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

Doctor of Philosophy, The Ohio State University, 2018, Industrial and Systems Engineering

Light weighting is a cornerstone of the automotive industry's push to achieve greater fuel economy, thereby conserving fossil fuel resources and decreasing CO2 emissions. Composites are the focus of much of the research in the light weighting space. Carbon fiber laminates in particular, are one of the leading material choices because they have a high strength to weight ratio, and exceptional energy absorption characteristics, coupled with being almost completely impervious to the effects of environmental factors. These highly desirable properties are contrasted by characteristics that have limited the use of carbon fiber composites in many situations. In the cost driven automotive industry, high material cost is one of the main limiting factors for the introduction of new technology. Additional hidden costs arise from the highly anisotropic material behavior. This leads to joining difficulties requiring exceptional increases in the time spent on design and simulation of composite material systems. The combination of these costs limits their use in many situations. Progress is constantly being made to improve carbon fiber material and production costs as well as the design and simulation systems for composite materials in general. One area that still has opportunities for substantial improvement is in the joining methods for composite structures. This was the basis of the authors' previously researched hybrid joining method. The focus of this research is to understand the strengthening mechanisms of multi-axial loads on the epoxy adhesive system used in composite joints. This is integral to the strength improvement of the previously investigated hybrid structural composite joining method. This was accomplished by investigating two main areas, the bulk epoxies under test using basic tests, and a simplified version of the hybrid joint under different compression values and inclusion/epoxy/thickness combinations. Bulk epoxies were tested using ASTM D638 co (open full item for complete abstract)

Committee: Jose Castro (Advisor); Rebecca Dupaix (Committee Member); Soheil Soghrati (Committee Member) Subjects: Industrial Engineering; Materials Science; Mechanical Engineering

PhD, University of Cincinnati, 2014, Arts and Sciences: Mathematical Sciences

The development of efficient numerical methods to approximate solutions of partial differential equation problems that exhibit high frequency oscillations or boundary layers is a challenging task. One promising approach that has gained considerable popularity in the last decade enriches finite element approximations spaces with special functions that capture the difficult solution behavior. This extended finite element method or XFEM is usually coupled with continuous finite elements but several recent papers have enriched the spaces in discontinuous Galerkin framework. Computational results with this extended discontinuous Galerkin method or XdG have been successful and been applied to a wide range of application problems. However, very few theoretical error analyses have been done on either XFEM or, in particular, XdG. Such analyses are provided in this thesis for the XdG method and applied to problems with high frequency solutions and others with boundary layers. Proofs are given showing the XdG approximations are more accurate than those from more standard finite element schemes. These results are provided for elliptic and parabolic problems with solutions that exhibit high frequency oscillations and elliptic problems where boundary layers are present in the solutions. These error estimates are provided in terms of the degree of the polynomials used in the approximation and the largest high frequency or severity of the boundary layer. Computational results for this new method are presented and confirm the theoretical findings.

Committee: Donald French Ph.D. (Committee Chair); Sookkyung Lim Ph.D. (Committee Member); Benjamin Vaughan Ph.D. (Committee Member) Subjects: Mathematics

PhD, University of Cincinnati, 0, Engineering and Applied Science: Mechanical Engineering

Accurate prediction of structural responses under combined, extreme environments often involves a wide range of spatial and temporal scales. In the traditional analysis of structural response problems, time dependent problems are generally solved using a semi-discrete finite element method. These methods have difficulty simulating high frequency ranges, long time durations, and capturing sharp gradients and discontinuities. Some limitations include time step constraints or a lack of convergence. The space-time finite element method based on time-discontinuous formulation extends the discretization into the temporal domain and is able to address some of these concerns. The constraints on the time-step are relaxed and the method has had some success in accurately capturing sharp gradients and discontinuities. For applications featured by multiscale responses in both space and time, the regular space-time finite element method is unable to capture the full spectrum of the response. An enriched space-time finite element method is proposed based on a coupled space-time approximation. Enrichment is introduced into the space-time framework based on the extended finite element method (XFEM). The effects of continuous enrichment functions are explored for high frequency wave propagation. Previous works are based primarily on enrichment in time. Numerical solvers are developed and benchmarked for the space-time system on high-performance platform. The method's robustness is demonstrated by convergence studies using energy error norms. Improvements are observed in terms of the convergence properties of the enriched space-time finite element method over the traditional space-time finite element method for problems with fine scale features. As a result, enrichment may be considered an alternative to mesh refinement. The numerical instability associated with the high condition number of the enriched space-time analogous stiffness matrices is studied. The factors affecting the (open full item for complete abstract)

Committee: Dong Qian Ph.D. (Committee Chair); Thomas Eason Ph.D. (Committee Member); Randall Allemang Ph.D. (Committee Member); Yijun Liu Ph.D. (Committee Member) Subjects: Mechanical Engineering

PhD, University of Cincinnati, 2011, Engineering and Applied Science: Mechanical Engineering

Multiscale methods based on coupled atomistic-continuum representations have received significant attention in recent years due to their unique approach in balancing accuracy with efficiency for a wide spectrum of problems in solid mechanics. Examples include dislocation-originated plasticity, fracture, shear band localization and many others. Motivated by these advances, a concurrent simulation approach employing the space-time finite element method and molecular dynamics (MD) is developed in this dissertation with a focus on lattice dynamics and fracture. A space-time version of MD is initially proposed based on the time discontinuous Galerkin space-time finite element method. In the multiscale simulations, MD is coupled with coarse scale space-time finite element simulation based on a coarse grained material model. For the numerical approximation, standard space-time shape functions are augmented with enrichment function(s) based on the problem physics by exploiting the partition of unity concept. With the appropriate enrichment function(s), fine scale physics such as phonons and fractures can be represented in the coarse scale simulation in spatial and temporal scales. The two simulations can employ different time steps; the unconditional stability of the method makes selection of a large time step possible. Coupling between the simulations is achieved with the introduction of a projection operator and bridging scale treatment. The proposed approach is first employed to solve lattice dynamics with a focus on wave propagation. It is shown that a reflectionless interface at the atomistic-continuum simulation interface is achieved. The enriched continuum simulation retains all the atomistic level details and is able to transmit this information to another distinct atomistic region within the domain resulting in an energy conserving simulation method. The method is applied to systems with both linear and nonlinear potentials. An important feature of this approach (open full item for complete abstract)

Committee: Dong Qian PhD (Committee Chair); Thomas Eason PhD (Committee Member); Donald French PhD (Committee Member); Yijun Liu PhD (Committee Member); David Thompson PhD (Committee Member) Subjects: Mechanics