Analysis of dielectric straight bending waveguides has been a difficult problem in the past. Traditionally the task for computing bending of optical waveguides is carried out by the beam propagation method (BPM). However, due its assumptions on one-way propagation and paraxial approximation, BPM is unable to consider the reflection of dielectric straight-bent waveguides when the bending angles are large. In a straight-bent waveguide, two coordinate systems are needed to fully describe the ongoing complex scattering process in the transition region of the waveguide. It is extremely hard to analyze such an unbounded problems with two incompatible coordinate systems even for those general-purpose methods like the finite-difference, finite-element. In this thesis, we use the analytic continuity method (ACM) to deal with the boundary conditions that both the tangential electromagnetic field components must be continuous across the bending line. This method can handle the mismatch of two coordinate systems and decrease the amount of calculation and error for small bending angles. From the two coupled integral equation we can derive matrix equation via Galerkin least squared error method. The main part of this thesis contains the derivation of the approximate formula of the transmission and reflection matrices (scattering matrices) for a micro-bent waveguide. We show numerical results of various two-corner bends using cascading of these scattering matrices.

Present day optical integrated circuits contain many continuously bending waveguides making it important to study EM field profiles of bending waveguides. The mostly widely used numerical method for analyzing bending waveguides is the beam propagation method (BPM). Although it can calculate very fast, BPM results are not accurate enough in many wide-angle applications due to BPM¡¦s intrinsic paraxial approximation. Recently, full-wave based finite-difference time-domain technique has become quite popular and has been used to study many optical devices. Unfortunately it can not be used to study smoothly bending waveguides due to huge computational resource requirements needed for these large optical devices. In the absence of reflection in a bending waveguide, other one way, wide-angle methods can be applied. In this thesis we propose two such methods to analyze different kinds of bending waveguides. We use full eigen-mode expansion technique (FEMET) when reflection is negligible. In cases where reflection is strong, we propose a cylindrical couple transverse-mode integral-equation (C-CTMIE) to do the job. Both FEMET and CTMIE methods are built on complete sets of circular layered modes of the underlying structure. These modes are not easy to solve because the standard cylindrical mode solver requires extensive references to Bessel functions of complex arguments and orders. Here in this thesis, we proposed to expand cylindrical layered modes from planar layered modes of an equivalent structure. In essence, we renormalize the existing planar layered waveguide modes and turn them into desired circular layered modes. We show that using a matrix eigenvector formulation, this relatively simple technique is not only quite fast but also produces very accurate results. Finally using these circular modes various S-bend waveguides are analyzed. We also present a design to minimize the radiation loss of a circular waveguide using whisper gallery modes.

Many waveguide components in the integrated optics are built with bending structures, such as Y-branches, couplers, tapered waveguides, etc. The bending angles are getting larger and larger in order to fill into a smaller integrated optical circuit. The influences of wide bending angles are no longer ignorable. Commercially available beam-propagation method (BPM) design tools are inadequate for simulating and optimizing the problem we consider. These include tightly curved waveguide sections, reflection/transmission from slanted end facets and U-turn reflectors. In this thesis, we applied the coupled transverse-mode integral-equation (CTMIE) formulation and mode matching method to study the field distribution in a 2-dimentional rectangular waveguide structure with perfect boundary conditions. The problem is first separated into parts and then converted into a block-diagonal matrix equation. By considering the symmetry of the bending structures, the original problem is broken down to two smaller problems each with it¡¦s own boundary conditions. The combined solutions provide the desired results.

No description available.

This thesis documents the development of a computational method for wave induced longitudinal bending in ships. First, there will be a discussion about the importance of longitudinal bending in ship design. The paper will then outline the basic physics at work in the system. It will review the wave forcing computation as well as the response of the vessel. It will then document the progression of the program, which was constructed in Fortran 90, as it solves the linear differential equation for the vessel bending caused by an incoming wave. The entire program then appears at the end of the paper. While the current program is not complete the theory behind it is valid and the code can be augmented to include non-linear components in the future.

No description available.

No description available.

No description available.

No description available.

Research Doctorate - Doctor of Philosophy (PhD) / Masonry walls will almost invariably be required to resist lateral out-of-plane loads due to the action of wind or earthquakes; less commonly walls may be subjected to water or earth pressure or blast loading. Of particular interest is the common case which arises when the walls are supported on two or more adjacent edges. Under these conditions the masonry is subjected to a complex state of biaxial (two-way) out-of-plane bending combined with vertical in-plane compression due to the self weight of the wall and any superimposed loads. Different approaches currently exist for the design of masonry wall panels subjected to out-of-plane loads. However, these approaches are all empirical and often yield widely varying design recommendations and there has been significant criticism by proponents of the different methods regarding the use of alternative approaches. In this study an extensive program of laboratory testing in parallel with numerical analysis was conducted to examine the bending, biaxial bending in particular, behaviour of masonry walls. The aim was to provide a better understanding of the behaviour at the fundamental level towards ultimately developing a fully rational biaxial-bending failure model that can predict behaviour under any simultaneous combination of bending moments in the two principal directions, along with a superimposed compression force on the bed joints. Experimentally, 'single joint' four brick unit specimens were studied comprehensively, using a newly commissioned test rig, by subjecting them to various vertical and horizontal bending moments both separately and in combinations, along with a superimposed compression force on the bed joints. These tests provided important information about the flexural behaviour of mortar joints and the torsional behaviour of bed joints. In addition, a complete set of characterization tests was also performed to study the fundamental material properties of masonry, which were important input parameters in the numerical modelling. Numerically, a 3D non-linear finite element micro-model with cohesive contact was proposed and implemented in the ABAQUS/Standard software package. Numerical viii analyses were performed to provide rational explanations to the bending behaviours observed in the four brick unit specimen tests and evaluate a newly proposed torsion shear test method. A simplified 3D non-linear finite element micro-model was also proposed to simulate the bending behaviour of small walls. Its effectiveness was clearly demonstrated in its application to masonry walls, with or without openings, subjected to both in-plane and out-of-plane loads.