A Study on Microstructures of Homogenization for Topology Optimization

This thesis studies topology optimization method employing the homogenization method, with a focus on different microstructures and their effects on the topology optimization solutions. In the thesis, different microstructure models were investigated. The strengths and weaknesses of each type of microstructures were discussed. Homogenization method was employed to formulate the homogenized properties of the material. The optimality criteria and schemes of updating the design variables in the topology optimization process were derived for the newly developed microstructures and existing microstructures for which the information is not available in the literature. New microstructure models of one-material and bi-material were established. Based on these studies, a computer software package called Homogenization with Different Microstructures (HDM) incorporating fifteen existing and the new microstructure models was developed. By using the software, a series of problems were studied and solutions given by different microstructure models were compared