Multi-grid reduced-order topology optimization

Additive printing allows the “single step” production of virtually any complex mechanical component. However, the manufacturing process involves a layer-by-layer deposition of material, which leads to an anisotropic mechanical behavior of the whole component. This would then entail a very fine 3D model to simulate the mechanical performance accurately. This simulation would also need to be integrated within an iterative design process in order to obtain the most efficient design. Both reasons explain the prohibitive number of calculations needed, which is currently beyond the capacities of existing software and computers. Recent research papers have opened promising pathways for integrating model reduction techniques within the overall topology optimization process. However, these approaches still present challenges such as choosing the minimum number and appropriate selection of the snapshots required to get accurate simulations. In this work, we present a methodology in the combined field of reduced-order modeling and topology optimization. The key idea consists of projecting the higher dimensional system of equations onto a lower dimensional space with the reduced basis vectors constructed using Proper Orthogonal Decomposition (POD). This reduced basis is updated in an incremental “on-the-fly” manner using alternatively costly high-fidelity and more rapid lower fidelity simulation snapshots. The variable-fidelity resolutions of successive approximations to the global system of equations are then integrated into the topology optimization process. The approaches are tested and computational savings and precision are compared, using both minimum compliance and compliant mechanism design benchmark problems.