Proceedings of the IASS Annual Symposium 2016 “Spatial Structures in the 21st Century” 26–30 September, 2016, Tokyo, Japan K. Kawaguchi, M. Ohsaki, T. Takeuchi (eds.)
Design of a composed origami-inspired deployable shelter: modeling and technological issues. Giulia CURLETTO1*, Luigi GAMBAROTTA2 1* Department of Civil, Chemical and Environmental Engineering Polytechnic School, University of Genoa Via Montallegro, 1 – 16145 Genoa, Italy
[email protected] 2 Department of Civil, Chemical and Environmental Engineering, University of Genoa
Abstract A novel and efficient approach to the design of foldable architectural structures based on rigid Origami is here proposed to obtain lightweight constructions. This kind of structures are made by rigid thin plates, easily assembled and transportable. In particular, a composed Origami in-plane structure is developed, testing two different typology of folding solutions. The model has been developed by applying parametric design, which allows to vary the geometric parameters to assess the sensitivity of the structural response, with the aim of finding the best structural morphology. Manufacturing issues have been integrated in this process to develop a feasible construction. Thin panels of composite material Hylite® have been considered as particularly interesting to develop a model in which panel’s core material can provide a hinge function, suitable to be used for deployable structures. Keywords: Origami, foldable structures, modular shelter, form-finding, parametric modeling
1. Introduction Rigid foldable structures inspired by Origami are becoming increasingly popular in Engineering and Architectural designs. Foldable principles are applicable to building structures for creating transformable spaces, which configuration continuously evolves during the deployment process. Foldable plates consist of triangular or quadrilateral panels connected together along their edges by cylindrical hinges, which allow the deployment mechanism according to an Origami pattern, as described by Schenk and Guest [13]. Although this model is potentially flexible, technological issues rarely enables the application of foldable principles to building structures. In case of folding motion, such as deployment mechanism, the thickness of the panels and its material has to be considered. Moreover, efficient hinges are required to be used as folds, and finally a mechanism to deploy the structure has to be developed. In the recent years, relevant foldable structures have been presented, proposing several materials, hinges, and deployment mechanism solutions. A bar steel structure connected by kinematic joints and a tensile shelter has been studied by De Temmerman et al. [7], a textile-reinforced concrete folded structure has been designed by Chudoba et al. [5], and a pedestrian bridge, whose deployment is realized using an hydraulic system has been realized by Heatherwick Studio [9]. The aim of this paper is to propose a novel and efficient approach to realize mobile structures easily transportable and assembled on site, using the potentiality of the material Hylite®, an aluminum Copyright © 2016 by Giulia Curletto, Luigi Gambarotta Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Proceedings of the IASS Annual Symposium 2016 Spatial Structures in the 21st Century
composite panel with a polypropylene core and aluminum outer skins. The main advantage of this material, in addition to its lightweight and thin panels, is the possibility to use the core layer as hinge, ensuring the folding motion operation on the material itself without add further components. This approach is applied to a specific project of a mobile modular shelter inspired by Origami technic, easily transportable, assembled and scalable.
2. An efficient design for foldable structures The design of foldable structures includes many aspects: geometric, structural and technological issues have to be integrated in a process that continuously evolves until to find the best configuration. Various parameters are included in modeling and construction steps, so the key point for the design is to identify the criteria of the project and the ideal methodology to apply. The method to design a suitable transformable structure is not straightforward but various iterations are required integrating all the relevant aspects. In this approach, specific criteria have been identified finding the priorities to respect, then computational parametric methodology has been chosen as the ideal approach for designing foldable structures. 2.1. Design criteria Nine criteria have been followed to evaluate the efficiency of the design, as proposed by Hanaor and Levy [8]. Briefly, these criteria suggest readily applicable flexible modular design, high component uniformity, compatible folding, structural efficiency, care about wear and tear to connections, minimal foundation, care about degree of freedom, simple articulation of joints and hinges and light equipment to assist in deployment and folding. The approach proposed in this paper, not only takes into account low weight, high compatibility and transportability, but also it aims to respect all the above criteria. 2.2. Parametric design The identification of a method to represent and model foldable structures is basic to a correct interpretation of its behavior, especially since Origami have a very complex geometry that requires detailed studies. Here, a specific approach based on parametric modeling using the visual scripting software Grasshopper [12] has been proposed, which is valid and reproducible for every Origami foldable structures. The core advantage of this approach is the possibility to draw and edit complex models and simultaneously extract updated data analysis, by changing geometric, technological and structural parameters and their relationship. The first step in modeling is focused on the identification of the geometric parameters that characterize the dimensions of the model, on the base modules to reproduce and on the relation between adjacent faces to guarantee the compatibility conditions. Once the parameters have been defined, the geometric drawing can be developed elaborating an efficient algorithmic sequence, as described by Curletto and Gambarotta [6]. The second step converts the geometry into the structure, mechanical data are assigned (using Grasshopper plug-in Geometry-Gym [10]) and the structural response is obtained using FEA. The results obtained using this approach and tools will be discussed in the following paragraphs.
