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.

Inflatable dams are flexible, cylindrical structures anchored to a foundation. They are used for a variety of purposes, e.g. diverting water for irrigation or groundwater recharging, impounding water for recreational purposes, and raising the height of existing dams or spillways. The vibration behavior of such dams is analyzed. Single-anchor inflatable dams with fins are considered. First, a static analysis is performed which yields the equilibrium shapes of the dam, both in the presence and absence of water. Then, a dynamic analysis is undertaken which analyzes the small vibrations of the inflatable dam about the equilibrium configuration, both in the presence of water (hydrostatic water as well as parallel flowing water) and absence of water. The dam is modeled as an elastic shell. It is assumed to be air-inflated and resting on a rigid foundation. The cross-sectional perimeter, material thickness, modulus of elasticity, and Poisson's ratio are given. The analysis is performed for different values of internal pressure and external water heads. Initially, the dam is assumed to lie flat. The internal pressure is then increased slowly until it reaches the desired value. Then the external water is applied and the equilibrium configuration is obtained. Small vibrations about this configuration are considered. The water is assumed to be inviscid and incompressible, and potential theory is used. The infinite-frequency limit is assumed on the free surface. A boundary element technique is utilized to determine the behavior of the water, and the finite element program ABAQUS is used to analyze the structural behavior. Both the cases of fluid at rest and flowing parallel to the dam are considered. The vibration frequencies and mode shapes are computed. The effect of the internal pressure of the dam is investigated, and the results are compared to those for the dam in the absence of external water. / Master of Science

Spacecraft structures rely on honeycomb panels to provide a light weight means to support the vehicle. Honeycomb panels can carry significant load but are most vulnerable to structural failure at their joints where panels connect. This research shows that predicting sandwich panel joint capability using finite element analysis (FEA) is possible. This allows for the potential elimination of coupon testing early in a spacecraft design program to determine joint capability. Linear finite element analysis (FEA) in NX Nastran was used to show that adhesive failure can be predicted with reasonable accuracy by including a fillet model on the edge of the fitting. Predicting the ultimate failure of a joint using linear FEA requires that engineering judgment be used to determine whether failure of certain bonds in a fitting will lead to ultimate joint failure or if other bonds will continue to carry the joint's load. The linear FEA model is also able to predict when the initiation of core failure will begin. This has the limitation that the joint will still be able to continue to carry significantly more load prior to joint ultimate failure even after the core has begun to buckle. A nonlinear analysis is performed using modified Riks' method in Abaqus FEA to show that this failure mode is predictable. The modified Riks' analysis showed that nonlinear post-buckling analysis of a honeycomb coupon can predict ultimate core failure with good accuracy. This solution requires a very high quality mesh in order to continue to run after buckling has begun and requires imperfections based on linear buckling mode shapes and thickness tolerance on the honeycomb core to be applied. / Master of Science

The vestibular system of vertebrates consists of the utricle, saccule, and the semicircular canals. Head movement causes deformation of hair cell bundles in these organs, which translate this mechanical stimulus into an electrical response sent to the nervous system. This study consisted of two sections, both utilizing a Fortran-based finite element program to study hair cell bundle response. In the first part, the effects of variations in geometry and material properties on bundle mechanical response were studied. Six real cells from the red eared slider turtle utricle were modeled and their response to a gradually increased point load was analyzed. Bundle stiffness and tip link tension distributions were the primary data examined. The cells fell into two groups based on stiffness. All cells exhibited an increase in stiffness as the applied load was increased, but cells in the stiffer group showed a greater increase. Tip link tensions in the compliant group were approximately 3 times as high as those in the stiffer group. Cells in the stiffer group were larger, with more cilia, and also had a higher stereocilia/kinocilium height ratio than the cells in the other group. The stereocilia/kinocilium height ratio was the most important geometric factor in influencing bundle stiffness. Modeling a bundle as just its middle row of stereocilia resulted in some decrease in stiffness, but more significantly, a stiffness that was virtually constant as applied load increased. Tip link tension distributions showed serial behavior in the core rows of stereocilia and parallel behavior in the outer rows; this trend intensified if the tip link elastic modulus was increased. It was demonstrated that full three-dimensional modeling of bundles is critical for obtaining complete and accurate results. In the second part of the study, tip link ion gates were modeled. Sufficient tension in a tip link caused that link's ion gate to open, increasing the length of the link and causing its tension to decrease or the link to go slack. The two parameters that were varied were tip link elastic modulus and tip link gating distance d (change in length of the link). Bundle stiffness drops of up to 25% were obtained, but only when tip links went slack after gate opening; tip link slackening was dependent on tip link gating distance. Higher tip link modulus resulted in higher stiffness drops. Variable tip link modulus and tip link pre-tensioning were modeled. Variable tip link modulus resulted in increased bundle stiffness, especially under high applied loads, and in some cases, resulted in greater bundle stiffness drops when ion gates opened. Tip link pre-tensioning had no noticeable effect on bundle response. No evidence against inclusion of pre-tensioning or variable tip link elastic modulus was found. / Master of Science

