Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
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Item Latching Microelectromechanical Shock Sensor Systems: Design, Modeling, and Experiments(2010) Currano, Luke Joseph; Balachandran, Balakumar; Yu, Miao; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Latching shock sensors are acceleration threshold sensors that trigger when the acceleration level exceeds the designed acceleration threshold. The latching mechanism provides a mechanical memory, which keeps the sensor in a triggered, or latched, state until the sensor is reset. The attractive feature of this type of sensor is that it does not require power during monitoring; power is only needed to query and reset the sensor. Several devices have been presented in the literature, but with limited experimental data and models that provide little to no insight into the dynamics of the latching event. The aim of this work is to further the understanding of the physics and design of micromechanical latching shock sensors by conducting a combination of careful experiments and development of original reduced-ordermodels. These efforts enable one to obtain a detailed picture of the latching dynamics for the first time. Latching shock sensors have been designed, fabricated, and experimentally evaluated in this work. The model predictions have been compared to the experimental results to verify the validity, including a quantitative comparison of the position of the shock sensor during a latching event captured via high-speed videography. This is the first time a latching event has been imaged in this class of sensors, and the first time, the model predictions of position versus time histories have been validated through experiments. The models have also been used to conduct detailed numerical studies of the shock sensor, amongst other things to predict a latch "bounce" phenomenon during an acceleration event. To understand more thoroughly how the various design parameters affect the latching threshold of the sensor, various parametric and optimization studies have also been conducted with the reduced-order models to guide designs of future latching acceleration threshold sensors.Item Global Optimization of Finite Mixture Models(2007-05-31) Heath, Jeffrey Wells; Fu, Michael; Jank, Wolfgang; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The Expectation-Maximization (EM) algorithm is a popular and convenient tool for the estimation of Gaussian mixture models and its natural extension, model-based clustering. However, while the algorithm is convenient to implement and numerically very stable, it only produces solutions that are locally optimal. Thus, EM may not achieve the globally optimal solution in Gaussian mixture analysis problems, which can have a large number of local optima. This dissertation introduces several new algorithms designed to produce globally optimal solutions for Gaussian mixture models. The building blocks for these algorithms are methods from the operations research literature, namely the Cross-Entropy (CE) method and Model Reference Adaptive Search (MRAS). The new algorithms we propose must efficiently simulate positive definite covariance matrices of the Gaussian mixture components. We propose several new solutions to this problem. One solution is to blend the updating procedure of CE and MRAS with the principles of Expectation-Maximization updating for the covariance matrices, leading to two new algorithms, CE-EM and MRAS-EM. We also propose two additional algorithms, CE-CD and MRAS-CD, which rely on the Cholesky decomposition to construct the random covariance matrices. Numerical experiments illustrate the effectiveness of the proposed algorithms in finding global optima where the classical EM fails to do so. We find that although a single run of the new algorithms may be slower than EM, they have the potential of producing significantly better global solutions to the model-based clustering problem. We also show that the global optimum matters in the sense that it significantly improves the clustering task. Furthermore, we provide a a theoretical proof of global convergence to the optimal solution of the likelihood function of Gaussian mixtures for one of the algorithms, namely MRAS-CD. This offers support that the algorithm is not merely an ad-hoc heuristic, but is systematically designed to produce global solutions to Gaussian mixture models. Finally, we investigate the fitness landscape of Gaussian mixture models and give evidence for why this is a difficult global optimization problem. We discuss different metrics that can be used to evaluate the difficulty of global optimization problems, and then apply them to the context of Gaussian mixture models.Item Damage Initiation and Evolution in Voided and Unvoided Lead Free Solder Joints Under Cyclic Thermo-Mechanical Loading(2007-02-05) Jannesari Ladani, Leila; Dasgupta, Abhijit; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The effect of process-induced voids on the durability of Sn-Pb and Pb-free solder interconnects in electronic products is not clearly understood and researchers have reported conflicting findings. Studies have shown that depending on the size and location, voids are not always detrimental to reliability, and in fact, may sometimes even increase the durability of joints. This debate is more intensified in Pb-free solders; since voids are more common in Pb-free joints. Results of experimental studies are presented in this study to empirically explore the influence of voids on the durability of Ball Grid Array (BGA) Pb-free solder joints. In order to