Abstract
Topology optimization is a free form design tool that identifies the optimized layout of materials for a given performance metric within a specified design domain without any prior knowledge. The technique has undergone significant improvements and has evolved along a number of different directions in recent years. Today, the technique is the most widely used tool for discovery of novel structures and material microarchitectures. One of the most common applications of topology optimization is in design of stiff structures under volume constraints. This includes design in both continuum and discrete domains and design at both structural and microstructural scales. In this thesis we propose a strategy to impose a hierarchy of length scales in weight-constraint maximum stiffness driven. This is done through an efficient approach without the need to add a prohibitive number of constraints to impose multiple length-scales. We illustrate the effectiveness of our strategy by applying it to two benchmark problems.