Structural optimization method based on cellular automata simulation

  • Tetsuya Toyoda Nagoya University
  • Eisuke Kita Nagoya University

Abstract

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.

Keywords

topology and shape optimization, cellular automata (CA), local rule, 2D eiastic problem, finite element method (FEM),

References

[1] K-J. Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, 1982.
[2] E.R. BerieKamp, J.H. Conway, R.K Guy. Winning Ways for Your Mathematical Plays, 1st edition. Academic Press Ltd., 1982.
[3] M. Garzon. Models of Massive Parallelism, 1st edition. Springer-Verlag, 1995.
[4] R. Gaylord, K Nishidate. Modeling Nature: Cellular Automata Simulations with Mathematica, 1st edition. Springer-Verlag, 1996.
[5] N. Inou. Optimal design methods based on biological information systems (in Japanese). Journal of Japan Society for Technology of Plasticity, 35(4): 316, 1994.
Published
Feb 21, 2023
How to Cite
TOYODA, Tetsuya; KITA, Eisuke. Structural optimization method based on cellular automata simulation. Computer Assisted Methods in Engineering and Science, [S.l.], v. 9, n. 2, p. 191- 203, feb. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1129>. Date accessed: 24 nov. 2024.
Section
Articles

Most read articles by the same author(s)