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.

The vestibular system consists of several organs that contribute to ones sense of balance. One set of organs, otoconial organs, have been shown to respond to linear acceleration (1949). Hair bundles (and hair cells), which are the mechano-electric transducers found within otoconial organs, respond to displacement of the overlying otoconial membrane (OM). Structure, position and orientation of the OM within the head may influence the stimulus of hair bundles by changing the deformation characteristics of the OM. Therefore, studying the deformation characteristics of the OM with finite element models presents a unique advantage: the ability to study how different variables may influence the deformation of the OM. Previous OM models have ignored complicated OM geometry in favor of single degree of freedom (De Vries 1951)or distributed parameter models (Grant et al. 1984; Grant and Cotton 1990; Grant et al. 1994). Additionally, OMs have been modeled considering three dimensional geometry (Benser et al. 1993; Kondrachuk 2000; 2001a), however OM layer thicknesses were assumed to be constant. Further, little research has investigated the effect of position and orientation of otoconial organs on the deformation of the OM (Curthoys et al. 1999), due to natural movement of the head. The effect of structure, position and orientation of the utricle of a red ear slider turtle on the stimulation of hair bundles in the OM is investigated here. Using confocal images, a finite element model of the utricle OM is constructed considering its full 3D geometry and varying OM layer thickness. How specific geometric variables, which are missing from other OM models, effect the deformation of the utricle OM is studied. Next, since hair bundles are part of the structure of the OM, their contribution to the deformation of the utricular OM is quantified. Then, using computed tomography of a turtle head and high speed video of turtle feeding strikes, acceleration at the utricle during natural motion is estimated. Finally, the effects of orientation of the utricle in the head on the stimulus of hair bundles within the organ is investigated. In summary, a model and methods are developed through which deformation of the turtle utricle OM through natural movements of the head may be studied. Variables that may contribute to utricle OM deformation are investigated. Utricle OM geometry, hair bundles, position and orientation all play a role in utricle OM deflection and therefore hair bundle stimulus. Their effects are quantified and their roles are discussed in this dissertation. / Ph. D.

Polymeric foam cores are widely used as core materials in sandwich panels subject to blast loads, where high strain rates of the order of 4000 /s are observed. Unlike metallic foams polymeric foams exhibit transversely isotropic response when tested in a laboratory setting. More specifically, they exhibit different hardening along the foam thickness than that in a direction transverse to the thickness. Furthermore, polymeric foams harden differently in tension and compression. In this thesis we adopt ideas from the constitutive model developed by Hoo Fatt et al. cite{hoofatt2}, which captures strain hardening, transverse isotropy and distinguishes the response in tension and in compression, to include isotropic strain rate hardening in our constitutive model. A one dimensional prototype of the model is used to aid in the physical explanation of various variables, and the model is generalized to three dimensions. The material model is implemented as a VUMAT (user defined) subroutine in the commercial finite element software ABAQUS Explicit. We show that the model works robustly in uniaxial deformations as well as in sandwich problems using the test data available in the literature. We provide values of the 39 material parameters for H45, H60, H80, H100, H130 and H200 foams. The constitutive relation is utilized in an optimization problem in which the surrogate optimizer is utilized to minimize the backface deflection of a blast loaded clamped sandwich plate of a fixed mass. The core in the optimized sandwich structure has a stratified configuration (not functionally graded) and has 24% less maximum back face deflection as compared to that in which the six core layers vary from highest density to lowest density or vice a versa. For a sandwich panel subject to a blast load, when the strain rate hardening effect are neglected, we observed a 12% reduction in the predicted peak deflection from that when strain rate effects are considered. It is counter intuitive and needs further investigation. / Master of Science / Sandwich panels are widely used in high performance structures requiring high stiffness, low weight and the ability to withstand blasts. Sandwich panels consist of several layers, and it is possible to vary the material and thickness of each layer to arrive at a sandwich panel design which performs optimally. In this thesis, we numerically find an optimum sandwich panel design so that it deflects the least when exposed to a given blast. The problem is studied using ABAQUS Explicit and the Surrogate Optimization solver built into MATLAB. The outer layers of the sandwich panel are made of a highly stiff material and their thicknesses are fixed. The remaining six inner layers are allowed to be any of six different H45, H60, H80, H100, H130, H200 Divinycell polymeric foams and are allowed to vary in thickness. In order to draw a fair comparison between the designs, we constrain the total mass of the sandwich panel to be 1 kg. In our quest to find the best sandwich panel design, we develop and implement, in ABAQUS Explicit, a custom mathematical model which captures the complex behavior of the polymeric foams. Experimental data in the literature and other techniques were utilized to check that this mathematical model accurately predicts the physical response of polymeric foams in different scenarios. The reader is given all of the theory and physical constants needed to use this mathematical model for the six foams. The optimal sandwich panel deflects 24% less than a baseline design, and it is found that the material properties of the six foams do not vary gradually as they did in the baseline designs.