published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

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Until the twentieth century, theories of elastic rods and shells arose from collections of geometric and mechanical assumptions and approximations. These theories often lacked internal consistency and were appropriate for highly proscribed and sometimes unknown geometries and deformation sizes. The pioneering work of Truesdell, Antman, and others converted mechanical intuition into rigorous mathematical statements about the physics and mechanics of rods and shells. The result is the modern, geometrically exact theory of finite deformations of rods and shells.In the latter half of the twentieth century, biomechanics became a major focus of both experimental and theoretical mechanics. The genesis of residual stress by non-elastic growth has significant impact on the shape and mechanical properties of soft tissues. Inspired by the geometry of blood vessels and adopting a formalism found in elasto-plasticity, mechanicians have produced rigorous and applied results on the effect of growth on finite elastic deformations of columns and hollow tubes. Less attention has been paid to shells.A theory of growing elastic plates has been constructed in the context of linear elasticity. It harnessed many results in the theory of Riemann surfaces and has produced solutions that are surprisingly similar to experimental observations. Our intention is to provide a finite-deformation alternative by combining growth with the geometrically exact theory of shells. Such a theory has a clearer and more rigorous foundation, and it is applicable to thicker structures than is the case in the current theory of growing plates.This work presents the basic mathematical tools required to construct this alternative theory of finite elasticity of a shell in the presence of growth. We make clear that classical elasticity can be viewed in terms of three-dimensional Riemannian geometry, and that finite elasticity in the presence of growth must be considered in this way. We present several examples that demonstrate the viability and tractability of this approach.

As many variable pricing projects are still in the implementation stage, long-run driver responses to the variable tolls are largely unknown. This research examined the long-run changes in driver behavior in an existing variable pricing project in Lee County, Florida. Using empirical evidence, it was found that over time the price elasticities of demand on the Lee County toll bridges have decreased from -0.42 to - 0.11 (Midpoint Memorial Bridge) and from -0.31 to -0.06 (Cape Coral Bridge) during the early morning discount period. The elasticities have decreased, but to a lesser extent, during the late morning and early afternoon discount periods. A discount period volume spreading ratio was also developed to analyze these changes. The results from this analysis confirmed the elasticity results. In addition to the empirical analysis of travel patterns discussed above, a telephone survey of drivers was conducted. The survey results indicated that certain driver characteristics such as higher frequency of trips, commute trip purpose, full-time employment status, more people in the household, higher education, and age between 25-34 years, were all indicators that the participant may increase his or her variable pricing usage over time. Other characteristics, including being retired and having a household income less than $16,000, were indicators that the driver may not increase variable pricing participation. Binary logit and semiparametric models were also developed to examine socio-economic and commute characteristics that may influence a driver increasing his or her participation in a variable pricing program. The results from these two variable toll bridges in Lee County indicated a decrease in variable toll price elasticity over time. However, these results may not be typical for variable pricing projects. Factors such as alternative routes, different traveler demographics, traffic congestion levels, and size of the toll discount may influence the results obtained from other variable pricing projects. However, the methodology developed in this research can be applied to other projects in order to determine those toll price elasticities of demand.

Shear wave (SW) imaging is an ultrasound elastogrpahy technique for estimating the elastic properties of biological tissues. Increasing the frequency would improve both the confinement of the radiation force generating the shear wave, and the imaging spatial resolution. The objectives of the study were to realize a simple high frequency (HF) system for the generation and detection of SW propagation and to implement this system to develop and characterize tissue-mimicking gelatin phantoms (TMGP) for HF SWI with elastic properties in the range of those encountered in biological tissue. A 5 MHz and 10 MHz focused transducer were used to induced SW’s in TMGP ranging from 4% to 12% gelatin with 3% silica for scattering and a 25 MHz single-element focused transducer recorded pulse-echo signals in order to capture the SW. The shear wave speeds in the TMGP were found to range linearly from 1.59-4.59 m/s in the 4% to 12% gelatin samples.

Shear wave (SW) imaging is an ultrasound elastogrpahy technique for estimating the elastic properties of biological tissues. Increasing the frequency would improve both the confinement of the radiation force generating the shear wave, and the imaging spatial resolution. The objectives of the study were to realize a simple high frequency (HF) system for the generation and detection of SW propagation and to implement this system to develop and characterize tissue-mimicking gelatin phantoms (TMGP) for HF SWI with elastic properties in the range of those encountered in biological tissue. A 5 MHz and 10 MHz focused transducer were used to induced SW’s in TMGP ranging from 4% to 12% gelatin with 3% silica for scattering and a 25 MHz single-element focused transducer recorded pulse-echo signals in order to capture the SW. The shear wave speeds in the TMGP were found to range linearly from 1.59-4.59 m/s in the 4% to 12% gelatin samples.

In this paper, we used the Autoregressive Distributed Lag (ARDL) model and the bounds test approach to estimate the elasticity of demand for natural gas in Western and Central Canada. The best model specification selected by Schwarz Information Criterion (SIC) for each province suggests that there exist long-run relationships between the dependent variable and independent variables for all provinces, except Ontario. Consumption per capita in these provinces can be explained by natural gas prices, electricity prices, income, and heating degree days (a measurement for the weather factor) in levels for the selected specification. The results show that natural gas demand is very inelastic with respect to natural gas prices and also with respect to heating degree days.

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