Sensitivity boundary integral equations with applications in engineering mechanics

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Zhang, Daming
Major Professor
Frank J. Rizzo
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Aerospace Engineering

The Department of Aerospace Engineering seeks to instruct the design, analysis, testing, and operation of vehicles which operate in air, water, or space, including studies of aerodynamics, structure mechanics, propulsion, and the like.

The Department of Aerospace Engineering was organized as the Department of Aeronautical Engineering in 1942. Its name was changed to the Department of Aerospace Engineering in 1961. In 1990, the department absorbed the Department of Engineering Science and Mechanics and became the Department of Aerospace Engineering and Engineering Mechanics. In 2003 the name was changed back to the Department of Aerospace Engineering.

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  • Department of Aerospace Engineering and Engineering Mechanics (1990-2003)

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In sensitivity analysis for problems involving thin domains or domains with cracks, conventional boundary integral equations must be supplemented and/or replaced by hypersingular ones. This is due to the fact that the conventional equations become nearly-degenerate for thin domains and actually degenerate for cracks. Such degenerate character follows from the close proximity to each other, or actual coincidence, of two defining surfaces in each case. Hypersingular boundary integral equations for sensitivity analysis are developed in two forms in this thesis, using a global regularization and a local regularization. The regularizations are facilitated by observing that the singularity order of the sensitivity BIE. formulas is no more than that of the ordinary BIE formulas. One motivation for this work is the computation of stress-intensity-factor sensitivities with respect to crack-growth. Other motivations would include optimization and design applications wherein sensitivities would be needed, but would otherwise be unavailable, for any reason, from conventional integral equations alone. In this thesis, examples of stress-intensity-sensitivities with respect to the size of a crack are given. Specifically, sensitivity values for a circular bar with an embedded penny-shaped crack under tension, bending, and torsion loadings are obtained and shown to be accurate. These examples verify the formulas and the codes developed in this dissertation.

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Wed Jan 01 00:00:00 UTC 1997