skip to main content


Title: From design to the fabrication of shellular funicular 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.  more » « less
Award ID(s):
1944691 2037097
NSF-PAR ID:
10314969
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proceedings of the Association for Computer-Aided Design in Architecture (ACADIA)
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. The authors of this research investigate the possibility of fabricating shell-based cellular structures using knitting techniques. Shellular Funicular Structures are two-manifold single-layer structures that can be designed in the context of graphic statics. These are efficient compression/tension-only structures that have been designed for a certain boundary condition. Although the shellular funicular structures are efficient geometries in transferring the forces, the fabrication process is challenging due to the geometric complexity of the structure. Since Shellular structures comprise a single surface, they are suitable candidates to be fabricated using knitting technique, a method by which yarn is manipulated to create a textile or fabric. Using knitting approach, one can fabricate shellular structures with minimum production waste in which the knit can work as a formwork for actual structure or act as a composite structure combined with bio-based resin. This research proposes a workflow to fabricate shellular structures using knitting that can be scaled up for industrial purposes. In this process, the designed shellular structures are divided into multiple sections that can be unrolled into planar geometries. These geometries are optimized based on the elastic forces in the knitted network and knitted and sewn to make a topologically complex geometry of the shellular systems. After assembling the knitted parts and applying external forces at the boundaries, the final configuration of the structural form in tension is achieved. Then this form is impregnated with custom bio-resin blends from chitosan, sodium alginate, and silk fibroin to stiffen the soft knit structures into a compressed system. Although this method is an efficient fabrication technique for constructing shellular structures, it needs to be translated into an optimized method of cutting, knitting, and sewing with respect to the complexity of the shellular geometry. As a proof of concept of the proposed workflow, a mesoscale shellular structure is fabricated. Keywords: Biocomposite Structures, Shellular Funicular Structures, Knitting, Graphic statics. 
    more » « less
  2. This paper introduces an interactive form-finding technique to design and explore continuous Shellular Funicular Structures in the context of Polyhedral Graphic Statics (PGS). Shellular funicular forms are two-manifold shell-based geometries dividing the space into two interwoven sub-spaces, each of which can be represented by a 3D graph named labyrinth [1]. Both form and force diagrams include labyrinths, and the form finding is achieved by an iterative subdivision of the force diagram across its labyrinths [2]. But this iterative process is computationally very expensive, preventing interactive exploration of various forms for an initial force diagram. The methodology starts with identifying three sets of labyrinth graphs for the initial force diagram and immediately visualizing their form diagrams as smooth and continuous surfaces. Followed by exploring and finalizing the desired form, the force diagram will be subdivided across the desired labyrinth graph to result in a shellular funicular form diagram (Figure 1). The paper concludes by evaluating the mechanical performance of continuous shellular structures compared to their discrete counterparts. 
    more » « less
  3. The recent development of three-dimensional graphic statics (3DGS) has greatly increased the ease of designing complex and efficient spatial funicular structural forms [1]. The reciprocal diagram based 3DGS approaches not only generate highly efficient funicular structures [2], but also result in planarity constraints due to the polyhedron nature of the reciprocal diagrams [3]. Our previous research has shown the feasibility of leveraging this planarity by using planar glass sheets to materialize the 10m-span, double-layer glass bridge [3]. This paper is framed as a proof of concept for the 10m bridge and explores the form-finding, detail configuration, fabrication constraints, and assembly logic by designing and constructing a small-scale bridge prototype with a span of 2.5m. The prototype is designed in a modular approach, where each polyhedral cell of the form is materialized using a hollow glass unit (HGU) (Figure 1a), which can be prefabricated and preassembled, and therefore, greatly simplifies the assembly of the whole bridge. The compression-only form of the prototype is generated using the PolyFrame beta [4] plug-in for Rhinoceros [5]. The form-finding is carried out with a comprehensive consideration of a variety of parameters, including fabrication constraints, assembly ease, construction cost, and practicality. To start the form-finding process, a group of closed convex force polyhedrons is aggregated, controlling the topology of the form diagram and the orientations of the form elements. By manipulating the face tilting angles of the force diagram, the supported edges at the end of the bridge are all made horizontal, reducing the difficulty of the support design. Then, vertex locations and edge lengths of the form diagram are constrained, determining the final dimensions of both the bridge and the cells. After getting the geometry of the bridge, the detail developments are streamlined. Each of the 13 HGUs consists of two flat deck plates and a series of side plates (Figure 1b). To interlock the adjacent cells and prevent possible sliding, a male-female connection mechanism is introduced to the conjoint side plates of the HGUs (Figure 1b). Additionally, to eliminate the direct contact of the glass parts and prevent the stress concentration, two softer transparent materials are involved for connecting purposes. Within each HGU, silicon-based binding agent is used to hold the glass parts together; between the neighboring HGUs, plastic sheets are placed as interface materials (Figure 1b). Figure 1. a) The 2.5m-span small-scale prototype dome, b) Exploded view showing deck plates, side plates, male-female connection, and interface material For the fabrication of the glass parts, 5-axis Waterjet cutting techniques are applied. While the glass sheets for the deck plates can be purchased from the market, the irregular side plates with male-female connections need to be made from kiln-cast glass. In terms of the Waterjet cutting constraints, there is a max cutting angle of 60 degrees from vertical. With respect to this, all the glass parts are examined during the design process to ensure they all satisfy the cutting angle requirements. Aiming to achieve a fast and precise assembly, several assistant techniques are developed. On the local HGU level, assembly connectors are designed and 3D-printed to help locate the glass parts. On the global prototype level, the assembly sequence of the HGUs are simulated to avoid interference. Besides, a labeling system is also established to organize the fabricated parts and guide the entire assembly process. The design and construction of this small-scale prototype provide important information for the future development of the full-scale bridge regarding the interlocking detail design, the fabrication constraints, and assembly logic. The actual structural performance of the prototype awaits further investigation through-loading experiments. 
    more » « less
  4. Abstract

