Inverse design of deployable origami structures that approximate a general surface

Abstract

Shape-morphing finds widespread utility, from the deployment of small stents and large solar sails to actuation and propulsion in soft robotics. Origami structures provide a template for shape-morphing, but rules for designing and folding the structures are challenging to integrate into broad and versatile design tools. Here, we develop a sequential two-stage optimization framework to approximate a general surface by a deployable origami structure. The optimization is performed over the space of all possible rigidly and flat-foldable quadrilateral mesh origami. So, the origami structures produced by our framework come with desirable engineering properties: they can be easily manufactured on a flat reference sheet, deployed to their target state by a controlled folding motion, then to a compact folded state in applications involving storage and portability. The attainable surfaces demonstrated include those with modest but diverse curvatures and unprecedented ones with sharp ridges. The framework provides not only a tool to design various deployable and retractable surfaces in engineering and architecture, but also a route to optimizing other properties and functionality.

arXiv comment45 pages, 11 figures

References in corpus (12)

• Point-Set Registration: Coherent Point Drift
• Programming Curvature using Origami Tessellations
• Geometric Mechanics of Periodic Pleated Origami
• Making Faces: Universal Inverse Design of Surfaces with Thin Nematic Elastomer Sheets
• The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami
• Programmed buckling by controlled lateral swelling in a thin elastic sheet
• Helical Miura Origami
• Curved geometries from planar director fields - Solving the two-dimensional inverse problem
• Programming complex shapes in thin nematic elastomer and glass sheets
• An additive algorithm for origami design
• Hidden symmetries generate rigid folding mechanisms in periodic origami
• Origami and materials science

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• Origami and materials science
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• Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity
• Bistability and equilibria of creased annular sheets and strips
• Flexible Kokotsakis Meshes with Skew Faces: Generalization of the Orthodiagonal Involutive Type
• A continuum geometric approach for inverse design of origami structures
• 2D-to-3D transformation of ring origami via snap-folding instabilities
• Area preserving Combescure transformations
• Lorentz transformation for the kinematics of degree-4 rigid origami vertices and compatibility of rigid-foldable polygons
• Lagrangian approach to origami vertex analysis: Kinematics
• Explosive rigidity percolation in origami