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Graduation date: 2000

No description available.

No description available.

This research focuses on improvements and application of 1D finite elements for nonlinear dynamic analysis of reinforced concrete frames under extreme loadings. The concept of force interpolation is adopted for the element formulation and a solution scheme developed based on a total secant stiffness approach that provides good convergence characteristics. The geometrical nonlinearities including 2nd order P-Delta effects as well as catenary action are considered in the element formulation. It is shown that geometrical nonlinearities may have a significant effect on member (structure) response within extreme loading scenarios. In the analysis of structures subjected to extreme loadings, accurately modelling of the post peak response is vital and, in this respect, the objectivity of the solution with softening must be maintained. The softening of concrete under compression is taken into account, and the objectivity preserved, by adopting a nonlocal damage model for the compressive concrete. The capability of nonlocal flexibility-based formulation for capturing the post-peak response of reinforced concrete beam-columns is demonstrated by numerical examples. The 1D frame element model is extended for the modelling of 3D framed structures using a simplified torque-twist model that is developed to take account of interaction between normal and tangential forces at the section level. This simplified model can capture the variation of element torsional stiffness due to presence of axial force, bending moment and shear and is efficient and is shown to provide a reasonable degree of accuracy for the analysis of 3D reinforced concrete frames. The formulations and solution algorithms developed are tested for static and dynamic analysis of reinforced concrete framed structures with examples on impact analysis of beams, dynamic analysis of frames and progressive collapse assessment of frames taken from the literature. The verification shows that the formulation is very efficient and is capable of modelling of large scale framed structures, under extreme loads, quickly and with accuracy.

ABSTRACT The quest to model wave propagation in various physical systems has produced a large set of diverse nonlinear equations. Nonlinear singular integro-differential equations rank amongst the intricate nonlinear wave equations available to study the classical problem of wave propagation in physical systems. Integro-differential equations are characterized by the simultaneous presence of integration and differentiation in a single equation. Substantial interest exists in nonlinear wave equations that are amenable to the Inverse Scattering Transform (IST). The IST is an adroit mathematical technique that delivers analytical solutions of a certain type of nonlinear equation: soliton equation. Initial value problems of numerous physically significant nonlinear equations have now been solved through elegant and novel implementations of the IST. The prototype nonlinear singular integro-differential equation receptive to the IST is the Intermediate Long Wave (ILW) equation, which models one-dimensional weakly nonlinear internal wave propagation in a density stratified fluid of finite total depth. In the deep water limit the ILW equation bifurcates into a physically significant nonlinear singular integro-differential equation known as the 'Benjamin-Ono' (BO) equation; the shallow water limit of the ILW equation is the famous Korteweg-de Vries (KdV) equation. Both the KdV and BO equations have been solved by dissimilar implementations of the IST. The Modified Korteweg-de Vries (MKdV) equation is a nonlinear partial differential equation, which was significant in the historical development of the IST. Solutions of the MKdV equation are mapped by an explicit nonlinear transformation known as the 'Miura transformation' into solutions of the KdV equation. Historically, the Miura transformation manifested the intimate connection between solutions of the KdV equation and the inverse problem for the one-dimensional time independent Schroedinger equation. In light of the MKdV equation's significance, it is natural to seek 'modified' versions of the ILW and BO equations. Solutions of each modified nonlinear singular integro-differential equation should be mapped by an analogue of the original Miura transformation into solutions of the 'unmodified' equation. In parallel with the limiting cases of the ILW equation, the modified version of the ILW equation should reduce to the MKdV equation in the shallow water limit and to the modified version of the BO equation in the deep water limit. The Modified Intermediate Long Wave (MILW) and Modified Benjamin-Ono (MBO) equations are the two nonlinear singular integro-differential equations that display all the required attributes. Several researchers have shown that the MILW and MBO equations exhibit the signature characteristic of soliton equations. Despite the significance of the MILW and MBO equations to soliton theory, and the possible physical applications of the MILW and MBO equations, the initial value problems for these equations have not been solved. In this thesis we use the IST to solve the initial value problems for the MILW and MBO equations on the real-line. The only restrictions that we place on the initial values for the MILW and MBO equations are that they be real-valued, sufficiently smooth and decay to zero as the absolute value of the spatial variable approaches large values.