    Owing to the fact that effective properties of low‐density cellular solids heavily rely on their underlying architecture, a variety of explicit and implicit techniques exists for designing cellular geometries. However, most of these techniques fail to present a correlation among architecture, internal forces, and effective properties. This paper introduces an alternative design strategy based on the static equilibrium of forces, equilibrium of polyhedral frames, and reciprocity of form and force. This novel approach reveals a geometric relationship among the truss system architecture, topological dual, and equilibrium of forces on the basis of 3D graphic statics. This technique is adapted to devise periodic strut‐based cellular architectures under certain boundary conditions and they are manipulated to construct shell‐based (shellular) cells with a variety of mechanical properties. By treating the materialized unit cells as representative volume elements (RVE), multiscale homogenization is used to investigate their effective linear elastic properties. Validated by experimental tests on 3D printed funicular materials, it is shown that by manipulating the RVE topology using the proposed methodology, alternative strut materialization schemes, and rational addition of bracing struts, cellular mechanical metamaterials can be systematically architected to demonstrate properties ranging from bending‐ to stretching‐dominated, realize metafluidic behavior, or create novel hybrid shellulars.

     
    more » « less
  5. Multi-layer spatial structures usually take considerable external loads with very limited material usage at all scales, and Polyhedral Graphic Statics (PGS) provides a method to design multi-layer funicular polyhedral structures. The structural forms usually materialized as space frames. Our previous research shows that the intrinsic planarity of the polyhedral geometries can be harnessed for efficient fabrication and construction processes using flat-sheet materials. Sheet-based structures are advantageous over the conventional space frame systems because sheets can provide more load paths and constrain the kinematic degrees of freedom of the nodes. Therefore, they can take a wider range of load compared to space frames. Moreover, sheet materials can be fabricated to complex shapes using CNC milling, laser cutting, water jet cutting, and CNC bending techniques. However, not all sheets are necessary as long as the load paths are preserved, and the system does not have kinematic degrees of freedom. To find a reduced set of faces that satisfies the requirements, this paper incorporates and adapts the matrix analysis method to calculate the kinematic degree of freedom of sheet-based structure. Built upon this, an iterative algorithm is devised to help find the reduced set of faces with zero kinematic degree of freedom. To attest the advantage of this method over bar-node construction, a comparative study is carried out using finite element analysis. The result shows that, with the same material usage, the sheet-based system has improved performance than the framework system under a wide range of loading scenarios. 
    more » « less