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Abstract
In this thesis multiscale 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 wellestablished topologyoptimization methods.
First, the theory of homogenizationbased topology optimization is discussed. The modeling of microscopic details is considered, as well as optimal microstructuresthat have extremal stiffness. This theory is welldeveloped and can be used to find an overall optimal material distribution at low computational cost. A downside of these optimal multiscale designs is that they cannot be manufactured on a single lengthscale. 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 singlescale microstructures are presented that are optimized for multiple anisotropic loading conditions. A method to approximate optimal microstructures on a singlescale is proposed, which are close (e.g. 1015%) 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 nearoptimal performance in the high porosity limit, while still being wellconnected. The performance difference between closed and openwalled 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 highresolution 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 multiscale design method are discussed with emphasis on the fullscale 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 leastweight 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.
First, the theory of homogenizationbased topology optimization is discussed. The modeling of microscopic details is considered, as well as optimal microstructuresthat have extremal stiffness. This theory is welldeveloped and can be used to find an overall optimal material distribution at low computational cost. A downside of these optimal multiscale designs is that they cannot be manufactured on a single lengthscale. 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 singlescale microstructures are presented that are optimized for multiple anisotropic loading conditions. A method to approximate optimal microstructures on a singlescale is proposed, which are close (e.g. 1015%) 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 nearoptimal performance in the high porosity limit, while still being wellconnected. The performance difference between closed and openwalled 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 highresolution 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 multiscale design method are discussed with emphasis on the fullscale 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 leastweight 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.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  166 
ISBN (Electronic)  9788774755494 
Publication status  Published  2018 
Series  DCAMM Special Report 

Number  S254 
ISSN  09031685 
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Projects
 1 Finished

Multiscale design methods for Topology Optimization
Groen, J. P., Sigmund, O., Aage, N., Lazarov, B. S., Jensen, J. S., Allaire, G. & Stingl, M. W.
01/01/2016 → 02/05/2019
Project: PhD