Parametric modeling in form finding and application to the design of modular canopies

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1 Mobile and Rapidly Assembled Structures IV 223 Parametric modeling in form finding and application to the design of modular canopies G. Curletto Department of Civil, Chemical and Environmental Engineering, Genoa University, Italy Abstract Designers of modular systems having complex form should consider integrated approaches mostly based on technology, structural mechanics and economy. Due to both the configuration complexity and structural behavior that may be subjected to instability collapse and considerable vibration, the analysis and design of these models may lead to results too complicated to be carried out, limiting the use of new forms. To overcome these obstacles, the use of versatile tools must be applied in both the modeling phase and the analysis phase. The design solutions pursued in the present paper are devoted to the use of parametric software such as Grasshopper, Karamba and Millipide in which, through the modification of parameters, it is possible to vary the construction shape and carry out the structural analysis, taking into account all the above-mentioned components. The present research considers the potential of these tools in the parametric structural optimum design of modular canopies for outdoor installations. The design process is ruled by a development of algorithms for modeling, analysis and optimization of structures, applied to modular service stations. The objective is to model a structure reproducible on a large scale, simple enough to be assembled on site, and inexpensive. It is a canopy designed to organic form in which two parts may be identified: a trunk and an assemblage of radial made up of a series of steel elements connected to each other, supporting a lightweight polycarbonate cover. The dimensional, technological and formal characteristics are provided through a series of structural optimizations controlled with parametric tools. Keywords: parametric modelling, form finding, structural optimization, modular canopy, service station, Grasshopper, Karamba, Galapagos. doi: /mar140181

2 224 Mobile and Rapidly Assembled Structures IV 1 Introduction Over the years the service station has become an institution and the petrol station an indispensable factor in the daily life of many people. Yet, despite the innovation of service stations, their architecture remains relatively unchanged. The similarities are due to the need to make a project easy to standardize and economical objectives often difficult to reach with innovative products [1]. During the 20th century, a process of artifact taxonomy evolved through the application of criteria of modularity and decomposability of the functional and spatial elements. Moreover, the evolution of the functional, figurative and constructive apparatus of the petrol station signals the progressive autonomy of the canopy, which is detached from the main volume of the service station building and has come to be viewed as an independent, self-contained accommodation in the yard. It grows both as a single and continuous element on discrete and numerous supports, both mushroom-shaped and with a central pillar. The objective is to design a product that is easy to standardize, economical, and in which engineering, structural and material considerations are motivated by the shape, the structure and the optimization analysis. The potentiality of parametric modeling has been studied, developing a model in which geometric and structural characteristics evolve continuously until the optimal solution according to the established parameters is found. The sketch of shape, the modeling of the structure and the component sizing are constrained by some objectives, which become basic parameters of project. 2 Design parameters Any design process has to deal with the issue of correctly formulating the parameters. It could be useful to identify and classify the main parameters so as to define the degrees of freedom and design variables which can be independent or associated. It is important to distinguish the following five classes of parameters, known as: Shape: Includes macro-scale and micro-scale meaning, the model as a whole as well as the study of the individual components and their interrelationships. Structure and Topology: Distinguishes the main supporting structure and the secondary elements; Relates to the assembly of the components and the boundary conditions imposed by the designer. Structural Behavior: Relationship between actions (snow, wind, quake), internal forces (stress) and deformations (displacements); Describes the mechanical characteristics of the model, providing information on the stress, the deformations, etc., taking into account the external forces. Material: Closely connected to structural behavior, it is related to the mechanical characteristics, the cost of extraction, production and processing, and to the aesthetic and formal characteristics sought by the designer.

