3. Electronic Theses and Dissertations (ETDs) - All submissions

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Subject: search.filters.subject.Finite element method.

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    The dual ema-fem approach to dynamic analysis.
    (1990) Grobler, Steven Robert
    It has been said that experimental modal analysis (EMA) "grew to prominence because the engineering community was incapable of properly analyzing the dynamics of commercially significant structures" [24]. The advent of powerful theoretical methods, such as the Finite Element Method (FEM) has not, however, resulted in the demise of EMA. In fact both FEM and EMA have undergone rapid growth and the merging of the two into an effective design and diagnostic tool has had a major impact on the engineering community's approach to dynamics related problems. In this study, the term dual has no mathematical connotations and is used to describe the complementary use of the techniques of EMA and FEM. The mining industry, worldwide, has experienced dynamics related problems in the operation of conveyances in vertical shafts. A study undertaken in South Africa investigated the behaviour of shaft steelwork and skips, resulting in a set of design guidelines for future shaft steelwork designs. This work only investigated the dynamic behaviour of skips. In this project, the ABAQUS and MODEL SOLUTION FEM codes were used to construct models of a. mine cage. An impact modal test was carried ant on the cage, using a GenRad 2515 CAT system, An impact hammer, suitable for exciting large structures, and a strain gauge force transducer were designed and built for the purpose of the test. The natural frequencies and mode shapes obtained from both FEM and EMA are compared by means of the modal assurance criterion (MAC). The test data is used to tune the model to produce accurate results. The model Could then be used (with minimal further test work) for predicting the response of the structure to dynamic loading or the effects of structural modifications.
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    Finite element analysis of compressible flows.
    (1995) Felthum, Luke T
    In this research a finite element analysis program was developed for the modelling of general compressible Euler flows. An explicit Taylor-Galerkin algorithm was used as the flow solver and was used in conjunction with a flux-corrected transport algorithm in order to obtain high shock resolution without numerical oscillations and overshoots. The solver was applied to two and three dimensional geometries. An axisymmetric extension of the Taylor Galerkin algorithm was also developed. For the two dimensional code, a fully automatic mesh generator was implemented which was able to generate meshes for completely arbitrary geometries, as well as an adaptive refinement algorithm which performs an error analysis on the solution and refines and coarsens the mesh appropriately in order to maintain an optimal mesh resolution. The automatic mesh generator dramatically reduced problem setup time and the adaptive refinement algorithm reduced compllter time by up to 90%" A number of test cases were performed covering a wide range of compressible flows including steady and unsteady flows in air, using the ideal gas model, and shocks in liquids, using the Tait model. Within the limitations of the inviscid and real gas assumptions made, accurate results were obtained,
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    Gauge gravity dualities at finite N
    (2014-07-30) Mabanga, Wandile
    In this dissertation we compute the anomalous dimensions for a class of operators, belonging to the SU(3) sector of the theory, that have a bare dimension of order N. For these operators the large N limit and the planar limit are distinct and summing only the planar diagrams will not capture the large N dynamics. Although the spectrum of anomalous dimensions has been computed for this class of operators, previous studies have neglected certain terms which were argued to be small. After dropping these terms diagonalizing the dilatation operator reduces to diagonalizing a set of decoupled oscillators. In this dissertation we explicitely compute the terms which were neglected previously and show that diagonalizing the dilatation operator still reduces to diagonalizing a set of decoupled oscillators.
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    Gauge-gravity duality at finite N
    (2014-06-12) Tarrant, Justine Alecia
    Recently it has been shown that N = 4 super Yang-Mills theory is integrable in the planar limit. Past arguments suggest the integrability is only present in the planar limit. However, this conclusion was shown to be incorrect. Two speci c classes of operators were studied in the O(N) sector. The rst were labelled by Young diagrams having two long columns. The second were labelled by Young diagrams having two long rows. This result was then generalized to p long rows or columns with p xed to be O(1) as N ! 1. For this case, the non-planar limit was found to be integrable. In this dissertation, we extend this work by considering p to be O(N). We have calculated the dilation operator for the case with two impurities.
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    Gauge/gravity duality at finite N
    (2013-07-29) Mohammed, Badr Awad Elseid
    In the past decade, the gauge/gravity duality has been extensively explored in the large N limit. In particular, the spectrum of anomalous dimensions have been compared with the energy spectrum of the dual string theory showing remarkable agreement. In this limit, for operators with a bare dimension of order 1, planar diagrams give the leading contribution to the anomalous dimension. To obtain the anomalous dimensions, one needs to diagonalize the dilatation operator. One of the methods used to accomplish this is integrability. This allows an exact computation of the spectrum of the anomalous dimensions. There is by now a great deal of evidence that N = 4 supersymmetric Yang-Mills (SYM) theory and N = 6 superconformal Chern Simons (ABJ(M)) theory are integrable in the planar limit. In this thesis we probe the gauge gravity duality at finite N using novel tools developed from the representation theory of symmetric and unitary groups. We start by studying the action of the nonplanar dilatation operator of N = 4 SYM theory and ABJ(M) theory. The gauge invariant operators we consider are the restricted Schur polynomials. In the case of N = 4 SYM theory, we obtain the spectrum of the anomalous dimension beyond the SU(2) sector at one loop, and in the SU(2) sector at two loops. In both cases, we obtain the spectrum at arbitrary (finite) N. We then obtain the spectrum of anomalous dimensions in the SU(2) sector of ABJ(M) theory at two loops. The class of gauge invariant operators we consider have classical dimension of order O(N). In both theories, the spectrum of the anomalous dimensions reduces to a set of decoupled harmonic oscillators at large N. This indicates, for the first time, that N = 4 SYM theory and ABJ(M) theory exhibit nonplanar integrability. We expect to recover non-perturbative quantum gravity effects, from the gauge/gravity duality, when N is finite. The non-planar integrability we discover here may play an important role in finite N studies of the gauge/gravity duality, and hence may play an important role in understanding non-perturbative string stringy physics. In addition, we study various classes of correlators in ABJ(M) theory. In this context, we derive extremal n-point correlators in ABJ(M) theory and we probe the giant graviton dynamics in these theories.
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