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The paper presents a method to generate and structurally optimize the shape of free form shells by means of a genetic algorithm. The shape of the shell is described with the aid of a NURBS representation and the algorithm modifies and improves it on the basis of the structural behaviour. A FEM analysis is performed for each individual and at each generation of the evolutionary process, in order to evaluate the structural behaviour in terms of maximum vertical displacement under a distributed load condition. The method is applied to a recent example of free-form architecture and the results are discussed referring in particular to the role of the architect as 'decision maker' in the evolutionary process. From this point of view the necessity to fit different requirements (structural, functional, aesthetic) involving the work of many professionals, can then be interpreted as a problem of multiobjective optimization.
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... Forming and optimizing gridshell structures have been very attractive problems in the past decades. Several approaches, such as inversion method [1], dynamic relaxation [2,4,11], force density method [3,12], and so forth [10,13], have been studied so far in the literature to address the problem of forming a grid shell structure. Moreover, various techniques from gradient-based to evolutionary methods have been employed for optimization of gridshells taking into account various aspects of a gridshell such as economic, structural, or aesthetic [11][12][13][14][15][16][17][18]. ...
... Several approaches, such as inversion method [1], dynamic relaxation [2,4,11], force density method [3,12], and so forth [10,13], have been studied so far in the literature to address the problem of forming a grid shell structure. Moreover, various techniques from gradient-based to evolutionary methods have been employed for optimization of gridshells taking into account various aspects of a gridshell such as economic, structural, or aesthetic [11][12][13][14][15][16][17][18]. The focus of this work is on the optimization problem, and it is assumed that the initial forms of the desired gridshells are given. ...
... This is why we employ evolutionary techniques in this work. Among the evolutionary techniques, genetic algorithms (GAs) have been used the most in optimization of gridshells [1,3,5,8,10,11,[13][14][15][16][17][18]. Another well-known evolutionary method is particle swarm optimization (PSO) to which less attention has been paid for improving the gridshell structures so far. ...
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Designing and optimizing gridshell structures have been very attractive problems in the last decades. In this work, two indexes are introduced as “length ratio” and “shape ratio” to measure the regularity of a gridshell and are compared to the existing indexes in the literature. Two evolutionary techniques, genetic algorithm (GA) and particle swarm optimization (PSO) method, are utilized to improve the gridshells’ regularity by using the indexes. An approach is presented to generate the initial gridshells for a given surface in MATLAB. The two methods are implemented in MATLAB and compared on three benchmarks with different Gaussian curvatures. For each grid, both triangular and quadrangular meshes are generated. Experimental results show that the regularity of some gridshell is improved more than 50%, the regularity of quadrangular gridshells can be improved more than the regularity of triangular gridshells on the same surfaces, and there may be some relationship between Gaussian curvature of a surface and the improvement percentage of generated gridshells on it. Moreover, it is seen that PSO technique outperforms GA technique slightly in almost all the considered test problems. Finally, the Dolan–Moré performance profile is produced to compare the two methods according to running times.
... Some examples include integration of energy, daylighting, and cost analysis in high rise buildings in [11]; integration of energy, financial, and spatial programming compliance performance in [12]; determination of heating energy and investment cost analysis of a house in [13]; assessment of heating, cooling, and lighting performance in an open space office building in [14]; and implementation of a computer program named ENER-RATE to compare the energy use, indoor air quality, thermal comfort, operating plant load, financial costs, and other environmental degradation of design alternatives in [15]. On the other hand, another group of researchers have clustered structurerelated issues together such as shape and sizing optimization of truss and frame structures in [16]; shape optimization of a free form shell surface inspired by the Kakamigahara Crematorium in [17]; shape optimization of the continuous surface that forms the roof of the greenhouse facility in Gringrin Fukuoka in [18]; and implementation of a generative structural design system named eifForm in roof trusses in [19]. There exists interdisciplinary studies bridging the structures and daylighting disciplines (and in some studies a third discipline) in large span roof systems together, such as dialectic form finding of a grid shell regarding energy efficiency and structural performance in [20]; consideration of daylighting, structural, and manufacturing aspect of origami structures used for long-span roofs in [21]; integration of daylight, thermal comfort, and structural performance of large roofs in urban spaces in [22]; and studies on structural and operational energy efficiency of long span roofs in [23] Many of the aforementioned studies focus on a specific design or optimization problem considering multiple objectives and multiple disciplines without attempting to generalize the approach. ...
