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Morphogenesis and Structural Optimization of Shell Structures with the Aid of a Genetic Algorithm
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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. ...
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.
... In contrast, optimization theory and FEA based structural shape optimization is capable of resolving the aforementioned issues, being a more generalized and rigorous choice of form finding. Some implementations of this approach can be seen in (Ding, 1986;Bletzinger and Ramm, 2001;Bletzinger et al, 2005;Uysal et al, 2007;Pugnale and Sassone, 2007;Tomás and Martí, 2010;Ding et al, 2017;Rombouts et al, 2019;Xia et al, 2019Xia et al, , 2021San et al, 2021;Meng et al, 2022), in which the optimizers range from gradient-based (e.g. gradient descent) to gradient-free (e.g. ...
Shape optimization is of great significance in structural engineering, as an efficient geometry leads to better performance of structures. However, the application of gradient-based shape optimization for structural and architectural design is limited, which is partly due to the difficulty and the complexity in gradient evaluation. In this work, an efficient framework based on automatic differentiation (AD), the adjoint method and accelerated linear algebra (XLA) is proposed to promote the implementation of gradient-based shape optimization. The framework is realized by the implementation of the high-performance computing (HPC) library JAX. We leverage AD for gradient evaluation in the sensitivity analysis stage. Compared to numerical differentiation, AD is more accurate; compared to analytical and symbolic differentiation, AD is more efficient and easier to apply. In addition, the adjoint method is used to reduce the complexity of computation of the sensitivity. The XLA feature is exploited by an efficient programming architecture that we proposed, which can boost gradient evaluation. The proposed framework also supports hardware acceleration such as GPUs. The framework is applied to the form finding of arches and different free-form gridshells: gridshell inspired by Mannheim Multihalle, four-point supported gridshell, and canopy-like structures. Two geometric descriptive methods are used: non-parametric and parametric description via B\'ezier surface. Non-constrained and constrained shape optimization problems are considered, where the former is solved by gradient descent and the latter is solved by sequential quadratic programming (SQP). Through these examples, the proposed framework is shown to be able to provide structural engineers with a more efficient tool for shape optimization, enabling better design for the built environment.
... These forms can be considered as design suggestions and used to inform further design iterations to develop an actual structural 14 design. The authors foresee two different ways of doing so: (1) parametrise an AI-generated form with control points and use optimisation tools -such as Genetic Algorithms -to improve its structural performance [50]; and (2) perturbate the latent code representing the AI-generated form with additional variables -using both input modes shown in Figure 11 -and run an optimisation process to search for more performative variations of such a form. ...
This paper presents the development and application of a computational design tool that can be used to explore an AI-generated design space for the conceptual design of shell and tensile structures. An AI model was trained to extract geometric features from a dataset of 40 well-known design precedents of shell and tensile structures and to construct a design space. The trained model was then endowed with an interface to allow the designer to explore the design space within CAD software. Unlike the majority of current approaches to parametric design and optimisation, the exploration of the design space-and therefore the interaction between the designer and the computational model-does not take place via design variables, but through visual input. The potential of this tool to support the conceptual design of shell and tensile structures is examined through an application involving iconic design precedents. The application shows that, unlike form-finding and optimisation, this tool generates design suggestions that are not performance-driven, and do not require the statement of the boundary conditions, which would predetermine the results. Despite this, such design suggestions can be considered plausible because they embed specific design knowledge resulting from a re-elaborating process of the main geometric features of the precedents used to train the AI model. These features include, for example, the shape of the openings, the number and location of the support points or the inversion of curvature, where present. The application results question the role of computational tools in conceptual design and illustrate an alternative strategy to explore the design space.
... The walkable roof of Fukuoka central "Grin Grin" Park in Japan designed by Toyo Ito and Associates used a similar approach using a Simulated Annealing as the optimization algorithm. The shell designed by Toyo Ito and Associates for Crematorium in Kakamigahara Crematorium applied the same approach but using a GA as the search mechanism (Pugnale and Sassone, 2007). Future experiments will include the test of the strategy in more constrained design settings and the examination of adequate search algorithms in such applications. ...
