This thesis presents numerical techniques which have been developed to analyse three dimensional problems in offshore engineering. In particular, the three dimensional liquefaction analysis of offshore foundations on granular soils is the main subject of the thesis. The subject matter is broadly divided into four sections: 1)Development of an efficient method for the three dimensional elasto?plastic finite element analysis of consolidating soil through the use of a discrete Fourier representation of field quantities. 2)Validation of the three dimensional method through analyses of shallow offshore foundations subjected to three dimensional loading and investigation of the yield locus for foundations on purely cohesive soils. 3)Formulation of governing equations suitable for three dimensional liquefaction analyses of offshore foundations founded on granular soil, presentation of a method for liquefaction analyses, and application of the method in modified elastic liquefaction analyses of offshore foundations. 4)Application of a conventional elasto?plastic soil model in the liquefaction analyses of offshore foundations using the three dimensional finite element method. The finite element method developed in this thesis provides a rigorous and efficient numerical tool for the analysis of geotechnical problems subjected to three dimensional loading. The efficiency of the numerical tool makes it possible to tackle some of the problems in geotechnical engineering which would otherwise need enormous computing time and thus would be impractical. The accuracy of the numerical scheme is demonstrated by solving the bearing capacity problem of shallow foundations subjected to three dimensional loading. The generalized governing equations and the numerical method for liquefaction analyses presented in this thesis provide a solid base for the analysis of offshore foundations subjected to cyclic wave loading where they are founded on potentially liquefiable soil. The practicability of the numerical scheme is also demonstrated by a modified elastic liquefaction analysis of offshore foundations. The liquefaction phenomenon is redefined in the context of the conventional Mohr?Coulomb model, so that a relatively simple and practical model for elasto?plastic liquefaction analysis is presented. The three dimensional finite element method together with the numerical scheme for liquefaction analysis and the elasto?plastic soil model provide a suitable practical engineering tool for exploring the responses of offshore foundations subjected to cyclic wave loading.

This thesis presents numerical techniques which have been developed to analyse three dimensional problems in offshore engineering. In particular, the three dimensional liquefaction analysis of offshore foundations on granular soils is the main subject of the thesis. The subject matter is broadly divided into four sections: 1)Development of an efficient method for the three dimensional elasto?plastic finite element analysis of consolidating soil through the use of a discrete Fourier representation of field quantities. 2)Validation of the three dimensional method through analyses of shallow offshore foundations subjected to three dimensional loading and investigation of the yield locus for foundations on purely cohesive soils. 3)Formulation of governing equations suitable for three dimensional liquefaction analyses of offshore foundations founded on granular soil, presentation of a method for liquefaction analyses, and application of the method in modified elastic liquefaction analyses of offshore foundations. 4)Application of a conventional elasto?plastic soil model in the liquefaction analyses of offshore foundations using the three dimensional finite element method. The finite element method developed in this thesis provides a rigorous and efficient numerical tool for the analysis of geotechnical problems subjected to three dimensional loading. The efficiency of the numerical tool makes it possible to tackle some of the problems in geotechnical engineering which would otherwise need enormous computing time and thus would be impractical. The accuracy of the numerical scheme is demonstrated by solving the bearing capacity problem of shallow foundations subjected to three dimensional loading. The generalized governing equations and the numerical method for liquefaction analyses presented in this thesis provide a solid base for the analysis of offshore foundations subjected to cyclic wave loading where they are founded on potentially liquefiable soil. The practicability of the numerical scheme is also demonstrated by a modified elastic liquefaction analysis of offshore foundations. The liquefaction phenomenon is redefined in the context of the conventional Mohr?Coulomb model, so that a relatively simple and practical model for elasto?plastic liquefaction analysis is presented. The three dimensional finite element method together with the numerical scheme for liquefaction analysis and the elasto?plastic soil model provide a suitable practical engineering tool for exploring the responses of offshore foundations subjected to cyclic wave loading.

Due to space limitations in urban areas, underground construction has become a common practice worldwide. When using deep excavations, excessive lateral movements are a major concern because they can lead to significant displacements and rotations in adjacent structures. Therefore, accurate predictions of lateral wall deflections and surface settlements are important design criteria in the analysis and design of excavation support systems. This research shows that the current design methods, based on plane strain analyses, are not accurate for designing excavation support systems and that fully three-dimensional (3D) analyses including wall installation effects are needed. A complete 3D finite element simulation of the wall installation at the Chicago and State Street excavation case history is carried out to show the effects of modeling: (i) the installation sequence of the supporting wall, (ii) the excavation method for the wall, and (iii) existing adjacent infrastructure. This model is the starting point of a series of parametric analyses that show the effects of the system stiffness on the resulting excavation-related ground movements. Furthermore, a deformation-based methodology for the analysis and design of excavation support systems is proposed in order to guide the engineer in the different stages of the design. The methodology is condensed in comprehensive flow charts that allow the designer to size the wall and supports, given the allowable soil distortion of adjacent structures or predict ground movements, given data about the soil and support system.

