PhD, University of Cincinnati, 2002, Engineering : Engineering Mechanics

Simulations of structural impact utilizing explicit finite element codes have high requirements for computational efficiency. Woven fabric composites have high impact resistance and toughness but complex microstructure. A micro-mechanical model of woven fabric composites is developed here. The geometrical simplifications and the low discretization of the microstructure lead to computational efficiency. The model is based on the stiffness homogenization technique. The elastic property prediction of the model is in good agreement with the experimental data. A computationally efficient fiber reorientation technique is developed and applied to unidirectional composites. An investigation of the effect of the fiber reorientation on the elastic properties of the woven composite model is carried out. The reorientation technique, material non-linearity, and stiffness degradation are implemented in progressive failure model development. The model is used in structure survivability simulations. Loosely woven neat fabrics of high modulus fibers are used as protectors against impacting bodies because of their flexibility and high strength. The homogenization and fiber reorientation techniques are implemented in a loosely woven fabric model. The model is validated in ballistic impact simulations and demonstrates reasonable behavior in airbag inflation simulations. The viscoelasticity of polymeric materials increases their strength and Young's modulus during impact. The viscoelasticity is included in another model of loosely woven fabrics. The model is based on a mechanism representing the crimped yarns of the fabric. The viscoelastic model of loosely woven fabrics is validated in ballistic impact simulations. The viscoelasticity of the fibers, the viscoplasticity of the matrix material and the progressive damage with strain softening are essential for energy dissipation in structure crashworthiness simulations. They are implemented in another model of woven fabric composites base (open full item for complete abstract)

Committee: Dr. Ala Tabiei (Advisor) Subjects: Engineering, Mechanical

Doctor of Philosophy, The Ohio State University, 2006, Computer and Information Science

Subsurface light transport in highly scattering media is a problem of great interest to both computer graphics and biomedical optics researchers. Specifically, computer graphics researchers strive to develop more accurate simulations of light physics to in turn generate more realistic synthetic images. Likewise, biomedical optics researchers are concerned with accurately simulating light propagation to aid in design of equipment for diagnostic medical use. The mathematical formulation for diffusive light transport is presented along with a derivation for both a finite difference and finite element numerical solution for two and three dimensions. Efficient implementations are proposed which use Cholesky factorization to efficiently update the light scatter calculations if the source changes. Furthermore, the use data structures are proposed to accelerate (by an order of magnitude) parts of the source calculation and finite element matrix construction proposed by current biomedical optics literature. Furthermore, a novel technique for grid refinement for the finite element formulation using hanging nodes is presented. This technique allows for simple mesh refinement while maintaining the flux continuity on the finite element formulation. In conjunction with this technique, a per-element error estimator derived from a Green's function is presented along with a discussion on why traditional Galerkin style a posteriori estimation techniques fail. These techniques can then be combined to drive an adaptive finite element grid refinement method. Finally, to demonstrate the practicality of these techniques are demonstrated on simulations of numerical phantoms whose geometry and scattering properties were selected using segmented MRI data of human tissues. Furthermore, the results are visually comparable to images derived from a real world device which visualizes subsurface vasculature in human tissue by transilluminating tissue with near infrared light.

Committee: Raghu Machiraju (Advisor) Subjects: Computer Science

Doctor of Philosophy, The Ohio State University, 2023, Electrical and Computer Engineering

We present a discussion on the reduced-order modeling of electromagnetic simulation in general, and kinetic plasma simulations in particular, using the Proper Orthogonal Decomposition technique. Computational electromagnetics has been an important tool for physicists and engineers since the mid-1960s, when the increasing availability of modern high-speed computers started to allow the numerical solution of practical problems for which closed-form analytic solutions did not exist or were impractical to calculate. The study of kinetic plasmas is of great interest both for theoretical exploration and technological applications such as design of vacuum electronic devices, the study of the interaction of space-borne assets and cosmic radiation, fusion experiments, among others. Due to the theoretical complexity of these problems and the difficulty in performing physical experiments, simulations are instrumental for obtaining new insights or developing new device designs by resolving the field and plasma behaviors when changes are made. Several variants of simulations exist, but particle-in-cell algorithms for solving particle dynamics coupled with finite-differences or finite-elements field solvers are particularly successful. Despite their success, such algorithms are still constrained by computational cost such as processing time and memory/storage limitations. The Proper Orthogonal Decomposition is a technique that extracts the spatiotemporal behavior from a function of interest or a set of data points. This spatiotemporal behavior is characterized by a set of coupled spatial and temporal modes, which makes the Proper Orthogonal Decomposition especially suitable for analyses and applications in dynamic systems; it has been used for creation of reduced-order models in the past, especially in the fluid dynamics community where it originated from but also in many other areas. We have explored the application of the Proper Orthogonal Decomposition technique to co (open full item for complete abstract)

