The roof of the Teshima Art Museum’s main building in Teshima, Kagawa Prefecture, is a reinforced concrete shell with a freeform curved surface in the shape of a water droplet, having a maximum span of 41.2m, a maximum rise 5.12m and thickness of 250mm. This paper discusses the structural planning, design and construction methods for implementing such shallow, thin RC shells with freeform curved surfaces. Especially, we described in detail about the stability analysis and the construction methods. This building is a very valuable actual example regarding earthquake-resistant design of the shell structure that is undeveloped in our country.

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In this paper, we describe the example of the tunnel-shaped form building that was designed by structural morphogenesis and constructed. The genetic algorithms(GA) is applied to the structural morphogenesis of the framed construction of this tunnel type. In the numerical result, we show various solution forms of the arch shape by giving some design constraints. An effective structural form for the structure, the design, and the function is searched from the combination of the obtained arch shape. This simple structural morphogenesis procedure will become the hint of the design tool that decides the building shape.

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 Biomimetic technology (biomimetics) has recently attracted a great deal of attention in engineering field. Also, in architecture field, as represented by shell structure, biomimetics has been used for a long time. In recent years, the buildings which floors are supported by the structure such as trees or seaweeds have been built (Tod's Omotesando Building, Sendai Mediatheque). On the other hand, it is conceivable that the topology optimization can be used for biomimetics in architecture field, because it has been observed that the shape obtained by the topology optimization is relatively close to the natural form. Therefore, in this paper, several numerical examples of computational morphogenesis of building structures using IESO (Improved Evolutionary Structural Optimization) method³⁾ are shown in order to verify the application possibility of the proposed method to the biomimetics.
 In IESO method, the design domain is divided in same eight-node brick elements (voxels), and in the optimization process, for solid element, it will be removed if the sensitivity number¹⁰⁾ is less than the threshold value. This threshold value is obtained from the equation proposed in extended ESO^12,13). This equation consists of the mean value of sensitivity number and the average deviation of sensitivity number with a control parameter. In the proposed method, the evolutionary volume ratio (reduction ratio) is given as an input data, and this control parameter is determined automatically in the program so as to satisfy the given reduction ratio approximately. Furthermore, in this paper, finishing algorithm is added to IESO. In this algorithm, first, the converged solution obtained by IESO is input, and then, the elements about 5% of the total elements of design domain are added according to the rule of CA method. Specifically, in order from the element which the sensitivity number is the greatest, the elements of the von Neumann neighborhood are added, and if the number of additional elements is greater than 5% of the total elements of design domain, this program is ended. Finally, the calculation of IESO is executed again with the smaller reduction ratio than the initial analysis (about 1/5～1/10).
 Several numerical examples have been shown in order to demonstrate the effectiveness of the proposed method, and the effectiveness for the application to the biomimetics. By the numerical example which is used for design competition for a new train station for Florence (Fig. 3), it is shown that natural and simple topology can be obtained by IESO (Fig. 4), and it is also shown that if the finishing algorithm is added to IESO, the compliance of the solution obtained by IESO is less than CA-ESO (Fig. 5～8). (It was shown in the previous paper³⁾ that the compliance of the solution obtained by SIMP is greater than CA-ESO.) In the next numerical examples, the structural morphologies which support the single or multi flat slab from various base support points is generated using IESO (Fig. 9～18). From these examples, it is shown that the structural morphologies like natural trees can be generated by IESO.
 It is concluded from these examples that IESO is one method which can be used for applying biomimetics to the building design.

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Scheme of computational morphogenesis for the shell structures with free curved surface is proposed, where the shape can be optimized for linear buckling load. In the proposed scheme, The problem in question has been mathematically formulated as linear buckling load factor maximization problem where coordinates of NURBS control points with respect to the shape of curved surface are adopted as design variables and Genetic Algorithm (GA) is utilized to solve this problem without any difficulties because no sensitivity analysis, in needed. Numerical examples are presented where the effectiveness of the proposed scheme and the structural characteristics is investigated.

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The scheme of computational morphogenesis for the shell structures with free curved surface is proposed, where shape, distribution of thickness and topology can be simultaneously optimized. In the proposed scheme, distribution of thickness is discretized based on those values at each node, and Non Uniform Rational B-Spline (NURBS) is utilized by which the number of unknowns can be controlled while the high degree of freedom for expression of the shape of the curved surface and distribution of thickness are maintained. Moreover, the contour lines with respect to shell thickness over the shell surface are utilized by which topology of shell structures can be not only scraped but also grown up. By using this method, shell structure optimized with respect to not only shape and shell thickness but also topology can be obtained. The problem in question has been mathematically formulated as strain energy minimization problem of which coordinate of NURBS control point with respect to the shape of the curved surface and distribution of thickness are adopted as the design variables and numerical examples are presented where the effectiveness of the proposed scheme is investigated.

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The scheme of computational morphogenesis for the shell structures with free curved surface is proposed, where shape and distribution of thickness can be simultaneously optimized. Generally, when nodal coordinates and shell thicknesses of finite element are adopted as design variables in structural optimization problem, computational cost generally becomes very large. In the proposed scheme, distribution of thickness is discretized according to the nodal points, and NURBS (Non Uniform Rational B-Spline) is utilized by which the number of unknowns can be controlled while the high degree of freedom for expression of the shape of the curved surface as well as the distribution of thickness are maintained. Consequently, the problem in question has been mathematically formulated as strain energy minimization problem where coordinates of NURBS control points with respect to both the shape of the curved surface and the distribution of thickness are adopted as design variables and numerical examples are presented where the effectiveness of the proposed scheme is investigated.

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