... According to Veltkamp et al., in design of free-form structures, the shape is the most effective to change the overall structural behaviour [41]. Shape optimization has been conducted for many shell structures including continuous shells [17,18] and grid shells [39,42]. For continuous shells, "a shape is defined by the oriented boundary curves (of two-dimensional structures) or boundary surfaces (of three-dimensional structures) of the body…and the optimal form of these boundaries is computed" [31]. ...
Article
Employing an interdisciplinary approach in design is an important part of the future of architecture. Therefore, taking a step toward better understanding the overlaps between disciplines, and formalizing the process of integration between disciplines accelerates progress in the field. In examining an interdisciplinary design approach using computational design and simulation tools, while considering shell structures as a special case for spanning large-span roofs, structural and daylighting discipline are considered. The aim is to understand what are the design parameters that co-exist in the structural and daylighting design disciplines, and how may these parameters be implemented in a parametric model created by designers. The parametric model that includes discipline specific parameters can later be used for interdisciplinary performance-based design. Implementing design parameters calls for an understanding of the ways in which parameters affect design and performance. This research considers the application of parametric design methods at the early stages of design for designing high-performance buildings.
... The genetic algorithm approach to structural topology optimization is applied in [32][33][34][35]. However, some attempts to design and optimize steel bar structures using visual scripts were undertaken in [24,36,37]. ...
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Rationalization in structural design in the field of steel structures mostly consists inreducing structural material. The aim of this work was to develop an algorithmic-aided, original and practical approach to shaping curvilinear steel bar structures of modular roofs, enabling their optimization. The first stage of shaping consists in creating algorithms that define the structures of shelters made of four roof units. Algorithmic definitions of the structures made it possible to obtain many variants of the roof structures with the adopted preliminary criteria. In order to evaluate the effectiveness of the individual variants, the genetic optimizations of the structures’ forms were carried out. Assuming that the structures were loaded with self-weights, the cross-sections of the structures’ members were optimized with the permissible deflections, while the structures’ weights were the optimization criteria. This allowed us to eliminate the design variants unfavorable in terms of shape and weight. In contrast, the structures with the most advantageous properties were then optimized for weight under snow and wind loads. The research allowed us to notice how the shapes of the structures influenced their efficiency. The dual approach proposed for shaping, which takes advantage of the generative design and consistent flow of information during shaping, allowed us to achieve better solutions compared to the traditional approach.
... It can be modelled as an NURBS surface and the coordinates of the NURBS control points can be used as variables. Generally speaking, NURBS control points are fewer in number than mesh nodes, and a single control point can affect the position of many mesh nodes at the same time [3] (Fig. 1, on the right). This strategy was already proposed in the 90 s by pioneers in the field of structural optimisation, such as Bletzinger and Ramm, who demonstrated the advantages of NURBS-based parametrisation [4]. ...
Article
This paper presents a comparison between human-defined and AI-generated design spaces through simple optimisation applications. A design space is a formal expression of a design idea. It is constructed by selecting a set of variables, which limit the search for suitable solutions to a design problem within a specific range of options. Most computational approaches to structural design are based on parametric modelling, which require the definition of a design space, and therefore an analytical formulation of a design idea. In structural optimisation, such approaches tend to limit the search for optimal solutions to a subset of the entire space of design possibilities, and do not necessarily prompt the designer’s creativity. Recent AI models, such as Variational Autoencoders (VAEs) (Kingma and Welling, 2014), have the potential to overcome some of the limitations described above. VAEs can construct design spaces by extracting implicit design variables from a dataset of design solutions. Such variables result from a learning process and are conditioned exclusively by the characteristics of the dataset, rather than by a human-formalisation of design thoughts. A VAE has been trained on an artificial dataset of shell structures to construct a design space, which has then been compared with a design space constructed through the explicit definition of design variables. The comparison has been performed by analysing the diversity of the solutions retrieved from both design spaces in two optimisation applications. The comparison demonstrates that optimisation based on AI-generated design spaces results in a greater diversity of design outputs than the predictable solutions provided by optimisation based on human-defined design spaces. Furthermore, such design outputs respond better to the selected performance criteria.
... In 2007, Pugnale and Sassone [97] described a method for morphogenesis and structural optimization of a reinforced concrete roof based on the application of a genetic algorithm. They performed a case study of the Kakamigahara crematorium in Gifu (Japan), designed by Toyo Ito with Mutsuro Sasaki. ...
