A Study on the Shape and Topology Optimization of Structures

Abstract

In an effort to find optimal topologies in the design of structures, the shape optimization problem has been relaxed by using the homogenization method[1]. The concept of the material density distribution is employed to relax the shape optimization problem. To find the relationship between the macroscopic effective material properties and the material density, a microsturcture is introduced and the homogenization method is used. In this way, the shape optimization problem is converted to the material distribution problem. Bendsoe and Kikuchi explored this approach using a microstructure with a rectangular hole[2]. There have been other works which employed the same approach[3–8].