COMPUTATIONAL MORPHOGENESIS OF CONTINUUM SHELL STRUCTURES USING IESO METHOD

The appearance of a concrete shell structure has developed the construction of free curved shell structures as many attractive architectures. However, in design of such continuum shell structures, it is difficult to find an optimal structure analytically. Because, in the optimal analysis, shape, thickness and topology of shell structure become design variables simultaneously. Therefore, in this paper, a simple method to find an optimal shell structure is proposed. In this method, a rectangular fixed design domain with given boundary conditions and body forces is modeled by voxel mesh, and strain energies of elements (voxels) are obtained by voxel finite element method. Next, elements with small strain energy are gradually removed by the Improved ESO (IESO) method. Finally, we can obtain a shell structure that shape, thickness and topology are optimized. In this paper, several numerical examples will be shown in order to verify the effectiveness of the proposed method. In the IESO method, the fixed design domain is divided in same eight-node rectangular elements (voxels), and in the optimization process, for solid element, it will be removed if the sensitivity number is less than the threshold value. This threshold value is obtained from the equation proposed in the extended ESO method2). 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 to satisfy the given reduction ratio approximately. In section 4, several numerical examples are shown to demonstrate the effectiveness of the proposed method. A basic numerical example shows that IESO can obtain a natural and simple topology. In addition, we analyze the case of giving vertical body force (gravity), analyze the case of giving the vertical gravity and vertical physical strength of 0.2 times the vertical weight in the vertical direction, and conduct the morphological creation corresponding to the seismic force. In next numerical examples, a cylindrical shell is created due to the setting of supported areas as parallel lines, and a spherical shell is created due to the setting of supported area as a circle. Therefore, various optimal shell structures can be generated by the IESO method. Moreover, it is shown that the complicated structure is created in applic