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1. A Method for Designing Multi-Layer Sheet-Based Lightweight Funicular Structures

   https://doi.org/10.20898/j.iass.2022.018  

   Lu, Yao ; Alsalem, Thamer ; Akbarzadeh, Masoud ( December 2022 , Journal of the International Association for Shell and Spatial Structures)

   Multi-layer spatial structures usually take considerable external loads with a small material usage at all scales. Polyhedral graphic statics (PGS) provides a method to design multi-layer funicular polyhedral structures, and the structural forms are 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 conventional space frame systems because sheets can provide more load paths and constrain the kinematic degrees of freedom of the nodes. Therefore, they are more capable of taking a wider variety of load cases compared to space frames. Moreover, sheet materials can be fabricated into 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 an efficient set of faces that satisfies the requirements, this paper first incorporates and adapts the matrix analysis method to calculate the kinematic degrees of freedom for sheet-based structures. Then, an iterative algorithm is devised to help find a reduced set of faces with zero kinematic degrees of freedom. To attest to the advantages of this method over bar-node construction, a comparative study is carried out using finite element analysis. The results show that, with the same material usage, the sheet-based system has improved performance than the framework system under a range of loading scenarios. 

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2. Funicular Glass Bridge Prototype: Design Optimization, Fabrication, and Assembly Challenges

   Yao Lu ; Alireza Seyedahmadian ; Philipp Amir Chhadeh ; Matthew Cregan ; Mohammad Bolhassani ; Jens Schneider ; Joseph Robert Yost ; Gareth Brennan ; Masoud Akbarzadeh ( January 2022 , Glass structures engineering)

   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. 

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3. The form-finding and fabrication of an ultra-thin funicular bridge prototype made up of hollow glass units

   LU, Yao ; CREGAN, Matthew ; CHHADEH, Philipp A ; SEYEDAHMADIAN, Alireza ; BOLHASSANI, Mohammad ; Schneider, Jens ; YOST, Joseph R ; AKBARZADEH, Masoud ( October 2021 , International Association of Shell and Spatial Structures)

   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. 

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4. Kerf Bending and Zipper in Spatial Timber Tectonics

   Liu, Y. ; Lu, Y. ; Akbarzadeh, M. ( September 2021 , Proceedings of the Association for Computer-Aided Design in Architecture (ACADIA))

   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. 

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5. Tortuca: An Ultra-Thin Funicular Hollow Glass Bridge

   Lu Yao ; Alireza Seyedahmadian ; Philipp Amir Chhadeh ; Matthew Cregan ; Mohammad Bolhassani ; Jens Schneider ; Joseph Robert Yost ; Gareth Brennan ; Masoud Akbarzadeh. ( January 2022 , Proceedings of the 42nd Annual Conference of the Association for Computer-Aided Design in Architecture (ACADIA))

   Akbarzadeh, Masoud ; Aviv, Dorit ; Jamelle, Hina ; Stuart-Smith, Robert (Ed.)

   Designed with Polyhedral Graphic Statics (PGS), a geometry- based structural form-finding method, Tortuca presents an efficient and innovative structural system constructed by the dry assembly of thirteen hollow glass units (HGU). It also proposes a new language for glass that is carefully treated, structurally informed, fabrication-aware, and environmentally responsible. Each HGU of Tortuca is made of 1 cm (3/8 inch) glass deck plates and 2 cm (0.7 inch) acrylic side plates precisely cut with 5-axis abrasive waterjet cutting and CNC milling to match the structural geometry. The structure spans 3.2 m (10.5 ft) with a mass of only 250 kg (550 lbs), where the float glass is the primary loadbearing material. Thanks to the efficiency and light weight of the construction system, a single person can assemble and disassemble the structure without needing a crane or additional labor. Moreover, this research explores the potential of using an extremely delicate material such as float glass for the primary structural system to encourage minimizing the material and energy demands in buildings and infrastructural projects. Additionally, it shows how utilizing the material in its purest format could simplify the recycling process after the life cycle of the structure has ended. Also, this research project is achieved by collaboration across different institutions, from design to engineering, from theoretical to practical, and from academia to industry. We appreciate the value of breaking disciplinary boundaries and joining forces from multiple fields. 

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