Multi-scale design methods for Topology Optimization

In this thesis multi-scale design methods for topology optimizations are presented. The goal of these methods is to find manufacturable designs, with a close to optimalstiffness at a reduced computational cost compared to well-established topologyoptimization methods.
First, the theory of homogenization-based topology optimization is discussed. The modeling of microscopic details is considered, as well as optimal microstructuresthat have extremal stiffness. This theory is well-developed and can be used to find an overall optimal material distribution at low computational cost. A downside of these optimal multi-scale designs is that they cannot be manufactured on a single length-scale. The main contribution of the research in this thesis is to develop and extend on new methods, such that these optimal designs can be interpreted on a single scale, while still being close to what is theoretically possible.
Simple and close to optimal single-scale microstructures are presented that are optimized for multiple anisotropic loading conditions. A method to approximate optimal microstructures on a single-scale is proposed, which are close (e.g. 10-15%) to the theoretical bounds. When used as starting guess for topology optimization these proposed microstructures can be further improved, outperforming topology optimized designs using classical starting guesses both in performance and simplicity.
Furthermore, a class of simple periodic truss lattice structures is presented that exhibit near-optimal performance in the high porosity limit, while still being well-connected. The performance difference between closed and open-walled microstructures is presented for anisotropic loading situations, where it is demonstrated that the maximum difference occurs when isotropic microstructures are considered. Furthermore, a method to interpret spatially varying microstructures on a single scaleis presented. Using this method high-resolution and near optimal designs canbe achieved on a standard PC in less than 10 minutes. An extension of this method to enforce a minimum feature size and a method to locally adapt the microstructure spacing are shown. The promise and drawbacks of this multi-scale design method are discussed with emphasis on the full-scale performance. Furthermore, the overall solution procedure is shown as well as an extension of the method to obtain coated designs, i.e. a solid shell surrounding porous infill material. In a similar work, the link between Michell’s theory of least-weight trusses and optimal laminates is exploited to extract a discrete frame structure from a continuum design. Subsequent frame optimization results in convergence towards known optimal solutions at low computational cost.