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In this thesis we analyze the buckling behavior of an infinitely long, thin, uniform, inextensible, elastic plate that has a steady current flowing along its length. We are concerned with the derivation of the nonlinear equations of motion using nonlinear continuum mechanics, and subsequent analysis of the buckling behavior of the plate under electromagnetic self-forces. In particular, we concentrate on how the body-forces that result from the applied current determine the buckled configurations. We derive both analytical and numerical results, and in the process develop a novel boundary value problem solver for integro-differential equations in addition to a predictor-corrector algorithm to continue solutions with respect to the control parameters. We take a relatively complex problem in magneto-solid mechanics and elasticity theory and form a realistic model that sheds light on the bifurcation and buckling behavior resulting from the electromagnetic-field- induced self-forces that are derived in their full, exact form using Biot-Savart Law. / Ph. D.

A three-dimensional finite element code to analyze coupled thermomechanical deformations of composites has been developed. It incorporates geometric nonlinearities, delamination between adjoining layers, and damage due to fiber breakage, fiber/matrix debonding, and matrix cracking. The three damage modes are modeled using the theory of internal variables and the delamination by postulating a failure envelope in terms of the transverse stresses; the damage degrades elastic moduli. The delamination of adjoining layers is simulated by the nodal release technique. Coupled nonlinear partial differential equations governing deformations of a composite, and the pertinent initial and boundary conditions are first reduced to coupled ordinary differential equations (ODEs) by the Galerkin method. These are integrated with respect to time with the Livermore solver for ODEs. After each time step, the damage in an element is computed, and material properties modified. The code has been used to analyze several static and transient problems; computed results have been found to compare well with the corresponding test results. The effect of various factors such as the fiber orientation, ply stacking sequence, and laminate thickness on composite's resistance to shock loads induced by underwater explosions has been delineated. / Ph. D.

The behavior of large and tightly interconnected power systems resembles, in certain circumstances, the behavior of a continuously distributed system. This resemblance motivated the derivation of continuum models, which were used to explain and predict disturbance propagation, un-damped power oscillations, and the stability of power systems. In this dissertation, we propose a one-dimensional continuum representation suitable for meshed power systems. Previous continuous representations of meshed power systems used two-dimensional spatial domains. Thus our approach has the potential to provide better resolution for comparable computational burden. It is important to note that, the computational burden required to obtain solutions for PDEs involved in the continuum representation varies notably with the solver implementation. The contributions of this dissertation are: a) Reviewing a previous continuum model and providing a detailed derivation for the one-dimensional version of it. b) Providing and describing in detail a parameter distribution technique adequate for the continuum approach. c) Identifying and documenting limitations on the continuum model voltage calculation. e) Providing a procedure to simulate the behavior of meshed power systems using the one dimensional continuum model. And f) Identifying and applying a numerical PDE solver for the continuum approach. / Ph. D.

In a large and dense power network, the transmission lines, the generators and the loads are considered to be continuous functions of space. The continuum technique provides a macro-scale analytical tool to gain an insight into the mechanisms by which the disturbances initiated by faults and other random events propagate in the continuum. This dissertation presents one-dimensional and two-dimensional discrete models to illustrate the propagation of electromechanical waves in a continuum system. The more realistic simulations of the non-uniform distribution of generators and boundary conditions are also studied. Numerical simulations, based on the swing equation, demonstrate electromechanical wave propagation with some interesting properties. The coefficients of reflection, reflection-free termination, and velocity of propagation are investigated from the numerical results. Discussions related to the effects of electromechanical wave propagation on protection systems are given. In addition, the simulation results are compared with field data collected by phasor measurement units, and show that the continuum technique provides a valuable tool in reproducing electromechanical transients on modern power systems. Discussions of new protection and control functions are included. A clear understanding of these and related phenomena will lead to innovative and effective countermeasures against unwanted trips by the protection systems, which can lead to system blackouts. / Ph. D.

