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A model has been developed to modify Euler-Bernoulli beam theory for wooden beams, using visible properties of wood knot-defects. Treating knots in a beam as a system of two ellipses that change the local bending stiffness has been shown to improve the fit of a theoretical beam displacement function to edge-line deflection data extracted from digital imagery of experimentally loaded beams. In addition, an Ellipse Logistic Model (ELM) has been proposed, using L1-regularized logistic regression, to predict the impact of a knot on the displacement of a beam. By classifying a knot as severely positive or negative, vs. mildly positive or negative, ELM can classify knots that lead to large changes to beam deflection, while not over-emphasizing knots that may not be a problem. Using ELM with a regression-fit Young's Modulus on three-point bending of Douglass Fir, it is possible estimate the effects a knot will have on the shape of the resulting displacement curve.
ContributorsSexton, Thurston Bryant (Author) / Takahashi, Timothy (Thesis director) / Jones, Donald (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2015-05
Description
In materials science, developing GeSn alloys is major current research interest concerning the production of efficient Group-IV photonics. These alloys are particularly interesting because the development of next-generation semiconductors for ultrafast (terahertz) optoelectronic communication devices could be accomplished through integrating these novel alloys with industry-standard silicon technology. Unfortunately, incorporating a maximal amount of Sn into a Ge lattice has been difficult to achieve experimentally. At ambient conditions, pure Ge and Sn adopt cubic (α) and tetragonal (β) structures, respectively, however, to date the relative stability and structure of α and β phase GeSn alloys versus percent composition Sn has not been thoroughly studied. In this research project, computational tools were used to perform state-of-the-art predictive quantum simulations to study the structural, bonding and energetic trends in GeSn alloys in detail over a range of experimentally accessible compositions. Since recent X-Ray and vibrational studies have raised some controversy about the nanostructure of GeSn alloys, the investigation was conducted with ordered, random and clustered alloy models.
By means of optimized geometry analysis, pure Ge and Sn were found to adopt the alpha and beta structures, respectively, as observed experimentally. For all theoretical alloys, the corresponding αphase structure was found to have the lowest energy, for Sn percent compositions up to 90%. However at 50% Sn, the correspondingβ alloy energies are predicted to be only ~70 meV higher. The formation energy of α-phase alloys was found to be positive for all compositions, whereas only two beta formation energies were negative. Bond length distributions were analyzed and dependence on Sn incorporation was found, perhaps surprisingly, not to be directly correlated with cell volume. It is anticipated that the data collected in this project may help to elucidate observed complex vibrational properties in these systems.
By means of optimized geometry analysis, pure Ge and Sn were found to adopt the alpha and beta structures, respectively, as observed experimentally. For all theoretical alloys, the corresponding αphase structure was found to have the lowest energy, for Sn percent compositions up to 90%. However at 50% Sn, the correspondingβ alloy energies are predicted to be only ~70 meV higher. The formation energy of α-phase alloys was found to be positive for all compositions, whereas only two beta formation energies were negative. Bond length distributions were analyzed and dependence on Sn incorporation was found, perhaps surprisingly, not to be directly correlated with cell volume. It is anticipated that the data collected in this project may help to elucidate observed complex vibrational properties in these systems.
ContributorsLiberman-Martin, Zoe Elise (Author) / Chizmeshya, Andrew (Thesis director) / Sayres, Scott (Committee member) / Wolf, George (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05