Simulations of the welding process for butt and tee joints using finite element analyses are presented. The base metal is aluminum alloy 2519-T87 and the filler material is alloy 2319. The simulations are performed with the commercial software SYSWELD+®, which includes moving heat sources, material deposit, metallurgy of binary aluminum, temperature dependent material properties, metal plasticity and elasticity, transient heat transfer and mechanical analyses. One-way thermo-mechanical coupling is assumed, which means that the thermal analysis is completed first, followed by a separate mechanical analysis based on the thermal history. The residual stress state from a three-dimensional analysis of the butt joint is compared to previously published results. For the quasi-steady state analysis the maximum residual longitudinal normal stress was within 3.6% of published data, and for a fully transient analysis this maximum stress was within 13% of the published result. The tee section requires two weld passes, and both a fully three-dimensional (3-D) and a 3-D to 2-D solid-shell finite elements model were employed. Using the quasi-steady state procedure for the tee, the maximum residual stresses were found to be 90-100% of the room-temperature yield strength. However, the longitudinal normal stress in the first weld bead was compressive, while the stress component was tensile in the second weld bead. To investigate this effect a fully transient analysis of the tee joint was attempted, but the excessive computer times prevented a resolution of the longitudinal residual stress discrepancy found in the quasi-steady state analysis. To reduce computer times for the tee, a model containing both solid and shell elements was attempted. Unfortunately, the mechanical analysis did not converge, which appears to be due to the transition elements used in this coupled solid-shell model. Welding simulations to predict residual stress states require three-dimensional analysis in the vicinity of the joint and these analyses are computationally intensive and difficult. Although the state of the art in welding simulations using finite elements has advanced, it does not appear at this time that such simulations are effective for parametric studies, much less to include in an optimization algorithm. / Master of Science

The interest in the use of aluminum as a structural material in marine applications has increased greatly in recent years. This increase is primarily due to the low weight of aluminum compared to other structural materials as well as its ability to resist corrosion. However, a critical issue in the use of any structural material for naval applications is its response to fire. Past experience has shown that finite element programs can produce accurate predictions of failure of structural components. Parameter studies conducted within finite element programs are often easier to implement than corresponding studies conducted experimentally. In this work, the compression-controlled failures of aluminum plates subjected to an applied mechanical load and an applied heat flux (to simulate fire) were predicted through the use of finite element analysis. Numerous studies were completed on these finite element models. Thicknesses of the plates were varied as well as the applied heat flux and the applied compressive stresses. The effect of surface emissivity along with the effect of insulation on the exposed surface of the plate was also studied. The influence of the initial imperfection of the plates was also studied. Not only were the physical conditions of the model varied but the element type of both the solid and shell models as well as the mesh density were also varied. Two different creep laws were used to curve fit raw creep data to understand the effects of creep in the buckling failure of the aluminum plates. These predictions were compared with experiments (from a previous study) conducted on aluminum plates of approximately 800mm in length, 200mm in width, 6-9mm in thickness and clamped at both ends to create fixed boundary conditions. A hydraulic system and a heater were used to apply the compressive load and the heat flux respectively. Comparisons between predicted and experimental results reveal that finite element analysis can accurately predict the compression-controlled failure of aluminum plates subjected to simulated fire. However, under certain combinations of the applied heat flux and compressive stress, the mesh density as well as the choice of element may have a significant impact on the results. Also, it is undetermined which creep curve-fitting model produces the most accurate results due to the influence of other parameters such as the initial imperfection. / Master of Science