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Application of cellular automata simulation to truss structure design

Kita E., Toyoda T., Tamaki T., Xie Y. M.

Computer Assisted Mechanics and Engineering Sciences

2004

Vol. 11, No. 4

321-335

In the cellular automata simulation, the object under consideration is divided into small cells and the simulation is performed according to the local rule which is defined as the local relationship among cells. In this paper, the concept of cellular automata is applied to the design scheme of truss structures. First, truss elements are considered as the cells of the cellular automata and the local rule is derived from the optimization problem. The objective functions are defined to minimize the total weight of the structure and to obtain even stress distribution in the whole structure. The constraint conditions are introduced in order to define the local rule. The present method is applied to the design of the plane and the three-dimensional truss structures such as Schwedler and Lamella Domes. The convergence histories of the total weight and the mean and the maximum stresses are shown in order to discuss the property of the present method.

Structural optimization method based on cellular automata simulation

Toyoda T., Kita E.

Computer Assisted Mechanics and Engineering Sciences

2002

Vol. 9, No. 2

191-203

This paper describes the topology and the shape optimization scheme of the continuum structures using the cellular automata simulation. The design domain is divided into small square cells. By considering the cells as the elements, the stress analysis of the structure is carried out by finite element method. Then, the design variables are updated according to the local rule and the stress distribution. The rule is defined as the simple relationship between a cell whose design variable is updated and its neighborhood cells. In this paper, we will discuss the formulation to analytically derive the rules from the optimization problems. The special constraint condition named as ``CA-constraint condition'' is introduced first and then, the global optimization problem for the whole structure is divided into the local problem for some neighboring cells. The derived rules are applied to the same numerical example in order to discuss the theoretical validity of the formulation and the feature of the rules.