WIT Press

Topology And Shape Optimization Using The Local Rule


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E. Kita, H. Saito, T. Tamaki, H. Shimizu & Y. M. Xie


This paper describes the design scheme of the three-dimensional structures based on the concept of the cellular automata simulation. The structural optimization in the present method is performed according to the local rule. The penalty function is defined from two 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 applied to a single load and the schemes to reduce the computational cost are discussed. 1 Introduction Some researchers have presented the application of the cellular automata simulation to the shape optimization [1, 2, 3, 4, 5, 6]. In the simulation, the design domain is divided into small square cells. The cell density is updated according to the local rule from the equivalent stress at the adjacent cells. The formulations to define the local rule can be classified into the experimental, the evolutionary, the biomechanical and the mathematical ones. In our laboratory, the mathematical formulation has been presented and applied to the design of the two-dimensional structure and the truss structure [6]. In this paper, we will applied the formulation to the design of the three-dimensional structure. The optimization problem is defined and then, the local rule is derived analytically from the objective functions and the constraint condition of the optimization problem. Finally, we will describe the algorithm to improve the computational cost.