This thesis seeks to determine the relationship between the parameters that define microstructures composed of a matrix with periodic elliptical inclusions and the macroscopic shapes obtained using structural topology optimization. Stiffness properties for a range of microstructures were obtained computationally through homogenization, and these properties were used to conduct topology 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 topology optimization. For example, when making a cantilever beam from a material with soft, horizontal inclusions, ensuring that the aspect ratio of the inclusions is 2.25 will yield the best result after topology optimization is applied. Optimality criteria such as this have important implications in composite component design