3. Geometry of the composed foldable structure Geometry of a rigid-foldable structure is described focusing on the relevant parameters that characterize the geometry and their mutual relationship. Rigid panels connected together along their edges by cylindrical hinges characterize foldable structures, whose behavior depends on their geometrical shape (plane or free form), shape of folding (longitudinal or pyramidal), number of folding convergent in a joint (1DOF or plus), and deployment (in-plane or in-space) [14]. These features classify Origami, suggesting different fields of application. For example Miura-Ori, Yoshimura, Waterbomb base are all common rigid foldable pattern but Miura-Ori and Waterbomb base have a deployment in all directions and the Yoshimura enables translational motion, so Miura-Ori has been widely applied in Engineering, 2
Proceedings of the IASS Annual Symposium 2016 Spatial Structures in the 21st Century
while Waterbomb base is suitable for smart materials and more complicated designs. This consideration demonstrates that the choice of the pattern is the first point for realizing an efficient model. The purpose of the proposed project is to realize a rectangular shelter with as much as possible independent dimensions in order to be easily adaptable and scalable, so different Origami have been investigated, studying the possibility to integrate two or more different pattern and their relative deployment process. The result is a combination of different folding to obtain a novel composed Origami structure (Fig.1) that best suits to realize a mobile shelter applicable in different contests.
Figure 1: Composed foldable geometry inspired by Origami pattern.
A longitudinal folding has been chosen for the central portion, where uninterrupted hinges connect parallel rigid panels. The lateral edges of the central portion are linked to a module that derives by Miura-Ori, as proposed by Yasuda et al. [15], but presents different relationship between panels dimensions (Fig. 2a). The fold pattern consists of a replication of a single module, so it can be expanded or constricted simply repeating the base module periodically. Geometric parameters and their mutual relationship can be studied only for a single module, considering that length L and height H are fixed, while width W of the base module and the number of modules n define the final width of the whole system, 𝑊 𝑛 (Fig. 2b).
Figure 2: (a) Decomposed model: central portion presenting longitudinal folding and lateral portions inspired by Miura-Ori; (b) Geometric parameters characterizing the geometry, with highlighted the base module.
A correct modelling of the geometry requires pointing out all the dimensions that interest the base module, considering the necessity to guarantee the compatibility condition between central and lateral portions during the deployment mechanism. Central part consists of two equal panels symmetric on 𝑋 3
Proceedings of the IASS Annual Symposium 2016 Spatial Structures in the 21st Century
direction (Fig. 3) having dimensions 𝑎, 𝑏 and angle α, all independent parameters that directly affect length and width of the whole model. Each lateral portion is composed by eight panels symmetric on 𝑋direction, having in common with the central part the dimension 𝑏 and the angle α. Four quadrilateral panels have the same dimensions 𝑏, 𝑐, while the smallest one have dimensions 𝑏, 𝑑. The value of 𝑐 directly affects the height of the model and the value of 𝑑 interests the length of the model, together with the central portion. Finally, the triangles have dimensions related to 𝑏 and α, the edges are 𝑏𝑐𝑜𝑠α, 𝑏𝑠𝑖𝑛α, 𝑏, respectively.
