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.

Several rubber diaphragms, of the same type used inside an hydraulic accumulator, failed a short time after they were mounted. While there is nothing special with these failures the cost, in some cases can be high. A closer look, at the damaged diaphragms reveal an interesting nonsymmetric radial deformation accompanied in some cases by cracks. Most of the analyses regarding the failures of rubber diaphragms offer explanations only from a chemical or material science point of view. We propose in this thesis a new perspective from a mechanical-structural engineering view. Therefore the main goal of the thesis is to investigate the deformation of a diaphragm and based on this analysis to propose an explanation for formation of the cracks. It is shown that the analysis of the diaphragm problem leads to a pseudo-nonconservative system and involves a buckling, a post buckling (dynamic snap-through), an eversion, and a load response analysis. The problem is approached numerically using the nite element method. The character of pseudo-nonconservativeness of the system requires, in this case, an update of the tangent stiffness matrix with a certain stiffness correction. This new correction is proposed also. The result is valid not only for this particular problem but for the entire class of problems to which the diaphragm belongs. This correction is implemented in an existing nite element program (NIKE3D) and used to analyze the diaphragm deformation. The results indicate that under the typical load condition for a diaphragm a certain deformation pattern occurs, and this can lead to the formation of cracks. This deformation matches extremely well with the actual deformed shape of a typical failed diaphragm. It is shown that the deformation pattern depends on the structural properties of the diaphragm rather than on the magnitude of the applied load. The nonsymmetry in the diaphragm deformation and the difference in the crack development is explained also. / Ph. D.

Short-term creep tests in tension and in compression were conducted on southern pine, Douglas-fir, yellow-poplar, and Parallam™ samples at temperatures ranging between 20 and 80° C and at 6, 9 and 12% moisture content. The principle of time-temperature superposition was applied to form a master curve that extended for a maximum of 2 years. The horizontal shift factors followed an Arrhenius relation with activation energies ranging between 75 and 130 kJ/mole. It was not possible to superpose the compliance curves at 70 and 80° C, this is attributed to the presence of multiple components in wood with different temperature dependence. Long-term creep tests were also conducted in tension and in compression at 20° C and 12% moisture content for over 2 years. The resulting compliance curves were fitted to the power law equation using a nonlinear fitting procedure. The results were compared with those of the short-term creep tests. Finite element analysis was conducted on selected wood structures to determine the effect of creep on serviceability and stability. / Ph. D.

The unit load is the form of most commercial and industrial products during storage and distribution. A simple form of a unit load, a palletized bulk bin is commonly used to transport fruit and vegetables from the point of harvest to processing facilities. These vibration sensitive products are often subjected to damaging vibrations during this period. Most damage occurs during the large accelerations associated with resonance, which occurs when the natural frequency of the unit load matches the input frequencies commonly encountered during transportation. A computer model, called RoPUL (resonance of palletized unit loads), of a palletized bulk bin loaded with fruit, was developed using finite element analysis techniques. Unit loads consisting of palletized bulk bins of apples and peaches were tested and RoPUL was found to accurately predict the resonant frequencies of these loads. Using RoPUL, the effects of product mass, container design, and pallet design on natural frequencies can be analyzed. As the input frequencies of most transportation modes is well documented, RoPUL can be used to help design a unit load to better protects vibration sensitive products during shipment. / Ph. D.

The purpose of this study is to investigate spatial wood structures, trace their response on equilibrium paths, identify failure modes, and predict the ultimate load. The finite element models of this study are based on the Crafts Pavilion dome (Triax) in Raleigh, North Carolina, and the Church of the Nazarene dome (Varax) in Corvallis, Oregon. Modeling considerations include 3-d beam finite elements, transverse isotropy, torsional warping, beam-decking connectors, beam-beam connectors, geometric and material nonlinearities, and the discretization of pressure loads. The primary objective of this study is to test the hypothesis that the beam-decking connectors (B-D connectors) form the weakest link of the dome. The beam-decking connectors are represented by nonlinear springs which model the load slip behavior of nails between the beam and the decking. The secondary objective of this study is to develop models that are sufficiently simple to use in engineering practice. / Ph. D.

Over the past several decades, the use of composite materials has grown considerably. Typically, fiber-reinforced polymer-matrix composites are modeled as being linear elastic. However, it is well-known that polymers are viscoelastic in nature. Furthermore, the analysis of complex structures requires a numerical approach such as the finite element method. In the present work, a triangular flat shell element for linear elastic composites is extended to model linear viscoelastic composites. Although polymers are usually modeled as being incompressible, here they are modeled as compressible. Furthermore, the macroscopic constitutive properties for fiber-reinforced composites are assumed to be known and are not determined using the matrix and fiber properties along with the fiber volume fraction. Hygrothermo-rheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Both the temperature and moisture are taken to be prescribed. Hence, the heat energy generated by the viscoelastic deformations is not considered. When the deformations and rotations are small under an applied load history, the usual engineering stress and strain measures can be used and the time history of a viscoelastic deformation process is determined using the original geometry of the structure. If, however, sufficiently large loads are applied, the deflections and rotations will be large leading to changes in the structural stiffness characteristics and possibly the internal loads carried throughout the structure. Hence, in such a case, nonlinear effects must be taken into account and the appropriate stress and strain measures must be used. Although a geometrically-nonlinear finite element code could always be used to compute geometrically-linear deformation processes, it is inefficient to use such a code for small deformations, due to the continual generation of the assembled internal load vector, tangent stiffness matrix, and deformation-dependent external load vectors. Rather, for small deformations, the appropriate deformation-independent stiffness matrices and load vectors to be used for all times can be determined once at the start of the analysis. Of course, the time-dependent viscoelastic effects need to be correctly taken into account in both types of analyses. The present work details both geometrically-linear and nonlinear triangular flat shell formulations for linear viscoelastic composites. The accuracy and capability of the formulations are shown through a range of numerical examples involving beams, rings, plates, and shells. / Ph. D.

