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Shell-like structures allow to elegantly and efficiently span large areas. Quad meshes are natural patterns to represent these surface objects, which can also serve for mapping other patterns. Patterns for these shells, vaults, grid- shells or nets can represent the materialised structure, the force equilibrium or the surface map. The topology of these patterns constrains their qualitative and quantitative modelling freedom for geometrical exploration. Unless topological exploration is enabled.
Parametric design supporting exploration and optimisation of the geometry of structures is spreading across the community of designers and builders. Unfortunately, topological design is lagging, despite some optimisation-oriented strategies for specific design objectives. Strategies, algorithms and tools for topological exploration are necessary to tackle the multiple objectives in architecture, engineering and construction for the design of structures at the architectural scale. The task of structural design is rich and complex, calling for interactive algorithms oriented towards co-design between the human and the machine. Such an approach is complementary and empowered with existing methods for geometrical exploration and topology optimisation.
The present work introduces topology finding for efficient search across the topological design space. This thesis builds on three strategies for topology finding of singularities in quad-mesh patterns, presented from the most high-level to the most low-level approach.
Geometry-coded exploration relies on a skeleton-based quad decomposition of a surface including point and curve features. These geometrical parameters can stem from design heuristics to integrate into the design, related to the statics system or the curvature of the shell, for instance.
Graph-coded exploration relies on the topological strips in quad meshes. A grammar of rules allows exploration of this strip structure to search the design space. A similarity-informed search algorithm finds design with different degrees of topological similarity. Designs optimised for single objectives can inform this generation process to obtain designs offering different trade-offs between multiple objectives. A two-colour search algorithm finds designs that fulfil a two-colouring requirement of two-colouring. This topological property allows a partition of the pattern elements that many structural systems necessitate.
String-coded exploration relies on the translation of the grammar rules into alphabetical operations, shifting encoding from a phenotype mesh to a genotype string. Modifications, or mutations, of the string transform the genotype and change the phenotype of the design. String or vector encoding opens for the use of search and optimisation algorithms, like linear programming, genetic algorithms or machine learning.
Keywords: structural design, topological exploration, patterns, quad meshes, singularities, topology finding, shells, gridshells.

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This paper explores how computational methods of representation can support and extend kagome handcraft towards the fabrication of interlaced lattice structures in an expanded set of domains, beyond basket making. Through reference to the literature and state of the art, we argue that the instrumentalisation of kagome principles into computational design methods is both timely and relevant; it addresses a growing interest in such structures across design and engineering communities; it also fills a current gap in tools that facilitate design and fabrication investigation across a spectrum of expertise, from the novice to the expert. The paper describes the underlying topological and geometrical principles of kagome weave, and demonstrates the direct compatibility of these principles to properties of computational triangular meshes and their duals. We employ the known Medial Construction method to generate the weave pattern, edge 'walking' methods to consolidate geometry into individual strips, physics based relaxation to achieve a materially informed final geometry and projection to generate fabrication information. Our principle contribution is the combination of these methods to produce a principled workflow that supports design investigation of kagome weave patterns with the constraint of being made using straight strips of material. We evaluate the computational workflow through comparison to physical artefacts constructed ex-ante and ex-post.

Buildings enclose and partition space and are built from assemblies of
connected components. The many different forms of spatial and material
partitioning and connectedness found within buildings can be represented by
topology. This paper introduces the ‘Topologic’ software library which
integrates a number of architecturally relevant topological concepts into a
unified application toolkit.
The goal of the Topologic toolkit is to support the creation of the lightest, most
understandable conceptual models of architectural topology. The formal
language of topology is well-matched to the data input requirements for
applications such as energy simulation and structural analysis. In addition, the
ease with which these lightweight topological models can be modified
encourages design exploration and performance simulation at the conceptual
design phase.
A challenging and equally interesting question is how can the formal language
of topology be used to represent architectural concepts of space which have
previously been described in rather speculative and subjective terms?

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This article presents a new structural solution for the design and construction of rigid and elastic gridshells with specific meshes. Four meshes with singularities are created based on the original geometry of a previous successful project designed in 2011 by the Navier Laboratory of the École des Ponts et Chaussées. The paper first investigates the meshes in a rigid gridshell to check the overall behavior of the structure. A FEM structural analysis is performed and the result proves the structural interest of the concept as the solutions with singularities are stiffer than the original configuration. The aim is to apply the same concept to an elastic gridshell and use the proposed meshes to limit the curvature and the stresses during the shaping process. The final part of the paper focuses on the deformation of the initial grid that results in a sort of polyhedral surface rather than a smooth shape. The paper shows that the mesh strategy is an essential step for the gridshell design as it allows the designer to have better control of the structural behavior. The final results encourage the application of such a design philosophy for future structures exploring its structural and architectural potential.

