Two-Scale Topology Optimization using Homogenization Theory (1st International Conference on Optimization Driven Architectural Design Jordan, November 5th - 7th, 2019)

The two scale topology optimization formulation is a mathematical procedure which focuses on finding the optimal layout of a structure, by changing the topological characteristics of the many different unit cells consisting it. These unit cells are most commonly referred to as the “the micro scale” part of the optimization problem and the structure as the “the macro scale” part. The optimization procedure used to define the topology of the unit cells is the topology optimization formulation, modified to combine the information deriving from the two different scales involved. In addition with topology optimization, the most common theory used for connecting the properties of the two separate scales is the theory of homogenization. By applying the homogenization theory in each optimization loop the different topologies of the micro scale produce elasticity tensors which are consequently used as material parameters for the elements consisting the macro scale. The main focus of the study is the comparison of different formulations for performing the two scale optimization procedure as well as the efficiency of the different topology optimization approaches and different solvers. In addition a 3D case study will be presented demonstrating the capabilities of the two scale topology optimization in more complex problems