The method of Continuum Sensitivity Analysis (CSA) with Spatial Gradient Reconstruction (SGR) is presented for calculating the sensitivity of fluid, structural, and coupled fluid-structure (aeroelastic) response with respect to shape design parameters. One of the novelties of this work is the derivation of local CSA with SGR for obtaining flow derivatives using finite volume formulation and its nonintrusive implementation (i.e. without accessing the analysis source code). Examples of a NACA0012 airfoil and a lid-driven cavity highlight the effect of the accuracy of the sensitivity boundary conditions on the flow derivatives. It is shown that the spatial gradients of flow velocities, calculated using SGR, contribute significantly to the sensitivity transpiration boundary condition and affect the accuracy of flow derivatives. The effect of using an inconsistent flow solution and Jacobian matrix during the nonintrusive sensitivity analysis is also studied. Another novel contribution is derivation of a hybrid adjoint formulation of CSA, which enables efficient calculation of design derivatives of a few performance functions with respect to many design variables. This method is demonstrated with applications to 1-D, 2-D and 3-D structural problems. The hybrid adjoint CSA method computes the same values for shape derivatives as direct CSA. Therefore accuracy and convergence properties are the same as for the direct local CSA. Finally, we demonstrate implementation of CSA for computing aeroelastic response shape derivatives. We derive the sensitivity equations for the structural and fluid systems, identify the sources of the coupling between the structural and fluid derivatives, and implement CSA nonintrusively to obtain the aeroelastic response derivatives. Particularly for the example of a flexible airfoil, the interface that separates the fluid and structural domains is chosen to be flexible. This leads to coupling terms in the sensitivity analysis which are highlighted. The integration of the geometric sensitivity with the aeroelastic response for obtaining shape derivatives using CSA is demonstrated. / Ph. D.

Novel aircraft configurations tend to be sized by physical phenomena that are largely neglected during conventional fixed wing aircraft design. High-fidelity fluid-structure interaction that accurately models geometric nonlinerity during a transient aeroelastic gust response is critical for sizing the aircraft configuration early in the design process. The primary motivation of this research is to develop a continuum shape sensitivity method that can support gradient-based design optimization of practical and multidisciplinary high-fidelity analyses. A local continuum sensitivity analysis (CSA) that utilizes spatial gradient reconstruction (SGR) and avoids mesh sensitivities is presented for shape design derivative calculations. Current design sensitivity analysis (DSA) methods have shortcomings regarding accuracy, efficiency, and ease of implementation. The local CSA method with SGR is a nonintrusive and element agnostic method that can be used with black box analysis tools, making it relatively easy to implement. Furthermore, it overcomes many of the accuracy issues documented in the current literature. The method is developed to compute design derivatives for a variety of applications, including linear and nonlinear static beam bending, linear and nonlinear transient gust analysis of a 2-D beam structure, linear and nonlinear static bending of rectangular plates, linear and nonlinear static bending of a beam-stiffened plate, and two-dimensional potential flow. The analyses are conducted using general purpose codes. For each example the design derivatives are validated with either analytic or finite difference solutions and practical numerical and modeling considerations are discussed. The local continuum shape sensitivity method with spatial gradient reconstruction is an accurate analytic design sensitivity method that is amenable to general purpose codes and black box tools. / Ph. D.

This work discusses the use of Positive Position Feedback (PPF) for Active Vibration Control as part of an Active Damage Control System (ADCS). Vibration control increases the fatigue life of a structure and decreases the in-plane stresses that can cause delamination in a composite. PPF is a collocated direct-output feedback control method that increases the effective damping in a structure. A simply-supported beam was used as the testbed which used strain gages as the sensing element and piezoelectric ceramics as the actuator. Initial investigations into sampled-data systems using PPF are presented. The issues addressed are: stability of the sampled system, the effects of the sampling rate on the system, and degradation from predicted analog performance. A digital design procedure for the tuning filters in the Z-plane is suggested if the sampling rate to be used is known. If the sampling rate varies significantly, to avoid redesigning the filters for each new sampling rate, they should be designed in the continuous-time and transformed to the Z-plane. The Tustin transformation was found to adequately map the poles and zeros of the compensator to the Z-plane for digital control. Experimental implementation of PPF on a simply-supported beam resulted in vibration suppression of three modes with a S180 controller. The beam was subjected to both a single-frequency harmonic disturbance and a broadband harmonic disturbance. One, two, and three-mode controllers were designed with disturbance suppression up to 15dB achieved. / Master of Science

No / Nonresponse bias in survey research can result in misleading or inaccurate findings and assessment of nonresponse bias is advocated to determine response sample representativeness. Four methods of assessing nonresponse bias (analysis of known characteristics of a population, subsampling of nonresponders, wave analysis, and linear extrapolation) were applied to the results of a postal survey of U.K. hospital organizations. The purpose was to establish whether validated methods for assessing nonresponse bias at the individual level can be successfully applied to an organizational level survey. The aim of the initial survey was to investigate trends in the implementation of radiographer abnormality detection schemes, and a response rate of 63.7% (325/510) was achieved. This study identified conflicting trends in the outcomes of analysis of nonresponse bias between the different methods applied and we were unable to validate the continuum of resistance theory as applied to organizational survey data. Further work is required to ensure established nonresponse bias analysis approaches can be successfully applied to organizational survey data. Until then, it is suggested that a combination of methods should be used to enhance the rigor of survey analysis.

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