Committee: Fernando Teixeira (Advisor); Casey Wade (Committee Member); Kubilay Sertel (Committee Member); Robert Burkholder (Committee Member) Subjects: Electrical Engineering; Electromagnetics

Doctor of Philosophy, The Ohio State University, 2021, Aero/Astro Engineering

Computational fluid dynamics provides quantitative insights that complement physical experiments and enable cheaper and faster design/analysis processes. However, problems of interest tend to be highly complex, manifesting multiple physical processes over a broad range of spatial and temporal scales. The consequence of this is the desire for fluid simulations spanning many temporal and spatial scales. Here, relevant physical phenomena include steep gradients – due to shock waves, boundary layers, and laminar to turbulent boundary layer transition – and the broadband response of turbulence. Despite continual advancement in computing power, tractable analysis of problems involving such phenomena depends upon parallel advancements in the efficiency of numerical solution strategies. In these contexts, the overarching goal of this research is to assess the numerical solution of fluid dynamic problems using an enriched finite element framework. Through an enrichment process, this framework enables the expansion of the approximation space associated with more traditional finite element methods to non-polynomials. Non-polynomial approximation spaces better enable solution-tailored approximations that can significantly reduce computational costs. For example, previous works applying enriched finite elements in other disciplines have resulted in highly efficient numerical simulation of problems containing steep gradients, discontinuities, and singularities. Application of enriched finite elements for fluid dynamics problems is nontrivial due to numerical challenges: (1) restrictions on allowable velocity-pressure discretization for the solution of incompressible flows and (2) non-physical spurious oscillations in numerical solutions for advection dominated problems. Therefore, an enriched finite element method must address these challenges. For applying enriched finite elements to fluid dynamics, this research focuses on (1) addressing the aforementioned numerical chal (open full item for complete abstract)

Committee: Jack McNamara (Advisor); Patrick O'Hara (Committee Member); Armando Duarte (Committee Member); Datta Gaitonde (Committee Member); Jen-Ping Chen (Committee Member) Subjects: Aerospace Engineering; Engineering; Fluid Dynamics; Mechanical Engineering

Master of Sciences, Case Western Reserve University, 2021, Applied Mathematics

A common inverse problem arising in various applications is the estimation of a distributed parameter, such as a source term of a coefficient function of a partial differential equation from indirect observations of the solution. The problem can be recast in the framework of Bayesian inference, and the ill-posedness of the problem is mitigated by providing a priori information encoded in the prior density. Often the a priori information involves the gradient of unknown, and since the computational modeling is often based on finite element method (FEM), a natural question is how to represent the gradient in a basis compatible with the FEM discretization. In this work, we consider a hierarchical Bayesian model particularly suitable for solving inverse problems involving sparsity. Moreover, we show that a natural way to implement a prior that favors solutions with restricted support of the gradient is to express the gradient field in terms of Whitney elements. The efficacy of the representation combined with hierarchical Bayesian models is demonstrated with computed examples.

Committee: Erkki Somersalo (Committee Chair); Daniela Calvetti (Committee Co-Chair); Weihong Guo (Committee Member) Subjects: Applied Mathematics

PhD, University of Cincinnati, 2018, Engineering and Applied Science: Aerospace Engineering