Thesis (MScEng)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Several transverse flux and longitudinal flux linear generator topologies exist for freepiston Stirling engine applications. In this thesis the transverse flux permanent magnet linear generators are investigated together with a back-to-back converter which can deliver the electrical energy from the linear generator to the electrical network. The transverse flux permanent magnet linear generator is geometrically optimised with the aim to maximise the power-to-weight ratio while maintaining preset power and efficiency levels. An optimised 3 kW linear generator is built and the measured results correlate to the simulation results. A close-loop current control scheme is introduced to control the current of the rectifier, which is part of the back to back converter. The transverse flux permanent magnet linear generator is connected to the input of the rectifier which has the ability to force a specific current from the generator. The measured results of the rectifier correlate to the results of the simulations that were done. The current control present some complications and it is suggested that another control scheme is used. A close-loop voltage control scheme is introduced for the control of the DC bus voltage. The DC bus is connected between the rectifier and the inverter, which is the other part of the back-to-back converter. A close-loop current control scheme is introduced to control the inverter current that flows from the inverter to the electrical network. The measured results of the inverter and the DC bus correlate to the results of the simulations that were done. The results of the system, including the generator, rectifier and inverter, tested as a unit is presented and discussed. / AFRIKAANSE OPSOMMING: Verskeie tranverse vloed en longitudinale vloed lineˆere generator topologie¨e bestaan vir vrysuier Stirling enjin toepassings. In hierdie tesis word ’n transverse vloed permanente magneet lineˆere generator ondersoek saam met ’n omsetter. Die omsetter dra die elektriese energie van die generator oor aan die elektriese netwerk. Die transverse vloed permanente magneet lineˆere generator word geometries geoptimeer met die doel om die drywing-tot-gewig verhouding te maksimiseer terwyl vasgestelde drywing en effektiwiteit vlakke behou word. ’n Geoptimeerde 3kW lineˆere generator prototipe is vervaardig en die gemete resultate is geverifieer met die simulasie resultate. ’n Geslote lus stroombeheer strategie word voorgestel om die stroom te beheer van die gelykrigter, wat deel is van die omsetter. Die transverse vloed permanente magneet lineˆere generator word aan die gelykrigter, wat die vermo¨e het om ’n spesifieke stroom uit die generator te forseer, se intree verbind. Die gemete resultate van die gelykrigter wat gebou is stem goed ooreen met die van die simulasies wat gedoen is. Die stroombeheer hou komplikasies in wat bespreek word. Dus word die gebruik van ’n alternatiewe stroombeheer voorgestel. ’n Geslote lus spannings beheer strategie¨e word voorgestel om die gs. busspanning te beheer. Die gs. bus is gekonnekteer tussen die gelykrigter en die wisselrigter, wat ook deel uitmaak van die omsetter. ’n Geslote lus stroom beheer word voorgestel om die stroom te beheer wat vanaf die wisselrigter na die elektriese netwerk toe vloei. Die gemete resultate van die wisselrigter en die gs. bus stem goed ooreen met die van die simulasies wat gedoen is. Die resultate van die hele stelsel, wat die generator, gelykrigter en die wisselrigter insluit, wat as ’n eenheid getoets is word weergegee en bespreek.

Continuous casting represents 96% of all steel products made worldwide. To cast new alloys, optimal process parameters must be determined that reduce quality issues. Traditionally, this is a time-consuming and expensive process due to the need to run multiple casting trials. Alternatively, numerical models can be used to help guide development of optimal process parameters. In this thesis, a 3D thermal-solute-mechanical finite element model has been created using the THERCAST software to simulate the casting process of a new advanced high strength steel grade at Stelco’s Lake Erie Works facility. The model represents the caster from mould to exit, and takes into account heat transfer from the mould, sprays, rolls, and ambient air. The model has been extensively validated using plant measurements from steel shim trials and pyrometer data. The model is used to investigate the evolution of temperature and shell thickness along the cast length, and the effect of spray cooling and casting speed on the surface temperature at unbending to predict transverse cracking during secondary cooling. It was found that the susceptibility to cracking increased with lower casting speed and increased water spray cooling. Increasing the casting speed had a negligible effect, and it was found to decrease with decreasing water spray cooling. This decreased water spray cooling is also accompanied by an increase in metallurgical length, so further work is required to determine appropriate safety factors to ensure the steel is completely solidified. However, preliminary results of solute and mechanical models are also presented. Further work is required to improve the predictions made by these simulations. / Thesis / Master of Applied Science (MASc)

