ID(s):
- 1706511
- PAR ID:
- 10058688
- Date Published:
- Journal Name:
- Nature Physics
- ISSN:
- 1745-2473
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We consider the zero-energy deformations of periodic origami sheets with generic crease patterns. Using a mapping from the linear folding motions of such sheets to force-bearing modes in conjunction with the Maxwell–Calladine index theorem we derive a relation between the number of linear folding motions and the number of rigid body modes that depends only on the average coordination number of the origami’s vertices. This supports the recent result by Tachi [T. Tachi,Origami6, 97–108 (2015)] which shows periodic origami sheets with triangular faces exhibit two-dimensional spaces of rigidly foldable cylindrical configurations. We also find, through analytical calculation and numerical simulation, branching of this configuration space from the flat state due to geometric compatibility constraints that prohibit finite Gaussian curvature. The same counting argument leads to pairing of spatially varying modes at opposite wavenumber in triangulated origami, preventing topological polarization but permitting a family of zero-energy deformations in the bulk that may be used to reconfigure the origami sheet.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1038/s41567-018-0150-8