Figure 3: Composed Origami pattern, with highlighted the base module and valley/mountain folds.
A significant parameter to consider is the angle of deployment 𝜃 that governs the expansion of the geometry ranging from 𝜃 = 0, indicating the unfolding configuration, to 𝜃 = 𝜋⁄2, indicating the fully compated configuration. Varying the value on the angle of deployment 𝜃 and the values of geometric parameters 𝑎, 𝑏, 𝑐, 𝑑 and α, different configurations are possible, so very flexible models are obtained (Fig. 4).
Figure 4: Example of models obtained by changing geometric parameters.
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Proceedings of the IASS Annual Symposium 2016 Spatial Structures in the 21st Century
4. Behavior of the composed foldable structure The design of foldable structures requires understanding the structural behavior of the model in terms of the geometric parameters in order to find the best configuration of deployment. Computational methods can strongly contribute to this aim, allowing drawing and modifying complex models and simultaneous carrying out the structural analysis. In this research, the parametric software Grasshopper and its plug-in Geometry-Gym have been applied to define structural data, including load condition, constraints, material etc. In such way, it is possible to import the model data with both geometric and structural characteristics into the finite element analysis package Ansys. An example has been considered concerning the composed Origami structure made by four modules and having whole in-plane dimensions 8.40x4.40m. The operating configuration to obtain a rectangular shelter, deployed at the configuration characterized by an opening angle of 𝜃 = 51.5°, has dimensions 5.40x3.00m and height 2.42m, (Fig. 5). It is subjected to vertical pressure representing the snow load of 2KN/m2 superimposed to its own weight. The finite element model is composed of triangles and restrained at the base with simple supports.
Figure 5: Finite element discretization of the composed Origami structure, (a) isometric view, (b) lateral view, (c) front view.
The structural behavior relative to the uniformly distributed forces acting on the top structure and representative of the snow load is shown (Fig. 6). The central V-shaped part of the composed foldable system presents a bending behavior, characterized by longitudinal tensile stress at the intrados with maximum value equal to 𝜎 = 1.6 𝐾𝑁/𝑐𝑚2 , and at the extrados a compressive stress with minimum value equal to 𝜎 = −1.67 𝐾𝑁/𝑐𝑚2 .
Figure 6: Normal stress field due to dominant bending in the horizontal foldable structural element.
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Proceedings of the IASS Annual Symposium 2016 Spatial Structures in the 21st Century
The lateral portions of the composed foldable system play the role of support and result on the average as compressed members. The corrugated shape of this structural portion makes the system safer to compressive buckling phenomena. Moreover, from the Figure 7, it is possible to observe that in some regions, where the horizontal foldable structure is connected to the vertical supports, tensile stresses appear as a consequence of inversion in the bending moment. Finally, in these lateral structural elements the minimum compressive stress and the maximum tensile stress take the value 𝜎 = −3.5 𝐾𝑁/𝑐𝑚2 and 𝜎 = 0.6 𝐾𝑁/𝑐𝑚2 , respectively.
Figure 7: Stress field in the support elements.
