This paper seeks to determine the relationship between the parameters that define microstructures composed of a matrix with periodic elliptical inclusions and the effectiveness of structural optimization through the application of existing methods. Stiffness properties for a range of microstructures were obtained computationally through homogenization, and these properties were used to conduct separate homogeneous topology optimization and heterogeneous microstructural optimization on two canonical structural problems. Effectiveness was evaluated on the basis of final total strain energy when compared to a reference configuration. Local minima were found for the two structural problems and various microstructure configurations, indicating that the microstructure of composites with elliptical inclusions can be fine-tuned for optimization. For example, when applying topology optimization to a cantilever beam made from a material with soft, horizontal inclusions, ensuring that the aspect ratio of the inclusions is 2.25 will yield the stiffest structure. In the case of heterogeneous microstructural optimization, one of the results obtained from this analysis was that optimizing the aspect ratio of the inclusion is much more impactful in terms of increasing the stiffness than optimizing the inclusion orientation. The existence of these optimal designs have important implications in composite component design.

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