3 Mobile and Rapidly Assembled Structures IV 225 Technology: Since the building requirements are generally pre-eminent during the design process, all the technological aspects are included in this class of parameters. Besides these, it is useful to consider another class equally important in the field of service stations namely standardization and commercialization of the product, which requires: modularity of the components, independent of the single canopy; economy; ease of transport and assembly; and innovation and distinction in the urban landscape. Proper management and control of the parameters and their interrelationship involves a complex design in which the alteration of any value has a direct consequence on the entire system. One of the useful methods to deal with this problem is to apply parametric tools, in which parametric models are easily modified through the initial variables and make it possible to quickly get very complex forms that incorporate the properties of materials, manufacturing constraints and logic composition. The methodology used to conduct the design is based on two steps: parametric design of the structure, so a study for the least number of parameters that best describe the model in all its characteristics; study of the optimal configuration, in order to determine the structure that best meets the requirements of the problem. 3 Tools for integrated parametric design This type of methodology can be performed with some newly developed software, such as Grasshopper which is applied to the modeling phase; Karamba, which is used for the structural analysis; and Galapagos, which enables to reach the optimal configuration. It is useful to briefly examine the characteristics of each of these tools in order to highlight both their potentials and limitations. 3.1 Shape design: Grasshopper Grasshopper, one of the most well-known plug-ins for Rhinoceros, obviates some limitations related to the flexibility of the basic form for particular formal requirements and the difficulty to obtain rapid changes of complex models. Unlike traditional programs, the algorithmic modeling requires a logical/mathematical approach because Grasshopper is a visual application (visual scripting), created to suggest to the designer the potential of scripting. Through a graphical method based on a series of algorithms, sequences of instructions have been defined and translated into three-dimensional models. This modeling approach through scripting provides the ability to define the project with mathematical functions, to generate parametric models easily modified through the initial variables, and to quickly create very complex shapes featuring repeated geometric elements [2 3].

4 226 Mobile and Rapidly Assembled Structures IV Figure 1: Example of algorithmic sequence defined by Grasshopper. 3.2 Structural analysis of parametric models: Karamba Currently, because of structural tools, it is possible to analyze complex parametric models [4]. Developed since 2011, Karamba, Millipide, Kangaroo and other applications enable designers to realize accurate analysis, automatically update the results for every variation of the design parameters, and to view real-time stress, tensions, strains and other external factors. In this paper the model has been analyzed with Karamba, which utilizes two basic elements: beams and surfaces [5]. The combination of these components produces a wide variety of structures in which it is possible to define not only geometric characteristics, but to integrate engineering components: material, restraints, loads acting on the surfaces etc. 3.3 Optimization of shape: Galapagos Recently, optimization in parametric environment has been a subject of interest to many researchers and its use is growing in the professional field [6]. The designer, in analyzing complex structures, identifies various problems objectives to solve that can be developed through the use of codes which support the search of the optimal configuration. In this field, the optimization exploits genetic algorithms (GA) for their ability to find solutions in complex environments; in fact, they are searching algorithms inspired by the mechanism of natural selection and reproduction. The basic idea is to simulate the evolution of a population of individuals, which represent candidate solutions to a specific problem, favoring the survival and reproduction of the best. Then GA develop a set of points (population), belonging to the domain of the function to be optimized, making sure that the information on each can be transmitted and combined with others. In relation to parameters, defined by a specific domain, the optimization process can be observed in order to search the optimal solution to the objective defined by the user [7 8]. The advantage of these algorithms is needing to know only the function that has to be optimized (objective function), making them more effective than conventional optimization techniques.

Mobile and Rapidly Assembled Structures IV 227 The scheme below describes the optimization process of two parameters (Prm 1 and Prm 2), in which the objective is to minimize/maximize a specific value

Finally, the software shows the combination of values belonging to a specific range, defined by the user.

5 Mobile and Rapidly Assembled Structures IV 227 The scheme below describes the optimization process of two parameters (Prm 1 and Prm 2), in which the objective is to minimize/maximize a specific value (objective function). Galapagos produces an optimization function, which is useful to examine specific values at each generation. Finally, the software shows the combination of values belonging to a specific range, defined by the user. During this process the range of values combination narrows in order to find the best solution for the problem. Figure 2: Optimization process. Upper left: principal components of Galapagos: parameters (Prm1 and Prm 2) and objective function. Upper right: optimization function with 100 generations. Bottom: combination of values for each generation in order to find the best solution. 4 Project: modular canopy for petrol stations The principles of parametric modeling are applied to the design of a canopy by developing a model whose features of form and structure evolve continuously until the optimal solution is found according to the established parameters. In addition to these technical aspects, a strong architectural and aesthetic component has been maintained in order to aid in the selection of some formal solutions over others. The search for the shape is conducted primarily through shells seen in both architecture and in nature, followed by a brief study on the configuration that enables the best protection from weather agents. In a second

228 Mobile and Rapidly Assembled Structures IV phase, the system is examined in order to determine the parameters that control the shape and its characteristics.

