GOTICA - generation of optimal topologies by irregular cellular automata

Abstract

In recent years the Cellular Automata (CA) concept has been successfully applied to structural topology optimization problems. In the engineering implementation of CA, the design domain is decomposed into a lattice of cells, and a particular cell together with the cells to which it is connected forms a neighborhood. It is assumed that the interaction between cells takes place only within the neighborhood and the states of cells are updated synchronously in subsequent time steps according to some local rules.The majority of results that have been obtained so far were based on regular lattices of cells. However, a practical engineering analysis and design in many cases require using highly irregular meshes for complicated geometries and/or stress concentration regions. The aim of the present paper is to extend the concept of CA towards the implementation of unstructured grid of cells related to non-regular mesh of finite elements. Introducing an irregular lattice of cells allows to reduce the number of design variables without loosing the accuracy of results and without an excessive increase of the number of elements caused by using a fine mesh for a whole structure. The implementation of non-uniform cells of Cellular Automaton requires a reformulation of standard local rules, for which the influence of the neighborhood on the current cell is independent of sizes of the neighboring cells.