Deployable gridshells are lightweight structures made of interconnected elastic beams. They can be actuated from a compact state to a freeform and volume-enclosing deployed shape. This thesis introduces C-shells, a novel class of deployable gridshells, which employs curved elastic rods connected at single-axis rotational joints. As opposed to their straight counterparts, C-shells are guaranteed to be assembled in a planar and stress-free configuration while showing a wide diversity in their deployed shapes. They may serve as temporary shelters, pavilions, or on a smaller scale, as deployable furniture or decorative elements.

This thesis presents a comprehensive framework for the forward exploration of C-shell designs, enabling designers to interactively search the shape space and generate deployable structures with diverse appearances and topologies. The framework combines human-interpretable manipulations of a reference linkage with an efficient physics-based simulation to predict the deployed shape and mechanical behavior of the structure. Preservation of the linkage deployability and smoothness of the edits are ensured through the use of conformal maps as design handles. The framework is implemented as a Rhino-Grasshopper plugin, providing visual and quantitative real-time feedback on the deployed state.

The inverse design of C-shells is also addressed, where the deployed shape is given, and the flat state of the structure is computed. This thesis introduces a two-step pipeline composed of a flattening method and a design optimization algorithm. The flattening algorithm is based on kinematic considerations underlying the deployment of C-shell. The method harmonizes a flat and a hypothetical deployed state constrained on a user-prescribed target surface. The flat beam layout is further adjusted to minimize the deviation of the deployed shape to the target surface while ensuring a low elastic energy deployed state, under some beam smoothness regularization. The proposed method is validated through scanned small-scale prototypes.

C-shells are made of curved rods, which entails additional material waste compared to straight beams. To address this issue, this thesis presents a rationalization method that splits the curved beams into smaller straight elements which can be grouped into a sparse kit of parts, while preserving user-provided designs. The original combinatorial problem of jointly assigning parts to elements and adapting the parts' geometry is relaxed into a two-step optimization process incorporating our physics-based simulation, making it tractable using continuous optimization techniques. The proposed method applies more generally to bending-active structures and is further demonstrated on orthogonal gridshells and umbrella meshes. Part reuse is assessed in a study of the trade-off between the number of parts and fidelity to the input designs.