A method is developed to fuse Computational Fluid Dynamics (CFD) simulations and experimental data through the use of Tikhonov regularization. Inviscid-Viscous Interaction and Thin-Layer Navier-Stokes Equation models are used to provide CFD solutions for the flow past NACA 0012 and RAE 2822 airfoils, respectively. The velocity profile within the boundary layer and the pressure coefficient on the surface of the airfoil are merged with the corresponding experimental data. A finite element approach is applied to accomplish the numerical solution of the Tikhonov regularization method. By using over- or under-relaxation technique, relatively few iterations are needed to achieve the convergence of the fusion method. The results demonstrate that a-priori CFD solutions of low fidelity can be improved by the experimental data with less computational cost compared with more sophisticated CFD models. Alternatively, the sparse and scattered experimental data are efficiently processed by utilizing CFD models as regularization. The limitations of the Tikhonov regularization method have been examined. The result shows that the fusion method has significant advantages over a nonlinear least-square polynomial approach for interpolating and extrapolating experimental data.

The goal of structural optimization is to find the best possible configuration for a given structure, which meets the objective function and set of constraints. In this work we presented a method based on the evolutionary structural optimization method (ESO) in which we improved the quality of the solution by avoiding the chain-like sets of elements which are sources of potential kinematic instabilities, and by refining the revised mesh so as to obtain accurate solutions as the volume removal proceeds. Solution error estimates are also developed to provide insight to the validity of the revised models. Then we applied our algorithms to several examples from the literature as well as to new axisymmetric problems.

Using object-oriented programming (OOP) techniques and philosophies, a collection of C++ tools for the rapid development of finite element applications has been created. The Object-Oriented Finite Element Analysis (OOFEA) toolkit provides both the geometrical and mathematical management tools necessary for this task in the form of useful class hierarchies, in particular, the OOFEA toolkit features methods for evaluating arbitrary weak forms provided by the user in order to solve particular problems of interest. A detailed description of the underlying concepts, philosophies and techniques used to develop the toolkit, as well as description of its contents and usage are included. A strong effort has been made to concentrate on its possibly beneficial usage in the computational fluid dynamics area. Hence, a number of sample CFD and heat transfer applications of increasing difficulty and interests are thoroughly discussed. Moreover, to demonstrate the toolkit capabilities of managing complex projects, a simulator for laminar and turbulent natural convective flows in enclosures has been developed and a numerical study of some of these flows has been conducted. Using a primitive variable approach, the Galerkin FEM is used to obtain the weak form of the coupled unsteady Navier-Stokes and energy equations for incompressible, viscous, Newtonian fluids in two and three dimensions. By including a k-$\epsilon$ turbulence model in the governing equations, the analysis of both laminar and turbulent convective flows in enclosures is possible. With the help of a semi-implicit time stepping scheme, combined with a projection scheme, the resulting systems of equations are solved iteratively using the preconditioned conjugate gradient (PCG) algorithm. Time accurate two-dimensional simulations have been performed for a differentially heated square cavity in the laminar and turbulent regimes, for air with a Prandtl number of 0.71, and values of the Rayleigh number ranging between 10$\sp3$ and 10$\sp{10}$. Consistency tests show that the simulator correctly implements the k-$\epsilon$ turbulence model, and the numerical results compare well with results reported in the literature. Furthermore, three-dimensional simulations have been performed for a differentially heated cubic cavity in the laminar regime for air with a Prandtl number of 0.71, and values of the Rayleigh number ranging from 10$\sp3$ to 10$\sp6$. The results obtained compare well with other results in the literature, and characterize some of the three-dimensional effects that are ignored in two-dimensional simulations. In particular, it can be observed that the three-dimensional effects can change the predicted dimensionless heat transfer rate by as much as 10%.

