An official website of the United States government
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
Bio-Based Composite Spatial Shell Structures
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
- Award ID(s):
- 2037097
- PAR ID:
- 10465097
- Date Published:
- Journal Name:
- Proceedings of the {IASS} Annual Symposium 2023
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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
-
Polyhedral Graphic Statics (PGS) is an effective tool for form-finding and constructing complex yet efficient spatial funicular structures. The intrinsic planarity of polyhedral geometries can be leveraged for efficient fabrication and construction using flat sheet materials, such as glass. Our previous research used PGS for the form-finding of a 3 m-span, modular glass bridge prototype to be built with thirteen unique hollow glass units (HGUs) in a compression-only configuration. This paper reports its design optimization, fabrication, and subsequent modular assembly process. The computational modeling of the geometries is facilitated with the efficient half-face data structure provided by PolyFrame, a software that implements PGS. Regular float glass and acrylic are selected as the main structural materials, and they are fabricated using 5-axis water jet cutting and CNC milling techniques. With the help of 3 M™ Very High Bond tape, the glass parts and acrylic parts are bonded as HGUs, which serve as the basic structural and assembly modules. Surlyn sheets are used as interface material to prevent glass-to-glass direct contact between HGUs. The digital model is also simulated using ANSYS to ensure the effectiveness of the design. Due to the lightweight of the HGUs, the assembly of the bridge can be done by one person without the requirement of any heavy construction machinery.more » « less
-
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
-
Machine knitting is a well-established fabrication technique for complex soft objects, and both companies and researchers have developed tools for generating machine knitting patterns. However, existing representations for machine knitted objects are incomplete (do not cover the complete domain of machine knittable objects) or overly specific (do not account for symmetries and equivalences among knitting instruction sequences). This makes it difficult to define correctness in machine knitting, let alone verify the correctness of a given program or program transformation. The major contribution of this work is a formal semantics for knitout, a low-level Domain Specific Language for knitting machines. We accomplish this by using what we call the "fenced tangle," which extends concepts from knot theory to allow for a mathematical definition of knitting program equivalence that matches the intuition behind knit objects. Finally, using this formal representation, we prove the correctness of a sequence of rewrite rules; and demonstrate how these rewrite rules can form the foundation for higher-level tasks such as compiling a program for a specific machine and optimizing for time/reliability, all while provably generating the same knit object under our proposed semantics. By establishing formal definitions of correctness, this work provides a strong foundation for compiling and optimizing knit programs.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