The resources involved in the construction and operation of buildings represent nearly 40% of the global emissions of greenhouse gases (GHG), making the building sector one of the primary contributors to global warming. This reality has led to the creation of many prescriptive regulatory and voluntary programs that aim to mitigate the environmental impact of the building sector while ensuring high standards for Indoor Environmental Quality (IEQ), particularly those regarding the thermal and visual comfort of building occupants. Thus, the design of high-performance buildings, i.e., resource- and energy-efficient buildings that yield high levels of IEQ, is a pressing need. This scenario pushes architects to simulate their projects’ environmental performance to better support design tasks in a process referred to as performance-based design.
This dissertation studies the integration of daylighting and Building Energy Simulation (BES) tools into performance-based design supported by computational design (CD) methods, particularly parametric design and Building Performance Optimization (BPO). The assumption is that the early integration of parametric, BES, and daylighting simulation tools can be highly effective in the design, analysis, and optimization of high-performance buildings.
However, the research argues that the current daylighting and Building Energy Simulation (BES) tools pose critical challenges to that desirable integration, thus hindering the deployment of efficient exploratory design methods such as Parametric Design and Analysis (PDA) and BPO. These challenges arise from limitations regarding (i) tool interoperability, (ii) computationally expensive simulation processes, and (iii) problem and performance goal definition in BPO.
The primary objective of the dissertation is to improve the use of daylighting and BES tools in PDA and BPO. To that end, the research proposes and validates five modeling strategies that directly tackle the limitations mentioned above. The strategies are the following: (i) Strategy A: Automatically generate valid building geometry for BES; (ii) Strategy B: Automatically simplify building geometry for BES; (iii) Strategy C: Abstract Complex Fenestration Systems (CFS) for BES; (iv) Strategy D: Assess glare potential of indoor spaces using a time and spatial sampling technique; and (v) Strategy E: Painting with Light - a novel method for spatially specifying daylight goals in BPO.
The research work shows that the strategies address the research problem and current limitations by (i) improving the interoperability between design and BES and daylighting simulation tools (Strategies A, B, and C); (ii) producing quick and adequate feedback on the daylight, thermal, and energy behavior of buildings (Strategies B, C, and D); and (iii) facilitating the spatial definition of performance goals in daylighting BPO workflows (Strategy E). These three important merits of the proposed strategies effectively contribute to improving the efficiency of using daylight and BES tools in the design, analysis, and optimization of high-performance buildings.
Finally, the dissertation discusses the merits and limitations of each strategy, provides useful guidelines and recommendations for their use in building design, and suggests future directions for further research.
... 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]. ...
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]. ...
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. ...
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. ...
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. ...
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.
Following the success of AI in statistical regression, image generation, and decision-making tasks, new computational tools based on AI have been proposed for design applications since 2014. Engineers have used AI models to improve the efficiency of software for structural analysis and optimisation, whereas architects have started exploring the potential of AI tools for image generation to support conceptual design.
This thesis aims to demonstrate that AI can support the design process at an even deeper level. In other words, AI models can autonomously learn design strategies and interact with a designer to suggest design options that are unconstrained and unbiased by a formal description of the design problem, which is often required in structural optimisation applications. AI models can also learn to produce technical descriptions of a design object, whereas current applications of AI in architectural design primarily focus on synthesising visual output. To do so, this thesis examines how AI models can be trained in architectural and structural design and how the trained AI models can be integrated with CAD software to support the design process.
This thesis takes the view that training AI in design can be considered as training a novice designer. Therefore, in line with early studies in AI in design conducted in the 1990s, this thesis examines how AI can simulate a designer’s cognition and, in particular, acquire design knowledge by simulating three learning mechanisms relevant to design education: expertise, playfulness, and analogical reasoning. In design education, expertise is related to studying and analysing design precedents; playfulness is linked to model-making, and analogical reasoning pertains to finding inspiration in domains other than architecture, such as nature, art, music, and literature.
Through a set of applications, the thesis shows how AI models can be trained in design by simulating the three learning mechanisms and how the trained AI models can be interfaced with CAD software.
The applications aim to open a new path for research in AI in design by demonstrating that AI can effectively simulate some aspects of human cognition and interact with a designer through an exchange of visual information. The designer can decide to use the outputs obtained through the interaction with these tools to inform different stages of the design process, which could include problem-framing and decision-making. Although no given tool can be guaranteed to expand a designer’s creativity or automatically lead to outstanding design solutions, the AI models described in this thesis reveal a certain degree of autonomy and thus have a higher potential than other computational techniques to support the design process at a deep level.
