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A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering, August 2019 / An extension to classical lamination theory (CLT) is presented to analyse the natural fre- quencies and critical buckling loads of simply supported functionally graded plates. The variation of the through-thickness properties of the plate is governed by a power law which is subsequently represented by a polynomial series of su cient order and varies according to the law of mixtures or the Mori-Tanaka Homogenization method. The sti ness matrices are found, from which the position of the neutral plane is established which allows for the governing equations for the natural frequency and critical buckling load to be derived using the Rayleigh-Ritz method. The natural frequency and critical buckling loads are determ- ined for various volume indices, aspect and span ratios and the accuracy thereof is validated against 2D, 3D and quasi-3D solutions found in literature. A comparison with CLT found that the present study produces natural frequencies and critical bucking loads which are more accurate and which converge faster than CLT. / NG (2020)

Analytical expressions for the deflection surface of symmetrically loaded circular and annular plates resting on discrete point supports are derived. The formulation of the problem is based on classical small deflection plate theory. It is also assumed, in the formulation, that the supports are situated equal distances apart on a single concentric circle. There is no restriction placed on the number of supports or on the size of the support circle which could be as large as the plate itself or as small as the size of the hole of the annular plate. The singularity effects associated with the concentrated supports on the plate problems considered here are accounted for in the solution, by drawing an analogy from the Michell's solution to a clamped circular plate subjected to an eccentric point load. This procedure yields solutions in much more suitable form for practical numerical problems than other known methods. In the case of circular plates on multipoint supports, explicit solutions are given to a number of loading conditions. Solutions to a uniformly loaded circular plate on multipoint supports are compared with the published experimental results; the conclusions are favorable. From the numerical data obtained for a uniformly loaded circular plate on multipoint supports, a procedure is outlined for obtaining contour maps of deformed uniformly loaded plates with discrete supports on two support circles. Solutions to annular plates on multipoint supports are derived for the first time. By utilizing this result, design charts are drawn to indicate the optimum size of the support circle, which would produce least peak-to-peak displacements for any given size of hole, and a specified number of supports. Contour maps associated with annular plates on three point supports are also drawn to illustrate the influence of support circle on the displacements. It was found that when there are a fewer number of supports and/or the size of the hole is small, the magnitude of peak-to-peak displacements and the size of the optimum support circle are considerably different from the associated quantities when the support is a continuous ring. / Ph. D.

The theory proposed in this thesis is an attempt to bridge the gap that exists between the linear and nonlinear theories of Elasticity. The theory is applied to the solution of a hubbed, clamped, circular plate made of polyurethane whose hub is subjected to a "large" axi~symmetrioc twist. This particular problem is attacked in the conventional manner of the generalized plane stress problem of linear elasticity. However, the strain displacement relations are formulated in the Eulerian manner and the displacement gradients are not assumed to be small. In addition, a more general stress~strain relationship than the conventional Hookean form is assumed. The solution is checked by experiment; and in addition, three auxiliary problems; the uniaxial compression problem, the uniaxial tension problem, and a shear problem are checked experimentally to further cheek the validity of the proposed theory when applied to the finite strain response of polyurethane. / Ph. D.

The objective of the study was to develop a modeling technique to idealize thin, orthotropic plates into an equivalent grid, suitable for the matrix-displacement method of analysis. The formulation is an alternative to the classical plate theory and finite element method. The grid model is unique compared to other grid formulations in its applicability to plates exhibiting material orthotropy in addition to isotropy and shape orthotropy. Further, the grid model has less members compared to the previous grid formulations. A function was developed to establish the grid member cross-sectional size for various boundary conditions and material properties. The maximum error between predicted and published theoretical and experimental deflections was 3% for plates in isotropic and advanced composite materials. The maximum error between predicted and experimental deflections for wood based composite plates was 20%. / Master of Science

From the results of the cases discussed, it can be concluded that the neglect of transverse-shear deformation and normal stress results in expressions for bending moments and deflection which may be seriously in error. / / Master of Science

The strength and behavior of gusset plates in buckling is evaluated herein based on data from the experimental investigations conducted by other researchers and the analytical work presented herein. A set of design guidelines has been recommended through the review of the current practice. Representative single and double brace gusset plates normally adopted for connections with compressive bracing/diagonal members in braced frames and trusses, were modeled and analyzed using linear and nonlinear finite element methods to determine the buckling loads. The buckling analysis data along with the test data indicated the occurrence of inelastic buckling of the gusset plates. Current design practice and a set of formulas for determination of gusset plate thickness have been reviewed. A set of guidelines has been recommended for the design and evaluating gusset plate buckling loads.

published_or_final_version / Civil and Structural Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy