COMPUTATIONAL MORPHOGENESIS OF BUILDING STRUCTURES USING IESO METHOD

Abstract

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 ESO12,13). 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.