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Computational Morphogenesis - Design of a free-form concrete shell
... The processes of human thoughts are complex and flow more like a river than follow a set of instructions. The emergence of unexpected architectural forms through optimisation is, therefore, a clear illusion because it is always an expert designer to call the shots throughout the process [2]. Mutsuro Sasaki wrote that structural forms designed through optimisation are mutable, fluid and organic and can hence be called flux structures, but he also described in his book how critical it is that architects and engineers collaborate throughout the optimisation process to create such fluid structural ideas [3]. ...
This paper describes a novel approach to structural optimisation based on learning design strategies rather than searching for optimal solutions. In the proposed approach, an AI agent is trained through Reinforcement Learning (RL) to explore a 3D modelling environment and iteratively morph a flat NURBS surface into a doubly-curved shell structure. At each iteration of the 3D modelling process, the agent computes the maximum structural displacement through FEM analysis: it learns to select modelling actions through this feedback and progressively improves the performance of the input surface. Unlike current applications of RL in structural design, where the AI agent generates design options by recombining a predefined set of design variables, our approach aims to create structural forms through the interaction of a designer and an AI agent within a 3D modelling environment. An application illustrates that our agent can interpret a preliminary structural form defined by a designer and iteratively transform such a form to improve its structural performance. The trained agent can hence transform the geometry and improve the structural performance of any open surface that features a square footprint and is defined through a sequence of modelling commands. Preliminary results suggest that this AI agent can be used for the development of more interactive tools for structural design and optimisation.
... In the last few decades, a great attention has been paid to sustainability and efficiency in the architecture, engineering, and construction (AEC) industry. In the field of structural engineering, design strategies based on optimization techniques are being widely utilized by designers [1][2][3][4][5][6] and studied by researchers [7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Often, structural optimization processes are thought to minimize the weight, the compliance, or in a more complex way, the cost, by fixing a given amount of material and boundary conditions, while ensuring that the constraint conditions imposed on structural performance are respected. ...
A great attention has been recently paid to sustainability and efficiency in the field of civil engineering. In this context, structural optimization processes combined with shape grammar constitute an important tool to support the design phase of large scale structures. This paper proposes shape grammars for the topology optimization of grid shells and diagrid tall buildings characterized by triangulated patterns, with the aim to minimize the structural weight. The structural feasibility of the generated solutions is assessed through numerical analyses, while the optimized patterns are identified by means of optimization processes based on genetic algorithm. The results are provided in terms of optimal geometrical patterns, structural weight, stiffness/strength checks. The approach is helpful to support the investigation of lightweight structural patterns and structurally efficient solutions. The method could be expanded and improved by considering the minimization of different objective functions that take into account both the weight and construction aspects.
... The survival of the fittest turns the evolutionary process into a stochastic search process intended to find the variables that can best guarantee an individual's survival under particular environmental conditions. The approach has gained ground in the field of computational morphogenesis and architectural design [8][9]. ...
