Date of Completion


Embargo Period



Julian Norato, Horea Ilies, Ying Li

Field of Study

Mechanical Engineering


Master of Science

Open Access

Campus Access


The objective of this thesis is to develop techniques to automatically generate initial designs and adaptively add geometric components in the geometry projection method. The geometry projection method is a topology optimization technique to design structures exclusively made of geometric primitives. To date, this method requires the designer to define an initial layout of geometric components for the optimization, a process that is typically cumbersome. In this work, we propose simple techniques to automatically generate initial layouts of bars for arbitrarily-shaped design regions. We also propose a separate technique whereby no geometric components are placed in the initial design, but they are adaptively seeded throughout the optimization. To determine the best location to nucleate geometric components, we use the topological derivative for arbitrarily shaped inclusions. The calculation of this topological derivative requires the computation of the Polya-Szego polarization tensor, which we obtain via the finite element solution of a variational problem. To determine the best orientation at which components should be introduced, we additionally solve an optimization in each finite element to determine the angle that minimizes the value of the topological derivative. We propose a heuristic scheme to adaptively seed components, and demonstrate it for the problem of minimizing compliance subject to a volume constraint in steady-state heat conduction and linear elasticity.

Major Advisor

Julian Norato