This dissertation primarily presents new procedures to analyze the lateral vibrations of rotary oil-well drilling assemblies. The methodology uses random vibrations theory to gain insight into the complicated downhole dynamics; it is also applicable to longitudinal, torsional and coupled vibrations. Furthermore, this dissertation discusses a novel technique to model drilling vibratory excitation mechanisms using digital filters, presents an error estimator for the mode superposition method, introduces drilling fundamentals and includes an extensive literature review on drilling vibrations and related topics. A finite-element system represents the drilling assembly; modal analysis yields its natural frequencies and mode shapes. Additional structural dynamics techniques enable the reduction of the system size and the approximation of the transfer function using the mode superposition method. Furthermore, Hertz's contact law allows considering the well-bore presence whenever the lateral displacement of any node along the drill-string exceeds its pre-assigned clearance. Accounting for contact between the drilling assembly and the formation introduces nonlinearity in the system. Next, the drill-string response to a harmonic excitation omitting and accounting for the effects of the well-bore presence is obtained. Further, auto-regressive moving-average (ARMA) filters permit modeling measurement-while-drilling data and synthesizing time histories compatible with the generated approximate power spectra. The influence of the bit type on excitation mechanisms leads to separate treatments of bottom-hole assemblies with drag bits and those with roller-cone bits. The ARMA-filter-generated time histories are artificial downhole excitations. Used in conjunction with Monte-Carlo simulations, they yield the response of the system to random excitations. The stochastic linearization method is adopted for generating a linear system equivalent, in a statistical sense, to the original nonlinear problem. The solution of the stochastic vibrations problem of the equivalent system is obtained with two solution procedures: the covariance matrix approach in the time-domain, and the spectral matrix technique in the frequency-domain. Numerical studies are used to assess the relative efficiency of the three solution methods. It is hoped that the developed approach will stimulate further interest in the suitability of stochastic dynamics methods for the inherently uncertain environment of oil-well drilling.

We present three innovative approaches for simulations of parachute fluid-structure interactions (FSI), which otherwise tend to be unstable because of extreme sensitivity of thin membrane structure to massive fluid dynamic forces. In the first approach, we use an iterative scheme in conjunction with augmented structural mass matrix to achieve convergence in coupling the fluid and the structure motion. In the second approach, we use a coupled formulation that includes the inter-dependence of fluid and structure motion. The dependence of flow on domain deformation is addressed iteratively in this approach. Finally in the third approach, we use a directly coupled formulation that fully incorporates the inter-dependence of fluid, structure and mesh motion. All the three approaches accurately predict parachute FSI and successful FSI simulations of soft landing of T-10, G-12 and G-11 parachutes are presented to provide corroborating evidence. To further improve the quality of FSI simulations, carried out using any of the three coupling approaches, we present more enhanced-discretization and solution techniques. We present definitions of the stabilization parameters used in SUPG and PSPG formulations based on local length scales that are shown to be accurate and less dissipative. We also present an Enhanced-Discretization Space-Time Technique (EDSTT) that has tremendous potential in saving significant amount of computational time as it allows us to use different time-step sizes in different regions of a computational domain. Complementary to EDSTT, we propose an Enhanced-Discretization Successive Update Method (EDSUM) which resolves small scale information in flow simulations. We have also described a variation of EDSUM that gives dramatic rates of convergence in solving linear equation systems. Another effort toward accurately solving linear equation systems is the Enhanced-Approximation Linear Solution Technique (EALST) that we propose for improving the convergence in selected regions of the flow. All these techniques are successfully tested on a variety of problems and the results obtained are unequivocally satisfactory.

A residual flexibility approach for the analysis of systems comprised of multiple components subjected to dynamic loading is presented. In it, the reactive forces at the junctions of the components are computed directly without the synthesis of component modes or the determination of system modes. This is accomplished by expressing the displacements at the junction coordinates of the components in terms of the retained component free-junction normal modes and a first-order account of the residual flexibility of the unretained modes. Once the components are represented in this manner, the requirement of displacement compatibility and force equilibrium at the junction coordinates is enforced. This leads to a set of junction-sized, simultaneous algebraic equations, similar in form to that of the flexibility formulation in statics, in terms of the unknown junction forces. The computed forces at a given time-step then serve to base-drive each component's equations of motion separately, hence the term decoupled analysis. Due to the formulation of the method, the nonlinear, nonclassically damped problem becomes a natural progression. The new method compares well to the traditional method of Component-Mode Synthesis for solutions to a nonclassically damped fixed-fixed beam comprised of two classically damped cantilevered beam components.

A method of evaluating super-convergent second derivative recovery methods in proposed. The second derivative and exact flux error of three super-convergent patch (SCP) options are compared to determine the more effective method. The three super-convergent patch options employed are: the element based patch (all neighbors), the element based patch (facing neighbors), and the nodal based patch (all element neighbors). To witness the behavior of the different SCP options, different boundary conditions and element types are evaluated. The value of each SCP option is further investigated by comparing the uniform mesh refinement with the more cost effective h-refinement method.

