Efficient Two-Scale Optimization of Manufacturable Graded Structures

A new method for the optimal design of inhomogeneous meso-structured components is presented. The method is based on a variant of the free material optimization (FMO) method. Instead of coupling a macroscopic model directly with the meso-scale in the framework of a two-scale approach, information from the meso-scale is incorporated into the FMO model by additional constraints. The FMO result, given in terms of optimized tensors, is interpreted by the inverse homogenization approach. Rather than only computing the meso-structure for each “FMO cell” independently, approximate continuity of the meso-structure is enforced. Thus, the final result is a manufacturable structurally graded material. The feasibility of the whole method is demonstrated by means of an academic example.