A bar cell in the form of an isosceles trapezoid suitable for solution of two dimensional problems is introduced involving two new concepts, one that of overlapping bars and the other of a variable angle parameter. Based on the Identity of corner displacements of the cell and a similarly shaped piece of plate in conditions of uniform stress, expressions for the bar areas are derived in terms of Poisson's ratio, the geometry of the cell and a variable angle parameter. The stiffness matrix of the cell is derived further by combining different displacement modes. Two methods of calculating stresses, one by the nodal displacements and the other by the nodal force concentrations, are described. Two examples involving a rectangular plate and a partial sector of a circular plate illustrate the application of the finite element method using trapezoidal bar as well as no-bar cells and their results are compared with the exact elasticity solution. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Molluscan shells show great diversity in colour, which is due to many different classes of chemical compounds. The identification of the pigments found in the molluscan shells of a diverse group of marine species was done in situ using Resonance Raman spectroscopy, and found to be unsubstituted polyacetylenes. Two South African species (D. serra and J. janthina) were chosen for extraction of the pigment-containing organic component, and it was found that the vibrational bands in the Raman spectra of the extracted component shifted relative to that obtained in the molluscan matrix, indicating structural changes in the pigmentary molecules upon extraction. Published correlations were used to evaluate the possible length of the conjugated chain, and a new correlation was established using previous reported data. The conjugated chain length predicted from the new correlation of the studied pigmentary molecules ranges between ten and twelve double bonds. Copyright 2011, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. Please cite as follows: Barnard, W 2006, A spectroscopic investigation of polyacetylenic molecules in the molluskan biogenic matrix, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-06262008-114600 / > E216/ag / Dissertation (MSc (Chemistry))--University of Pretoria, 2008. / Chemistry / unrestricted

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An analysis is presented of the linear and geometrically nonlinear static response of "thin" doubly-curved shells of revolution, under internal pressure loading. The analysis is based upon direct numerical integration of the governing differential equations, written in first-order state vector form. It is assumed that the loading and response of the shell are both axially symmetric; the governing equations are thus ordinary differential equations. The geometry of the shell is limited in the analysis by the assumptions of axisymmetry and constant thickness. The shell is allowed to have general composite laminate construction, elastic supports at the edges and internal ring stiffeners. In addition, the analysis allows for the possibility of circumferential line loads at discrete locations along the dome meridian. The problem is a numerically unstable two-point boundary value problem; integrations are performed using the technique of multiple shooting. A development of the multiple shooting technique known as stabilized marching is given. Results achieved by use of the multiple shooting technique are verified by comparison to results of finite element analysis using the finite element analysis codes STAGS and ABAQUS. Parametric studies are performed for ellipsoidal domes constructed of symmetric, 8-ply laminates. The parametric studies examine the effects of dome geometry for a quasi-isotropic laminate first, then examine whether material properties may be adjusted to create a "better" design. Conclusions and recommendations for future work follow. / Ph. D.

Crosslinked polymers or elastomers are examples of soft, synthetic material that can bend, crease, snap, wrinkle in response to external stimulus like pH, humidity, electric field or swelling. If a droplet of favorable solvent is placed on top of a thin, elastomer beam, it bends drastically to accommodate the excessive swelling stress. Keeping the solvent and its volume constant if we just increase the thickness of the beam, microscopic surface creases appear on the top surface. In this thesis, we experimentally characterize this transition between global bending to surface creasing. Closing of Venus flytrap leaves is a classic example of well known snap-through instability. A knowledge of the timescale of snapping is crucial in designing advanced functional materials. We perform the simplest experiment of poking an soft, elastomer arch at its apex till it snaps. Combining our experiments with analytical model we are able to predict the purely geometric nature of the snapping timescale. We also develop a simple scaling law that captures the dynamics of jumping toy poppers. / Master of Science

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Improvements to isogeometric blended shells are introduced which blend traditional Reissner-Mindlin shells, and Kirchhoff-Love shells, with an exact interpolation of the shell director increment. A gradient extraction operator is introduced which allows derivatives of basis functions to be exactly expressed as a linear combination of the basis functions themselves. Several benchmarks are investigated and the new blended shell is compared with different shell elements in ABAQUS and NASTRAN. In addition, the effect of different quadrature schemes is included in the comparisons. The new isogeometric blended shell performs comparably in some benchmarks, and even outperforms commercial shell finite elements in some benchmarks. Future improvements to the formulation are discussed.