Two-scale topology optimization using homogenization theory

Abstract

Homogenization theory forms the basis for solving the topology optimization problem (TOP) of composite structures. The simplest repeating unit of the microstructure, that if isolated represents exactly the macroscopic behavior of the structure, is called the unit cell. Scope of homogenization is to determine the macroscopic properties of the non-homogeneous unit cell. In this study, homogenization is implemented on a 3D lattice unit cell, with the radius of the unit cell being the varying parameter of the homogenization procedure. Different values of the radius result to different configurations, hence, to different equivalent properties of the unit cell. Therefore, a fitting process takes place in order to accurately model the variations of the obtained effective properties with respect to the design variable. The corresponding, homogenization-based TOP is posed and the resulting geometries for several case studies are presented.