Numerical methods for computational physics have been applied for many years in the fields of turbomachinery and acoustics. The computational approach to addressing problems in these fields has strongly influenced improvements in performance and advancements in understanding for the systems and physical processes that govern such applications. Particularly within the turbomachinery community, the spectrum of numerical methods being applied is dominated by second-order accurate finite-volume and finite-difference discretizations of the governing equations. These have been quite successful and their robustness has been important in their adoption within industrial engineering as tools for design and analysis. At the same time, such approaches are very dissipative and require dense computational grids to resolve sharp features and capture wave propagation. As problems become more complex and inter-related, the numerical methodologies for analysis tools that are used to address such problems and inform solutions must improve in their fidelity, accuracy, and mathematical rigor. At the same time, high-order finite-element methods have experienced significant attention in the computational fluid dynamics community for their mathematical formalism, localized approach for obtaining high-order accuracy, and amenability to adaptation of the numerical grid and accuracy of the numerical approximation. The challenges of such approaches are to achieve efficiency and stability for the numerical method. The result of many research efforts in this area has pushed the applicability of high-order finite-element methods into many fields and they are approaching the point where they might soon find routine application to industrial problems for engineering design and analysis. This dissertation details the development and application of an implicit discontinuous Galerkin method to applications in turbomachinery and acoustics. This is carried out for the purpose of advancing the ap (open full item for complete abstract)

Committee: Paul Orkwis Ph.D. (Committee Chair); Shaaban Abdallah Ph.D. (Committee Member); John Benek Ph.D. (Committee Member); Mark Turner Sc.D. (Committee Member); Eric Wolf Ph.D. (Committee Member) Subjects: Aerospace Materials

Doctor of Philosophy (PhD), Ohio University, 2018, Civil Engineering (Engineering and Technology)

Inverts of many corrugated metal culverts in North America eventually deteriorate due to a combination of abrasive soil particles transported by the flow and exposure to moist (low resistivity) soils. In some areas, drainage water is acidic which exasperates the degradation process further. A traditional and economic method for sustaining lifespan of such deteriorated culverts has been to pave the invert using concrete reinforced with wire mesh (as specified by ODOT CMS 611.11). Structural benefits of this practice were examined in this dissertation by conducting field live load tests and three-dimensional computer simulations. Responses of in-service steel culverts to applied static axle loads were studied and compared among the intact state, the severely deteriorated state, and the rehabilitated state. It was confirmed that invert paving can restore the structural integrity of deteriorated metal culverts back to their intact status. Additionally, ultimate load bearing capacity of corrugated steel pipes was examined by performing a series of extreme load tests. It was observed that excessive reinforcement, more than that specified by ODOT CMS 611.11, is needed to restore metal culverts under extreme load applications. Finally, a closed form solution was presented to aid in the design of the invert pavement for deteriorated metal culverts.

Committee: Teruhisa Masada Dr. (Advisor) Subjects: Civil Engineering

BS, Kent State University, 2018, College of Arts and Sciences / Department of Mathematical Sciences

Our goal will be to find a weak solution to the Beltrami flow. A Beltrami flow in three-dimensional space is an incompressible (divergence free) vector field that is everywhere parallel to its curl. That is, curl(B) = λ B for some function. These flows arise naturally in many physical problems. In astrophysics and in plasma fusion Beltrami fields are known as force-free fields. They describe the equilibrium of perfectly conducting pressure-less plasma in the presence of a strong magnetic field. In fluid mechanics, Beltrami flows arise as steady states of the 3D Euler equations. Numerical evidence suggests that in certain regimes turbulent flows organize into a coherent hierarchy of weakly interacting superimposed approximate Beltrami flows. Given the importance of Beltrami fields, there are several approaches to proving existence of solutions, for instance use the calculus of variations, and use fixed point arguments. In this thesis we instead use a Hilbert space approach through the Lax-Milgram lemma.

Committee: Benjamin Jaye (Advisor); Andrew Tonge (Committee Member); Dexheimer Veronica (Committee Member); Jeremy Williams (Committee Member) Subjects: Applied Mathematics; Astrophysics

Master of Science in Mechanical Engineering (MSME), Wright State University, 2016, Mechanical Engineering

The continually growing market for metal components fabricated using additive manufacturing (AM) processes has called for a greater understanding of the effects of process variables on the melt pool geometry and microstructure in manufactured components for various alloy systems. Process Mapping is a general approach that traces the influence of process parameters to thermal behavior and feature development during AM processing. Previous work has focused mainly on Ti-6Al-4V (Ti64), but this work uses novel mathematical derivations and adapted process mapping methodologies to construct new geometric, thermal, and microstructural process maps for Ti64 and two nickel superalloy material systems. This work culminates in the production of process maps for both Inconel 718 (IN718) and Inconel 625 (IN625) that were developed via both experimental and analytical data, and the tools used in the established process mapping approach have been thoroughly explored. This has resulted in a non-dimensional template for solidification behavior in terms of material solidification parameters and AM process parameters. The optimized non-dimensional approach presented here will increase the efficiency of future process map development and will facilitate the comparison of process maps across alloy systems and AM processes, laying the ground work for integrated AM feature control and evaluation of current and future materials for AM application.

