Origami Cylinders

by Friedrich Bös
Doctoral thesis
Date of Examination:2017-07-06
Date of issue:2018-05-02
Advisor:Prof. Dr. Max Wardetzky
Referee:Prof. Dr. Max Wardetzky
Referee:Prof. Dr. Gert Lube
Referee:Ph.D. Etienne Vouga
Persistent Address: http://dx.doi.org/10.53846/goediss-6849

 

 

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Abstract

English

Origami, the age-old art of folding intricate three-dimensional structures from flat material, has found numerous applications in e.g. the design of deployable structures and mechanical metamaterials.  This thesis investigates the axial compressibility of cylindrical origami, i.e., cylindrical structures folded from a single rectangular sheet of paper. It is shown via purely geometric arguments that a general fold pattern has only finitely many strain-free cylindrical embeddings. Therefore, continuous deformations must either induce elastic strain or deform the preexisting folds. A counterexample shows that the obtained necessary flexibility conditions are sharp. The results restrict the space of possible constructions for designing rigid-foldable deployable structures and metamaterials. Despite this rigidity result, origami cylinders are nevertheless observed to compress apparently isometrically. In a second step, this apparent flexibility is modeled by replacing hard rigidity constraints with simple soft constraints in a way inspired by physical experiments, numerical simulations, and theoretical arguments. The resulting energy minimization problem is solved in two different ways: numerically using the particular geometry of the feasible set and qualitatively using topological arguments about the set of critical points. The results exhibit marked buckling phenomena reproducible in experiments, indicating a geometric as opposed to a physical origin. The model can be used for rapid prototyping in the design of foldable cylindrical structures with a prescribed strain response to axial compression.
Keywords: Origami; Deployable Structures; Rigid Origami; Computational Physics
 
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