5. Technology of the composed foldable structure Despite the wide research on foldable shapes, applications are not so common in Architecture and Civil Engineering, because of difficulties to transform geometric models into real structures: different parameters are considered and technological issues arise. The conversion of a foldable geometry into a structure essentially requires to convert surfaces to rigid-panels and edges to cylindrical hinges. Folding mechanism involves complex kinematics, where all folds have simultaneous motion. Moreover, since rigid-Origami structures have been mainly studied in Academia, there is no industrial standardization for connections, joints etc. Finally, issues related to the choice of material and thickness of the plates need to be discussed. Deployable structures require lightweight materials, for ease of both transportation and manipulation. The thickness of the panels is an important point, because when the structure is approaching the closure, contacts between the adjacent faces takes place. In the recent years some attempts have been developed, testing different materials such as concrete, cardboard and wood, as proposed by Robeller et al. [11]. Several strategies for dealing with thick elements have been proposed, for instant Tachi [14] proposed to apply double-layered panels of constant thickness by offsetting the boundary shape avoiding collision during folding motion. Solutions to deploy simultaneously the whole system have been evaluated using hydraulic systems or folding machines [5, 9]. In this research the design is based on the use of an innovative material that provides an hinge function, obtaining a lightweight system composed only by panels linked together. Moreover, the structure exhibits maximum flexibility and modularity of the components, facilitating to assume various configurations. 5.1. Material selection The choice of material has a considerable impact on the model, it affects not only structural behavior and technological solutions, but it has a strong aesthetic effect. Different are the possible solutions to be applied on foldable structures: concrete, wood, cardboard, textiles, and all of them have an impact on the final perception of the Architecture. The choice of the material is here related both to technological 6
Proceedings of the IASS Annual Symposium 2016 Spatial Structures in the 21st Century
and architectural considerations. The aim is to realize a lightweight foldable system, easily transportable, deployable and assembled on site with as little energy as possible, as exposed by Curletto and Gambarotta [6]. Another important criterion is the ease of reproduction and the modularity of the elements to facilitate the standardization of the shelter. For these reasons, a new material has been investigated, Hylite® [1] is an aluminum-plastic-aluminum laminate material, composed by a polypropylene core. Hylite® benefits include very low thickness of 2mm, ideal for lightweight structures, and high dimensional stability, as discussed by Burchitz et al. [4]. It was developed to replace steel or aluminum plates in applications where high flexural rigidity is required. It was elaborated to have low weight per unit area with equivalent rigidity of steel and aluminum (Table 1). As shown, if steel and aluminum plates are compared with 1.2/0.8 Hylite® on the basis of equal flexural stiffness, Hylite® is 5% lighter than steel and 30% lighter than aluminum sheet. Table 1: Comparison of steel, aluminum and hylite weight at equal flexural rigidity [4]. Steel
Aluminum
1.2/0.8 Hylite
Thickness, mm
0.74
1.08
0.2/0.8/0.2
Specific weight, kg/m2
5.8
2.9
1.82
Maximum elongation, %
30-40
20-25
18-20
Foldable structures require panels of a light and stiff material, so the material index 𝑀𝑏 , as proposed by Ashby [2] has to be evaluated: 𝑀𝑏 = 𝐸
1⁄3
⁄𝜌 ,
(1)
where 𝐸 is the modulus of elasticity and 𝜌 is the material density. The index 𝑀𝑏 suggests the best material to use for a minimum weight and Hylite® combines excellent flexural rigidity with low weight (Fig. 8a, as proposed by Boesenkool et al. [3]).
Figure 8: (a) Bending modulus against density of lightweight, high-stiffness design [3] , (b) material for elastic hinges [2].
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Proceedings of the IASS Annual Symposium 2016 Spatial Structures in the 21st Century
Nevertheless, the core advantage of this material, suitable for the foldable structure here proposed, regards to use of the panel’s core as hinge (Fig. 9a-b). Locally removing the aluminum skins of an Hylite® plate provides an elastic hinge integrated into the sandwich panel. The material that can be bent to the smallest radius without yielding or failing is the ideal one to be applied as hinge, This property can be evaluated with the index 𝑀ℎ , as demonstrated by Boesenkool et al. [3]: 𝜎 𝑀ℎ = 𝑓⁄𝐸 , (2) where 𝜎𝑓 is the failure strength (Figure 8b). As shown, the best choice for elastic hinges are all polymeric materials, however materials like polyethylene, polypropylene or nylon are not rigid enough to be applied in structural applications.
Figure 9: (a) Example of hinge realized on a plate of Hylite®, (b) scheme of hinge function.
