Browsing by Subject "Applied Mechanics"

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    Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells
    (1987) Eve, Robin Andrew; Reddy, B Daya
    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.
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    Numerical investigation of the edge profile in hot-rolling
    (1992) Veale, John; Mercer, Colin Douglas; Martin, J B
    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.
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    The rheological characterisation of non- Newtonian slurries using a novel balanced beam tube viscometer
    (1986) Slatter, Paul Thomas; Lazarus, J M
    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 .