Committee: Nathan Klingbeil Ph.D. (Advisor); Joy Gockel Ph.D. (Committee Member); Raghavan Srinivasan Ph.D. (Committee Member) Subjects: Engineering; Materials Science; Mechanical Engineering

Master of Sciences, Case Western Reserve University, 2016, EMC - Mechanical Engineering

The present work is aimed at developing a dynamic adaptive mesh refinement (DAMR) method for the study of failure mechanisms in brittle materials within the eigenfracture framework. A mesh refinement method based on boundary representation technique (B-rep) and Delaunay triangulation is developed. In addition, a flip algorithm is employed to guarantee the quality of the refined mesh. The mesh refinement algorithm is verified in an example of static adaptive mesh generation of polycrystalline structures that are created by using Voronoi tessellation. Furthermore, the DAMR method is built upon the combination of the adaptive mesh refinement algorithm and the eigenfracture approach. In the DAMR, the energy release rate G is used as the adaption. Finally, the DAMR method is validated by comparing to mode-I and mixed mode fracture experiments on concrete materials. The simulation results show excellent agreement with experimental measurements and more accurate predictions than the original eigenfracture approach.

Committee: Bo Li (Committee Chair); Vikas Prakash (Committee Member); John Lewandowski (Committee Member) Subjects: Mechanical Engineering

Master of Science, The Ohio State University, 2015, Civil Engineering

This thesis presents the development and application of a multidimensional (2-D & 1-D) kinematic wave model in a discontinuous Galerkin framework for simulating overland flow and runoff due to torrential rainfall. The objective of this work is to improve on (1) the modeling approach involving many small-scale rivers and channels and (2) the accuracy of flooding caused by storm surge coupled with torrential rainfall. The overland flow is modeled using the 2-D kinematic wave equations derived from the 2-D depth averaged shallow water equations. In areas of the domain where flow converges into channels, the edges of 2-D elements are used as 1-D channels for flow routing. To best represent complex topography, domains are discretized using an application co-developed by the author called Admesh+, an automatic unstructured mesh generator for shallow water models. Admesh+ produces high-quality meshes with the appropriate amount of refinement where it is needed to resolve all of the geometry and flow characteristics of the domain. The mesh generation technique utilizes high-resolution digital elevation maps (DEMs) to automatically produce unstructured meshes with elements arranged to best represent shorelines, channel networks and watershed delineations. The development of the multidimensional overland flow model and mesh generation techniques are presented along with comparisons of model results with various analytic solutions and experimental data.

Committee: Ethan Kubatko (Advisor) Subjects: Civil Engineering

Master of Science, The Ohio State University, 2015, Mechanical Engineering

In the last few decades, the finite element method (FEM) has become one of the most important computational tools for the simulation of engineering problems. Due to the increasing popularity of this method, a heavy body of research has focused its attention to the development of advanced FEM-based techniques for the treatment of complex phenomena, including intricate morphologies. This thesis introduces a hierarchical interface-enriched finite element method (HIFEM) for the mesh-independent treatment of the mentioned type of problems. The HIFEM provides a general, and yet easy-to-implement algorithm for evaluating appropriate enrichment in elements cut by multiple interfaces. In the automated framework provided by this method, the construction of enrichment functions is independent of the number and sequence of the geometries introduced to nonconforming finite element meshes. Consequently, the HIFEM algorithm eliminates the need to modify/remove existing enrichment every time a new geometry is added to the domain. The proposed hierarchical enrichment technique can accurately capture gradient discontinuities along material interfaces that are in close proximity, in contact, or intersecting with one another using nonconforming finite element meshes for discretizing the problem. The main contribution of this thesis is the development and implementation of the two-dimensional higher-order HIFEM, and in particular the development of a new hierarchical enrichment scheme for six-note triangular elements. Furthermore, this manuscript presents a new enrichment scheme to simulate strong discontinuities (cracks) in linear elastic fracture mechanics problems. Special attention is given to the available strategies to improve the level of precision and efficiency of the simulations. A detailed convergence study for the enrichment technique that yields the highest precision and the lowest computational cost is also presented. Finally, the author illustrates the application of the (open full item for complete abstract)