A technique was developed for analyzing and developing mechanical properties for porous geomaterials subjected to the high pressures encountered in penetration and blast-type loadings. A finite element (FE) code was developed to verify laboratory test results or to predict unavailable laboratory test data for porous media loaded to multikilobar stress levels. This FE program eliminates a deficiency in the process of analyzing and developing mechanical properties for porous geomaterials by furnishing an advanced analysis tool to the engineer providing properties to material modelers or ground shock calculators. The FE code simulates quasi-static, axisymmetric, laboratory mechanical property tests, i.e., the laboratory tests are analyzed as boundary value problems. The code calculates strains, total and effective stresses, and pore fluid pressures for fully- and partially-saturated porous media. The time dependent flow of the pore fluid is also calculated. An elastic-plastic strain-hardening cap model calculates the time-independent skeletal responses of the porous solids. This enables the code to model nonlinear irreversible stress-strain behavior and shear-induced volume changes. Fluid and solid compressibilities were incorporated into the code, and partially-saturated materials were simulated with a "homogenized" compressible pore fluid. Solutions for several verification problems are given as proof that the program works correctly, and numerical simulations of limestone behavior under drained and undrained boundary conditions are also presented. / Ph. D.

Sizings, a thin polymer coating applied to the surface of the carbon fiber before impregnation with the matrix, have been shown to affect the mechanical performance of the composite. These sizings affect the processability of the carbon fiber that translates into a composite with less fiber breakage and improved fiber/matrix adhesion. In addition, the interdiffusion of the sizing and the bulk matrix results in the formation of an interphase. This interphase can alter damage initiation and propagation that can ultimately affect composite performance. The overall objective of the work detailed in this thesis is to ascertain the effects that thermoplastic sizing agents have on composite performance and determine the phenomenological events associated with the effects. All of the thermoplastic sizings had improved processability over the traditional G' sizing. These improvements in processability translated into a composite with less fiber damage and improved surface quality. In addition, all of the thermoplastic sizings outperformed the industrial benchmark sizing G' by at least 25% in static tensile strength, 11% in longitudinal flexure strength, and 30% in short beam shear strength. All moduli were found to be unaffected by the addition of a sizing. The interphase formed in K-90 PVP sized carbon fiber composites was fundamentally predicted from the constitutive properties of K-90 PVP/Derakane™ interdiffusion and fundamental mass transport equations. The K-90 PVP sizing material interdiffusing with the Derakane™ matrix was found to be dissolution controlled. The dissolution diffusion coefficient had an exponential concentration dependence. Fundamental mass transport models were utilized to predict the interphase profile. The predicted K-90 PVP interphase concentration profile displayed steep gradients at the fiber/matrix interface but essentially no gradients at points distant from the fiber surface. The predicted mechanical property profile was essentially flat for the modulus but did show a steep gradient in the strain-to-failure and shrinkage properties. However, the K-90 PVP interphase compared to the unsized/pure Derakane™ interphase showed improvements in strength and strain-to-failure and a reduction in cure shrinkage without significantly affecting the interphase tensile or shear moduli. / Ph. D.

A two part study is performed to investigate the application of reliability-based design optimization (RBDO) approach to design elastic-plastic stiffener beams with Tsection. The objectives of this study are to evaluate the benefits of reliability-based optimization over deterministic optimization, and to illustrate through a practical design example some of the difficulties that a design engineer may encounter while performing reliability-based optimization. Other objectives are to search for a computationally economic RBDO method and to utilize that method to perform RBDO to design an elastic-plastic T-stiffener under combined loads and with flexural-torsional buckling and local buckling failure modes. First, a nonlinear elastic-plastic T-beam was modeled using a simple 6 degree-of-freedom non-linear beam element. To address the problems of RBDO, such as the high non-linearity and derivative discontinuity of the reliability function, and to illustrate a situation where RBDO fails to produce a significant improvement over the deterministic optimization, a graphical method was developed. The method started by obtaining a deterministic optimum design that has the lowest possible weight for a prescribed safety factor (SF), and based on that design, the method obtains an improved optimum design that has either a higher reliability or a lower weight or cost for the same level of reliability as the deterministic design. Three failure modes were considered for an elastic-plastic beam of T cross-section under combined axial and bending loads. The failure modes are based on the total plastic failure in a beam section, buckling, and maximum allowable deflection. The results of the first part show that it is possible to get improved optimum designs (more reliable or lighter weight) using reliability-based optimization as compared to the design given by deterministic optimization. Also, the results show that the reliability function can be highly non-linear with respect to the design variables and with discontinuous derivatives. Subsequently, a more elaborate 14-degrees-of-freedom beam element was developed and used to model the global failure modes, which include the flexural-torsional and the out-of-plane buckling modes, in addition to local buckling modes. For this subsequent study, four failure modes were specified for an elasticplastic beam of T-cross-section under combined axial, bending, torsional and shear loads. These failure modes were based on the maximum allowable in-plane, out-ofplane and axial rotational deflections, in addition, to the web-tripping local buckling. Finally, the beam was optimized using the sequential optimization with reliabilitybased factors of safety (SORFS) RBDO technique, which was computationally very economic as compared to the widely used nested optimization loop techniques. At the same time, the SOPSF was successful in obtaining superior designs than the deterministic optimum designs (either up to12% weight savings for the same level of safety, or up to six digits improvement in the reliability for the same weight for a design with Safety Factor 2.50). / Ph. D.