quantify the detailed influence of size, location, and volume fraction of voids, extensive modeling is conducted, using a continuum damage model (Energy Partitioning model), rather than the existing approaches, such as fracture mechanics, reported in the literature. The E-P approach is modified in this study by use of a successive initiation method, since depending on their location and size; voids may influence either the time to initiate cyclic fatigue damage or time to propagate fatigue damage, or both. Modeling results show competing interactions between void size and location, that results in a non-monotonic relationship between void size and durability. It also suggests that voids in general are not detrimental to reliability except when a large portion of the damage propagation path is covered with either a large void or with many small voids. In addition, this dissertation also addresses several fundamental issues in solder fatigue damage modeling. One objective is to use experimental data to identify the correct fatigue constants to be used when explicitly modeling fatigue damage propagation in Pb-free solders. Explicit modeling of damage propagation improves modeling accuracy across solder joints of vastly different architectures, since the joint geometry may have a strong influence on the ratio of initiation-life to propagation-life. Most solder fatigue models in the literature do not provide this capability since they predict failure based only on the damage accumulation rates during the first few cycles in the undamaged joint. Another objective is to incorporate into cyclic damage propagation models, the effect of material softening caused by cyclic micro-structural damage accumulation in Pb-free solder materials. In other words the model constants of the solder viscoplastic constitutive model are continuously updated with the help of experimental data, to include this cyclic softening effect as damage accumulates during the damage-propagation phase. The ability to model this damage evolution process increases the accuracy of durability predictions, and is not available in most current solder fatigue models reported in the literature. This mechanism-based microstructural damage evolution model, called the Energy Partitioning Damage Evolution (EPDE) model is developed and implemented in Finite Element Analysis of solder joints with the successive initiation technique and the results are provided here. Experimental results are used as guidance to calibrate the Energy Partitioning fatigue model constants, for use in successive initiation modeling with and without damage evolution. FEA results show 15% difference between the life predicted by averaging technique and successive initiation. This difference could significantly increase in the case of long joints such as thermal pads or die-attach, hence validating the use of successive initiation in these cases. The difference between using successive initiation with and without damage evolution is about 10%. Considering the small amount of effort that has to be made to update the constitutive properties for progressive degradation, it is recommended that softening be included whenever damage propagation needs to be explicitly modeled. However the damage evolution exponents and the corresponding E-P model constants obtained in this study, using successive initiation with damage evolution, are partially dependent on the specimen geometry. Hence, these constants may have to be re-calibrated for other geometries.Item Extending the Levy Processes to Multiasset Products Pricing(2006-11-27) Xia, Qing; Madan, Dilip B.; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Levy processes have gained great success in pricing single asset options. In this thesis, we introduce a methodology enabling us to extend the single asset pricing technique based on Levy processes to multiasset cases. In our method, we assume the log-return of each asset as a linear sum of independent factors. These factors are driven by the Levy processes, and the specific Levy process we are studying in this thesis is the Variance Gamma (VG) process. We recover these factors by a signal processing technique called independent component analysis (ICA), from which we get the physical measure (P measure). To price the contingent claims, we still need the risk-neutral measure (Q measure). We bridge the gap between physical measure and risk-neutral measure by introducing the transformation of measure between the P measure and the Q measure. We next write each asset as the linear sum of factors under risk-neutral measure. Thus, we may calibrate the measure change parameters simultaneously through individual listed option data. With the measure change parameters (from P measure to Q measure) being recovered, we're able to price multiasset products by doing Monte Carlo simulation. In this thesis, we also explore the possibility of extending Levy processes to multiasset product pricing by applying the copula method. Generally speaking, the copula method enables us to introduce the dependence structure for arbitrary marginal distributions. The probabilistic interpretation of copulas is that we may apply the copula method to write the multivariate distributions for any marginal distributions. We consider examples from two different copula families - the elliptical copula family and Archimedean copula family. We studied Gaussian and Clayton one factor copulas as the examples from these two classes. We calibrated the correlation parameters for both methods and found them inconsistent across different strikes and maturities. And like the volatility