Committee: Soheil Soghrati Prof. (Advisor); Rebecca Dupaix Prof. (Committee Member); Marcelo Dapino Prof. (Committee Member) Subjects: Materials Science; Mathematics; Mechanical Engineering

Doctor of Philosophy, Case Western Reserve University, 2014, Applied Mathematics

Piezoelectricity is a property of certain materials that allows the conversion of mechanic deformation into electric voltage potential, and vice versa. The wide use of piezoelectric materials, e.g., in transducer technology and energy harvesting makes the design problem of optimizing the material parameters and geometry an important target in scientific computing. In energy harvesting in particular, the design of devices with impedance resonances in a predetermined range is of special interest: Matching the resonances with the ambient vibration frequencies may lead potentially to higher efficiency of the device. Material scientist can rely on numerical simulations in the design and production of piezoelectric devices. Numerical simulations employ numerical techniques like finite element methods to generate information about the design starting from an input of material parameters. In the context of this thesis, these material parameters include the elastic, electromagnetic and piezoelectric constants. Because the quantitative values of the material parameters are often determined from simplified experiments based on some assumptions, the reliability of the results of the simulations depends on the validity of these assumptions. Optimization based approaches to the numerical acquisition of the material parameters normally give a single set of values which, in turn, identifies one specific material as the approximation of the target. From a practical point of view this may be too restrictive, because it leaves little flexibility when trying to develop materials with a certain desired response. In this thesis we approach the inverse problem of material characterization for piezoelectric materials from a Bayesian perspective. The main question addressed in this thesis is, how to choose the elastic, electromagnetic, and piezoelectric material parameters so that a target resonance frequency is achieved, and the band-pass impedance response outside the resonance (open full item for complete abstract)

Committee: Erkki Somersalo Dr (Advisor); Daniela Calvetti Dr (Advisor) Subjects: Applied Mathematics; Materials Science; Mathematics

Master of Science in Engineering (MSEgr), Wright State University, 2003, Mechanical Engineering

Daily, Jeremy S., M.S. Egr., Department of Mechanical and Materials Engineering, Wright State University, 2003. Plastic Dissipation Energy in Mixed-Mode Fatigue Crack Growth on Ductile Bimaterial Interfaces. A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This and previous energy-based approaches in the literature suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under Mode I loading. The goal of the current study is to extend the dissipated energy approach to steady-state crack growth under mixed-mode loading conditions, with application to cyclic delamination of ductile interfaces in layered materials. The total plastic dissipation per cycle is obtained by 2-D elastic-plastic finite element analysis of a stationary crack in a general mixed-mode specimen geometry under constant amplitude loading. Both elastic-perfectly plastic and bi-linear kinematic hardening constitutive behaviors are considered, and numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant mechanical properties and mixed-mode loading conditions. In addition, numerical results are presented for the case of fatigue crack growth along a bonded interface between materials with identical elastic, yet dissimilar plastic properties, including mismatches in both kinematic hardening modulus and yield strength. Finally, the approach is generalized to include mismatches in both elastic and plastic properties, and results for the dimensionless plastic dissipation per cycle are reported over the complete design space of bimaterial interfaces. The results of this thesis are of interest in soldering, welding, coating, electronic packaging, and a variety of layered manufacturing applications, where mismatches in both elastic and plastic properties can exist between the deposited material (open full item for complete abstract)

Committee: Nathan Klingbeil (Advisor) Subjects: Engineering, Mechanical

MS, University of Cincinnati, 2011, Engineering and Applied Science: Civil Engineering

