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The study of normal impedance of perforated plate acoustic liners including the effect of bias flow was studied. Two impedance models were developed, by modeling the internal flows of perforate orifices as infinite tubes with the inclusion of end corrections to handle finite length effects. These models assumed incompressible and compressible flows, respectively, between the far field and the perforate orifice. The incompressible model was used to predict impedance results for perforated plates with percent open areas ranging from 5% to 15%. The predicted resistance results showed better agreement with experiments for the higher percent open area samples. The agreement also tended to deteriorate as bias flow was increased. For perforated plates with percent open areas ranging from 1% to 5%, the compressible model was used to predict impedance results. The model predictions were closer to the experimental resistance results for the 2% to 3% open area samples. The predictions tended to deteriorate as bias flow was increased. The reactance results were well predicted by the models for the higher percent open area, but deteriorated as the percent open area was lowered (5%) and bias flow was increased. A fit was done on the incompressible model to the experimental database. The fit was performed using an optimization routine that found the optimal set of multiplication coefficients to the non-dimensional groups that minimized the least squares slope error between predictions and experiments. The result of the fit indicated that terms not associated with bias flow required a greater degree of correction than the terms associated with the bias flow. This model improved agreement with experiments by nearly 15% for the low percent open area (5%) samples when compared to the unfitted model. The fitted model and the unfitted model performed equally well for the higher percent open area (10% and 15%). / 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.

The Eshelby-Stroh formalism is used to analyze the generalized plane strain quasistatic deformations of an anisotropic, linear elastic laminated plate.The formulation admits any set of boundary conditions on the edges and long faces of the laminate. Each lamina may be generally anisotropic with as many as 21 independent elastic constants. The three dimensional governing differential equations are satisfied at every point of the body.The boundary conditions and interface continuity conditions are satisfied in the sense of a Fourier series. Results are presented for three sample problems to illustrate the versatility of the method. The solution methodology is generalized to study the deformation of finite rectangular plates subjected to arbitrary boundary conditions. The effect of truncation of the series on the accuracy of the solution is carefully examined. Results are presented for thick plates with two opposite edges simply supported and the other two subjected to eight different boundary conditions. The results are compared with three different plate theories.The solution exhibits boundary layers at the edges except when they are simply supported. Results are presented in tabular form for different sets of edge boundary conditions to facilitate comparisons with predictions from various plate theories and finite element formulations. The Eshelby-Stroh formalism is also extended to study the generalized plane deformations of piezothermoelastic laminated plates. The method is capable of analyzing laminated plates with embedded piezothermoelastic patches. Results are presented for a thermoelastic problem and laminated elastic plates with piezothermoelastic lamina attached to its top surface. When a PZT actuator patch is attached to an elastic cantilever substrate, it is observed that the transverse shear stress and transverse normal stress are very large at the corners of the PZT-substrate interface. This dissertation is organized in the form of three self-contained chapters each of which will be submitted for possible publication in a journal. / Ph. D.

Analytical expressions for the deflection surface of symmetrically loaded circular and annular plates resting on discrete point supports are derived. The formulation of the problem is based on classical small deflection plate theory. It is also assumed, in the formulation, that the supports are situated equal distances apart on a single concentric circle. There is no restriction placed on the number of supports or on the size of the support circle which could be as large as the plate itself or as small as the size of the hole of the annular plate. The singularity effects associated with the concentrated supports on the plate problems considered here are accounted for in the solution, by drawing an analogy from the Michell's solution to a clamped circular plate subjected to an eccentric point load. This procedure yields solutions in much more suitable form for practical numerical problems than other known methods. In the case of circular plates on multipoint supports, explicit solutions are given to a number of loading conditions. Solutions to a uniformly loaded circular plate on multipoint supports are compared with the published experimental results; the conclusions are favorable. From the numerical data obtained for a uniformly loaded circular plate on multipoint supports, a procedure is outlined for obtaining contour maps of deformed uniformly loaded plates with discrete supports on two support circles. Solutions to annular plates on multipoint supports are derived for the first time. By utilizing this result, design charts are drawn to indicate the optimum size of the support circle, which would produce least peak-to-peak displacements for any given size of hole, and a specified number of supports. Contour maps associated with annular plates on three point supports are also drawn to illustrate the influence of support circle on the displacements. It was found that when there are a fewer number of supports and/or the size of the hole is small, the magnitude of peak-to-peak displacements and the size of the optimum support circle are considerably different from the associated quantities when the support is a continuous ring. / Ph. D.

The theory proposed in this thesis is an attempt to bridge the gap that exists between the linear and nonlinear theories of Elasticity. The theory is applied to the solution of a hubbed, clamped, circular plate made of polyurethane whose hub is subjected to a "large" axi~symmetrioc twist. This particular problem is attacked in the conventional manner of the generalized plane stress problem of linear elasticity. However, the strain displacement relations are formulated in the Eulerian manner and the displacement gradients are not assumed to be small. In addition, a more general stress~strain relationship than the conventional Hookean form is assumed. The solution is checked by experiment; and in addition, three auxiliary problems; the uniaxial compression problem, the uniaxial tension problem, and a shear problem are checked experimentally to further cheek the validity of the proposed theory when applied to the finite strain response of polyurethane. / Ph. D.