It has always been enigmatic which processes control the accretion of the North American terranes towards the Pacific plate and the landward migration of the San Andreas plate boundary. One of the theories suggests that the Pacific plate first cools and captures the uprising mantle in the slab window, and then it causes the accretion of the continental crustal blocks. The alternative theory attributes the accretion to the capture of Farallon plate fragments (microplates) stalled in the ceased Farallon-North America subduction zone. Quantitative judgement between these two end-member concepts requires a 3D thermomechanical numerical modeling. However, the software tool required for such modeling is not available at present in the geodynamic modeling community. The major aim of the presented work is comprised basically of two interconnected tasks. The first task is the development and testing of the research Finite Element code with sufficiently advanced facilities to perform the three-dimensional geological time scale simulations of lithospheric deformation. The second task consists in the application of the developed tool to the Neogene deformations of the crust and the mantle along the San Andreas Fault System in Central and northern California. The geological time scale modeling of lithospheric deformation poses numerous conceptual and implementation challenges for the software tools. Among them is the necessity to handle the brittle-ductile transition within the single computational domain, adequately represent the rock rheology in a broad range of temperatures and stresses, and resolve the extreme deformations of the free surface and internal boundaries. In the framework of this thesis the new Finite Element code (SLIM3D) has been successfully developed and tested. This code includes a coupled thermo-mechanical treatment of deformation processes and allows for an elasto-visco-plastic rheology with diffusion, dislocation and Peierls creep mechanisms and Mohr-Coulomb plasticity. The code incorporates an Arbitrary Lagrangian Eulerian formulation with free surface and Winkler boundary conditions. The modeling technique developed is used to study the aspects influencing the Neogene lithospheric deformation in central and northern California. The model setup is focused on the interaction between three major tectonic elements in the region: the North America plate, the Pacific plate and the Gorda plate, which join together near the Mendocino Triple Junction. Among the modeled effects is the influence of asthenosphere upwelling in the opening slab window on the overlying North American plate. The models also incorporate the captured microplate remnants in the fossil Farallon subduction zone, simplified subducting Gorda slab, and prominent crustal heterogeneity such as the Salinian block. The results show that heating of the mantle roots beneath the older fault zones and the transpression related to fault stepping, altogether, render cooling in the slab window alone incapable to explain eastward migration of the plate boundary. From the viewpoint of the thermomechanical modeling, the results confirm the geological concept, which assumes that a series of microplate capture events has been the primary reason of the inland migration of the San Andreas plate boundary over the recent 20 Ma. The remnants of the Farallon slab, stalled in the fossil subduction zone, create much stronger heterogeneity in the mantle than the cooling of the uprising asthenosphere, providing the more efficient and direct way for transferring the North American terranes to Pacific plate. The models demonstrate that a high effective friction coefficient on major faults fails to predict the distinct zones of strain localization in the brittle crust. The magnitude of friction coefficient inferred from the modeling is about 0.075, which is far less than typical values 0.6 – 0.8 obtained by variety of borehole stress measurements and laboratory data. Therefore, the model results presented in this thesis provide additional independent constrain which supports the “weak-fault” hypothesis in the long-term ongoing debate over the strength of major faults in the SAFS. / Seit jeher rätselhaft sind die Prozesse, die die Akkretion der Nordamerikanischen Terranen in Richtung der Pazifischen Platte sowie die Wanderung der Plattengrenze der San-Andreas-Verwerfung in Richtung Festland bestimmen. Eine Theorie besagt, dass sich die Pazifische Platte erst abkühlt und den aufsteigenden Mantel im „Slab Window“ fängt und somit die Akkretion der kontinentalen Krustenblöcke bewirkt. Die andere Theorie geht von einer Akkretion durch das Fangen von Teilen der Farallon-Platte (Mikroplatten) aus, die in der inaktiven nordamerikanischen Farallon-Subduktionszone fest stecken. Die quantitative Beurteilung dieser beiden gegensätzlichen Konzepte erfordert eine thermomechanische numerische 3-D-Modellierung. Das dafür benötigte Software Tool steht jedoch der geodynamischen Modellierung derzeit noch nicht zur Verfügung. Das Hauptziel der vorliegenden Arbeit umfasst im Wesentlichen zwei miteinander verbundene Aufgaben. Die erste besteht in der Entwicklung und Erprobung des Finite-Element-Codes, dessen Eigenschaften den hohen Anforderungen an die Ausführung der dreidimensionalen Simulationen lithosphärischer Deformation auf geologischer Zeitskala gerecht werden müssen. Die zweite Aufgabe ist die Anwendung des entwickelten Tools auf die neogenen Deformationen der Kruste und des Mantels entlang der San-Andreas-Verwerfung in Zentral- und Nordkalifornien. Die Modellierung auf geologischer Zeitskala lithosphärischer Deformation bringt für die Software Tools in Bezug auf Konzept und Durchführung zahlreiche Herausforderungen mit sich. Unter anderem gilt es, den Brittle-Ductile-Übergang in einem einzigen Modell sowie die Gesteinsrheologie in einer breiten Spanne unterschiedlicher Temperaturen und Spannungen adäquat darzustellen und die extremen Deformationen der freien Oberfläche und internen Grenzen aufzulösen. Im Rahmen der vorliegenden Arbeit erfolgte die erfolgreiche Entwicklung und Erprobung des neuen Finite-Element-Codes (SLIM3D). Dieser Code beinhaltet eine gekoppelte thermomechanische Behandlung von Deformationsprozessen und ermöglicht eine elasto-visko-plastische Rheologie mit Diffusion, Dislokation, Peierls Kriechmechanismen und Mohr-Coulomb-Plastizität. Der Code verbindet eine Arbitrary Lagrangian-Eulerian kinematische Formulierung mit freien Oberflächen- und Winkler-Randbedingungen. Das entwickelte Modellierungsverfahren wird für die Untersuchung der Aspekte verwendet, die die neogene lithosphärische Deformation in Zentral- und Nordkalifornien beeinflussen. Die Modellanordnung konzentriert sich auf die Interaktion zwischen drei großen tektonischen Elementen in dieser Region: die Nordamerikanische Platte, die Pazifische Platte sowie die Gorda-Platte, die sich in der Mendocino-Triple-Junction treffen. Unter anderem verdeutlicht die Modellierung den Einfluss des Aufsteigens der Asthenosphäre in das sich öffnende „slab window“ der übergelagerten Nordamerikanischen Platte. Die Modelle beziehen auch die angelagerten Überreste der Mikroplatten in der fossilen Farallon-Subduktionszone, die vereinfachte subduzierende Gorda-Platte sowie markante Heterogenitäten der Kruste, wie beispielsweise den „Salinian Block“, mit ein. Die Ergebnisse zeigen, dass die Erwärmung der Mantellithosphäre unter den älteren Störungszonen sowie die Transpression eine Abkühlung im „Slab Window“ als alleinige Begründung für die Ostwärtsbewegung der Plattengrenze nicht zulassen. Aus Sicht der thermomechanischen Modellierung bestätigen die Ergebnisse das geologische Konzept, welches durch das mehrmalige Fangen von Mikroplatten den Hauptgrund für die Wanderung der Plattengrenze der San-Andreas-Verwerfung in Richtung Festland über die letzten 20 Millionen Jahre sieht. Die Überreste der Farallon-Platte, die in der fossilen Subduktionszone gefangen sind, verursachen im Mantel eine wesentlich stärkere Heterogenität als die Abkühlung der Asthenosphäre und stellen somit den effizienteren und direkteren Weg für die Anlagerung der nordamerikanischen Gebiete an die Pazifische Platte dar. Die Modelle demonstrieren, dass ein hoher effektiver Reibungskoeffizient an großen Störungen nicht in der Lage ist, die eindeutigen Zonen der Dehnungslokalisierung in der spröden Kruste vorherzusagen. Die Größe des Reibungskoeffizienten, die sich aus der Modellierung ableitet, beträgt etwa 0,075 und ist damit wesentlich kleiner als die durch unterschiedliche Bohrlochmessungen und Labordaten ermittelten Spannungswerte zwischen 0,6 und 0,8. Daher liefern die in dieser Arbeit präsentierten Ergebnisse der Modelle in der seit langem geführten Debatte über die Stärke von großen Störungen in der San-Andreas-Verwerfung eine zusätzliche unabhängige Begründung der „Weak-Fault“-Hypothese.

