Three-dimensional structural design based on cellular automata simulation

This paper describes the design scheme of the three-dimensional structures based on the concept of the cellular automata simulation. The cellular automata simulation is performed according to the local rule. In this paper, the local rule is derived in the mathematical formulation from the optimization problem. The cell density is taken as the design variable. Two objective functions are defined for reducing the total weight of the structure and obtaining the fully stressed structure. The constraint condition is defined for defining the local rule. The penalty function is defined from the objective functions and the constraint condition. Minimization of the penalty function with respect to the design parameter leads to the local rule. The derived rule is applied to the design of the three-dimensional structure first. The final structure can be obtained successfully. However, the computational cost is expensive. So, in order to reduce the computational cost, the material parameters c1 and c2 and the value of the cell rejection criterion (CRC) are changed. The results show that the computational cost depends on the parameters and the CRC value.