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3D concrete printing (3DCP) structural components for construction assemblies are known for reduced material use and enhanced efficiency and design freedom. This article investigates the limitations in the geometrical and toolpath design of 3DCP structural components and presents an automated and comprehensive approach to their toolpath design and optimization. It exploits hierarchical geometric data structures and graph algorithms to achieve the following features: (1) By analyzing the overhang of toolpaths, the method offers quantitative criteria for determining the buildability of the components and predicting failure, thus assisting design decisions. (2) It provides toolpath offsetting and filleting methods that can enhance the dimensional accuracy of the print concerning layer line textures and overfills. (3) For branching and porous geometries, the method creates as-continuous-as-possible toolpaths with minimal stop-starts based on their topologies, thus reducing seam defects. (4) It converts the toolpath into efficient visualization meshes representing layer line textures and toolpath meshes compatible with finite elements analysis. The proposed method is implemented as a plug-in software within the environment of Grasshopper® for Rhino® to facilitate designers and engineers working with 3DCP. The effectiveness and versatility of the tool are demonstrated through the toolpath design and printing of four sets of examples. The tool reduces the number of toolpaths by 90% for a typical 80 mm nozzle and takes 0.21 s per meter of toolpath to slice, analyze overhang, generate continuous printing toolpaths, and visualize the print. 

This paper aims to advance the field of additive manufacturing by producing multimaterial objects with intricate topological features and polylithic material distribution through an integrated approach. First, we develop a Single-Nozzle Multi-Filament (SNMF) system equipped with active mixing to blend multiple filaments and deposit a programmable mixture. The system can also deposit gradient transitions between different materials within a single print. Second, we establish a numerical model to represent the material transitional behavior and validated it with experiments. The model enables the precise control of the material transitional interface to ensure high material fidelity. Third, we propose three strategies for designing and modeling multimaterial objects catering to different application scenarios, including image sampling, 2D discrete patches, and 3D surface division. The system’s capabilities were validated through six case studies designed and fabricated through the above approaches for distinct application scenarios, demonstrating the successful materialization of complex designs with multiple functionalities. 

In this research study, the fracture strength of flat 10 mm thick annealed glass sheets having an abrasive water-jet cut surface and bearing against a transparent interface material is experimentally investigated. The transparent interface material is necessary to provide axial-compressive force continuity in modular compression-dominant all- glass shell structures. A series of short glass columns were tested in axial compression under a variety of load cases, which included cyclic, creep, and monotonic-to-fracture loading. A target glass fracture bearing stress of 36.6 MPa is identified and represents an upper bound bearing stress for annealed glass compression members failing in a flexural buckling mode. The study concludes the transparent thermoplastic material, known as Surlyn, was able to achieve a fracture strength that exceeds the target value and that the fracture strength is not affected by cyclic or creep loading. Consequently, column-related failure limit states will occur before glass fracture is associated with interface bearing. Glass fracture occurs in Type-I mode, reflecting the presence of interface tensile stress. Furthermore, the monotonic bearing stiffness in the service range of 5 to 15 MPa is increased by 20 % and 16 % for samples subjected to cyclic and creep loading, respectively, relative to monotonic-only samples. 

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. 

Nature has always been the master of design skills to which humans only aspire to, but new approaches bring that aspiration closer to our reach than ever before. Through 4.5 billion years of iterations, nature has shown us its extraordinary craftsmanship, breeding a variety of species whose body structures have gradually evolved to adapt to natural phenomena and make full use of their unique characteristics. The dragonfly wing, among body structure is an extreme example of efficient use of materials and minimal weight while remaining strong enough to withstand the tremendous forces of flight. It has long been the object of scientific research examining its structural advantages to applying their principles to fabricated designs.1 We can imitate its form and create duplicates, but thoroughly understanding the dragonfly wing’s mechanism, behavior and design logic is no trivial task. 

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. 

Special Issue: Machine Hallucinations: Architecture and Artificial Intelligence Nature has always been the master of design skills to which humans only aspire, but new approaches bring that aspiration closer to our reach than ever before. Through 4.5 billion years of iterations, nature has shown us its extraordinary craftsmanship, breeding a variety of species whose body structures have gradually evolved to adapt to natural phenomena and make full use of their unique characteristics. The dragonfly wing, among body structures, is an extreme example of efficient use of materials and minimal weight while remaining strong enough to withstand the tremendous forces of flight. It has long been the object of scientific research examining its structural advantages to apply its principles to fabricated designs.1 We can imitate its form and create duplicates, but thoroughly understanding the dragonfly wing’s mechanism, behavior, and design logic is no trivial task. 

The Auxetic materials are structural systems with a negative Poisson’s ratio. Such materials show unexpected behavior when subjected to uni-axial compression or tension forces. For instance, they expand perpendicular to the direction of an applied compressive force. This behavior is the result of their internal structural geometry. These materials, with their unique behavior, have recently found many applications in the fields of sensors, medical devices, sport wears, and aerospace. Thus, there is a lot of relevant research in the artificial design of auxetic metamaterials and the prediction of their behavior [2]. Since the behavior of these materials heavily relies on the geometry of their internal structure, the geometry-based methods of structural design, known as graphic statics, are very well suited to derive their geometry or describe their behavior. Nevertheless, graphic statics has never been used in the design of such materials. For the first time, this paper provides an introduction to the use of graphic statics in the design and form-finding of auxetic metamaterials. The paper explains multiple equilibrium states of various auxetic structures using algebraic formulations of 2d/3d graphic statics [1, 3]. Moreover, it sheds light on the geometric behavior of auxetic materials by changing the force diagram of graphic statics. Therefore, it suggests a novel approach in predicting the changes in the geometry of the material under various loading conditions by controlling the force equilibrium geometrically. 

This paper introduces a web-based interactive educational platform for 3D/polyhedral graphic statics (PGS) [1]. The Block Research Group (BRG) at ETH Zürich developed a dynamic learning and teaching platform for structural design. This tool is based on traditional graphic statics. It uses interactive 2D drawings to help designers and engineers with all skill levels to understand and utilize the methods [2]. However, polyhedral graphic statics is not easy to learn because of its characteristics in three-dimensional. All the existing computational design tools are heavily dependent on the modeling software such as Rhino or the Python-based computational framework like Compass [3]. In this research, we start with the procedural approach, developing libraries using JavaScript, Three.js, and WebGL to facilitate the construction by making it independent from any software. This framework is developed based on the mathematical and computational algorithms deriving the global equilibrium of the structure, optimizing the balanced relationship between the external magnitudes and the internal forces, visualizing the dynamic reciprocal polyhedral diagrams with corresponding topological data. This instant open-source application and the visualization interface provide a more operative platform for students, educators, practicers, and designers in an interactive manner, allowing them to learn not only the topological relationship but also to deepen their knowledge and understanding of structures in the steps for the construction of the form and force diagrams and analyze it. In the simplified single-node example, the multi-step geometric procedures intuitively illustrate 3D structural reciprocity concepts. With the intuitive control panel, the user can move the constraint point’s location through the inserted gumball function, the force direction of the form diagram will be dynamically changed from compression-only to tension and compression combined. Users can also explore and design innovative, efficient spatial structures with changeable boundary conditions and constraints through real-time manipulating both force distribution and geometric form, such as adding the number of supports or subdividing the global equilibrium in the force diagram. Eventually, there is an option to export the satisfying geometry as a suitable format to share with other fabrication tools. As the online educational environment with different types of geometric examples, it is valuable to use graphical approaches to teach the structural form in an exploratory manner.