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

   https://doi.org/10.1007/s40940-022-00177-x  

   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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4. Deterministic and stochastic control of kirigami topology

   https://doi.org/10.1073/pnas.1909164117  

   Chen, Siheng; Choi, Gary P. T.; Mahadevan, L. (February 2020, Proceedings of the National Academy of Sciences)

   Kirigami, the creative art of paper cutting, is a promising paradigm for mechanical metamaterials. However, to make kirigami-inspired structures a reality requires controlling the topology of kirigami to achieve connectivity and rigidity. We address this question by deriving the maximum number of cuts (minimum number of links) that still allow us to preserve global rigidity and connectivity of the kirigami. A deterministic hierarchical construction method yields an efficient topological way to control both the number of connected pieces and the total degrees of freedom. A statistical approach to the control of rigidity and connectivity in kirigami with random cuts complements the deterministic pathway, and shows that both the number of connected pieces and the degrees of freedom show percolation transitions as a function of the density of cuts (links). Together, this provides a general framework for the control of rigidity and connectivity in planar kirigami. 

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5. 3D Transformable Modular Kirigami Based Programmable Metamaterials

   https://doi.org/10.1002/adfm.202105641  

   Li, Yanbin; Zhang, Qiuting; Hong, Yaoye; Yin, Jie (July 2021, Advanced Functional Materials)

   Abstract Kirigami, the ancient paper art of cutting, has recently emerged as a new approach to construct metamaterials with novel properties imparted by cuts. However, most studies are limited to thin sheets‐based 2D kirigami metamaterials with specific forms and limited reconfigurability due to planar connection constraints of cut units. Here, 3D modular kirigami is introduced by cutting bulk materials into spatially closed‐loop connected cut cubes to construct a new class of 3D kirigami metamaterials. The module is transformable with multiple degrees of freedom that can transform into versatile distinct daughter building blocks. Their conformable assembly creates a wealth of reconfigurable and disassemblable metamaterials with diverse structures and unique properties, including reconfigurable 1D column‐like materials, 2D lattice‐like metamaterials with phase transition of chirality, as well as 3D frustration‐free multilayered metamaterials with 3D auxetic behaviors and programmable deformation modes. This study largely expands the design space of kirigami metamaterials from 2D to 3D. 

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