6 228 Mobile and Rapidly Assembled Structures IV phase, the system is examined in order to determine the parameters that control the shape and its characteristics. Finally, it is possible to make a detailed analysis, from macro-scale to micro-scale, in which the cover components are sized, studying the connection system, transport and assembly. 4.1 Definition of the shape: from concept to modeling An accurate study of past models is essential for proper planning. The history of architecture provides many examples of innovative solutions regarding service stations: grid-shell surfaces; mushroom-shaped covers developed with different technologies and materials; and organic shapes for example, branching trees and gills which support the caps of mushrooms. In relation to patterns, integrated with the desire to create a modular, autonomous and innovative canopy, a continuous coverage has been designed as a modular element supported by a central pillar, and developed in a radial pattern. Another important problem to consider is the connection between canopies and the need for a solution that will ensure the best protection against weather agents. As mentioned, it is important to develop the geometry with some parameters easily identified and defined within a certain range, for the purpose of checking the geometric features as the parameters vary. So the model is developed in Grasshopper, assuming a continuous surface in mushroom shape, produced from the rotation of a generating curve whose curvature is governed by the coordinates of three points P 1, P 2, P 3 design parameters. After that, it is useful to divide the surface into two parts: the trunk and radial pattern. So the first step is to create a cylinder with a hollow section for the trunk, while the radial pattern is composed by 12 segments of equal size, copying the one obtained by the 30- degree rotation of the base curve. This constructive choice on one hand facilitates the assembly and transport, and on the other hand ensures the standardization of the components. Figure 3: Modeling of the generating curve and division of the canopy in trunk and radial pattern.

7 Mobile and Rapidly Assembled Structures IV 229 The shape is generated using NURBS modeling, so to realize the structural analysis, it is necessary to convert it into planned juxtaposed surfaces, called Mesh, connected by a triangular grid. Consequently, it is possible to define the material and the cross-section characteristics, to impose constraints and to analyze the structure. 4.2 Study of the structural behavior: from the definition of characteristics to the analysis The project has integrated from the beginning of the shape study, material and structural behavior in one single process. These components can be added directly with the shape using the Karamba plug-in, in order to understand both the potentials and limitations. To realize a correct analysis, the following characteristics have been considered: supporting steel structure, a resistant material against stress and external actions, easily assembled with welded or bolted joints; rectangular hollow sections (height 8 cm, base 4 cm and thickness 3 mm); cover plates of polycarbonate; structure constrained at the base. Analyzing the current system subjected to the load combination of shelf-weight and external forces is not rigid enough, presenting high vertical displacements on the outer edge. Therefore it is necessary to improve the structure with an optimization process in order to increase the structural rigidity. Using Galapagos, the overall shape of the canopy has been improved operating at the macro-scale and subsequently, the section of the weight-bearing structure has been optimized, working at the micro-scale. 4.3 Finding the optimal configuration: shape and section optimization Galapagos enables one to consider the parameters of shape, section, etc., defined in a certain range of variation, finding the combination of values that best corresponds to the requirements imposed by the designer. In order to develop the analysis, it is important to properly determine the parameters of the system and the load combination, for which it is required to maximize the structural stiffness of the canopy. In the present case, five parameters have been defined, which correspond to the coordinates of the three points P 1, P 2, P 3 guide points of the generating curve. In this specific case, the load combination includes self-weight and external actions like snow and wind. The following scheme describes the five parameters for which the model is optimized, for the radius and the height of the canopy, whose values correspond to the points coordinates just mentioned. Finally, the range of variation of each parameter is defined as approximately 0.02 m.

8 230 Mobile and Rapidly Assembled Structures IV Figure 4: Determination of the five parameters and their ranges of variation. The result is described in the following table, which presents a sequence of states in the optimization process to 100 generations. Note that the process significantly changes the value of the maximum displacement in the first 20 generations, later stabilizing in subsequent stages. Figure 5: Graph shows the values of the maximum displacement. As a result of the optimization process, to further increase the structural rigidity, according to such requirements, it is useful to query the system no longer on the already great overall shape, but on the supporting structure sections of the most-stressed radiating portion. In fact structural mechanics shows that one of the possibilities for strengthening a system is to increase the section height, so as to increase its modulus. Observing the maximum vertical displacement on the outer perimeter of the canopy, it is advisable to thicken the rays in the central part, where their curvature renders them most vulnerable to stress. It is of no use to increase the size of the entire section only to limit the growth of the self-weight in the most stressed part. Working with Grasshopper, the 12 rays have been identified, dividing each of them into eight equal parts, so as to define different height sections. Aiming to increase the structural rigidity, the parameters of the project are the height sections, selecting a variation range between 0.08 and 0.30 m.

