Geometric Control in Topology Optimization

Topology optimization is the search for the optimal material distribution in a specified design domain, which means that an objective function is minimized, taking into account certain constraints. This type of design optimization has great potential in various branches of engineering: it comes with a high degree of design freedom, resulting in high-performance designs - but also in complex geometries. Reliable techniques for geometric control in topology optimization are still lacking, while this kind of control is often needed because of buildability concerns, functional demands, or aesthetic preferences.

In this PhD project, new methods will be developed to tackle three types of geometric requirements: (1) minimum/maximum length scale, i.e. the minimum/maximum allowable cross-section for solid features or perforations, (2) restrictions related to specific manufacturing processes, e.g. for mould removal in casting or for tool accessibility in milling, and (3) pattern repetition, e.g. the design of a perforated structure with a limited number of perforation shapes. Two approaches are envisaged: a filter-based approach, where  unwanted geometric features are removed during the optimization, and a constraint-based approach, where the geometric requirements are explicitly included as constraints in the optimization problem. Four example problems, formulated in 2D and 3D, and spanning different areas of structural engineering, will be used as test cases.