Ph.D. Proposal

Cameron Smith

(Professor Graeme Kennedy)

Topology Optimization for Structural Stability with Geometric Nonlinearity and Inverse Design for Frequency Response

Mon. Dec. 8

9:00 a.m.

Weber 200

Abstract: 

The stability and resonance behavior of structures are well-studied phenomena within the field of structural engineering. Understanding their impact on structural response is critical for performance and safety concerns. For aerospace structures, safety factors are often utilized to ensure designs avoid the critical buckling load or operate outside of resonance regions. This approach often leads to designs that are heavier than required, which diminishes the payload capacity for vehicles. Topology optimization is one solution to optimally distribute material that can satisfy design requirements for stability and vibration while simultaneously reducing the amount of material used. The current state of the art in topology optimization has considered these criteria, including maximizing or constraining the critical buckling load factor from both linear and nonlinear analyses and designing structures to possess specific natural frequencies and mode shapes. However, to further advance the field and apply topology optimization to other applications, several gaps can be addressed. To design more robust structures under compressive loading, particularly those that are close to the buckling point, post-buckling behavior should be considered. The computational cost associated with tracing the full nonlinear solution path can be avoided by incorporating an initial post-buckling analysis into the topology optimization procedure that still accounts for geometric nonlinearity. Additionally, to identify structures with specific frequency response behavior, inverse design techniques can be applied using topology optimization. Using statistical measures, this approach could identify designs that satisfy requirements for both natural frequencies and mode shapes, with a potential application for developing mass simulators for rideshare payloads. Finally, since the distribution of material contributes to a structure's stiffness properties, which affects stability and resonance, topology optimization can ensure designs are appropriate for both disciplines.

Committee:
Dr. Graeme Kennedy (advisor), School of Aerospace Engineering
Dr. Claudio Di Leo, School of Aerospace Engineering
Dr. Keegan Moore, School of Aerospace Engineering
Dr. Kai James, School of Aerospace Engineering
Dr. Daniel Tortorelli, Lawrence Livermore National Laboratory