Article
Conceptual architectural design is a complex process that draws on past experience and creativity to generate new designs. The application of artificial intelligence to this process should not be oriented toward finding a solution in a defined search space since the design requirements are not yet well defined in the conceptual stage. Instead, this process should be considered as an exploration of the requirements, as well as of possible solutions to meet those requirements. This work offers a tour of major research projects that apply artificial intelligence solutions to architectural conceptual design. We examine several approaches, but most of the work focuses on the use of evolutionary computing to perform these tasks. We note a marked increase in the number of papers in recent years, especially since 2015. Most employ evolutionary computing techniques, including cellular automata. Most initial approaches were oriented toward finding innovative and creative forms, while the latest research focuses on optimizing architectural form.
... 29 Many studies that have investigated shell design have considered their structural performance. 30,31 Once a shell is perforated, daylighting is introduced to the space. Perforated shell structures exhibit an especially pronounced interdependence between the parameters of form, structure, and required daylighting. ...
Article
Many computational studies generate an array of solutions for a design problem paired with their structural or daylighting performance. An enormous investment of effort and computational time is required to create these simulation-based datasets. However, the generated data is usually bound to the specific case studies they were created to explore. Can this data be useful for application to other design cases? This study employed a generative algorithm to fill a database with perforated shell structures covering a courtyard. A shell by Heinz Isler was chosen to be mapped onto the generated solution space based on its performance. The study found that this method is effective for predicting daylight performance, while structural performance modifications can be a source of inspiration for designing other structural forms.
... Focusing on shells' performance, many studies have considered structural optimization either in grid shells [29][30][31] or continuous shells [27,32,33]. Many other studies have integrated assessment of shell structural performance with other disciplines, such as energy-related design aspects (including solar radiation control [34]), or acoustics [14], as summarized in Table 1. ...
Article
In this work, a computational interdisciplinary design approach is used to integrate assessment of the structural and environmental performance of perforated concrete shell structures. Design parameters that co-exist in these disciplines and relevant performance criteria are identified. Questions result: how do these design parameters affect performance? What is the tradeoff between performance in each? Computer-aided design tools are used for form generation and performance assessment. Statistical analyses are used to study the sensitivity of performance to each parameter. Finally, the perforation ratio is found to be the most significant parameter affecting both disciplines; a value ≤ 10% to 20% is recommended for shell structures when translucent glazing is installed without shades in a Boston-type climate.
... In a research study, the shape of a free form shell was modeled using a NURB (Non-uniform rational basis spline) surface inspired by the Kakamigahara Crematorium designed by Toyo Ito. The shell was then structurally optimized by means of a genetic algorithm (Pugnale & Sassone, 2007). In another research study, Richardson & Adriaenssens (2014) conducted shape optimization of a gridshell related to x-and y-coordinates of the nodes. ...
Thesis
With the advancement of computational design tools paired with performance assessment technologies, taking an interdisciplinary design approach at the early stages of design is largely facilitated. The Master Builder whose role has been fragmented between multiple professionals of many disciplines is being recreated, this time by facilitating seamless collaboration among a plethora of minds and perspectives. In this mode of collaboration, studying disciplinary tradeoffs also becomes part of the design process. This calls for a new design approach with an understanding of other disciplines. A building needs to stand up and needs to be illuminated, thus the structural and daylighting disciplines are associated with the purpose of architectural design. Despite the interaction between the two, there is little research showing the overlaps. Understanding this integration helps designers better understand how making a decision affects other stakeholders. This dissertation is at the intersection of computational design, structural performance, and daylighting performance assessment. Shells are the ideal typology for investigating this interrelation as their form is related with force flow, while adding holes to the shell’s surface not only introduces daylight but also affects force flow thus structural performance. By employing a computational interdisciplinary design approach, and by choosing perforated concrete shell structures as the main structural typology, I ask: How can the designer identify the design parameters that are shared between the discipline of architecture and an engineering discipline? What are the design parameters that co-exist in the structural and daylighting design disciplines? How may these parameters be used by designers? How do the design parameters affect performance in structural and daylighting discipline? What is the tradeoff between performance in structural and daylighting design? How can the results of a specific design case be useful for application to other design cases that do not necessarily have the same boundary conditions? This research demonstrates how daylighting performance can be affected in the design of shell structures, a typology that is mainly driven by its structural design criteria in the literature. Also important is its demonstration of how a continuous shell can be perforated to the point at which becomes a grid shell; therefore, continuous and grid shells are two ends of a spectrum rather than two distinct structural typologies. A high-level significance of this dissertation is its marriage of the structural and daylighting disciplines and demonstration of how the two are closely related in shells by the perforation ratio. I find that perforation ratio is the most significant parameter that affects both disciplines and a number between 10% to 20% is the recommended limit for shell structures when translucent glazing is installed without any external or internal shading. One of the most significant contributions of this research is its methodological approach, which uses a formalized framework for categorizing design parameters in the structural and daylighting disciplines and then identifying overlapping design parameters. This design method, presented as a roadmap is the fundamental new component arising from this research. The final contribution of this dissertation explores how a generated solution space may become useful for other design projects which do not necessarily have the exact same boundary conditions. By abstracting the boundary conditions of new projects to match those in the solution space, the designer can examine possibilities and compare how making a decision in one field may affect performance in other fields.