9 Mobile and Rapidly Assembled Structures IV 231 Figure 6: Region of increased rigidity. After the determination of parameters, the optimization of the system can be fulfilled, setting the basic and thickness section and placing the height values as variables. Below are described the values of section height as a result of the optimization process. In the central portion, the height coincides with the maximum value of the domain, and with the minimum value in the border part. Figure 7: Optimum model section with the optimized heights. To ensure the quality of the result for checking the solution provided by Galapagos, it is highly recommended to define the correct domain of the variables and to establish the optimization function. Finally, after the optimization processes, the structural behavior of the canopy has been analyzed in the points of maximum stress, verifying the resistance and the rigidity of the system when subjected to external forces.

10 232 Mobile and Rapidly Assembled Structures IV 4.4 Description of the components and their function After verifying the soundness of the structure, the canopy s details have been described, defining the individual components, their technical characteristics and assembly: Figure 8: Exploded view with specified components of the canopy. base: a steel plate that fastens the trunk to the floor; trunk: a steel structure composed of 12 rectangular, hollow section elements connected by four circles, the purpose being to add strength (must be considered a single element); rays: 12 steel elements with variable section connected to the trunk, which form the main structure resistant; beams: small size elements arranged between rays creating a concentriccircle structure; tie-beams: a network of steel wires crossing the radial pattern which are connected to the rays, in order to maintain a rigid system under the effect of external actions; coverage: a few-millimeters-thick surface made of polycarbonate and secured to the radial pattern, that provides protection against weather agents;

Mobile and Rapidly Assembled Structures IV 233 outer circle: frame in steel useful to connect and bind the rays of the canopy, and to secure the coverage.

11 Mobile and Rapidly Assembled Structures IV 233 outer circle: frame in steel useful to connect and bind the rays of the canopy, and to secure the coverage. Another important factor to ensure the correct operation of the canopy is the drainage of the rainwater that is constituted by two elements: a flat cable, which allows collecting the water, and a drain tube, fixed along the trunk to make it flow until ashore. In addition to geometrical aspects, a strong engineering approach has been maintained in order to guarantee the construction of each component of the canopy. In fact, the interaction between Grasshopper and its plug-ins enables to create a model in which geometric and engineering aspects are integrated. 4.5 Modularity and connection system After defining the elements of the canopy and its operation, it is important to analyze the connection system between adjacent canopies in order to design a larger service station. The best protection from the weather agents has to be guaranteed, with minimal changes in the cover components. For this reason, it is better to juxtapose canopies at the same height, matching one of the twelve sides of the radial pattern and studying the coverage triangular connection. Additional component connection has not been applied, because modifying some segments is a more affordable way to realize it. The polycarbonate coverage has been extended using segments, with a slight slope of the elements to ensure the flow of rainwater. The outer circle has also been modified, becoming a strengthening element of the system, and connecting the canopies. Figure 9: Perspective view and connection between canopies.

12 234 Mobile and Rapidly Assembled Structures IV 5 Conclusions In this paper, formal and structural issues have been developed describing the relationship between these two components. Tools to achieve an integrated design have been investigated, offering parametric modeling as one of the solutions that best integrates physical, constructive, structural and technological components. The first part focuses on the description of these tools, such as Grasshopper, Karamba and Galapagos, which allow the creation of complex shapes in which the parameters and all characteristics are easily editable. Afterward, the theoretical considerations have been applied to the design of a modular canopy for service stations. The choices and motivations have been described to realize the model starting from the initial step through the definition of the details. The potential of parametric design has been exploited developing a model whose shape and structure features evolve continuously until the optimal solution is found, according to the established parameters. In addition to these parametric aspects, it has been decided to keep a strong architectural and aesthetic component to narrow the field of formal solutions. In conclusion, a new approach to digital technology has been described to capture a mastery of every phase of design and to exploit the potential of these tools in order to realize controlled and detailed model in each component. References [1] Minale M., How to Design a Successful Petrol Station, Hoepli, Londra, [2] Tedeschi A., Parametric Architecture with Grasshopper, Le Penseur, [3] Grasshopper, Algorithmic Modeling for Rhino, [4] Khabazi Z., Generative Algorithms using Grasshopper, [5] Karamba, Parametric Engineering, [6] Pugnale A., Sassone M., Morphogenesis and Structural Optimization of Shell Structures with the Aid of a Genetic Algorithm, Journal of the International Association for Shell and Spatial Structures, Vol. 48, n. 155, December [7] Sarkisian M., Long E., Shook D., Doo C.S., Optimization Tools for the Design of Structures, 20th Analysis & Computation Specialty Conference, ASCE 2012, pp [8] Koza J. R., Genetic Programming. On the Programming of Computers by Means of Natural Selection, the MIT Press, Cambridge, 1992.

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