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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)

This thesis presents a study of two basic modes of deformation of a thin sheet: wrinkling and crumpling, viewed primarily in the context of an elastic sheet confined by capillary forces on a drop of liquid. First, it provides a brief conceptual background in the relevant physics of thin sheet mechanics and capillarity and introduces the general principles of wrinkling and crumpling. The problem of confining a circular sheet on an increasingly curved spherical drop is presented as a vehicle to explore these principles. At finite curvature, the sheet is seen to wrinkle around its outer edge. At large confinement, characteristic features of crumpling gradually dominate the pattern. The experimental observations in both regimes are analyzed separately. Analysis of images of the sheet in the wrinkled regime yield data for the number and length of the wrinkled zone, as a function of the experimental control parameter, the pressure. The length of the wrinkles is correctly described by a far-from-threshold theory, which describes a limiting regime in thin-sheet mechanics, distinguished by high 'bendability'. The validity of this theory is verified by the data for highly bendable, ultrathin sheets for the first time. The theory is based on the assumption that the wrinkles completely relax compressive stresses and therefore preserve the cylindrical symmetry of the stress field. The emergence of crumpling from the wrinkled shape is explored via evolution of visible features in the sheet as well as gaussian curvature measurements obtained by analyzing height maps from optical profilometry. The emergence of several length scales, increasing asymmetry in curvature distribution, the failure of wrinkle extent prediction and formation of d-cones associated with crumpling are all measured to locate the transition to a crumpled state. The value of gaussian curvature at the center of the sheet appears to follow the cylindrically symmetric prediction over the whole range of the experiment, suggesting that the onset of crumpling events does not affect the global shape of the sheet. Finally, analogous wrinkling and crumpling behavior of particle-laden interfaces is discussed. The spontaneous formation of conical defects in a curved 2D crystal is compared to the crumpling of a sheet on a drop, and insight from thin sheet mechanics is applied to the mysterious wrinkling of particle rafts. Some future directions for measuring wrinkling of sheets on negative curvature surfaces and deformations of fluid interfaces are proposed.

<p> This thesis deals with the analytical and experimental study of buckling strength, of thin walled channel struts, of different geometrical dimensions. The influence of the dimensions of the columns on the buckling strength has been studied.</p> <p> The experimental work consisted of testing different channels of thin sheeting to failure. Comparison has been made with the previous work done and a comparison is made between the theoretical predicted values and the experimental results. The Appendix includes detailed mathematical procedure and matrices formulations.</p> / Thesis / Master of Engineering (MEngr)

<p> A report follows in which five different conditions of support of stepped crane columns were investigated. In each case the curvature or moment equations representing the column in its just-buckled condition are determined. The general solution of each differential equation is then found and solved in terms of the boundary conditions to obtain a transcendental equation which gives the critical buckling length. This transcendental equation is solved for the lowest possible value to get the critical buckling length. This lowest value is compared to the Euler critical buckling value in order to get the effective length factor.</p> / Thesis / Master of Engineering (MEngr)

No / This paper presents the buckling behaviour and design of axially loaded concrete filled steel elliptical hollow sections. The experimental investigation was conducted using normal and high strength concrete of 30, 60 and 100 MPa. The current study includes both the stub and slender column tests. Based on the existing design guidance in Eurocode 4 for composite columns, the proposed design equations were found to provide an accurate and consistent prediction of the cross section and buckling capacity of the composite concrete filled steel elliptical hollow sections in axial compression.

