Alignable lamella gridshells

Alignable lamella gridshells are 3D grid structures capable of collapsing into a planar strip. This feature significantly simplifies on-site assembly and also ensures compactness for efficient transport and storage. However, designing these structures still remains a challenge. This paper tackles the inverse design problem of alignable lamella gridshells leveraging concepts from differential geometry and Cartan's theory of moving frames. The study unveils that geodesic alignable gridshells, where lamellae are disposed tangentially to the surface, are limited to forming shapes isometric to surfaces of revolution. Furthermore, it demonstrates that alignable gridshells with lamellae arranged orthogonally to a surface can be realized only on a specific class of surfaces that meet a particular curvature condition along their principal curvature lines. Finally, drawing on these theoretical findings, this work introduces novel computational tools tailored for the design of these structures.