Abstract

Cellular automata (CA) paradigm has been successfully applied to solve the topology and sizing optimization problems of truss structures and continuum bodies. In a conventional uniform Cellular Automata (CA) model, a unit cell's behavior is updated based on information from its eight immediate neighboring nodes (in 2D configuration). However, this neighborhood system may not always be suitable for representing real truss structures. To address this limitation, a non-uniform CA approach has been proposed in this research study for the optimization of truss structures.
The proposed non-uniform CA approach is based on non-identical cells, each of which is defined by a center node and members connecting the center node of the cell to all other nodes in its immediate neighborhood. This differs from the Moore neighborhood concept used in the conventional uniform CA approach, which only considers the eight immediate neighboring nodes. It has been shown that the proposed non-uniform CA approach provides a more realistic representation of truss structures and improves the optimization process.
Moreover, conventional CAs rely on a fixed grid, thus with respect to design optimization of discrete structures, they can only be used for sizing and topology of the structure while the layout optimization cannot be conducted as the coordinates of the nodes remain unchanged throughout the optimization process. In this research study, a novel non-uniform CA design optimization algorithm has been formulated to solve the general problem of topology, sizing and layout optimization of truss structures subject to both stress and displacement constraints. Several benchmark case studies have been provided to demonstrate the efficiency and accuracy of the proposed design optimization methodology.