Topology And Shape Optimization Using
The Local Rule
Author(s)
E. Kita, H. Saito, T. Tamaki, H. Shimizu & Y. M. Xie
Abstract
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.
Keywords
Related Book
Other papers in this volume
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