smile and skew in the Black-Scholes model, we call it the skew and smile effect of correlation for one factor copula method.Item Characterization and Modeling of the Magnetomechanical Behavior of Iron-Gallium Alloys(2006-08-31) Atulasimha, Jayasimha; Flatau, Alison; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Magnetostrictive Iron-Gallium alloys (Galfenol) demonstrate moderate magnetostriction (~350 ppm) under very low magnetic fields (~100 Oe), have very low hysteresis, high tensile strength (~500 MPa), high Curie temperature (~675°C), are in general machinable, ductile and corrosion resistant. Therefore, they hold great promise in active vibration control, actuation, stress and torque sensing in helicopters, aircrafts and automobiles. To facilitate design of magnetostrictive actuators and sensors using this material, as well as to aid in making it commercially viable, it is necessary to perform a comprehensive characterization and modeling of its magnetomechanical behavior. This dissertation addresses some of these issues, focusing primarily on quasi-static characterization and modeling of the magnetomechanical behavior of single-crystal FeGa alloys with varying gallium content and along different crystallographic directions, and studying the effect of texture on the magnetomechanical behavior of polycrystals. Additionally, improved testing and modeling paradigms for magnetostrictive materials are developed to contribute to a better understanding and prediction of actuation and sensing behavior of FeGa alloys. In particular, the actuation behavior (λ-H and B-H curves) for 19, 24.7 and 29 at. % Ga <100> oriented single crystal FeGa samples are characterized and the strikingly different characteristics are simulated and explained using an energy based model. Actuation and sensing (B-σ and є-σ curves) behavior of <100> oriented 19 at. % Ga and <110> oriented 18 at. % Ga single crystal samples are characterized. It is demonstrated that the sensing behavior can be predicted by the model, using parameters obtained from the actuation behavior. The actuation and sensing behavior of 18.4 at. % Ga polycrystalline FeGa sample is predicted from the volume fraction of grains close to the [100], [110], [210], [310], [111], [211] and [311] orientations (obtained from cross-section texture analysis). The predictions are benchmarked against experimental actuator and sensor characteristics of the polycrystalline sample.Item Weakly Compressible Navier-Stokes Approximation of Gas Dynamics(2006-08-07) Jiang, Ning; Levermore, Charles David; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation addresses mathematical issues regarding weakly compressible approximations of gas dynamics that arise both in fluid dynamical and in kinetic settings. These approximations are derived in regimes in which (1) transport coefficients (viscosity and thermal conductivity) are small and (2) the gas is near an absolute equilibrium --- a spatially uniform, stationary state. When we consider regimes in which both the transport scales and $\mathrm{Re}$ vanish, we derive the {\em weakly compressible Stokes approximation} --- a {\em linear} system. When we consider regimes in which the transport scales vanish while $\mathrm{Re}$ maintains order unity, we derive the {\em weakly compressible Navier-Stokes approximation}---a {\em quadratic} system. Each of these weakly compressible approximations govern both the acoustic and the incompressible modes of the gas. In the fluid dynamical setting, our derivations begin with the fully compressible Navier-Stokes system. We show that the structure of the weakly compressible Navier-Stokes system ensures that it has global weak solutions, thereby extending the Leray theory for the incompressible Navier-Stokes system. Indeed, we show that this is the case in a general setting of hyperbolic-parabolic systems that possess an entropy under a structure condition (which is satisfied by the compressible Navier-Stokes system.) Moreover, we obtain a regularity result for the acoustic modes for the weakly compressible Navier-Stokes system. In the kinetic setting, our derivations begin with the Boltzmann equation. Our work extends earlier derivations of the incompressible Navier-Stokes system by the inclusion of the acoustic modes. We study the validity of these approximations in the setting of the DiPerna-Lions global solutions. Assuming that DiPerna-Lions solutions satisfy the local conservation law of energy, we use a relative entropy method to justify the weakly compressible Stokes approximation which unifies the Acoustic-Stokes limits result of Golse-Levermore, and to justify the weakly compressible Navier-Stokes approximation modulo further assumptions about passing to the limit in certain relative entropy dissipation terms. This last result extends the result of Golse-Levermore--Saint-Raymond for the incompressible Navier-Stokes system.Item The Performance of Multivariate Quality-Control Charts for Autocorrelated Bivariate Data(2006-06-02) Wu, Chen-Hsiang; Zantek, Paul; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)To monitor the mass production process, several quality control charts are constructed. Two of the most recognized schemes are the multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) schemes. Originally, we assume that the observations from the production process are independent. However, sometimes the observations are autocorrelated. In this article, a vector autoregressive model VAR (m) is applied. Here we want to study the impact of autocorrelations on both schemes. We also want to know about which scheme is more efficient when