Novel local rules of Cellular Automata applied to topology and size optimization

Bogdan Bochenek (1) , Katarzyna Tajs-Zielinska (2)

1 Institute of Applied Mechanics
2 Institute of Applied Mechanics

Cellular Automata are mathematical idealization of physical systems in which the design domains are divided into lattices of cells, states of which are updated synchronously in discrete time steps according to some local rules. The principle of the Cellular Automata is that global behaviour of the system is governed by cells that only interact with their neighbours. Because of its simplicity and versatility the method has been found as useful tool for structural design, especially that Cellular Automata methodology can be adopted both to optimal sizing and topology optimization. This paper presents application of Cellular Automata concept to topology optimization of plane elastic structures. As to the optimal sizing the design of columns exposed to loss of stability is discussed as well. A new local update rule is proposed, selected optimal design problems are formulated, and finally the paper is illustrated by results of numerical optimization.

Mots clés: Physical Sciences

Domaines: Sciences de l'ingénieur [physics]

Bogdan Bochenek, Katarzyna Tajs-Zielinska. Novel local rules of Cellular Automata applied to topology and size optimization. Engineering Optimization, 2011, pp.1. ⟨10.1080/0305215X.2011.561843⟩. ⟨hal-00712748⟩