Novel local rules of cellular automata applied to topology and size optimization

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 for both optimal sizing and topology optimization. This article presents the application of the 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 also discussed. A new local update rule is proposed, selected optimal design problems are formulated, and finally the article is illustrated by results of numerical optimization.