the observations are autocorrelated.Item AN EMBEDDED BOUNDARY FORMULATION FOR LARGE-EDDY SIMULATION OF TURBULENT FLOWS INTERACTING WITH MOVING BOUNDARIES(2005-11-01) Yang, Jianming; Balaras, Elias; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A non-boundary-conforming formulation for simulating transitional and turbulent flows with complex geometries and dynamically moving boundaries on fixed orthogonal grids is developed. The underlying finite-difference solver for the filtered incompressible Navier-Stokes equations in both Cartesian and cylindrical coordinates is based on a second-order fractional step method on staggered grid. To satisfy the boundary conditions on an arbitrary immersed interface, the velocity field at the grid points near the interface is reconstructed locally without smearing the sharp interface. The complications caused by the Eulerian grid points emerging from a moving solid body into the fluid phase are treated with a novel ``field-extension'' strategy. To treat the two-way interactions between the fluid and structure, a strong coupling scheme based on Hamming's fourth-order predictor-corrector method has been developed. The fluid and the structure are treated as elements of a single dynamical system, and all of the governing equations are integrated simultaneously, and iteratively in the time-domain. A variety of two and three-dimensional fluid-structure interaction problems of increasing complexity have been considered to demonstrate the accuracy and the range of applicability of the method. In particular, forced vibrations of a rigid circular cylinder including the harmonic in-line vibrations in a quiescent fluid and the transverse vibrations in a free-stream, and the vortex-induced vibrations of an elastic cylinder with one and two degrees of freedom in a free-stream are presented and compared with reference simulations and experiments. Three-dimensional DNS and LES of fluid flows involving stationary complex geometries include the flow past a sphere at $Re=50 \sim 1,000$, the transitional flow past an airfoil with a $10^\circ$ attack angle at $Re=10,000$. Then, the turbulent flow over a traveling wavy wall at $Re=10,170$ are simulated are compared with the detailed DNS using body-fitted grid in the literature. Finally, the simulation of the transitional flow past a prosthetic mechanical heart valve with moving leaflets at $Re=4,000$ has been performed. All results are in good agreement with the available reference data.Item A Ceramic Damage Model for Analyses of Multi-Layered Ceramic-Core Sandwich Panels Under Blast Wave Pressure Loading(2005-05-10) Lee, Keejoo; Lee, Sung W.; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A damage model for ceramic materials is developed and incorporated into the geometrically nonlinear solid shell element formulation for dynamic analyses of multi-layered ceramic armor panels under blast wave pressure loading. The damage model takes into account material behaviors observed from multi-axial dynamic tests on Aluminum Nitride (AlN) ceramic. The ceramic fails in a brittle or gradual fashion, depending upon the hydrostatic pressure and applied strain-rate. In the model, the gradual failure is represented by two states: the initial and final failure states. These states are described by two separate failure surfaces that are pressure-dependent and strain-rate-dependent. A scalar damage parameter is defined via using the two failure surfaces, based on the assumption that the local stress state determines material damage and its level. In addition, the damage model accounts for the effect of existing material damage on the new damage. The multi-layered armor panel of interest is comprised of an AlN-core sandwich with unidirectional composite skins and a woven composite back-plate. To accommodate the material damage effect of composite layers, a composite failure model in the open literature is adopted and modified into two separate failure models to address different failure mechanisms of the unidirectional and woven composites. In addition, the effect of strain-rates on the material strengths is incorporated into the composite failure models. For finite element modeling, multiple eighteen-node elements are used in the thickness direction to properly describe mechanics of the multi-layered panel. Dynamic analyses of a multi-layered armor panel are conducted under blast wave pressure loadings. The resulting dynamic responses of the panel demonstrate that dynamic analyses that do not take into account material damage and failure significantly under-predict the peak displacement. The under-prediction becomes more pronounced as the blast load level increases. Numerical analyses also indicate that the multi-layered armor design, while tailored for penetration resistance, performs poorly against blast shock wave. An alternative design is proposed and its performance is compared with the original design. Computational modeling of the fundamental material behaviors of ceramics would help expanding the use of ceramics to other structural applications, via enabling designers to efficiently explore design options.Item TRAVELING WAVE SOLUTIONS FOR A COMBUSTION MODEL(2005-05-04) Davis, Brian M; Trivisa, Konstantina; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)From the compressible Navier-Stokes equations for a reacting mixture, we reduce the system to obtain a one-dimensional 2-species polytropic gas combustion model. We examine the equilibria and determine their stability as well as identify the conditions that provide for the existence and uniqueness of a traveling wave/shock layer solution.