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Several rubber diaphragms, of the same type used inside an hydraulic accumulator, failed a short time after they were mounted. While there is nothing special with these failures the cost, in some cases can be high. A closer look, at the damaged diaphragms reveal an interesting nonsymmetric radial deformation accompanied in some cases by cracks. Most of the analyses regarding the failures of rubber diaphragms offer explanations only from a chemical or material science point of view. We propose in this thesis a new perspective from a mechanical-structural engineering view. Therefore the main goal of the thesis is to investigate the deformation of a diaphragm and based on this analysis to propose an explanation for formation of the cracks. It is shown that the analysis of the diaphragm problem leads to a pseudo-nonconservative system and involves a buckling, a post buckling (dynamic snap-through), an eversion, and a load response analysis. The problem is approached numerically using the nite element method. The character of pseudo-nonconservativeness of the system requires, in this case, an update of the tangent stiffness matrix with a certain stiffness correction. This new correction is proposed also. The result is valid not only for this particular problem but for the entire class of problems to which the diaphragm belongs. This correction is implemented in an existing nite element program (NIKE3D) and used to analyze the diaphragm deformation. The results indicate that under the typical load condition for a diaphragm a certain deformation pattern occurs, and this can lead to the formation of cracks. This deformation matches extremely well with the actual deformed shape of a typical failed diaphragm. It is shown that the deformation pattern depends on the structural properties of the diaphragm rather than on the magnitude of the applied load. The nonsymmetry in the diaphragm deformation and the difference in the crack development is explained also. / Ph. D.

Shallow light penetration in tissue has been a technical barrier to the development of photothermal therapies for cancers in the epithelial tissues and skin. This problem can potentially be solved by utilizing minimally invasive probes to deliver light directly to target areas potentially > 2 mm deep within tissue. To develop this solution, fiber optic microneedles capable of delivering light for therapy were manufactured. We have manufactured fiberoptic microneedles by tapering silica-based optical fibers employing a melt-drawing process. These fiberoptic microneedles were 35 to 139 microns in diameter and 3 mm long. Some of the microneedles were manufactured to have sharper tips (tip diameter < 8 microns) by changing the heat source during the melt-drawing process. All of the microneedles were individually inserted into ex vivo porcine skin samples to demonstrate the feasibility of their application in human tissues. Skin penetration experiments showed that sharp fiber optic microneedles with a minimum average diameter of 73 microns and a maximum tip diameter of 8 microns were able to penetrate skin without buckling. Flat microneedles, which had larger tip diameters, required a minimum average diameter of 125 microns in order to penetrate through porcine skin samples. Force versus displacement plots showed that a sharp tip on a fiber optic microneedle decreased the skin's resistance during insertion. Also, the force acting on a sharp microneedle increased more steadily compared with a microneedle with a flat tip. Melt-drawn fiberoptic microneedles provided a means to mechanically penetrate dermal tissue and deliver light directly into a localized target area. We also described an alternate fiberoptic microneedle design with the capability of delivering more diffuse, but therapeutically useful photothermal energy using hydrofluoric acid etching of optical fibers. Microneedles etched for 10, 30, and 50 minutes, and an optical fiber control was compared for their ability to deliver diffuse light using three techniques. First, red light delivery from the microneedles was evaluated by imaging the reflectance of the light from a white paper. Second, spatial temperature distribution of the paper in response to near-IR light (1,064 nm, 1 W, CW) was recorded using infrared thermography. Third, ex vivo adipose tissue response during 1,064 nm, (5 W, CW) irradiation was recorded with bright field microscopy. Increasing etching time decreased microneedle diameter (from 125 to 33 microns), resulting in increased uniformity of red and 1,064 nm light delivery along the microneedle axis. For equivalent total energy delivery, microneedles with smaller diameters reduced carbonization in the adipose tissue experiments. However, thin fiberoptic microneedles designed to minimize tissue disruption and deliver diffuse therapeutic light are limited in their possible clinical application due to a lack of mechanical strength. Fiberoptic microneedles have been embedded in an elastomeric support medium (polydimethylsiloxane, PDMS) to mitigate this issue. The critical buckling force of silica microneedles with 55, 70, and 110 microns diameters and 3 mm length were measured with and without the elastomeric support in place (N = 5). Average increases in the mechanical strength for microneedles of 55, 70, and 110 microns diameters were measured to be 610%, 290%, and 33%, respectively. Aided by mechanical strengthening through an elastomeric support, microneedles with 55 microns diameter were able to repeatedly penetrate ex vivo porcine skin. / Ph. D.