Design of variable-stiffness composite layers using cellular automata

Benefits of directional properties of fiber reinforced composites could be fully utilized by proper placement of the fibers in their optimal spatial orientations. This paper investigates an application of a cellular automata (CA) based strategy for the optimal design of curvilinear fiber paths to improve in-plane response of composite laminae within the context of structural design. Applied to structural design, CA are iterative numerical techniques that use local rules to update both field and design variables to satisfy equilibrium and optimality conditions. In the present study, displacement update rules are derived using a local finite element model governing the equilibrium of the cell neighborhood. Local fiber orientation angles are treated as continuous design variables, and their spatial distribution is determined based on a minimum compliance design formulation. A heuristic pattern-matching technique is implemented along with the local optimality condition to maintain fiber orientation continuity in order to improve manufacturability. Numerical examples for in-plane compliance design of composite layers are used to demonstrate the methodology and improvements that can be achieved through optimal placement of fiber paths.