Sensitivity boundary integral equations with applications in engineering mechanics
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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.