... • Secondly, the fitness of a candidate geometry must be determined. Often an FE analysis is used to give a structural performance value, such as deflection (Pugnale and Sassone, 2007;Veenendaal and Block, 2014) or total strain energy (Liu et al., 2012;Tomás and Martí, 2010b). Alternatively, the self-weight might be the fitness value, subject to a given structural constraint such as a stress limit (Banichuk et al., 2006;Beghini et al., 2014;Uysal et al., 2007). ...
Thesis
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Rapid urbanisation and population growth is driving unprecedented levels of building construction. Over the next 40 years, approximately 230 billion square meters of new floor area will be constructed globally, a doubling of existing building stock. Already, the production of concrete and steel accounts for a third of worldwide industrial CO2 emissions, representing a major opportunity, and responsibility, for structural engineers to contribute towards a low-carbon future through efficient design. A significant majority of the structural material in a typical building exists within the floors, making these a prime target for material reductions. This dissertation shows that thin shell concrete floors are a viable alternative to typical slabs and beams in multi-storey buildings. Switching the dominant structural behaviour from bending to membrane action increases efficiency, enabling significant embodied carbon reductions. A system is proposed featuring pre-cast textile reinforced concrete shells of uniform thickness and shallow depth, supported at columns, with a network of prestressed steel tension ties. A lightweight foamed concrete fill is cast above the shells to provide a level top surface and transfer floor loads to the shell. The structural behaviour of this system is explored through a series of computational and experimental investigations, leading to refinement of the design, exploration of construction methods and the development of a complete design methodology incorporating novel theoretical work. The shells feature optimised singly-curved groin vault geometry. This provides efficient structural performance whilst simultaneously minimising construction complexity. Thus, a practical and scalable solution is proposed, which is shown to offer considerable embodied carbon savings over typical concrete and steel floor structures. This work provides a robust platform for future refinement and large-scale implementation of thin-shell concrete floors for sustainable buildings.
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This study looks into some practical implications of using evolutionary algorithms for optimization of free-form concrete shells in search of methods for automating design representation and determining the number of design variables. This study reports the insights and learnings from a set of numerical experiments, by changing the number of parameters, on thickness optimization of a barrel roof shell subjected to self-weight, an additional snow load, and an earthquake response spectrum. The practical advantages and challenges of two methods, parametric and direct representations, are analysed, and a spectrum of methods between these two extremes are investigated through experiments. The results demonstrate how changing the number of variables affects the quality of the design and the performance of the algorithm and why a systematic problem-dependent method for finding the best design representation and number of variables outside this spectrum can be beneficial.
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Evolutionary structural optimisation (ESO) method is based on the idea that by gradually removing inefficient materials, the structure evolves towards an optimum. Bi-directional ESO (BESO) allows for adding efficient materials in the evolution. This paper investigates the ESO and BESO methods in solving the topology optimisation of continua structures with a constraint on the global stiffness. Based on the work on stiffness optimisation with fixed load conditions, this paper focuses on problems considering design dependent loads. The dependence can be due to transmissible loads, inclusions of structural self weight and surface loads. Sensitivity analysis and evolutionary procedure for problems of fixed load conditions are modified to accommodate the load variation condition. A number of examples are presented for verification. The results demonstrate that ESO and BESO are effective in solving the optimisation with design dependent loads. BESO has the flexibility of balancing solution quality and computing time.
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