Publication
Shape-morphing structures can transform between multiple geometric configurations, enabling a wide range of applications in architecture, robotics, personalizable medical devices, emergency shelters, and space technology. This thesis presents computational inverse design frameworks that incorporate geometric insights and physics-based simulation for three novel shape-morphing structures: 3D weaving with curved ribbons, umbrella meshes, and surface-based inflatables. Our method leverages the potential of digital fabrication technology and optimizes the geometry of the fabrication states to encode the 3D shape, motion, and functionality of these structures.
In 3D weaving, we construct smooth free-form surface structures using optimized curved ribbons. By optimizing the geometry of planar ribbons, we obtain assemblies of interwoven ribbons that closely approximate a large variety of target surfaces and that settle reliably back into the target shapes even after external deformation. Umbrella meshes are a new type of volumetric deployable structure that transforms from a compact block into a bending-active 3D surface. We employ insights from conformal geometry to find good initializations for the design parameters. Then we apply numerical optimization to improve the design such that the deployed structures encode both the intrinsic and extrinsic curvature of the target surfaces. Surface-based inflatables are composed of two layers of nearly inextensible sheet material joined together along carefully selected fusing curves. We build a computational framework that employs numerical homogenization to characterize the behavior of parametric families of periodic inflatable patches. We create a database of geometrically diverse fusing patterns and develop a two-scale optimization method to search for fusing curves with good structural properties such that the inflated structures with these fusing curves best approximate input target surfaces.
For each shape-morphing structure, we first apply geometric abstractions to explain their unique transformation behavior and gain intuition into efficiently exploring the design space. We then develop robust simulation algorithms to model the complex interaction between the elastic components of these structures. By employing unit-cell-based analysis, we characterize the effective design parameters and create databases of unit cells with mappings from their geometric features to mechanical properties. Our inverse design algorithms integrate these simulation methods and unit-cell analysis to globally optimize the geometry of the fabrication states. In addition to improving each material system and enabling specific applications in architecture and mechanical engineering, these computational approaches also yield fundamental contributions in numerical analysis and optimization algorithms. We validate our approach through a series of physical prototypes and design studies to demonstrate the broad range of new woven g