4D Printing for Freeform Surfaces: Design Optimization of Origami and Kirigami Structures

A self-folding structure fabricated by additive manufacturing can be automatically folded into a demanding 3D shape by actuation mechanisms such as heating. However, 3D surfaces can only be fabricated by self-folding structures when they are flattenable. Most generally designed parts are not flattenable. To address the problem, we develop a shape optimization method to modify a non-flattenable surface into flattenable. The shape optimization framework is equipped with topological operators for adding interior/boundary cuts to further improve the flattenability. When inserting cuts, selfintersection is locally prevented on the flattened 2D pieces. The total length of inserted cuts is also minimized to reduce artifacts on the finally folded 3D shape.