A finite element model of a fiber reinforced polymer (FRP) bridge in Hamilton County, Ohio was conducted using the computer program SAP2000. The purpose of the model was to determine the vertical deflection under a specified truck loading and to compare the analytical results from the model with load test results of the actual bridge, which spanned approximately 20 feet. The bridge superstructure was composed of eight separate panels that were assembled on site. The panels were constructed of a sandwich panel deck with integral beams spaced approximately two feet on center with the panels themselves being approximately seven and a half feet wide. The finite element model utilized shell elements to represent the different FRP components of the bridge such as the top and bottom faces of the deck along with the beam webs and flanges. The material properties input into the model for the shell elements were provided by the manufacturer. A mesh sensitivity analysis was conducted to identify an adequate discretization of the bridge without creating an excessive amount of elements in the model. Once this was accomplished, the entire bridge was then modeled with the applied loading to mimic the truck loading tests to which the actual bridge was subjected in order to assess the validity of the finite element model. The results of the model showed good agreement with the experimental results, validating the model.

Committee: Richard Miller PhD (Committee Chair); Gian Rassati PhD (Committee Member); Bahram Shahrooz PhD (Committee Member) Subjects: Civil Engineering

MS, University of Cincinnati, 2006, Engineering : Mechanical Engineering

Even with the ever-increasing and affordable computational power, detailed atomistic analysis of large domains using molecular dynamics remains prohibitively expensive. This motivates the use of continuum type of simulation methods such as the finite element method in order to reduce the computational expense. However, the accuracy in FEM simulation is often unsatisfactory. As a result, efforts are being made to combine the advantages of the simulation methods at different scales into a multiscale framework. The main goal for this thesis is to develop a coupled atomistic-continuum formulation for a nanoscale system. The main challenge is in attaining a reflectionless boundary at the interface of the molecular dynamics and finite element simulation. The finite element mesh is generally much coarser than the atomic spacing. Thus it can't represent the fine scale portion of the displacement, resulting in incorrect information being supplied to the atomistic simulation which subsequently leads to reflection of phonons at the interface. Most of the research effort so far has been towards attaining a reflectionless boundary at the interface of the two simulations by using variety of methods. In all these approaches, the focus has been to achieve accurate description of the system in the region where we have molecular dynamics. The regions where the finite elements are used don't give very accurate results. In this thesis a space-time description for a 1D atomistic system is developed. We have considered a system having harmonic interatomic potential with nearest neighbor interaction only. The objectives for the space-time formulation development are two folds: first, we aim at overcoming the time scale limit by constructing approximation in the time domain. Secondly with the introduction of fine scale variables, we provide a multiscale description of the field variable. This is the key in achieving a truly reflectionless boundary condition. More specifically we have devel (open full item for complete abstract)

Committee: Dr. Dong Qian (Advisor) Subjects: Engineering, Mechanical

Doctor of Philosophy, The Ohio State University, 2009, Mechanical Engineering

Magnetostrictive materials have the ability to transfer energy between the magnetic and mechanical domains. They deform in response to magnetic fields and magnetize in response to stresses. Further, their stiffness and permeability depend on both magnetic field and stress. Galfenol, an alloy of iron and gallium, is an emerging magnetostrictive material which is unique for its combination of high magnetomechanical coupling and steel-like structural properties. Unique among smart materials, Galfenol can serve both as a structural element and as an actuator or sensor. This work presents nonlinear characterization and modeling of magnetization and strain of Galfenol, and a 3-D system-level model for Galfenol-based transducers. Magnetomechanical measurements are presented which reveal that Galfenol constitutive behavior is kinematically reversible and thermodynamically irreversible. Magnetic hysteresis resulting from thermodynamic irreversibilities is shown to arise from a common mechanism for both magnetic field and stress application. Linear regions in constant-stress magnetization curves are identified as promising for force sensing applications. It is shown that the slope of these linear regions, or the magnetic susceptibility, is highly sensitive to stress. This observation can be used for force sensing; the 19-22 at. % Ga range is identified as a favorable Galfenol composition for sensing, due to its low anisotropy with moderate magnetostriction and saturation magnetization. A thermodynamic framework is constructed to describe the magnetization and strain. An elementary hysteron, derived from the first and second laws, describes the underlying nonlinearities and hysteresis. Minimization of the energy of a single magnetic domain gives expressions for the hysteron states and accurately describes features of the constitutive behavior, including the stress dependence in the magnetization regions and the stress dependence of the location of the burst magnetization regio (open full item for complete abstract)

