A Study on Topological Optimization of Structure Using Cantor Function As Teaching Function

In order to obtain better structural designs, it is important to carry out optimization from primary parts of those designs. Especially, designs of topologies of structures were depended on intuition of the designers and they were not always best fitted to the requirements of the structure. These days, designs of topologies of the structures become important to meet those purposes. In this study, we will propose a new method to obtain optimum topology of the structure to satisfy their requirements by growth and degeneration tutored by Cantor function as teaching function. Cantor function is the one which is very famous as an introduction of the fractal. By operating its order, it is very easy to manipulate its division among 0 and 1. We set skipping and restarting rules of growth and degeneration, and criteria of convergence. We applied the proposed method to the problem similar to the one well-known as Mitchell truss problem to compare the results obtained by the proposed method. From these numerical examples, we can obtain quite similar topological results to the homogenization method in small number of iteration. There, the proposed method has advantages in computational time, cost and memory. More over, we can see the growth of the topology. Although we demonstrate the proposed method in a few examples, we can say that the proposed method can derive optimum oriented topology even with this simple scheme efficiently.