Spacecraft structures are subject to a series of load environments during their service life, with the most severe of these occurring during the spacecraft's launch and ascension through the atmosphere. In particular, acoustic loads imposed on stowed satellites within the launch vehicle fairing can result in high mechanical loads on sensitive spacecraft hardware. These acoustic loads have the potential to damage important components and as such it is necessary to accurately characterize and predict the acoustic launch environment for a given mission. This research investigates the Sound Pressure Level (SPL) that can be measured in and around spacecraft cavities resulting from a known excitation and the resultant structural responses. Linear finite element analysis (FEA) is coupled with the Boundary Element method (BEM) to analyze spacecraft acoustic environments and corresponding structural responses at low frequencies on the order of the structural modes. Analytical capability for predicting acoustic environments inside the launch vehicle has improved significantly in recent years; however, while it is easy to perform an analysis and obtain results, the modeling effort can become unnecessarily complicated and analytical data can be hard to interpret. This work seeks to alleviate unnecessary complexity in the low-frequency regime of acoustic modeling by examining the fundamentals of coupled BEM-FEM analysis and applying simplification to a spacecraft model where possible to achieve results verified against direct field acoustic testing (DFAT) methods. / Master of Science

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<p>In this thesis we study hybrid numerical methods to be usedin computational electromagnetics. We restrict the methods tospectral domain and scattering problems. The hybrids consist ofcombinations of Boundary Element Methods and Geometrical Theoryof Diffraction.</p><p>In the thesis three hybrid methods will be presented. Onemethod has been developped from a theoretical idea to anindustrial code. The two other methods will be presented mainlyfrom a theoretical perspective. We will also give shortintroductions to the Boundary Element Method and theGeometrical Theory of Diffraction from a theoretical andimplementational point of view.</p><p><b>Keywords:</b>Maxwell’s equations, Geometrical Theoryof Diffraction, Boundary Element Method, Hybrid methods,Electromagnetic Scattering</p>

Pitting corrosion is a form of highly localized corrosion that can lead to crack and failure of a structure. Study on pitting corrosion is necessary in order to predict and prevent the risk of failure of structure susceptible to corrosion. In this thesis, a combination of Cellular Automata (CA) and Boundary Element Method (BEM) was developed to simulate pitting corrosion growth under certain environment. It is assumed that pitting corrosion can be simplified to electrochemical corrosion cell. The distribution of potential around this corrosion cell can then be simulated by BEM. This distribution potential represents cathodic and anodic reactions around the corrosion cell. A CA model was developed that uses transition rules reflecting mechanism of pitting corrosion. The CA model has two types of cell states, one reflecting BEM simulation results and the other reflecting the status of corrosion cell (anode, cathode, and passive metal’s surface). For every CA iteration, the CA decides the state of the corrosion cells (the location and size of anode, cathode) while BEM simulate the level of electrochemical activity at discrete location on the surface (represented by potential distribution). In order to demonstrate the methodology, a simple case of rectangular corrosion cell with varied dimensions and under different polarization functions is considered. Results show certain shapes tend to grow at certain type environment and these pits are comparable to commonly observed pit shapes. In addition, stress analysis was carried out to investigate the severity of corrosion pits of varying shapes and sizes. Results show that certain pits induced highly varying stress concentration as it grows over time, while others have more steady increase of stress concentration.

Neste trabalho utiliza-se a formulação direta do Método dos Elementos de Contorno aplicada ao problema de flexão de placas com vinculação interna. Através da utilização da teoria baseada nas hipóteses de Reissner é possível atender em cada ponto, a três condições físicas de contorno. Admite-se a aplicação de cargas transversais distribuídas e concentradas, além de momentos distribuídos em linha. Os elementos de contorno apresentam geometria linear com aproximação quadrática para as variáveis de contorno. As equações integrais dos deslocamentos são escritas para pontos de colocação dispostos fora do domínio, evitando-se assim problemas de singularidades. O sistema de equações algébricas originado da análise de placas via MEC é modificado para incorporar o enrijecimento produzido pela vinculação interna. Primeiramente é analisado o enrijecimento produzido por apoios internos pontuais ou distribuídos em áreas pequenas e, em seguida, é estudada a associação da placa com uma estrutura qualquer, formada por barras. O enrijecimento produzido por esta estrutura é obtido utilizando-se o Método dos Elementos Finitos. Finalmente, são apresentados alguns exemplos simples que mostram a boa precisão da técnica utilizada. / The direct formulation of the Boundary Element Method is applied to the analysis of internally restrained plates in bending. By employing Reissner\'s theory, the three boundary conditions are satisfied at each point. Loading conditions include concentrated or uniformly distributed loads as well as linearly distributed moments. The boundary elements are geometrically linear with quadratic approximation for the boundary variables. The displacement integral equations are written for collocation points outside the domain thus avoiding any singularity problem. The resulting system of algebraic equations is modified to include the stiffening effects. Plates with internal point restraints and restrained over small areas are analyzed as well as plates connected to others structures made up of bars. In this last case, the stiffening effect is calculated through the Finite Element Method. The results obtained in simple problems indicate the accuracy of the procedure.

