Zusammenfassung Englisch Origami, the age-old art of folding intricate three-dimensional structures from flat material, has found numerous applications in e. This thesis investigates the axial compressibility of cylindrical origami, i.
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 hard single sheet origami 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 hard single sheet origami to axial compression.