In conclusion, in comparison with polymers, Hylite® has higher rigidity of outer skins in aluminum, while in comparison with metals the integrated hinges in polypropylene give a core advantage in folding, so it can be considered as the ideal material to be applied for lightweight foldable structures. 5.2. Fabrication, assembly and elevation The efficient fabrication of the elements composing the system and their assembly process ensures high quality standards and rapid delivery. Three panels of Hylite® of dimensions 3.00 × 1.30 m compose the base module of the structure (Fig. 10a). A central panel is linked to the adjacent through an efficient bolting. The first panel has the function of cover, while the adjacent panels work as supports to connect the overall system with the base structure (Fig.10b). The proposed solution enables the modularity of the whole structure, because of the possibility to connect as many panels as desired. All elements can be factory made and easily transported and installed on site, following the scheme below (Fig. 10c). First, each module is composed linking the three panels of Hylite® together. Then, each module is connected to the base structure, which restraints the system at the desired configuration of deployment. Finally, panels can be connected together through bolting, composing the overall structure.
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Proceedings of the IASS Annual Symposium 2016 Spatial Structures in the 21st Century
Figure 10: (a) Base module panels, (b) assembled structure, (c) assembly and elevetion process.
6. Conclusion This paper aims to propose an approach for designing foldable structures integrating geometric, technological and structural aspects. A project of a new foldable system has been developed, presenting an innovative configuration, inspired by Origami pattern. The structure provides maximum flexibility in planning and facilitates different variations in site configuration, depending from the relation between geometric parameters. An innovative composite material is considered, Hylite® has the core advantage to provide a hinge function without the application of additional components for cylindrical hinges realization, with structural and aesthetic benefits. All elements are factory made and easily transported and installed on site, providing costs benefits and ensuring high quality standards and rapid delivery. A prototype of the proposed system is in production, remaining object of discussion for future works.
References [1] 3AComposites, Hylite®, aluminum composite panel, http://www.display.3acomposites.com/en/products/hylite/characteristics.html, (accessed 13 June 2016). [2] Ashby MF., Materials selection in mechanical design, II ed., Butterworth-Heinemann, 116-119, 1999. [3] Boesenkool R., Hurkmans A., The development of a lightweight deep-drawable steel-plastic-steel sandwich, Proc. of EUROMAT97, 5th European conference on advanced materials and processes and applications, Maastricht, 53-57, 1997. [4] Burchitz I., Boesenkool R., Van der Zwaag S., Tassoul M., Highlights of designing with hylite, a new material concept, Materials and Design, 26, 271-279, 2005. [5] Chudoba R., Van der Woerd L., Schmerl M., Hegger J., Oricrete: modeling support for design and manufacturing of folded concrete structures, 2013. 9
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[6] Curletto G., Gambarotta L., Rigid foldable origami structures: integrated parametric design and structural analysis, IASS2015 (Annual International Symposium on Future Visions), 524185, Amsterdam 17-20 Aug 2015. [7] De Temmerman N., Mollaert M., Van Mele T., De Laet L., Design and analysis of a foldable mobile shelter system, International Journal of Space Structures, 22 (3), 161-168, 2007. [8] Hanaor A., Levy R., Evaluations of deployable structures for space enclosures, International Journal of Space Structures, 16 (4), 211-229, 2001. [9] Heatherwick Studio, Rolling Bridge, design of a pedestrian bridge, 2004, www.heatherwick.com/rolling-bridge/, (accessed 13 June 2016). [10] Mirtschin J., GeometryGym, OpenBIM tools for architects, engineers and the construction industry, https://geometrygym.wordpress.com/, (accessed 13 June 2016). [11] Robeller C., Weinand Y., Interlocking Folded Plate – Integral Mechanical Attachment for Structural Wood Panels, International Journal of Space Structures, 30 (2), 111-122, 2015. [12] Rutten D. Robert McNeel & Associates, Grasshopper, algorithmic modeling for Rhino, www.grasshopper3d.com, (accessed 13 June 2016). [13] Schenk M., Guest S. D., Origami folding: a structural engineering approach. Origami 5: 5th International Meeting of Origami Science, Mathematics and Education 5OSME, 291-303, 2011. [14] Tachi T., Rigid-foldable thick Origami, Proceedings of the 5th International Conference on Origami in Science, Mathematics and Education 5OSME, 253-263, 2011. [15] Yasuda H., Yein T., Tachi T., Miura K., Taya M., Folding behaviour of Tachi–Miura polyhedron bellows, Proc. Royal Soc. A, 469, 20130451, 2013.
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