Student Name: Cameron S. Smith

Advisor: Dr. Graeme Kennedy

Milestone: PhD Thesis Final Examination (Defense)

Degree Program: Aerospace Engineering

Title: Topology Optimization using a Hierarchical Gradient-Based Framework with Applications Involving Eigenvalue Problems

Abstract: Structural optimization presents a solution for the design of novel structures that maximize performance criterion for a variety of engineering applications. Topology optimization is a subset of this field that seeks to identify the optimal material layout that simultaneously optimizes the shape, size, and topology of structural features. Combined with advancements in additive manufacturing, topology optimization is poised to enhance next-generation structural design. This is particularly applicable for aerospace vehicles, as topology optimization can reduce structural weight without compromising performance, enabling more mass to be allocated to the payload. However, reducing structural material has critical design implications for both structural stability and vibration response, necessitating the development of optimization methodologies that can account for these phenomena. Furthermore, to enable rapid design optimization, it is essential to have software architectures that can enable the development of new formulations and approaches for topology optimization. This dissertation directly addresses these areas through concentrated research thrusts. First, a lightweight framework is introduced, which standardizes the process of formulating computational procedures intended for optimization. The software was designed for engineering systems that are described by directed acyclic graphs, and it is centered around the adjoint method to enable total derivative computation for gradient-based design optimization. A hierarchical approach is employed to facilitate the construction of new computational procedures and optimization formulations. Furthermore, it is designed to supplement preexisting software tools by providing the flexibility to integrate other libraries and packages into the framework. The developed framework is particularly applicable for topology optimization problems, but its scope extends beyond this field to benefit broader multidisciplinary design optimization. Using the hierarchical framework to orchestrate the computational procedures, topology optimization applications that involve the solution of eigenvalue problems are explored. Specifically, structural stability and vibration are targeted, as these two disciplines are highly relevant for the design of aerospace structures. A novel approach using Koiter asymptotic theory to predict the initial post-buckling response is developed and integrated into continuum-based topology optimization problems. This method provides additional information during optimization about a structure's response after buckling at a reduced computational cost compared to fully nonlinear solution techniques. Additionally, resonance behavior is studied, particularly in the context of inverse design to achieve desired natural frequency properties. The formulation of a modified ordered directed Hausdorff distance is presented, which compares two natural frequency spectra using nearest neighbor matching and provides greater flexibility than an ordered matching approach. Using this quantity, an inverse design methodology is discussed that is applicable for both structural design and damage identification. Both of these applications of topology optimization present new design strategies that can enable the development of optimized structures in support of next-generation aerospace design.

Date and time: 2026-11-18, 1 PM ET

Location: Montgomery Knight 317

Committee:
Dr. Graeme Kennedy (advisor), School of Aerospace Engineering
Dr. Claudio V. Di Leo, School of Aerospace Engineering
Dr. Kai A. James, School of Aerospace Engineering
Dr. Keegan J. Moore, School of Aerospace Engineering
Dr. Daniel A. Tortorelli, University of Illinois Urbana-Champaign