Scale-Related Topology Optimization from Unit Cell Homogenization to Superelement Model

1. Abstract The integrated lightweight design optimization of structural layout and material microstructures are discussed in this paper. By analyzing the basic features of such a two-scale problem, it is found that the optimal solution strongly depends upon the scale of the material unit cell (UC) or named representative volume element (RVE). In fact, the effective material properties predicted by the traditional homogenization method are limit values that can characterize only the effects of the material volume fraction and the topology of the microstructure regardless of the influence of the unit cell scale. From this consideration, we introduce the superelement (SE) concept as a macro representative volume element to describe the material unit cell of micro-scale. By changing the scale and aspect ratio of the superelement, design optimizations of both materials and structures can be unified and the scale-related effect can be revealed in the final result of integrated design of materials and structures. Numerically, 2D problems concerning the stiffness maximization with cellular core design optimization are considered to illustrate the approach. 2.