Exploration of Data Clustering Within a Novel Multi-Scale Topology Optimization Framework

Date of Award


Degree Name

M.S. in Mechanical and Aerospace Engineering


Department of Mechanical and Aerospace Engineering


Robert Lowe


High performance aircraft endure harsh conditions and require intelligently designed materials to survive complex, multi-physics loadings. Multi-scale topology optimization is a method of tailoring a material to potentially meet the requirements imposed by such conditions. The proposed design framework not only separates material design into a macroscale and mesoscale, but performs the analyses and optimizations of each separately, which allows for a larger structural design space. After a study to determine the constraints of the design space, an analysis at the macroscale defines ideal properties of representative volume elements (RVEs, voxels), which constitute the mesoscale. A function then generates a physical, realizable voxel geometry to match those ideal properties. Matching a geometry to each set of properties described by the optimized solution would be a computationally expensive process. However, applying data clustering methods to the macroscale analysis results combines like data points to simplify the problem to a specified number of voxel types, ideally at minimal cost to the objective function. The clustered solution varies from the original optimized solution but facilitates a feasible voxel geometry generation process. Four data clustering methods are compared to identify the one best suited for a test run of the design framework and to investigate their performance given different datasets from various test cases. K-means clustering, Spectral clustering, DBSCAN (Density-Based Spatial Clustering of Applications with Noise), and OPTICS (Ordering Points to Identify Clustering Structure) are all compared by their impact on the objective function of optimizations (structural compliance, in these cases) of a block in uniaxial tension, a Michell truss, and a half-span Messerschmitt-Bolkow-Blohm (MBB) beam (commonly known as a three-point bend test). Findings include evidence that data clustering successfully simplifies the number of unique mesoscale designs with a negligible effect on the objective function of the optimization, and that K-means clustering performs best in all three test cases. For uniaxial tension boundary conditions, K-means clustering achieves a 97.33% decrease in voxel type with only a 0.024% increase in compliance. The Michell Truss test case sees a 3.605% increase in the objective function for a 99.33% drop in unique RVE designs. Finally, there is an observed 89.33% decrease in voxel type corresponding to a 0.2495% increase in compliance for an MBB beam. To complete the path of the design framework, the K-means-clustered solution to the three-point bend problem is additively manufactured for mechanical testing in the manner for which it was optimized. The test article is observed to behave nonlinearly, especially in contrast to results of a linear finite element simulation (FEA) of modeled conditions. Methods to increase FEA fidelity are identified, and next steps follow to compare accurately simulated results to validate the design optimization. Comprehensively, these investigations help characterize the effectiveness of data clustering methods in aiding the inter-scale communication of a multi-scale topology optimization design framework suited for the design of hypersonics.


Aerospace Materials, Aerospace Engineering, Mechanical Engineering, Multi-scale topology optimization, Data clustering, High-performance aerospace materials, Additively manufactured architected materials, Custom three-point bend test fixture

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