Axial flux permanent magnet (AFPM) machines have recently attracted significant attention due to several reasons, such as their specific form factor, potentially higher torque density and lower losses, feasibility of increasing the number of poles, and facilitating innovative machine structures for emerging applications. One such machine design, which has promising, high efficiency particularly at higher speeds, is of the coreless AFPM type and has been studied in the dissertation together with more conventional AFPM topologies that employ a ferromagnetic core. A challenge in designing coreless AFPM machines is estimating the eddy current losses. This work proposes a new hybrid analytical and numerical finite element (FE) based method for calculating ac eddy current losses in windings and demonstrates its applicability for axial flux electric machines. The method takes into account 3D field effects in order to achieve accurate results and yet greatly reduce computational efforts. It is also shown that hybrid methods based on 2D FE models, which require semi-empirical correction factors, may over-estimate the eddy current losses. The new 3D FE-based method is advantageous as it employs minimum simplifications and considers the end turns in the eddy current path, the magnetic flux density variation along the effective length of coils, and the field fringing and leakage, which ultimately increases the accuracy of simulations. After exemplifying the practice and benefits of employing a combined design of experiments and response surface methodology for the comparative design of coreless and conventional AFPM machines with cores, an innovative approach is proposed for integrated design, prototyping, and testing efforts. It is shown that extensive sensitivity analysis can be utilized to systematically study the manufacturing tolerances and identify whether the causes for out of specification performance are detectable. The electromagnetic flux path in AFPM machines is substantially 3D and cannot be satisfactorily analyzed through simplified 2D simulations, requiring laborious 3D models for performance prediction. The use of computationally expensive 3D models becomes even more challenging for optimal design studies, in which case, thousands of candidate design evaluations are required, making the conventional approaches impractical. In this dissertation a new two-level surrogate assisted differential evolution multi-objective optimization algorithm (SAMODE) is developed in order to optimally and accurately design the electric machine with a minimum number of expensive 3D design evaluations. The developed surrogate assisted optimization algorithm is used to comparatively and systematically design several AFPM machines. The studies include exploring the effects of pole count on the machine performance and cost limits, and the systematic comparison of optimally designed single-sided and double-sided AFPM machines. For the case studies, the new optimization algorithm reduced the required number of FEA design evaluations from thousands to less than two hundred. The new methods, developed and presented in the dissertation, maybe directly applicable or extended to a wide class of electrical machines and in particular to those of the PM-excited synchronous type. The benefits of the new eddy current loss calculation and of the optimization method are mostly relevant and significant for electrical machines with a rather complicated magnetic flux path, such is the case of axial flux and of transvers flux topologies, which are a main subject of current research in the field worldwide.

