Date of Award

May 2020

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering


John F. Dannenhoffer III

Second Advisor

Melissa Green


Design optimization, Gradient-based optimization, Level-set method, Parameterized level-set function, Radial basis functions, Topology optimization

Subject Categories



Recently, there have been many developments made in the field of topology optimization. Specifically, the structural dynamics community has been the leader of the engineering disciplines in using these methods to improve the designs of various structures, ranging from bridges to motor vehicle frames, as well as aerospace structures like the ribs and spars of an airplane. The representation of these designs, however, are usually stair-stepped or faceted throughout the optimization process and require post-process smoothing in the final design stages. Designs with these low-order representations are insufficient for use in higher-order computational fluid dynamics methods, which are becoming more and more popular. With the push for the development of higher-order infrastructures, including higher-order grid generation methods, there exists a need for techniques that handle curvature continuous boundary representations throughout an optimization process.

Herein a method has been developed for topology optimization for high-Reynolds number flows that represents smooth bodies, that is, bodies that have continuous curvature. The specific objective function used herein is to match specified x-rays, which are a surrogate for the wake profile of a body in cross-flow. The parameterized level-set method is combined with a boundary extraction technique that incorporates a modified adaptive 4th-order Runge-Kutta algorithm, together with a classical cubic spline curve-fitting method, to produce curvature-continuous boundaries throughout the optimization process. The level-set function is parameterized by the locations and coefficients of Wendland C2 radial basis functions. Topology optimization is achieved by implementing a conjugate gradient optimization algorithm that simultaneously changes the locations of the radial basis function centers and their respective coefficients. To demonstrate the method several test cases are shown where the objective is to generate a smooth representation of a body or bodies that match specified x-rays. First, multiple examples of shape optimization are presented for different topologies. Then topology optimization is demonstrated with an example of two bodies merging and several examples of a single body splitting into separate bodies.


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