A force-driven generative grammar rule is proposed as a design exploration method for planar networks in static equilibrium within non-convex domains. The aim is to enrich the catalog of unconventional structural typologies. Empty or partial networks in equilibrium are used as the starting point of the process. The rule's successive application always leads to complete networks but ensures static equilibrium throughout the process. Overall, it operates as a form-finding engine for planar trusses and helps designers to gain knowledge and develop intuition about structural design. A number of case studies highlight the factors that affect: the number of iterations, the exploratory power, as well as the additional parameters that are required to apply a rule. Extension of the method to more general applications is eventually suggested. 1 Introduction and problem statement Design is an ill-structured problem [1] characterized by open-ended expectations, emerging constraints, non-quantifiable features, the absence of global optimality and contradicting solution paths. Designers tame this complexity through creative processes, such as design exploration. Design exploration frames the systematic, iterative generation of design candidates, in order to extend and/or gain knowledge about the problem. Traditionally, this knowledge only sources from the designer's own experience and/or references he/she has been influenced by. For that, the process itself is prone to premature design fixation, i.e. the inception of familiar features leading to the generation of similar designs that only represent a tiny fraction of the actual solution space. The tendency for premature design fixation is likely to coexist with a lack of creativity and the introduction of hard technical constraints and objectives , e.g. in the case of structural design. Nowadays, regardless of the numerous computational tools and the ubiquity of computers in design professions, computers are still far from being considered as collaborative partners during the structural design process. As a matter of fact, most built structures are incepted by human logic and experiences, while computers remain confined to means of design, exceling at computerized drafting and representation [2], or as means of technical assessment and optimization. Computational logic is rarely exploited to assist the generation of new designs. In order to influence design, parametric logic allows the variation of a finite set of numerical values within predefined domains, usually set by the constraints [3]. Though this approach offers the possibility to alter design candidates, the scope of design freedom and exploration are limited by the available input parameters and the way their parameterization leads to the solution. In addition, current design workflows seldom provide instant structural feedback. Consequently, prospective ways for architects and engineers to improve the structural design process may consider the: ▪ Exploitation of technological advances; replace computerized approaches by computational ones and make the most out of them. ▪ Investment on rule-based rather than on variable-based design; parameters define the design logic itself, not only the input variables. ▪ Integration of structural evaluation within the creative process; avoid the structural feedback as a discrete and disconnected subsequent step but consider structurally-informed generations. ▪ Elevate the designer and the computer as two collaborating partners; each contributing with specific, unparalleled skills. Following these principles, this paper presents a force-driven grammar rule, for the generative, interactive , and conceptual design of planar trusses. Its successive application within an algorithmic framework operates as a form-finding engine, capable of generating numerous design candidates in
... Although the shells are materially efficient structures, the complication of the shell theory prohibits them to be widely applied [1] (let alone the fabrication of the doubly curved surfaces). By the development of computational methods and techniques, numerical algorithms are able to analyze the statics of the shells by discretizing the continuous surfaces into finite elements [2] and sometimes reconstruct them back to smooth NURBS surfaces [3]. However, the design of smooth shells is still restricted to a few analytical solutions. ...
Membrane shells, which have minimized bending moments under certain load conditions, are regarded as ideal structural forms in terms of material efficiency. Most of the existing numerical form-finding methods are based on discretizing membranes into finite panels or funicular networks and focusing on gravitational loading only. In order to obtain smooth shells and to consider horizontal loads, this paper presents a method to find the equilibrium forms of the membrane shells by solving Pucher's equation. Radial base functions (RBFs) is utilized to represent stresses and shapes of the membranes, and a least square method is applied to find the controlling coefficients which allow the functions to fit the boundary conditions (e.g. zero stresses at the free edges) and the governing equation. When all the parameters are carefully chosen, the stress and shape functions can achieve sufficient accuracy. The presented method has been preliminarily implemented to find shells on a triangle ground plan incorporating horizontal loads. The form-found geometries are then analyzed by finite element models. The result confirms that the form-found shells have the stress distributions similar to the prescribed stresses.
... Yet, with the rapid growth of advanced artificial intelligence tools, studies evolved towards automatic generation of design solution, especially through the implementation of evolutionary optimization [28,16,49,21]. Specifically in the field of shell design, successful applications include the use of genetic algorithms for the optimization of axisymmetric and free form shells, [4,51,41], as well as in the optimization of other structural elements, such as trusses [47]. ...
Thin shells are crucially dependent on their shape in order to obtain proper structural performance. In this context, the optimal shape will guarantee performance and safety requirements, while minimizing the use of materials, as well as construction/maintenance costs.
Thin shell design is a team-based, multidisciplinary, and iterative process, which requires a high level of interaction between the various parties involved, especially between the Architecture and Engineering teams. As a result of technological development, novel concepts and tools become available to support this process. On the one hand, concepts like Integrated Project Delivery (IPD) show the potential to have a high impact on multidisciplinary environments such as the one in question, supporting the early decision-making process with the availability of as much information as possible. On the other hand, optimization techniques and tools should be highlighted, as they fit the needs and requirements of both the shell shape definition process and the IPD concept. These can be used not only to support advanced design stages, but also to facilitate the initial formulation of shape during the early interactions between architect and structural engineer from an IPD point of view.