Submitted to the Department of Electrical Engineering in Fulfilment of the Requirements for the Magister Technologiae in Electrical Engineering at the CAPE PENINSULA UNIVERSITY OF TECHNOLOGY SUPERVISOR: E. VOSS NOVEMBER 2013 / Radial and peripheral displacement of stator teeth in electrical machines is known to be the cause of undesired vibration which leads to noise. This thesis serves to investigate the possibility of physically measuring the radial displacement of stator teeth caused by electromagnetic forces which, to the author’s knowledge, has not yet been achieved. A simplified practical approach is adopted in order to address the inherent difficulties attached to this problem, and the measurement of displacement is done by means of an experimental rig where a tooth is subjected to magnetic force acting over an air gap. Three experiments are carried out, each comprising ten tests, the results of which are compared in order to gain some idea as to the magnitudes of displacement which can be expected over a range of applied air gap flux densities. The aim of this work is to observe the displacement response of magnetised EM core material when acted upon by forces, and to see if the measured results agree with the elastic displacement predicted by a wellknown formula. It will be shown that although the measured results are in the same range as the predicted results, there is a deviation from the predicted linearity due to certain characteristics of the force rig, which are explained. The chosen measurement method is capacitive displacement and is shown to be a viable alternative to the more commonly used search coils and vibrometers in past literatures, especially when measuring displacements on the nano-scale. In addition, this study shows the importance of using 3D finite element software to simulate the electromagnetic model when saturation is present in the core of the test specimen. The important findings of this work are discussed in detail, and some ideas put forward, in an attempt to establish a starting point for future related work in the measurement of electromagnetic forceinduced displacement of stator teeth in electrical machines.

This thesis is aimed on three-dimensional finite element time domain analysis. Vector finite elements are used for analysis of cavity resonator made from PEC and filled with vacuum. Results are compared with classical “nodal” finite elements and with published literature.

No description available.