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published_or_final_version / Civil Engineering / Master / Master of Philosophy

A finite element formulation for the shear-deformable analysis of beams, plates and shells, based on a strain energy expression defined in terms of total and flexural displacement components, is presented. The effects of transverse shear deformation are considered while the normal strain is neglected. The finite element representation requires independent descriptions of total and flexural displacement components. The flexural strain energy term involves second derivatives of flexural displacement component and thereby necessitates slope-compatible shape functions. This requirement is relaxed by adopting the 'discrete Kirchhoff' hypothesis for the flexural displacement component. An element of triangular shape is formulated for the analysis of laminated composite plates and shallow shells. Numerically exact integration is employed in the calculation of element stiffness matrix and corresponding load vectors. The resulting finite element possesses twelve degrees of freedom at each corner node of the triangle. Numerical results obtained for an extensive range of thickness and planform aspect ratios, laminate configurations, mesh sizes, edge conditions, types of loading and geometry of the structure demonstrate the efficacy of the finite element formulation. The element is applicable to a full range of thicknesss ratios. The present formulation is employed for dynamic and stability analysis of beams, as a precursor to the inclusion of these effects in the analysis of plates and shells.

The research work presented here deals with problems associated with finite element analysis of laminated composite thin-shell structures. The specific objective was to develop a thin shell finite element to model the linear elastic behavior of these shells, which would be efficient and simple to use by the practicing engineer. A detailed discussion of the issues associated with the development of thin shell finite element has been presented. It has been pointed out that the problems encountered with formulation of these elements stem from the need for satisfaction of the interelement normal slope continuity and the rigid body displacement condition by the assumed displacement functions. These difficulties have been surmounted by recourse to the discrete Kirchhoff theory approach and an isoparametric representation of the shell middle surface. A detailed derivation of the strain energy density in a thin laminated composite shell, based on a linear shear deformation theory formulated in a general curvilinear coordinate system, has been presented. The strain-displacement relations are initially derived in terms of the displacement and rotation vectors of the shell middle surface, and are subsequently expressed in terms of the cartesian components of these vectors to enable an isoparametric representation of the shell geometry. A three-node curved triangular element with the tangent and normal displacement components and their first-order derivatives as the final nodal degrees of freedom has been developed. The element formulation, however, starts with the independent interpolation of cartesian components of the displacement and rotation vectors using complete cubic and quadratic polynomials, respectively. The rigid-body displacement condition is satisifed by isoparametric interpolation of the shell geometry within an element. A convergence to the thin shell solution is achieved by enforcement of the Kirchhoff hypothesis at a discrete number of points in the element. A detailed numerical evaluation through a number of standard problems has been carried out. Results of application of the "patch test solutions" to spherical shells demonstrate a satisfactory performance of the element under limiting states of deformation. It is concluded that the DKT approach in conjunction with isoparametric representation results in a simple and efficient thin shell element.

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The silk fibres spun by insects and spiders have intrigued scientists for many years. Their mechanical performance is remarkable when one considers that the fibres are spun under ambient conditions from aqueous protein solutions without requiring many of the harsh processing conditions used in the production of man-made fibres. Yet, despite this interest, very little is known about the initial structure of the precursor proteins prior to spinning. One reason for this lies in the difficulty of handling the native proteins without accidental aggregation. Therefore in this thesis a novel sample preparation protocol for native silk is developed and small angle scattering (SAS) techniques are combined with circular dichroism (CD) and atomic force microscopy (AFM) to examine the structure and morphology of the proteins with different mechanical properties and thus biological function in nature. This work highlights the importance of studying native, functional proteins, at close to in vivo conditions, since clear differences in the structure and interaction of native and reconstituted silks can be attributed to the additional processing which reconstituted silks have undergone in order to be solubilised. Indeed native silk proteins are found to be more inherently non-interacting at quite high protein concentrations than reconstituted silk. Upon dilution, inter-chain interactions can be observed by SAS and CD as the protein is driven from its equilibrium conformation. This interaction and the shear-induced assembly of these proteins are also followed by AFM. Interestingly, native silk proteins from spider and silkworms retain a semiflexible conformation in solution. Indeed by comparing the silks from the major and minor ampullate, flagelliform and cylindriform glands of Nephila edulis with the cocoon silk of Bombyx mori silkworms, important insights are gained into how their flexibility suggests similarities in the local environment of the protein chains thereby dictating the hierarchical structure of silk fibres.

