Basics of Shape and Topology Optimizations

Structural optimization has been widely utilized in many industries such as mechanical and automotive industries. Structural optimization is classified into sizing, shape and topology optimization methods. In shape optimization, the shape boundaries of the target structure is explicitly represented and updated using an optimization method. In topology optimization, the optimization problem is replaced by a material distribution problem, and the topological changes can be performed during the optimization procedure. Comparing two optimizations, topology optimization can drastically improve the structural performance while shape optimization can provide practical structural solutions. In this paper, the concepts and basics of shape and topology optimizations, and their applications are discussed.