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.

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.

Masonry vaults, mechanically efficient structures, are challenging to build because they require significant tailored falsework as temporary structures for centering, guidework, and scaffolding, which decreases construction productivity and increases financial cost and environmental impact. Traditional building techniques combined with recent digital technologies can eliminate such temporary construction. An integrated digital design and construction approach that leverages the benefits of four construction strategies (namely, thin-tile vaulting, loxodrome tessellation, augmented reality, and prefabricated spine) within a 4D funicular design framework is presented in this paper and illustrated by a large-scale demonstrator, innixAR. This structure demonstrates that the combination of the vernacular craft of thin-tile vaulting with augmented reality technology to produce a digital guidework, informing a 4D funicular design process that considers the entire construction sequence from a prefabricated spine, minimizes the required falsework, making the construction of masonry vaults more efficient and affordable. This approach is benchmarked against alternative conventional vault falsework. Combining thin-tile vaulting and prefabricated spine allowed a reduction of 82% of the falsework mass, making transport lighter. Whereas combining digital guidework and prefabricated spine allowed a reduction of 91% of the falsework elements, making assembly faster. This research contributes to the development of structures that are efficient both mechanically and constructionally.

This paper investigates the feasibility of adapting ancient historical construction techniques to cooperative robotic assembly methods to minimize centering requirements in masonry vaults. First, an overview of seven historical techniques is presented. Next, a classification framework is introduced to evaluate the automation potential of these methods, identifying the rib network as the most promising candidate. This is followed by two computational case studies on the cooperative robotic construction of planar masonry arches and multi-arch rib networks. These studies evaluated the impact of robotic reachability and support payload on the feasibility of centering-free construction. A conclusion based only on these simulation results is that high-payload fixed robots, in comparison to medium-payload mobile setups, allow for the construction of larger and more complex rib structures. This research is of relevance to architects and engineers interested in using a cooperative robotic fabrication framework to reduce centering in masonry vault construction.

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.

The response of vaulted structures with dry-joints such as arches and shells can be predicted using graphical methods, limit state analysis, and rigid block analysis. However, these approaches assume material deformations are negligible. While acceptable for conventional masonry structures, there is a growing body of work investigating segmented vaulted structures where the segments comprise a large portion of the overall span. In such cases, material deformations and non-linearities can play a significant role. Typical analysis tools available are usually difficult to use and are not widely used by industry practitioners. In this paper, a modelling approach using a widely used finite element analysis package (LS-DYNA) is presented, using an ‘out-of-the-box’ approach for parameter tuning and modelling. This was then benchmarked against five experimental tests of dry-joint arches undergoing support displacements and a segmented concrete shell with large segments tested under a central point load. Crucially, the segmented shell exhibited imperfect dry-joints, with gaps occurring throughout various locations. A method of modelling and assessing such imperfections in a simple and practical manner is investigated through the use of a positive penetration allowance in the contact surfaces. The results show that the modelling approach is able to predict the collapse mechanism and failure support displacement for arches well, with further experimental tests required for 3D systems. It is envisioned that this work will add to the number of tools designers will have for analysing segmented vaulted structures with dry-joints.

Concrete shell structures offer a mechanically efficient solution as a building floor system to reduce the environmental impact of our buildings. Although the curved geometry of shells can be an obstacle to their fabrication and implementation, digital fabrication and affordable robotics provide a means for the automation of their construction in a sustainable manner at an industrial scale. The applicability of such structures is demonstrated in this paper with the realisation of a large-scale concrete shell floor system, completed by columns, tie rods, and a levelled floor. The shell was prefabricated off-site in segments that can be transported and assembled on-site, and which can be disassembled to enable a circular economy of construction. This paper presents the conceptual and structural design; the automation of fabrication, thanks to an actuated, reconfigurable, reusable mould and a robotic concrete spraying process; the strategy and sequence of assembly and disassembly on-site using standard scaffold elements; and the sustainability assessment using life-cycle analysis. This prototype offers a reduction of about 50% of cradle-to-gate embodied carbon benchmarked against regular flat slabs before further improvement and optimisation.

The fabrication of doubly curved concrete shells traditionally poses challenges in terms of material deposition and formwork manufacturing. Recent advances in digital fabrication techniques including robotics in construction have created tools to better tackle these challenges. We present a digital fabrication system to accurately deposit cementitious materials onto doubly curved surfaces using robotic concrete spraying in a process for prefabrication of structural shell components we call ARCS (Automated Robotic Concrete Spraying). Using inputs of a generic variable thickness shell volume, a robotic path is generated to deposit material onto the formwork surface where required. Paths are generated on the surface using geodesic lines as guides in order to create iso-curves for evenly spaced spray paths. Additionally, layers are incrementally deposited to allow for variable thicknesses across the surface. This approach is flexible enough such that additional features can be embedded onto the shell such as ribs. We demonstrate this automated fabrication process on a 1.8 m by 1.8 m scale shell specimen.

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.

The construction industry is responsible for nearly half of the UK’s carbon emissions, mainly due to the large amount of concrete used. Traditional formwork methods for concrete result in prismatic building elements with a constant cross-section, but the shear forces and bending moments that beams have to withstand are far from constant along their length. Up to 40% of the concrete in a typical beam could be removed. An iterative optimisation process has been implemented in a parametric modelling framework to generate and analyse optimal forms for non-prismatic beams that take into account the constraints imposed by the fabrication process, namely the use of fabric formwork. The aim of the resulting design tool is to facilitate the adoption of non-prismatic elements by the construction industry.