In bubble dynamics, an underwater bubble may evolve from being singly-connected to being toroidal. Furthermore, two or more individual bubbles may merge to form a single large bubble. These dynamics involve significant topological changes such as merging and breaking, which may not be handled well by front-tracking boundary element methods. In the level set method, topological changes are handled naturally through a higher-dimensional level set function. This makes it an attractive method for bubble simulation. In this paper, we present a method that combines the level set method and the boundary element method for the simulation of bubble dynamics. We propose a formulation for the update of a potential function in the level set context. This potential function is non-physical off the bubble surface but consistent with the physics on the bubble surface. We consider only axisymmetric cavitation bubbles in this paper. Included in the paper are some preliminary results and findings. / Singapore-MIT Alliance (SMA)

In this paper a precorrected FFT-Fast Multipole Tree (pFFT-FMT) method for solving the potential flow around arbitrary three dimensional bodies is presented. The method takes advantage of the efficiency of the pFFT and FMT algorithms to facilitate more demanding computations such as automatic wake generation and hands-off steady and unsteady aerodynamic simulations. The velocity potential on the body surfaces and in the domain is determined using a pFFT Boundary Element Method (BEM) approach based on the Green’s Theorem Boundary Integral Equation. The vorticity trailing all lifting surfaces in the domain is represented using a Fast Multipole Tree, time advected, vortex participle method. Some simple steady state flow solutions are performed to demonstrate the basic capabilities of the solver. Although this paper focuses primarily on steady state solutions, it should be noted that this approach is designed to be a robust and efficient unsteady potential flow simulation tool, useful for rapid computational prototyping. / Singapore-MIT Alliance (SMA)

<p>Steady-state sound fields in enclosures, with specular and diffuse reflection boundaries, are modeled with a first-principle energy-intensity boundary element method using uncorrelated broadband directional sources. The specular reflection field is represented by a limited set of spherical harmonics that are orthogonal on the half-space. The amplitudes of these harmonics are determined by a Lagrange multiplier method to satisfy the energy conservation integral constraint. The computational problem is solved using an iterative relaxation method starting from the 3-D diffuse reflection solution. At each iteration, directivity harmonics are estimated by post-processing and the influence matrix is refined accordingly. For internal sources, simple first reflection images improve accuracy with virtually no penalty on computation time. Monotonic convergence occurs in relatively few relaxation steps. Extrapolating to an infinite number of boundary elements and iterations gives very accurate results. The method is very computationally efficient. Results are compared to exact benchmark solutions obtained from a frequency-by-frequency modal analysis, and a broadband image method, demonstrating high accuracy. The method of absorption scaling is verified for complicated 3-D cases, and showing that the spatial variation in rooms is largely determined by source position and the relative distribution of absorption, but not the overall absorption level.</p> / Dissertation

This research investigates effects of tensile stresses in liquids. Areas of application include bearing lubrication and polymer processing, in which liquids may be subjected to hydrostatic tension or large shear stresses. A primary thrust of this research is the development of a criterion for liquid failure, or cavitation, based upon the general state of stress in the liquid. A variable pressure, rotating inner cylinder, Couette viscometer has been designed and used to test a hypothesized cavitation criterion. The criterion, that cavitation will occur when a principal normal stress in a liquid becomes more tensile than some critical stress, is supported by the results of experiments with the viscometer for a Newtonian liquid. Based upon experimental observation of cavitation, a model for cavitation inception from crevice stabilized gas nuclei, and gaseous, as opposed to vaporous, cavitation is hypothesized. The cavitation inception model is investigated through numerical simulation, primarily using the boundary element method. Only Newtonian liquids are modeled, and, for simulation purposes, the model is reduced to two dimensions and the limit of negligible inertia is considered. The model includes contact line dynamics. Mass transport of dissolved gas through the liquid and in or out of the gas nucleus is considered. The numerical simulations provide important information about the probable nature of cavitation nucleation sites as well as conditions for cavitation inception. The cavitation criterion predicts cavitation in simple shear, which has implications for rheological measurements. It can cause apparent shear thinning and thixotropy. Additionally, there is evidence suggesting a possible link between shear cavitation and extrusion defects such as sharkskin. A variable pressure capillary tube viscometer was designed and constructed to investigate a hypothesized relationship between shear cavitation and extrusion defects. Results indicate that despite the occasional coincidence of occurrence of cavitation and sharkskin defects, cavitation cannot explain the onset of extrusion defects. If nuclei are removed, then liquids can withstand a negative hydrostatic pressure. A falling body viscometer has been constructed and used to investigate the effect of negative pressures on viscosity. It is found that current pressure viscosity models can be accurately extrapolated to experimentally achievable negative pressures.

Based on a full-wave formulation, a vector boundary element method (VBEM) is proposed to model the photonic crystal fibers (PCFs) (microstructured fibers). The accuracy and efficiency of the approach are confirmed by comparing the results calculated with those in previous literatures. With employing the VBEM, the guiding characteristics, including the effective indexes, vector mode patterns, and the polarization properties of the PCFs are investigated. There polarization characteristics of the PCFs with elliptical air holes (EPCFs) and the one ring air-hole EPCF embedded in the step-index core are studied and discussed. In addition, based on the VBEM formulations, a novel and efficient numerical approach to calculate the dispersion parameters of the PCFs is also proposed. The effect of the PCF geometrical structure on the group velocity dispersion property is reviewed, and then the one-ring defect and two-ring defect PCFs are studied and designed for the ultra-flattened dispersion applications. As an example, a four-ring (two-ring defect) PCF with flattened dispersion of ¡Ó0.25 ps/km/nm from 1.295£gm to 1.725£gm wavelength is numerically demonstrated.