The last decade has seen significant advances in the development of Vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs). The emergence of enabling technologies, in addition to the practical usefulness of such systems has driven their development to a point where numerous technology demonstrators and commercial products are now in existence. Of particular interest has been the development of small scale, VTOL UAVs commonly referred to as mini and micro-VTOL UAVs. The versatility and agility of such vehicles offers great potential for the use in clustered, urban environments. Despite recent advancements, the autonomous navigation of VTOL UAVs remains a very challenging research area. The dynamics of VTOL UAVs are heavily nonlinear, underactuated and non-minimum phase. This, coupled with the aggressive maneuvers that such vehicles are expected to execute provides a stimulating problem in dynamic control. This is particularly true in the case of micro-VTOL UAVs. The fast, nonlinear nature of these systems render classical, linear control approaches inadequate. The past twenty years has seen great interest in the development of nonlinear control strategies. This has led to the emergence of a number of standard design tools, most notably feedback linearisation and Lyapunov-based, backstepping approaches. Such design techniques offer a framework for the derivation of model based control laws capable of achieving global stabilisation and trajectory tracking control for heavily nonlinear systems. Recently, there has been significant interest in the application of such nonlinear control paradigms for the stabilisation and control of VTOL UAVs. The aim of this thesis is to further the application and analysis of nonlinear control design techniques for the control of VTOL UAVs. In particular, focus is placed on Lyapunov-based, backstepping-type control approaches. The first half of this thesis investigates Lyapunov-based control strategies that cast the closed-loop VTOL dynamics into a globally stable, cascade structure. This work was directly inspired by, and builds on, a variety of previously published works. Firstly, an alternative design approach to that previously published is presented, resulting in an improved closed-loop dynamic structure. Although inspired by the VTOL system, this idea may be generalised for the control of a broad class of systems, and is presented as such. A singularity issue arising in the cascade control of VTOL vehicles is then investigated, and a novel approach to overcome this issue is formulated. The second half of this thesis is dedicated to the trajectory tracking control of VTOL UAVs at velocities where the influence of aerodynamics is significant. In general, the aerodynamic models of VTOL UAVs are heavily nonlinear and poorly known. The use of such models in a backstepping framework that uses explicit differentiation of these models for dynamic inversion is questioned, due to the potential sensitivity of such nonlinear models. Consequently, an alternative approach utilising coupled filters to avoid such sensitivity issues is proposed. All control designs formulated in this thesis are accompanied by proofs guaranteeing their global stability, and numerical simulations demonstrating their time domain response characteristics. / http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1298413 / Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 2007

Nonlinearities exist in all process control systems. The use of linear control techniques is valid only in a narrow range of operation. Therefore, in this thesis, multivariable nonlinear control techniques are considered. The target process is the single effect evaporative process of the liquor burning unit in Alcoa's alumina refinery in Kwinana and the proposed triple effects unit in the Wagerup refinery. Two types of nonlinear control strategies using differential geometry were studied, namely, the input output linearization (Kravaris and Soroush, 1990) and the input state linearization (Hunt et al, 1983a). The research has successfully demonstrated the superiority and simplicity of the nonlinear controller through simulations and plant implementations. An integrated software package using MAPLE V.3 as the computing environment was developed to automate the solution algorithms and to graphically simulate the closed loop dynamics of different processes using the two nonlinear control strategies.The issue of robustness of the nonlinear controller was addressed by developing a procedure called uncertainty vector adjustment. The effectiveness of the new strategy was successfully demonstrated on the simulated liquor burning process. Furthermore, the stability of the adjustment technique was proved and its theoretical bounds were established using Lyapunov function analysis.A comparative study of geometric nonlinear filter and extended Kalman filter was conducted to reduce the requirement of full state feedback necessary for nonlinear control using either input output linearization or input state linearization. The simulation of the single effect evaporation unit of the liquor burning process showed that the geometric nonlinear filter is superior to the extended Kalman filter in terms of nonlinear tracking performances.The plant trials of the input output linearization ++ / in Alcoa's Kwinana alumina refinery demonstrated the practicability and feasibility of implementing nonlinear control in an industrial setting and also fostered a closer gap between academia and industry. The trials established guidelines for implementing a global linearizing controller on site, including conversion of the relevant constraints and the output of an industrial proportional and integral controller to the equivalent proportional and integral action required by the nonlinear controller. The results showed that the performance of the nonlinear controller was better than the current linear controller on site in terms of responsiveness and resistance to disturbances. Hence, the nonlinear control strategy enables the process to settle faster.All in all, efforts have been made in this thesis to minimise the use of abstract mathematical language and, in some cases, simplify the language so that nonlinear control theory can be understood by a wider range of audience, especially industrial practitioners. It is hoped that the insights provided in the dissertation will encourage more industrial implementations of nonlinear controllers and forge more interaction to close the widening gap between academic and industrial practice in process control.Keywords: nonlinear control, differential geometry, symbolic algebra, evaporator process, uncertainty vector adjustment, geometric nonlinear filter.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (leaves 111-116).

Thesis (Ph. D.)--University of Adelaide, Dept. of Applied Mathematics, 1987. / Includes bibliographical references (leaves 70-72).