The shape of an elastic boundary deformed by transmural pressure

Hoskin, Danny (2018) The shape of an elastic boundary deformed by transmural pressure. Masters thesis, University of East Anglia.

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Abstract

This thesis is an exploration of some problems involving flexible boundaries subjected to transmural pressure differences. During the thesis, we explore a few example problems with the common theme of finding the shape profile of these flexible boundaries. We begin with the problem of a cross section of an elastic tube that is subjected to a pressure difference between the inside and outside pressures. This chapter is based on Flaherty et al. [10], but is essential to the thesis as a whole as we use the structure here to define the governing equations for the flexible boundary that we will refer to throughout the rest of the chapters. We then look at these circular cross sections as a fluid annulus where we have fluid contained between two of these flexible boundaries, and this fluid flow causes the pressure differences. The thesis then takes the governing elastic equations (again with the transmural pressure differences) but instead of an enclosed ring, we have a setup where the boundary is fixed at two points. Interestingly here we discover the existence of non-symmetric solutions that have not been found before. The setup of the elastic boundary that is fixed is then extended by passing a flow across the elastic boundary to create the pressure differences, firstly as a weak flow perturbation analysis and then via numerical computation.

Item Type: Thesis (Masters)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Gillian Aldus
Date Deposited: 11 Jan 2019 10:05
Last Modified: 11 Jan 2019 10:05
URI: https://ueaeprints.uea.ac.uk/id/eprint/69553
DOI:

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