This paper proposes a methodology aimed at enhancing the interactive and iterative process associated with the early stages of thin shell design, supported by an integrated framework. The latter is based on several tools, namely Rhinoceros 3D, Grasshopper, and Robot Structural Analysis. In order to achieve full integration of the support tools, a custom devised module was developed, so as to allow interoperability between Grasshopper and Robot Structural Analysis. The system resorts to various technologies targeted at improving the shell shape definition process, such as formfinding techniques, parametric and generative models, as well as shape optimization techniques that leverage on multi criteria evolutionary algorithms. The proposed framework is implemented in a set of fictitious scenarios, in which the best thin reinforced concrete shell structures are sought according to given design requirements. Results stemming from this implementation emphasize its interoperability, flexibility, and capability to promote interaction between the elements of the design team, ultimately outputting a set of diverse and creative shell shapes, and thus supporting the pre-design process.
Structural optimization techniques are becoming popular and effective approaches for the design of constructions, able to support architects and structural designers in the complex process of searching competitive solutions, usually in terms of structural weight, cost and accounting for specific structural/functional requirements. In case of gridshells, the structural weight is strictly related to the susceptibility of the structure to global buckling, which is often the governing design criterion. The susceptibility to global buckling is mainly due to the global stiffness of the structures, primarily related to the stiffness of the joints, to the boundary conditions, and to the presence of imperfections. In this context, the paper presents design strategies based on optimization techniques that specifically take into accounts the presence of semi-rigid, rigid and hinged joints in order to guarantee light solutions safe from global buckling phenomena. In particular, two approaches are proposed: the joint stiffness approach, which considers the gridshell composed by semi-rigid joints, all characterized by the same rotational stiffness, and the rigid/hinged approach, which considers the gridshell composed by most hinged joints, and by a low number of rigid joints arranged in optimal positions. The approaches have been applied to a case study characterized by different boundary conditions, different rise-to-span ratios and also considering both perfect and imperfect shapes. The results of the proposed optimization processes highlight the beneficial effect of a finite value of the rotational stiffness of the joints in the susceptibility of the gridshell to global buckling phenomena, leading to light structural solutions.
Gridshell are fascinating examples of structures able to combine aesthetic qualities and optimal structural performances thanks to a complete merging between “shape” and “structure”. To make gridshell structurally efficient is their capacity to cover large spans with light systems, exploiting the inherent strength of a double curvature shell. The design of gridshell is often the result of strategies based on both form-finding and structural-optimization techniques, sometimes combined together to obtain efficient structural solutions and architectural conception of space. Pre-tensioned rods, in some cases incorporated in the structure of gridshell, could particularly influence the structural performance of gridshell in terms of both its global deformability and stress distribution within its members. Consequently, pre-tensioned rods, when present, represent additional structural components to necessarily consider in the design optimization process of gridshell. Aim of the present paper is, first, to analyze the influence of pre-tensioned rods in the design optimization of gridshell and, then, to propose an optimization procedure for gridshell equipped with pre-tensioned rods. To this end, some simple gridshell examples and the case study of the Smithsonian Museum canopy in Washington are analyzed in the paper. The obtained results underline the importance of considering the presence of pre-tensioned rods both in the phase finalized to find the free-form shape and, moreover, in the structural optimization process.
Before the introduction of NURBS-based CAD software and optimisation, the design of form-resistant structures was based on the use of either experimental tools (physical form-finding) or analytical surfaces, and architects were challenged in the articulation of spaces from the intrinsic characteristics/rules of structural forms. An outstanding example of this kind is provided by the Church of Longuelo, which was built by architect Pino Pizzigoni in Italy, between 1961-1966. It was conceived as composed by two major elements – an irregular frame and a set of shells suspended to it. The entire design process was based on the calculation of the frame on which the shells have been just added as a dead load. This paper presents one possible way to redesign the church parametrically. Comparison with the original design is not performed at the final formal level, which can logi-cally differ, but around the concepts behind the project. The aim is to show how current digital design and optimisation tools are affecting the way architects design. But, at a higher level, the purpose is also to highlight where conceptual design is now taking place in the process.
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