Designing Fractal Origami Tessellations Through Eigen Analysis

This article investigates a method of designing fractal origami tessellations through eigen analysis. Foldable structures with hierarchical geometric features could be beneficial in applications where a graded functionality is desired. A representative unit in an origami tessellation is modeled as networked truss elements with torsional springs at fold lines. Eigen analysis and nonlinear mechanics analysis of the representative unit with fractal boundary conditions reveal the foldability of a given fractal origami crease pattern out of its flat state. This configuration can be used to construct a folded fractal origami tessellation with a desired number of fractal levels, which can then be used to evaluate its functional merit. The design process is demonstrated for the design of a fractal origami tessellation with tailored boundary shape change (from rectangular to trapezoidal) through folding, that could be used as an enabling mechanism for an adaptive wing section.