[Truncated abstract] The study reported in this thesis extends the scaled boundary finite-element method to firstorder and second-order wave diffraction problems. The scaled boundary finite-element method is a newly developed semi-analytical technique to solve systems of partial differential equations. It works by employing a special local coordinate system, called scaled boundary coordinate system, to define the computational field, and then weakening the partial differential equation in the circumferential direction with the standard finite elements whilst keeping the equation strong in the radial direction, finally analytically solving the resulting system of equations, termed the scaled boundary finite-element equation. This unique feature of the scaled boundary finite-element method enables it to combine many of advantages of the finite-element method and the boundaryelement method with the features of its own. ... In this thesis, both first-order and second-order solutions of wave diffraction problems are presented in the context of scaled boundary finite-element analysis. In the first-order wave diffraction analysis, the boundary-value problems governed by the Laplace equation or by the Helmholtz equation are considered. The solution methods for bounded domains and unbounded domains are described in detail. The solution process is implemented and validated by practical numerical examples. The numerical examples examined include well benchmarked problems such as wave reflection and transmission by a single horizontal structure and by two structures with a small gap, wave radiation induced by oscillating bodies in heave, sway and roll motions, wave diffraction by vertical structures with circular, elliptical, rectangular cross sections and harbour oscillation problems. The numerical results are compared with the available analytical solutions, numerical solutions with other conventional numerical methods and experimental results to demonstrate the accuracy and efficiency of the scaled boundary finite-element method. The computed results show that the scaled boundary finite-element method is able to accurately model the singularity of velocity field near sharp corners and to satisfy the radiation condition with ease. It is worth nothing that the scaled boundary finite-element method is completely free of irregular frequency problem that the Green's function methods often suffer from. For the second-order wave diffraction problem, this thesis develops solution schemes for both monochromatic wave and bichromatic wave cases, based on the analytical expression of first-order solution in the radial direction. It is found that the scaled boundary finiteelement method can produce accurate results of second-order wave loads, due to its high accuracy in calculating the first-order velocity field.
| Identifer | oai:union.ndltd.org:ADTP/221436 |
| Date | January 2007 |
| Creators | Li, Boning |
| Publisher | University of Western Australia. School of Civil and Resource Engineering |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Copyright Boning Li, http://www.itpo.uwa.edu.au/UWA-Computer-And-Software-Use-Regulations.html |
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