Browsing by Subject "Geometric"
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Item Measurement of internal and external geometric imperfections of lined pipes(2015-05) Harrison, Benjamin Duncan; Kyriakides, S.; Liechti, KennethCarbon steel pipe is often lined with a thin layer of non-corrosive material to protect it against corrosion from sour hydrocarbons. The product is commonly assembled by mechanical expansion of a liner shell bringing it into contact with the inner surface of a seamless steel pipe. During installation and operation, lined pipelines can experience bending or compressive deformations large enough to cause the liner to buckle and collapse inside an intact outer pipe. It has been demonstrated that such buckling instabilities are very sensitive to small initial geometric imperfections in the liner. Liner imperfections in 8- and 12- inch lined pipes have been measured using custom scanning devices and have been characterized by trigonometric Fourier series. These measurement schemes revealed that the imperfection geometry is dominated by imperfections in the circumferential direction, whereas axial imperfections are of relatively small amplitude and short wavelength. Imperfection amplitudes were determined to be on the order of 0.2% of the OD for both pipes studied. Liner geometry of the 8-inch pipe can be approximated as a shape, and the 12-inch pipe can be approximated as a shape. In general, the imperfection geometry of the interior surface follows that of the exterior surface, presumably due to the nature of the manufacturing process. The main source of the imperfections is from the piercing, rolling, and external finishing of the carrier pipe. Following the expansion process by which the liner is installed, interior surface imperfection of the carrier pipe is “transferred” to the liner. Overall, the interior surface is found to more imperfect than the exterior. Finite element models of a 12-inch lined pipe that incorporate liner imperfections defined by the results from this study demonstrate their detrimental effect on liner wrinkling and collapse.Item Power series coefficients of some classical functions(Texas Tech University, 2006-08) Williams, Alexander S.; Barnard, Roger W.; Pearce, Kent; Solynin, Alexander Y.; Williams, BrockIn this thesis we consider several problems pertaining to extremal conditions arising in Geometric Function Theory. First, we extend the known extremal conditions of a particular function space to a slightly more general space and determine the condition of equality. Next, we discuss the current status of the Krzyz conjecture with a new observation. In the following chapter, we develop a mechanism to translate an extremal function of one space into another space and apply it to a special case of the Krzyz conjecture. The last chapter of the paper is devoted to discussing the current status of Brannan's conjecture with some observations that might lead to its proof.