The objective of this paper is to discuss the characteristics of a family of space structures that are referred to as 'nexorades'. Typically, a nexorade is constructed from scaffolding tubes, connected together with swivel couplers. An important application of nexorades is for shelters of various sizes and shapes for temporary or permanent purposes. In such a shelter, the structural skeleton is provided by a nexorade and the cover is provided by a membrane material.
In optimization, multiple objectives and constraints cannot be handled independently of the underlying optimizer. Requirements such as continuity and differentiability of the cost surface and yet another conflicting element to the decision process. While "better" solutions should be rated higher than "worse" ones, the resulting cost landscape must also comply with such requirements.
Evolutionary algorithms (EA'S), which have found application in many areas not amenable to optimization by other methods, possess many characteristics desirable in a multiobjective optimizer, most notably at the concerted handling of multiple candidate solutions. However, EA's are essentially unconstrained search techniques which require the assignment of a scalar measure of quality or fitness to such candidate solutions.
After reviewing current evolutionary approaches to multiobjective constrained optimization, the paper proposes that fitness assignment be interpreted as, or at least related to, a multicriterion decision process. A suitable decision making framework based on goals and priorities is subsequently formulated in terms of a relational operator, characterized and shown to encompass a number of simpler decision strategies. Finally, the ranking of an arbitrary number of candidates is considered. The effect of preference changes on the cost surface seen by an EA is illustrated graphically for a simple problem. The paper concludes with the formulation of a multiobjective genetic algorithm based on the proposed decision strategy. Niche formation techniques are used to promote diversity among preferable candidates and progressive articulation of preferences is shown to be possible as long as the genetic algorithm can recover from abrupt changes in the cost landscape.
Evolutionary Structural Optimization (ESO) method is one of the powerful and promising techniques for pursuing the optimal structural form. Although it is easy to carry out the calculation of ESO, there have been remained some weak points in its evolutionary process, by which inefficiency of calculation is caused or unreasonable solutions are generated. The authors have already proposed a new method through the usage of the contour lines, which is named Extended ESO method, in order to remove such defects of the original ESO as well as to enable the structures to not only be scraped off but also grow up toward the final optimal structures. In this paper, extension for 3-dimensional structures of the Extended ESO method is proposed and the effectiveness of the proposed scheme is shown through some numerical examples as well as the application to the actual structural design project.
Design is a complex engineering activity, in which computers are more and more involved. The design task can often be seen as an optimization problem in which the parameters or the structure describing the best quality design are sought.Genetic algorithms constitute a class of search algorithms especially suited to solving complex optimization problems. In addition to parameter optimization, genetic algorithms are also suggested for solving problems in creative design, such as combining components in a novel, creative way.Genetic algorithms transpose the notions of evolution in Nature to computers and imitate natural evolution. Basically, they find solution(s) to a problem by maintaining a population of possible solutions according to the ‘survival of the fittest’ principle. We present here the main features of genetic algorithms and several ways in which they can solve difficult design problems. We briefly introduce the basic notions of genetic algorithms, namely, representation, genetic operators, fitness evaluation, and selection. We discuss several advanced genetic algorithms that have proved to be efficient in solving difficult design problems. We then give an overview of applications of genetic algorithms to different domains of engineering design.
This paper describes the application of genetic algorithm to the shape optimization of axisymmetric shells. The primary problem of axisymmetric shell optimization under fracture mechanics constraint is formulated as the weight (volume of shell material) minimization under stress intensity constraints. It is assumed that the shells are made from quasi-brittle materials and through-thickness crack presence is admitted. Taking into account the fact of incomplete information concerning crack arising (size, location and orientation) this paper presents some numerical results based on a guaranteed approach.
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.
This paper discusses the adaptive approach in genetic algorithms (GAs). It is tried to show how the adaptive approach affects the performance of GAs, suggesting some improvements in both the penalty function, and mutation and crossover. A strategy is also considered for member grouping to reduce the size of the problem. Some practical design of space truss examples taken from technical literature are optimized by the algorithm suggested in the current work. Design constraints such as displacement, tensile stress and stability given by national specifications are incorporated and the results are compared with the ones obtained by previous studies. It is concluded that the member grouping together with the adaptive approach increase the probability of catching the global solution and enhance the performance of GAs.