Cellular Automata for Design of Two-Dimensional Continuum Structures

The implementation of Cellular Automata (CA) techniques for the analysis and design of two-dimensional continuum structures under in-plane loading is presented. The paper summarizes the basic elements of the CA and the specific formulation used for thin isotropic plates. Analysis and design rules are presented that satisfy static equilibrium and fulfill a fully-stressed material failure condition. The update rules are based on the deformation of an equivalent truss structure, and the relation between the thickness of the isotropic plate and the cross-sectional areas of the truss members are derived so mat the strain energy due to in-plane deformation is modeled correctly. Example results are presented which verify the accuracy of the modeling technique by a comparison to a closed-form stress functional solution. Additionally, design studies based on topology optimization and thickness sizing are performed, which demonstrate the applicability of the CA environment for efficient design of structures