Research report submitted to the Faculty of Engineering and the Built Environment, University of Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering Johannesburg 2017 / This report investigates the seismic response of catenary vaults. Through a series of tests, the inherent seismic resilience of catenary vaults was assessed and a number of reinforcement strategies were investigated to improve this. An analytical model, based on the virtual work method, was developed by Ochsendorf (2002) for the assessment of circular voussoir arches. This model was adapted for catenary vaults. This model is used to calculate the minimum lateral acceleration required to cause the collapse of a catenary vault (λmin) for any catenary profile. The model indicates that there is a linear relationship between cross sectional depth of the arch and λmin until the depth to ratio passes approximately 0.3, where the change in λmin becomes exponential. Using the model, it is also predicted that λmin decreases exponentially with an increase in the height to width ratio up to a value of approximately 1.6. After this point λmin linearly decreases with increased height to width ratios and approaches zero. The first series of tests involved subjecting unreinforced catenary vaults to seismic loading. In these tests the frequency of vibration was varied and the stroke was kept constant. From the results of the tests, it was found that there was no frequency at which the vaults underwent excessive vibration due to resonance. It was observed that during seismic loading, hinges form at locations where pre-existing cracks occur despite the higher computed λmin values for these positions. The tests also indicate that the vaults’ behaviour changes drastically with each hinge that forms. In the next series of tests the frequency was set and the stroke was increased. The vaults were subjected to seismic loading at 2 Hz and 6 Hz, representative of low and high frequencies respectively. The tests indicated that the collapse acceleration of arches subjected to vibration at 2 Hz was lower than that of the vaults subjected to vibrations at 6 Hz. Despite this, the stroke, representing ground movement, required to cause collapse at 2 Hz was substantially higher than that of the 6 Hz tests. This indicates that the duration of load cycles has an effect on the collapse acceleration. In comparing the computed collapse acceleration, λmin, with the actual collapse accelerations, it was found that the computed values are highly conservative. Yet this is expected as the model is based on an infinite duration of lateral loading. It was found that the analytical model was more accurate for low frequency tests as compared to high frequency tests in terms of the predicted hinge locations. Finally, three reinforcement strategies were investigated using basalt fibre geogrid. This was found to be an economical and viable reinforcement material. The first strategy consisted of laying the geogrid over the arch and securing it at the arch base. The second was the same as the first with the addition of anchors which held the geogrid down. The final strategy involved prestressing the arch using the geogrid. The latter 2 methods were found to be the most effective, with observed collapse accelerations being over 60% higher than that of the same unreinforced arch. The anchorage solution was found to be the most viable due to the substantially higher technical input required for the prestressing solution. / MT2017

Photocopy of typescript. / Digitized by Kansas Correctional Industries

O presente trabalho relaciona-se à modelagem viscoelástica estrutural, objetivando-se a simulação numérica, com ênfase às estruturas de concreto. Faz-se, inicialmente, uma revisão dos modelos reológicos básicos unidimensionais para facilitar o entendimento das características intrínsecas da resposta viscoelástica das estruturas, tais como o fenômeno de fluência. Dentre as teorias que permitem levar em conta a idade do concreto no instante da aplicação do carregamento, são apresentadas a da hereditariedade e a do envelhecimento. Apresentam-se, em seguida, as funções de fluência e relaxação em notação apropriada à implementação numérica, combinada com o Método dos Elementos Finitos. Alguns aspectos da integração numérica das relações constitutivas ao longo do tempo são discutidos, com a apresentação, em particular, de um esquema de solução explícito fundamentado na Técnica dos \'Núcleos Degenerados\'. Finalmente, exemplos constituídos da análise de treliças planas ilustram a aplicabilidade dos modelos e procedimentos numéricos comentados. / The present work is related to structural viscoelastic modeling aiming numerical simulation, with emphasis on concrete structures. First of all, a revision of unidimentional basic reologic models is given, in order to enhance the inherent features of structural viscoelastic response, such as creep phenomenon. Among the theories able to consider the concrete age at the instant of loading, the hereditary and the aging theories are here presented. After that, the creep and relaxation functions are given in appropriate notation for numerical implementation, combined with the Finite Element Method. Some aspects of time numerical integration of constitutiva relations are discussed, mainly an explicit solution scheme based on the so called Degenerate Kernel Technic. Finally, examples consisting of plane trusses analysis illustrate the applicability of the models and numerical procedures commented.

"December 2004" / Includes bibliographical references. / 1 v. (various pagings) : / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / On understanding fundamental mechanisms that control the behaviour of composite structures. / Thesis (D.E.)--University of Adelaide, School of Civil and Environmental Engineering, 2005