Several structural systems rely on a specific hierarchy between their constitutive elements, which results in topological constraints on the feasible patterns that can describe them. Folded, corrugated, or creased surface structures require this bipartition, also called two-colouring, between independent wavy and smooth directions. Finding a valid pattern for complex design problems is not straightforward and identifying relevant ones is important as creasing can either strengthen or weaken a structure. This paper presents a way of tackling such a design problem, by focusing on the roof of the Great Courtyard of the British Museum, revisiting this structure with a creased shell to increase its bending stiffness in the key directions. The methodology includes two-colour topology finding of corrugated patterns, parametric structural analysis, and simple structural optimisation through data analysis for topological combination, which opens new research avenues for performance-informed topological exploration.

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Structural design is a search for the best trade-off between multiple architecture, engineering, and construction objectives, not only mechanical efficiency or construction rationality. Producing hybrid designs from single-objective optimal designs to explore multi-objective trade-offs is common in the design of structural forms, constrained to a single parametric design space. However, producing topological hybrids offers a more complex challenge, as a combinatorial problem that is not encoded as a finite set of real numbers but as an unbonded series of grammar rules. This paper presents a strategy for the generation of hybrid designs of quad-mesh pattern topologies for surface structures. Based on a quad-mesh grammar, an algebra is introduced to measure the distance between designs, find their similar features, and enumerate designs with different degrees of topological similarity. Structural design applications are shown to highlight the use of topologically hybrid designs as a surrogate for obtaining multi-objective trade-offs.

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This paper presents a formwork system consisting of a bending-active gridshell that simultaneously serves as falsework and integrated reinforcement for realising a ribbed funicular concrete skeleton shell. Encased by a knitted textile shuttering, the formwork system was demonstrated through KnitNervi, an architectural-scale, funnel-shaped demonstrator measuring 9 m in diameter and 3.3 m in height. The gridshell is materialised from straight steel rebar actively bent into curvilinear, double-layered rebar cages. Regular stirrups and pairs of inclined stirrups forming triangulated shear connectors provide the necessary shape control and stiffness for the load-bearing falsework. The rebar cages define the shape of the concrete ribs by supporting a knitted closed sectional mould and stay in place to structurally reinforce the resulting ribs. The focus of this paper lies on the falsework and reinforcement system with its interrelated design drivers. The geometric design includes the funicular form finding of the target shell with Thrust Network Analysis and the incremental form finding of the bending-active gridshell with its informed assembly sequence towards the funicular target with Finite Element Analysis. The engineering of the falsework demonstrates its sufficient load-bearing capacity and deflection control to support the weight of the wet concrete at an architectural scale. Sensitivity studies reveal the effectiveness of activating the double layer through the shear-connecting stirrups, the relevance of the internal connection design, and the geometric integrity during a potential stepwise casting sequence. The construction of the demonstrator verified the shape control and fabrication design. In only 36 h, the bespoke falsework gridshell was efficiently assembled from its kit-of-parts of standard rebar elements with adequate precision, logistics, time, and material resources. It was relatively lightweight, compact for transport, and employed low-tech construction techniques common to the rebar industry. Its structural geometry and informed bending-active logic enabled its efficient construction without digital fabrication or wasteful, costly moulds, which typically present the bottleneck for custom concrete structures. The resulting funicular concrete skeleton shell saves structural mass, hence embodied carbon, compared to unarticulated bending-dominant typologies. The overarching motivation of the research is to outline a strategy that could mitigate the environmental impact of the construction sector, applicable to a broad range of technological contexts.

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Topology-optimisation strategies for structural design of discrete surface structures result in unstructured patterns that require post-rationalisation to limit the number and complexity of the various structural elements. Fabrication-related objectives still demand further processing. Designers need topology exploration, before topology optimisation, following a generative-design approach that is decoupled from density tuning and shape design, to produce high-quality patterns. Such an approach allows to flexibly embed multiple design constraints, benefit from state-of-the-art form-finding algorithms and explore design trade-offs of the multiple requirements related to architecture, engineering and construction. This research investigates a parameterisation strategy to encode topological exploration of structured patterns based on quad meshes. The focus is set on singular vertices, which connect an irregular number of blocks, cables, or beams. Singularities are independent from pattern density and geometry, and have a fundamental influence on the qualitative and quantitative performance of the structure. We introduce an L-system encoding a quad-mesh grammar into a string that describes topological transformations of these singularities. Design applications to a net and a gridshell demonstrate the influence of singularities on the design of surface structures, and highlight the flexibility and generality of the approach in terms of geometrical processing and performance metrics. Beyond exploration, this parameterisation strategy opens to novel applications of search and optimisation methods for generative design of singularities in structural patterns.

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Facing the challenges of our environmental crisis, the AEC sector must significantly lower its carbon footprint and use of first-use resources. A specific target is the reduction of the amount of concrete used. Funicular structures that base their strength on their structurally-informed geometry allow for material efficiency. However, a bottleneck for their construction lies in their costly and wasteful formworks and complex reinforcement placement. This research presents an alternative flexible formwork system consisting of a bending-active gridshell falsework and fabric shuttering for ribbed funicular concrete shells. The falsework becomes structurally integrated as reinforcement and is designed as two connected layers offering shape control and sufficient stiffness to support the wet-concrete load. The paper focuses on the development of a design-to-fabrication workflow and a graph-based data structure for gridshell falsework and reinforcement in the computational framework COMPAS. The implementation utilises, customises and creates packages for the form finding of the ribbed shell with TNA and the gridshell with FEA. The research is based on a demonstrator realised in the context of the Technoscape exhibition at the Maxxi Museum in Rome, Italy. The computational workflow was used to design this system and translate it for materialisation. The demonstrator serves as proof-of-concept for the novel material-efficient construction system. Its key to efficiency lies in the structurally-informed geometry for both the formwork and the resulting ribbed concrete shell.

