No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

Any structural analysis which gives stresses and displacements for some predefined structure is governed by some physical domain of loading, geometry and boundary conditions. Let this domain be called the structures "problem space." In applying finite element analysis, the solution to any one problem space may be one of many admissible solutions all of which satisfy some given set of boundary conditions. Admissibility is determined by the stated problem with its boundary conditions along with computer storage capacity considerations. Obtaining the most exact approximate solutions is one of major concern to insure adequate results. This problem has been approached from a number of viewpoints [4-9] all of which employ some version of minimum potential energy [5, 10]. This report is a study of current approaches to this problem and their effect on finite element grid optimizations. Selected optimizations [4-9] are shown to be effective in producing better solutions but it is noted that the implementation of these optimizations may be difficult. To survey the situation two fixed problem spaces of a tapered beam and a cantilever beam are chosen for investigation. Conclusions based on this study display that optimizations methods applied to a finite element model give an optimum space arrangement that is a function of the selected element geometry and displacement function. When changes in the element geometry are introduced a new optimum results. Comparing test problem results leads to some speculation employing uniform strain energy as a better guide to "first guess" grid arrangement and a recommendation for further investigation in this direction.

<p> The thesis proposes a novel method for the computation of the design sensitivity of microwave network parameters. The approach is based on the finite-element method. When combined with the iterative update method (the Broyden method) during the gradient-based optimization process, the approach requires practically no overhead for the computation of the response Jacobian, thus accelerating the optimization. </p> <p> The efficiency and accuracy of the gradient-based optimization and the tolerance analysis greatly depend on the computation of the design sensitivity. However, common commercial full-wave electromagnetic solvers do not provide sensitivity information. With them, the design sensitivities are computed from the response themselves using finite-difference or higher-order approximations at the response level. Consequently, for each design parameter of interest, at least one additional full-wave analysis is performed. </p> <p> The proposed self-adjoint sensitivity analysis (SASA) is so far the most efficient way to extract the sensitivity information for the network parameters with the finite-element method. As an improvement of the adjoint-variable method (AVM), it eliminates the additional system analyses. With one single full-wave analysis, the sensitivities with respect to all design parameters are computed. This significantly improves the efficiency of the sensitivity computations. </p> <p> When employed in gradient-based optimization, the computational overhead of the SASA can be further reduced. Instead of the finite-difference approximation, the system matrix derivatives are updated iteratively using the Broyden update. This reduces the computational overhead of the sensitivity analysis to practically zero. Further, several switching criteria between the Broyden update and the finite-difference approximation of the system matrix derivatives is proposed to guarantee the robust convergence of the optimization algorithm. This leads to our Broyden/finite-difference SASA (B/FD-SASA). </p> <p> The efficiency in terms of CPU time as well as the accuracy of the SASA is verified by several numerical examples, where the reference results are provided through the traditional finite-difference approximations. Also, the efficiency of the B/FD-SASA is validated by a filter design example and a microwave imaging example, with implementations exploiting different gradientbased optimization algorithms. </p> / Thesis / Master of Applied Science (MASc)

Yes / Ophthalmologists rely on a device known as the Goldmann applanation tonometer to make intraocular pressure (IOP) measurements. It measures the force required to press a flat disc against the cornea to produce a flattened circular region of known area. The IOP is deduced from this force using the Imbert-Fick principle. However, there is scant analytical justification for this analysis. We present a mathematical model of tonometry to investigate the relationship between the pressure derived by tonometry and the IOP. An elementary equilibrium analysis suggests that there is no physical basis for traditional tonometric analysis. Tonometry is modelled using a hollow spherical shell of solid material enclosing an elastic liquid core, with the shell in tension and the core under pressure. The shell is pressed against a rigid flat plane. The solution is found using finite element analysis. The shell material is anisotropic. Values for its elastic constants are obtained from literature except where data are unavailable, when reasonable limits are explored. The results show that the force measured by the Goldmann tonometer depends on the elastic constant values. The relationship between the IOP and the tonometer readings is complex, showing potentially high levels of inaccuracy that depend on IOP.

The hair cell, a specialized cell in the inner ear, is responsible for hearing and balance. The hair cell is an exquisite sensor that captures mechanical stimuli and generates neurosensory signals. A theory called gating theory has been developed and widely used to analyze the experimental data of hair cell transduction. Despite increasing knowledge about molecular structures of hair cells, the mechanical model in the gating theory remained simple. Efforts to make the most of the recent findings regarding the hair cell structures led to the development of hair cell finite element (FE) model (Cotton & Grant, 2000, 2004a, b). I have extended this approach by adding channel kinetics and structural dynamics to the FE structural model of the hair cell. I have expanded the previous static and passive model to a dynamic and active model. It is the most detailed hair cell structural model and includes up-to-date knowledge of the hair cell structure such as the stereocilia and various extracellular links. In order to observe the dynamic response of hair bundles in the endolymph fluid, I have included fluid drag in the model. Link nonlinearity has been added to reflect recent observations (Tsuprun 2003). The lateral links stiffen as they stretch and prevent contact between stereocilia when they compress. In addition to these structural features, I added channel kinetics such as the fast adaptation. In my study, the Ca²⁺ diffusion kinetics plays a key role in the hair cell adaptations. The Ca²⁺ association rate to the fast adaptation modulator is postulated to govern the fast adaptation. I assumed that two factors--the tip link tension and the Ca²⁺ concentration at the tip of stereocilia govern the hair cell mechanoelectric transduction. My dissertation comprises three parts--structure, dynamics and mechanotransduction of hair cells. First, the mechanical properties of hair bundle were sought by comparing my FE model with other experiments. The quantified Young's modulus of stereocilia and the stiffness of tip link agree well with other recent estimates. The stiffness of other structural elements (upper lateral and shaft links) was newly estimated through this effort. Second, I established equations of motion for the hair bundle in the fluid. Two possible loading conditions to the hair bundle were simulated. Two different hair bundles were subjected to a point load and a load induced by fluid flow. The results showed that some vestibular hair cells' transduction might be dominated by the fluid-induced force. Finally, I observed the hair cell transduction in various stimulus conditions. The results showed that the hair cell's sensitivity highly depends on the stimulus method. The fluid-jet stimulus activated fewer channels than the glass fiber and made the hair cell less sensitive. A faster stimulus opened more channels and made the hair cell more sensitive. The resting tension in the tip link, which is believed to be controlled by the Ca²⁺ concentration, also affected the hair cell sensitivity. A higher resting tension, equivalent to a lower Ca²⁺ concentration, tended to make the hair cell more sensitive. In conclusion, I developed a new tool to study the hair cell mechanoelectric transduction. My hair cell computational model enables us (1) to study how the hair cells' morphological variations are related to their function; (2) to investigate the hair cell mechanoelectric transduction at the single channel level, in silico, as opposed to the statistical approach; (3) to test the response of hair cells under in situ force boundary conditions. / Ph. D.