Hysteresis is a phenomenon which is widely observed in a variety of physical systems. It introduces a nonlinear and multivalued behavior in systems, making their modeling and control problematic. This thesis underlines the significance of dynamic hysteresis modeling from the perspectives of analysis and control. Toward that end, a widely accepted definition of hysteresis is adopted and some important properties of hysteresis are presented. Five general hysteresis models are discussed, along with some damping and friction models. Their properties are compared and contrasted. The Duhem model is shown to be a versatile dynamic hysteresis model, and it is adapted to two distinct physical systems. First, the evolution of dynamic hysteresis modeling of harmonic drive is studied, and a new dynamic model, based on Duhem model, is developed. It is more accurate than previous models and is used to prove, via the method of describing functions, that PID regulation control of harmonic drive can cause a limit cycle due to hysteresis. Second, a dynamic hysteresis model, based on Duhem model, is proposed for a shape memory alloy actuator, which yields a complete dynamic model of the actuator, linking its temperature, strain and electrical resistance together. Therefore, this thesis provides a foundation for dynamic hysteresis modeling in engineering systems and brings out the salient features of dynamic hysteresis modeling from the perspectives of analysis and control.

Flow-generated noise, especially rotorcraft noise has been a serious concern for both commercial and military applications. A particular important noise source for rotorcraft is Blade-Vortex-Interaction (BVI) noise, a high amplitude, impulsive sound that often dominates other rotorcraft noise sources. In this thesis the research is to formulate and implement efficient computational tools for the development and study of optimal control and design strategies for complex flow/acoustic systems with emphasis on rotorcraft applications, especially BVI noise control problem. The main purpose of aeroacoustic computations is to determine the sound intensity and directivity far away from the noise source. However, the computational cost of using a high-fidelity flow-physics model across the full domain is usually prohibitive and it might also be less accurate because of the numerical diffusion and other problems. Taking advantage of the multi-physics and multi-scale structure of this aeroacoustic problem, we develop a multi-model, multi-domain (near-field/farfield) method based on a discontinuous Galerkin discretization. In this approach the coupling of multi-domains and multi-models is achieved by weakly enforcing continuity of normal fluxes across a coupling surface. For our interested aeroacoustics control problem, the adjoint equations that determine the sensitivity of the cost functional to changes in control are also solved with same approach by weakly enforcing continuity of normal fluxes across a coupling surface. Such formulations have been validated extensively for several aeroacoustics state and control problems. A multi-model based optimal control framework has been constructed and applied to our interested BVI noise control problem. This model problem consists of the interaction of a compressible vortex with Bell AH-1 rotor blade with wall-normal velocity used as control on the rotor blade surface. The computational domain is decomposed into the near-field and far-field. The near-field is obtained by numerical solution of the Navier-Stokes equations while far away from the noise source, where the effect of nonlinearities is negligible, the linearized Euler equations are used to model the acoustic wave propagation. The BVI wave packet is targeted by defining an objective function that measures the square amplitude of pressure fluctuations in an observation region, at a time interval encompassing the dominant leading edge compressibility waves. Our control results show that a 12dB reduction in the observation region is obtained. Interestingly, the control mechanism focuses on the observation region and only minimize the sound level in that region at the expense of other regions. The vortex strength and trajectory get barely changed. However, the optimal control does alter the interaction of the vortical and potential fields, which is the source of BVI noise. While this results in a slight increase in drag, there is a significant reduction in the temporal gradient of lift leading to a reduction in BVI sound levels. (Abstract shortened by UMI.)

Harmonic drive gear reducers were developed during the mid-1950's and are used in many industrial and military applications. The harmonic drive is a compact, "in-line" gear reducer capable of producing reduction ratios of up to 320:1. The devices are known for their efficiency and precision, but they also possess undesirable qualities characterized by nonlinear behavior. These undesirable aspects include the presence of both static and dynamic friction, flexibility (compliance), and kinematic, or positional, error. In the thesis, the mechanical design of a test platform for the study of the system nonlinearities was developed and fabricated. Experimental testing through computer controlled data acquisition validated the apparatus as a system for the examination and control of kinematic error. A new model for kinematic error was developed for the test system. Observations were made concerning the way in which flexibility effects the magnitude of the kinematic error. PD control schemes were implemented in both motor state and local state feedback control efforts. The load state feedback effort successfully compensated for the effects of kinematic error during regulation of the load position. The experimental results were compared to a model and discussed in detail.