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This paper presents the design, engineering and digital fabrication strategies for a circular pedestrian bridge to be built as part of “De Groene Boog” development of the A16 highway north of Rotterdam, The Netherlands. The bridge is designed as a lightweight funicular unreinforced concrete gridshell with openings based on the principle of a three-hinged arch extrapolated to 3D geometry. In its realisation, it demonstrates a model of circular construction using recent material developments (such as recycled concrete) and an efficient flexible formwork system using knitted textiles. The presented design and fabrication process is developed collaboratively by the Block Research Group at ETH Zurich and De Groene Boog. The structure is commissioned by the Dutch Ministry of Infrastructure and Water Management (Rijkswaterstaat).@en

This paper describes the structural design, digital fabrication and construction of KnitCandela, a free-form, concrete waffle shell with KnitCrete, a falsework-less formwork approach using a custom prefabricated knitted textile as multi-functional, structural shuttering layer and a form-found cable net as the main load-bearing formwork. The digitally designed and fabricated textile provided integrated features for inserting and guiding elements such as cables and inflatables that helped shape the sophisticated mould. With a total weight of only 55 kg, the 50 m² formwork was easy and compact to transport. On site, the formwork was tensioned into a timber and steel rig, the pockets were inflated, and then coated with a thin layer of custom-developed, fast-setting cement paste. This paste served as a first stiffening layer for the textile, minimising the formwork's deformations during further concrete application. Fibre-reinforced concrete was manually applied onto the formwork to realise a 3 cm-thick shell with 4 cm-deep rib stiffeners. The novel approach, for the first time applied at architectural scale in this project, enables the building of bespoke, doubly-curved geometries in concrete, with a fast construction time and minimal waste, while also reducing the cost and labour of manufacturing complex parts.

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The patterns of many structural systems must fulfil a property of two-colourability to partition their elements into two groups. Such examples include top versus bottom layers of continuous beams in elastic gridshells, corrugated versus non-corrugated directions in corrugated shells or warp versus weft threads in woven structures. Complying with such constraints does not depend on the geometry but on the topology of the structure, and, more specifically, on its singularities. This paper presents a search strategy to obtain patterns that fulfil this topological requirement, which represent only a fraction of the general design space. Based on an algebra for the exploration of the topology of quad meshes, including a grammar and a distance, a topology-finding algorithm is proposed to find the closest two-colour quad-mesh patterns from an input quad-mesh pattern. This approach is expressed as the projection to the two-colourable subspace of the design space. The distance underlying the definition of the projection measures the similarity between designs as the minimum number of topological grammar rules to apply to modify one design into another. A design application illustrates how two-colour topology finding can complement workflows for the exploration of structural patterns with singularities informed by the system's topological requirements.

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A novel formwork system is presented as a material saving, labour reducing and cost-effective solution for the casting of bespoke doubly curved concrete geometries. The approach uses a custom knit technical textile as a lightweight stay-in-place formwork with integrated solutions for the insertion of additional elements, and is fabricated as a nearly seamless fabric. Using weft knitting as the textile formation technique minimises the need for cutting patterns, sewing, welding or gluing, when compared to conventional weaving and gives the possibility to integrate channels, openings, have varying widths and directional material properties, thus broadening the geometric design space. The system has been tested through a small-scale concrete footbridge prototype, built using a pre-stressed hybrid knitted textile and a bending-active structure that acted as a waste-free, stay-in-place, self-supporting formwork. Through the gradual buildup of strength in thin layers of concrete, formwork deformations during casting were minimised. This allowed for low tensioning levels of the fabric and the possibility to use higher pressure (e.g. during shotcreting) in applying the subsequent concrete without intermediate support from below. The computational design and fabrication of the knitted textile formwork included integrated channels for the insertion of bending-active rods, tensioning ribbons and features for controlling the concrete casting. The analysis and process of increasing the stiffness of the lightweight and flexible formwork is presented. The hybrid approach results in an ultra-lightweight formwork that is easily transportable and significantly reduces the need for falsework support and scaffolding, which has many advantages on the construction site.

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Knitting offers the possibility of creating 3D geometries, including non-developable surfaces, within a single piece of fabric without the necessity of tailoring or stitching. To create a CNC-knitted fabric, a knitting pattern is needed in the form of 2D line-by-line instructions. Currently, these knitting patterns are designed directly in 2D based on developed surfaces, primitives or rationalised schemes for non-developable geometries. Creating such patterns is time-consuming and very difficult for geometries not based on known primitives. This paper presents an approach for the automated generation of knitting patterns for a given 3D geometry. Starting from a 3D mesh, the user defines a knitting direction and the desired loop parameters corresponding to a given machine. The mesh geometry is contoured and subsequently sampled using the defined loop height. Based on the sampling of the contours the corresponding courses are generated and the so-called short-rows are included. The courses are then sampled with the defined loop width for creating the final topology. This is turned into a 2D knitting pattern in the form of squares representing loops course by course. The paper shows two examples of the approach applied to non-developable surfaces: a quarter sphere and a four-valent node.@en

This paper presents initial results of research focused on developing a novel type of formwork for concrete based on pre-stressed fabric formwork principles. It aims at creating geometries that are fabricated in one piece by knitting technical fibers, which could ultimately be used as reinforcement for concrete. This approach would result in a spatial textile that minimises the need for patterning, sewing, welding or gluing compared to a conventional approach to fabric formwork and textile reinforcement based on woven fabrics. It makes it possible to create directional material properties aligned to the internal force flow. This paper presents an overview of the proposed prefabrication technique and exemplifies its feasibility through small-scale experiments.@en