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This paper directly links the abstract geometry of structural form-finding to the fabrication-aware design of discrete shells and spatial structures for 3D concrete printing through a bidirectional approach, where it creates surface-toolpath twins for the components, optimizing the buildability of the parts and their surface quality. The design-to-production process of efficient structural systems for 3D printing is often a top-down unidirectional process involving form-finding, segmentation, and slicing, where results face printability challenges due to incompatibility between the initial geometry and the printing system, as well as material constraints. We introduce surface-toolpath twins that can be interconverted and synchronized through efficient slicing and surface reconstruction algorithms to allow the combination of optimizations and modifications on either part of the twin in flexible orders. We provide two core methods for fabrication rationalization: (1) global buildability optimization on the surface mesh by normal-driven shape stylization and (2) local surface quality optimization on toolpath curves through intra-layer iterative adjustments. The result is a bidirectional design-to-production process where one can plug and play different form-finding results, assess and optimize their fabrication schemes, or leverage knowledge in fabrication design, model toolpath curves as sections, reconstruct surfaces, and merge them into form-finding and segmentation in an inverse way. The proposed framework enables the integration of form-finding expertise with fabrication-oriented design, allowing the realization of spatial shell structures with complex topologies or extreme geometrical features through 3D concrete printing. 

Space frames are widely used in spatial constructions as they are lightweight, rigid, and efficient. However, when it comes to the complex and irregular spaces frames, they can be difficult to fabricate because of the uniqueness of the nodes and bars. This paper presents a novel timber space frame system that can be easily manufactured using 3-axis CNC machines, and therefore increase the ease of the design and construction of complex space frames. The form-finding of the space frame is achieved with the help of polyhedral graphic statics (PGS), and resulted form has inherent planarity which can be harnessed in the materialization of the structure. Inspired by the traditional wood tectonics kerf bending and zippers are applied when devising the connection details. This system's design approach and computational process are described, and a test fabrication of a single node is made via 3-axis CNC milling and both physically and numerically tested. The structural performance shows its potential for applications in large-scale spatial structures. 

Shellular Funicular Structures (SFSs) are single-layer, two-manifold structures with anticlastic curvature, designed in the context of graphic statics. They are considered as efficient structures applicable to many functions on different scales. Due to their complex geometry, design and fabrication of SFSs are quite challenging, limiting their application in large scales. Furthermore, designing these structures for a predefined boundary condition, control, and manipulation of their geometry are not easy tasks. Moreover, fabricating these geometries is mostly possible using additive manufacturing techniques, requiring a lot of support in the printing process. Cellular funicular structures (CFSs) as strut-based spatial structures can be easily designed and manipulated in the context of graphic statics. This paper introduces a computational algorithm for translating a Cellular Funicular Structure (CFS) to a Shellular Funicular Structure (SFS). Furthermore, it explains a fabrication method to build the structure out of a flat sheet of material using the origami/ kirigami technique as an ideal choice because of its accessibility, processibility, low cost, and applicability to large scales. The paper concludes by displaying a design and fabricated structure using this technique. 

The recent development of three-dimensional graphic statics using polyhedral reciprocal diagrams (PGS) has greatly increased the ease of designing complex yet efficient spatial funicular structural forms, where the inherent planarity of the polyhedral geometries can be harnessed for efficient construction processes. Our previous research has shown the feasibility of leveraging this planarity in materializing a 10m-span, double-layer glass bridge made of 1cm glass sheets. This paper presents a smaller bridge prototype with a span of 2.5m to address the larger bridge’s challenges regarding form-finding, detail developments, fabrication constraints, and assembly logic. The compression-only prototype is designed for prefabrication as a modular system using PolyFrame for Rhinoceros. Thirteen polyhedral cells of the funicular bridge are materialized in the form of hollow glass units (HGUs) and can be prefabricated and assembled on-site. Each HGU consists of two deck plates and multiple side plates held together using 3M™ Very High Bond (VHB) tape. A male-female glass connection mechanism is developed at the sides of HGUs to interlock each unit with its adjacent cells to prevent sliding. A transparent interface material is placed between the male and female connecting parts to avoid local stress concentration. This novel construction method significantly simplifies the bridge’s assembly on a large scale. The design and construction of this small-scale prototype set the foundation for the future development of the full-scale structure.