Committee: Marcelo Dapino PhD (Advisor); Joseph Heremans PhD (Committee Member); Ahmet Kahraman PhD (Committee Member); Menq Chia-Hsiang PhD (Committee Member) Subjects: Engineering; Materials Science; Mechanical Engineering

Master of Science (MS), Ohio University, 2010, Civil Engineering (Engineering and Technology)

This work studies the response of jointed plain concrete pavement to traffic loading as well as temperature variations, using the three-dimensional FE program EverFE2.24. The traffic loading is modeled using ODOT single axle dump truck rolling on top of the pavement, while the environmental loading is modeled using temperature measurements by thermocouples inserted throughout the depth of the slab. Picking a reference point in the temperature data, the change in stresses with respect to time has been computed and compared with the field data. Performing a fatigue analysis, the temperature is found to be considerably more detrimental to the concrete pavement compared to axle loads. Measurement of the surface temperature, especially in the top, is evaluated to be critical in convergence of EverFE2.24 model. The 3D FE program EverFE2.24 results followed the trend of the measured data from the field.

Committee: Shad Sargand PhD (Committee Chair); Teruhisa Masada PhD (Committee Member); Eric Steinberg PhD (Committee Member); Martin Mohlenkamp PhD (Committee Member) Subjects: Civil Engineering

Doctor of Philosophy, University of Akron, 2009, Electrical Engineering

Over the last decades, there has been an ever increasing interest in nano-focusing oflight and subwavelength resolution overcoming the classical diffraction limit. Examples of that are scanning near-field optical microscopy (SNOM) and “perfect lenses” with negative-index materials. Development of scanning techniques, better performing probes for SNOM and engineering of effective material parameters depends on numerical modeling more than ever before. More accurate models and precise simulations are required to obtain quantitative rather than just qualitative results. This dissertation discusses numerical challenges of nano-scale structure simulations with enhanced and strongly localized electric field distributions. In particular, the thesis focuses on the simulation of scattering-type apertureless SNOM in the mid-infrared and field distributions in plasmon-enhanced Raman spectroscopy in the visible range. Although the ideas of field enhancement are similar (sharp, optionally plasmon-coated, object causing a strong localized enhancement in the vicinity of an AFM tip), applicable models and the nature of computational and engineering challenges are different. For the plasmon-enhanced SNOM, the quasi-static and the full-wave FEM analyses are compared and a qualitative agreement is shown. The optical response of the AFM tip is shown to correlate with the amplitude of the local field distribution. This allows one to use dark field microscopy for tip testing. Several tip designs proposed in the literature were analyzed using the quasi-static approximation; parametric analysis and optimization were performed for selected tips. Numerical challenges due to the multi-scale nature of the problem and multiple scattering in scattering-type SNOM are exemplified in 3D simulations of a realistic cantilevered AFM tip in the mid-infrared. The finite element method (FEM) with adaptive meshing is shown to be a useful tool, but the computation resources of a st (open full item for complete abstract)

Committee: Igor Tsukerman PhD (Advisor) Subjects: Electrical Engineering; Electromagnetism; Optics

Master of Science, University of Akron, 2008, Electrical Engineering

The Finite Element Method (FEM) is an extremely powerful and versatile computa-tional technique. The standard (nodal) FEM, however, cannot be used universally in computational electromagnetics. In particular, the method fails to solve for the full vector Maxwell equations. The introduction of the vector FEM overcame most of the problems associated with nodal FEM. The present thesis extends some of the work done by Z. Ren and N. Ida on tetrahedral finite elements to hexahedral elements. The goal of the present thesis is twofold. First, to provide detailed mathematical and theorethical background, required to better understand the construction of the p-th order 1-form basis functions from a geometrical point of view. Second, to con- struct higher order basis functions for hexahedral elements, conforming in the space H(curl, Ω). To take full advantage of the insights the vector elements provide, one has to master the theory of differential forms, which is much more general tool than that of the vector analysis. The basis functions that are constructed in the present work are designed to model correctly the range space and null space of the exterior differential operator. They are hierarchical, so they can be used in p-refinement al- gorithms. In addition, by virtue of their construction the basis functions match the continuity conditions of the physical quantity modeled.

Committee: Nathan Ida PhD (Advisor) Subjects: Electrical Engineering; Electromagnetism; Engineering