The largest cost in manufacturing PEM fuel cells for automotive applications is due to the bipolar plate. The current graphite material used for the bipolar plate is very brittle and difficult to machine to the rigorous specifications needed for fuel cell stacks. This paper introduces the development of a fuel cell test stand for simultaneous testing of six individual fuel cells. To establish a long-term performance evaluation, the fuel cells incorporate a baseline graphite material that undergoes testing in the fuel cell environment. The graphite is an industry standard material that should not corrode when subjected to continual testing. The baseline model will be used in development of novel composite materials that will be tested under the same conditions for comparison to the graphite. Furthermore, the new materials and applied manufacturing methods could reduce the overall cost of fuel cell stacks in the future. Funding for this project was generously donated by the Virginia Center for Innovative Technology and the National Science Foundation. / Master of Science

Four plates with centrally located circular holes were manufactured using a fiber placement technique. With two plates the fibers were steered around the holes in curvilinear trajectories. With the two other plates the fibers were placed in the conventional straight line format. For the case of the curvilinear trajectories, the fibers were continuous from one end of the plate to the other, whereas for the straight trajectories the fibers were cut by the presence of the hole. Two plates, a curvilinear fiber plate and a straight fiber plate, were tested in tension. The two other plates were tested in compression. The straight fiber plates were considered as baseline cases. Since the plates were thin, compression testing resulted in buckling and post buckling. The current work focuses on the analysis of these four plates and a comparison between the analysis and experimental results. Because of a spatial dependence of the A and D stiffness matrices for the curvilinear fiber cases, the analyses were conducted using finite element methods, and included a failure criterion. A scheme to improve the plate design is also considered. / Master of Science

Load testing was performed on a one-third scale model steel fiber reinforced concrete post-tensioned flat plate. The specimen had nine 10ft x 10ft x 3in. bays along with a 2ft-6in. overhang. Distributed loading was applied with a whiffle tree loading system at each bay and overhang section. Throughout the test, crack widths, crack locations, deflections, concrete strains, and reinforcing bar strains were monitored. The post-tensioned flat plate was designed to just meet the maximum allowable stress requirements of ACI 318. Minimal quantities of hairline cracks were observed after stressing the slab, and up through service-level loads, the cracks grew slightly in length and width. The slab behaved elastically through service-level loading. As factored-level loading was approached, the slab began to behave inelastically as indicated by both the load-deflection plots and the load-strain plots. A total ultimate load of 282psf (174psf of applied load) was reached when concrete crushing occurred. A 0.20in. wide full-length crack was observed running on the bottom surface of the slab between column lines 1 and 2, and a full-length crack was observed at column line 2 on the top surface of the slab. These two cracks were the leading contributors to the slab's failure. The performance of the SFRC post-tensioned flat plate indicated that considerations should be made to remove requirements for negative moment reinforcement in post-tensioned flat plates when SFRC is used. Also, the requirements for positive moment reinforcement should be modified. Additionally, the SFRC post-tensioned flat plate exhibited excellent levels of ductility. More experimentation should be conducted to determine if the maximum tensile stress in ACI 318 can be increased for post-tensioned flat plates with SFRC. / Master of Science / Load testing was performed on a one-third scale model steel fiber reinforced concrete (SFRC) post-tensioned flat plate. Post-tensioned flat plates are a type of concrete structural system typically used as flooring. This system typically employs high-strength steel strands, which are stretched to introduce compression into the concrete, which helps prevent the onset of cracking. The specimen had nine 10ft x 10ft x 3in. bays along with a 2ft-6in. overhang. Distributed loading was applied with a whiffle tree loading system at each bay and overhang section. The whiffle tree loading system was used to allow actuators to spread out the vertical loading on the slab. During the test, crack widths, crack locations, deflections, concrete strains, and reinforcing bar strains were monitored. The post-tensioned flat plate was designed to just meet the maximum allowable stress requirements of the governing standard, ACI 318. Minimal quantities of hairline cracks were observed after stressing the slab, and up through service-level loads, the cracks grew slightly in length and width. As larger loads were applied, the cracks grew and the effects of these cracks on the slab were evidenced in the deflection and strain measurements. A total ultimate load of 282psf (174psf of applied load) was reached when concrete crushing occurred. A 0.20in. wide full-length crack was observed running on the bottom surface of the slab between column lines 1 and 2, and a full-length crack was observed at column line 2 on the top surface of the slab. These two cracks were a driving force in the slab’s failure. The performance of the SFRC post-tensioned flat plate indicated that considerations should be made to change the requirements for negative and positive moment reinforcement in post-tensioned flat plates when SFRC is used. Additionally, the SFRC post-tensioned flat plate exhibited great performance after significant cracking was present. More experimentation should be conducted to determine if the maximum allowable tensile stress in ACI 318 can be increased for post-tensioned flat plates with SFRC.

The objective of the study was to develop a modeling technique to idealize thin, orthotropic plates into an equivalent grid, suitable for the matrix-displacement method of analysis. The formulation is an alternative to the classical plate theory and finite element method. The grid model is unique compared to other grid formulations in its applicability to plates exhibiting material orthotropy in addition to isotropy and shape orthotropy. Further, the grid model has less members compared to the previous grid formulations. A function was developed to establish the grid member cross-sectional size for various boundary conditions and material properties. The maximum error between predicted and published theoretical and experimental deflections was 3% for plates in isotropic and advanced composite materials. The maximum error between predicted and experimental deflections for wood based composite plates was 20%. / Master of Science