Topology optimization based on reduction methods with applications to multiscale design and additive manufacturing

Advanced manufacturing processes such as additive manufacturing offer now the capability to control material placement at unprecedented length scales and thereby dramatically open up the design space. This includes the considerations of new component topologies as well as the architecture of material within a topology offering new paths to creating lighter and more efficient structures. Topology optimization is an ideal tool for navigating this multiscale design problem and leveraging the capabilities of advanced manufacturing technologies. However, the resulting design problem is computationally challenging as very fine discretizations are needed to capture all micro-structural details. In this paper, a method based on reduction techniques is proposed to perform efficiently topology optimization at multiple scales. This method solves the design problem without length scale separation, i.e., without iterating between the two scales. Ergo, connectivity between space-varying micro-structures is naturally ensured. Several design problems for various types of micro-structural periodicity are performed to illustrate the method, including applications to infill patterns in additive manufacturing.