An analysis of the finite deformation of an elastic body using the finite element method is investigated. The governing nonlinear equations of equilibrium are derived through the principle of virtual work using a Lagrangian description. A general incremental virtual work equation is obtained, and then linearized to permit the use of direct solution techniques. A residual loading term is defined which represents the nonsatisfaction of equilibrium of the solution obtained at the end of an increment using the linear incremental virtual work equation. The residual loading term is used to control the divergence of the linearized incremental solution from the exact equilibrium solution, through the self-correcting solution technique. The finite element method is introduced in general for three dimensional analysis, and is then specialized for two dimensional, plane elasticity analysis. Two eight degree of freedom rectangular finite elements are developed using a bilinear assumed displacement field. The first element is numerically integrated using Gaussian quadrature, while the second employs a nonuniform integration scheme in order to improve this element's performance. Four finite deformation problems are analysed using the procedure presented in this thesis, and the results are compared with available closed form solutions. The problems analysed are those of a uniformly loaded infinite plate strip having either simply supported longitudinal edges or fixed longitudinal edges, a cantilever beam under a uniformly distributed load, and lastly a cantilever beam with a para-bolically distributed end load. Excellent agreement was obtained between the finite element analysis results and the closed form solutions. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

During the hot-rolling of aluminium ingot into sheet, the material elongates in the rolling direction as it is reduced vertically. The spread which occurs in the lateral direction during the multiple pass schedules used in industry is minimal. However, the deformation on these edges is important. During the initial passes a concave profile develops - the material near the surfaces spreads outward while the material at the centre moves inward. The concave profile can lead to defects in the final product; these are the 'roll over' of material from the edges to the top and bottom surfaces, the fold over of material in the centre of the edge, and the formation of vertical edge cracks. To remove these the edges are trimmed at the end of the process. Research work in this area was motivated by the possibility of identifying means of reducing the amount of material that needs to be trimmed. The objectives of this thesis are to develop techniques of simulating the rolling, and to use these to investigate the deformation mechanisms which lead to the concave edge profile. Models of the rolling were developed using the general purpose, non-linear finite element code ABAQUS. To reproduce the edge profiles accurately requires large three-dimensional models, for which the explicit dynamic method was found to be the most suitable. The results of the analyses were used to investigate the mechanisms which lead to the concave edge profile. In the roll-gap the work-load arches through the ingot; and for roll passes with small reductions a stress pattern occurs which leads to the concave edge profile. In this pattern the stresses of highest magnitude at the surfaces are compressive stresses in the vertical direction, while in the centre of the ingot they are orientated in the rolling direction and are tensile. Thus deformation occurs by vertical compression near the surfaces, and by stretching in the rolling direction at the centre. At the edges the material is not constrained laterally; and due to the Poisson effect, the material spreads outward near the surfaces, and moves inward at the centre. The effect of certain variables on the edge profile were investigated with the modelling. The friction between the work-rolls and the ingot was found to have significant influence on the amount of lateral surface spread. Work hardening, strain rate and temperature effects in the material lead to variations in the yield stress through the height of the ingot. These effects were included in the modelling and were found to affect the shape of the profile, but to a lesser extent than the friction.

The novel Balanced Beam Tube Viscometer (BBTV), developed at the University of Cape Town, has been further developed and refined. Extensive work has been done in the following areas: (i) The effective length of the BBTV tubes. (ii) Interpretation of the data obtained using the BBTV in both the laminar and turbulent flow regimes. (iii) Comparison with the rotary type viscometer. Kaolin clay and uranium tailings slimes slurries of different particle size range and concentration have been successfully characterised by yield- pseudoplastic rheologies using the BBTV. The BBTV is in fact a miniature pipeline and it has been shown that it is capable of producing valid turbulent flow data and indicating the laminar/turbulent transition region in the two tube sizes .

Bibliography: pages 132-135. / In deriving asymptotic error estimates for a conforming finite element analyses of static thin elastic shell problems, the French mathematician Ciarlet (1976) proposed an approach to the formulation of such problems. The formulation he uses is based on classical shell theory making use of Kirchhoff-Koiter assumptions. The shell problem is posed in two-dimensional space to which the real problem, in three-dimensional space, is related by a mapping of the domain of the problem to the shell mid-surface. The finite element approximation is formulated in terms of the covariant components of the shell mid-surface displacement field. In this study, Ciarlet's formulation is extended to include the eigenvalue problem for the shell. In addition to this, the aim of the study is to obtain some indication of how well this approach might be expected to work in practice. The conforming finite element approximation of both the static and eigenvalue problems are implemented. Particular attention is paid to allowing generality of the shell surface geometry through the use of an approximate mapping. The use of different integration rules, in-plane displacement component interpolation schemes and approximate geometry schemes are investigated. Results are presented for shells of different geometries for both static and eigenvalue analyses; these are compared with independently obtained results.

Nanofluids are a novel class of heat transfer fluids in which nanoparticles are dispersed in traditional heat transfer fluids. They offer enhanced thermophysical, rheological and radiative properties. These enhancements have resulted in recent research being centred on the application of nanofluids to various systems. An example of such systems is the solar volumetric flow receiver in which great efficiency improvements have been reported. To explain this efficiency increase, researchers have evaluated the impact of enhanced radiative properties of nanofluids while largely neglecting that of enhanced thermophysical properties. This study looks at the impact of enhanced thermophysical properties on the performance of nanofluid-based solar volumetric receivers. Particular focus is drawn to the impact of temperature dependent conductivity and volumetric specific heat capacity. Copper oxide - water nanofluid is employed as its temperature dependent properties have been characterised. [Please note: this thesis file has been deferred until June 2016]

Bibliography: leaves 112-116. / The problem of the backreaction resulting from particle creation by black holes is examined from several vantage points. We first focus attention on the occurrence of the Berry phase in certain situations. This gives some insight into the geometry of quantum mechanics. Then we turn our attention to the analysis of quantum fields in black hole spacetimes. This brings us to the renormalisation of the stress- tensor via analytic methods. Finally, we draw on recent results to show how the Berry phase comes into play.

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