Topology optimization is a rapidly growing field and is extensively used in the product development cycle. The goal of topology optimization is to attain the best distribution of material for a given objective function with certain constraints. In this thesis, we use the hybrid cellular automata (HCA) methodology as a tool for topology optimization.
The HCA paradigm integrates local design rules from the cellular automata framework with a grid-based computational method like finite element analysis. The updating process is achieved through local communication among the automata based on a set of pre-defined rules; this leads the structure to an equilibrium state at which point no further updating is required.
In this work, we discuss the use of the HCA approach to solve two different problems: design of materials with prescribed constitutive properties, and design of structures with minimum mass and compliance. The problem of designing of periodic materials can be formulated as an inverse homogenization problem, where the goal is to design the base cell of structure such that the macroscopic properties of the material match the prescribed values. The second problem is formulated with an objective function considering the structure's mass and compliance. Several numerical experiments illustrating the HCA approach and its efficacy are discussed.