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This paper investigates the use of robotics with sensing mechanisms in combination with industrial sewing techniques to explore new strategies for the fabrication of thin wooden shells.

Contemporary innovations in structural form-finding and fabrication techniques are leading to design of freeform masonry architecture. These new forms create new challenges in laying out tessellation patterns, especially if structural, fabrication and construction requirements as well as aesthetical considerations are taken into account. Addressing these challenges, we review historic stone-cutting strategies and their geometric principles, forming the base for the development of two new discretisation approaches for given thrust surfaces, allowing for various degrees of user control. First, we introduce a tessellation approach based on primal, anisotropic triangular meshes and their dual counterparts. Second, an alternative tessellation approach based on transverse cutting curves is presented. Using a simple set of geometric rules, both methods enable the design of rigid, staggered bonds with locally force-flow aligned block configurations to avoid sliding failures. For this research, the tessellation design of the Armadillo Vault, an unreinforced, dry-assembled, cut-stone stone shell, served as a case study to demonstrate the feasibility of our methods in the context of a full-scale architectural project.

In the research field of segmented timber shells, two construction systems have lately received much attention, which both expose interesting structural and constructional characteristics: planar plate structures made of thin plywood and actively bent plywood structures. The research presented in this article combines elements of both approaches, resulting in a construction system for segmented shell structures with elastically bent elements. The increasing complexity of this approach requires a sophisticated design process, which integrates fabrication constraints as well as structural feedback. As a consequence, form-finding strategies of bending-active timber shells are discussed, with a special focus on the programming of the stiffness distribution in order to fulfil geometrical requirements. The authors also reflect on the specific structural challenges of joining thin sheets of plywood by transferring traditional textile connection methods to timber construction. Investigations of biological role models such as the sand dollar led to transfers of constructional principles on different levels. The resulting construction system was validated through the design and construction of a full-scale architectural prototype.

The term ‘configuration’ refers to an arrangement of parts. For example, the elements of a structure constitute a configuration and so do the atoms of a molecule and the components of an electrical network. The most common usage of the term configuration is in reference to geometric compositions that consist of points, lines, surfaces and so on. The term ‘configuration processing’ refers to the skill of dealing with creation and manipulation of configurations. In particular, the term ‘formex configuration processing’ implies configuration processing with the aid of ‘formex algebra’. Formex algebra is evolved to perform processes needed for configuration processing, just as the ordinary algebra is evolved to perform operations needed for creation and manipulation of numerical models. The term ‘formex’ is derived from the word ‘form’ and it is meant to imply a ‘representation of form’. This article has two main objectives. The first objective is to provide a general feeling of how the elements of formex algebra perform configuration processing. This objective is achieved through simple examples, without involvement in too many details. It will be seen that working with parameters is a natural characteristic of formex configuration processing. Thus, a formex solution is, normally, for a class of problems rather than an individual one. This would allow consideration of different variants of a configuration by simply changing the values of the parameters. It will also be seen the ease with which freeforms can be created. The coverage also includes information about ‘Formian’ which is the name of the computer software for formex configuration processing. The second objective of this article is to record the story of the development of formex algebra from the beginnings in the mid-1970s to the middle of the second decade of the 21st century, covering some 40 years of development. Formex configuration processing is an effective and elegant conceptual tool for generation and manipulation of forms. However, there are also other approaches to configuration processing. In particular, there are now a number of highly successful software systems for configuration processing using various tactics. Formex algebra will be a natural complement for these systems.

Since shape grammars were first described about forty five years ago, several types of grammars have emerged. The goal of this paper is to provide a framework that gathers together the main existing types of grammars. The categorization is preceded by a glossary of 19 terms related to shape grammars. Then, 44 types are placed into 13 chronologically-ordered categories. Each type is characterized with its name, a short description, the reference to the original paper, three examples of existing grammars of the type, and simple illustrative grammars. The types are organized using a classification guide in the form of a checklist, which is filled according to an existing shape grammar as an example.