The available experimental evidence demonstrates the extreme nonlinear material behaviour of reinforced concrete structures. These nonlinear effects are attributed to the collective behaviour of the constituent materials in addition to factors such as cracking, crushing, aggregate interlock, creep, shrinkage, bond slip and rate of loading. Analytical methods have been improved in the past two decades as a result of the availibility of more powerful computers. It is, therefore, feasible to model these nonlinear features in order to conduct an analysis of the behaviour of reinforced concrete structures. The present research is concerned with some of these nonlinear effects. These include the formulation of a constitutive model for the three-dimensional stress-strain relationships of concrete and the mathematical modelling of cracked and crushed concrete. The proposed models have been implemented into a finite element system for the analysis of reinforced and pre-stressed concrete structures. Chapter One is a general introduction to structural nonlinearities and the finite element method. The structure of the thesis is also outlined. Chapter Two reviews available theoretical approaches used for the formulation of the concrete behaviour and assesses their relative advantages. The theory of plasticity is discussed in greater depth as it forms the foundation of the work in Chapter Three. A three-dimensional concrete yield surface is developed in Chapter Three. This yield surface is used in the theory of hardening plasticity to establish the incremental constitutive relationships for concrete. Furthermore, this model is extended to represent the strain-softening effect in concrete. The hardening and softening rule which has been developed is based on experimental results obtained from the literature. The results of the proposed model are compared with these experimental data. The cracking and crushing of concrete have been studied in Chapter Four. A rough crack model is developed for concrete and crack stress-displacement relationships due to aggregate interlock are formulated. A mathematical model is proposed for the effect of dowel forces in cracked reinforced concrete structures. The effect of bond stress between a steel bar and concrete has been introduced by a tension-stiffening factor and suitable formulations has been proposed. The results from the crack related models have also been compared with experimental data from the literature. Finally, stiffness matrices for cracked plain and reinforced concrete have been developed using a smeared crack approach. The concrete constitutive model and the crack model developed in Chapters Three and Four have been implemented into a finite element program for the numerical analyses given in Chapter Five. This implementation has been carried out for plane stress and axisymmetric solid stress problems. A reinforced concrete beam and a prestressed concrete reactor vessel have been analysed and the results compared with experimental data. Finally Chapter Six presents the overall conclusions and recommendations for further research.

A new modal method capable of analysing the aeroelastic response of rotorcraft in both steady and manoeuvring flight is developed. Particular emphasis is given to the correct modelling of the dynamic interactions between the rotor and the fuselage. This is achieved via the use of complex rotor modes, which allows the effects of hub motion to be incorporated. The modal Lagrangian equation for a single rotating blade using real modes as state variables is first derived. The important non-linear terms based on an ordering scheme are retained. This aeroelastic model is then extended to adopt the complex rotor modes as state variables. This concept, which is both new and analytically demanding, is furnished with minimum algebra. A generalised proof of complex modes orthogonality and its application to the coupled rotor-fuselage dynamic system are provided. Important conclusions drawn from this proof include: A set of complex left-hand eigenvectors are required, together with the right-hand set, in order to reduce the system response equations to an uncoupled modal form suitable for a solution; and It is necessary for the modes analysis to be re-formulated as an eigenvalue problem replacing the transfer matrix solution procedure. An orthogonalisation procedure is employed to reduce the complex system response equations to the uncoupled modal form. The procedure not only simplifies the algebraic process, but also identifies exactly the forcing functions present in the dynamic system modelled. However, for consistency wi th the dynamic model, it is necessary to restrict the blade model to a straight beam with small pre-deformed angles. The need to treat both the complex coupled and reactionless mode sets simultaneously, when they are defined in different reference frames, requires special attention to the solution of the modal responses. A numerical technique is developed for filtering the applied forces and hence identifying the forcing for the respective mode types. The fundamental issue regarding the true definition of angle of attack used for aerodynamic calculation is also addressed. The second order pseudo-torsion term must be removed from the incidence expression to ensure the aerodynamic loads are calculated correctly. The determination of the blade structural loads using both Modal Summation and Force Integration methods is discussed and described. A novel numerical technique, based on curve fitting using Chebyshev polynomials coupled with analytical integration, is devised and shown for the first time to minimise the inherent numerical problems associated with Force Integration. Finally, applications of the analytical model to include the effects of hub motion on vibratory loads calculation and to determine loads in an extreme manoeuvre are successfully demonstrated. The use of rotor modes by including transmission flexibility in a rotor dynamic model in loads calculation is also provided. These correlations establish the important milestone on the ability of this model to improve vibration prediction and to simulate manoeuvring flight. They also demonstrate the potential applications of this model. Recommendations for future research are also made.

This research work presents a series of investigations into the structural, dynamic and aeroelastic behaviour of composite wings. The study begins with a literature review where the development of aeroelastic tailoring and specific applications of the technology are discussed in detail. A critique of methods for the determination of cross-sectional rigidity properties follows for beams constructed of laminated and thin-walled materials. Chordwise stiffness is shown to be an important parameter that must be considered as it has a significant effect on the amount of bending-torsion coupling present in a beam and, as a consequence, on the value of torsional rigidity. The free vibration characteristics of such beams are then examined using the dynamic stiffness matrix method. Natural frequencies and mode shapes of various beams are studied using the fibre angle, β, and the bending-torsion coupling which is measured (in this study) by the non-dimensional parameter ψ, as design variables. The results show that ψ has only a marginal effect on the natural frequencies of composite beams (wings) but can significantly modify the mode shapes of such beams. It can be used to decouple modes which are geometrically (inertially) coupled in the same way as mass balancing but without a weight penalty. It can also be used to abate the unfavourable coupling introduced by sweep angle. Classical flutter and divergence of swept and unswept uniform cantilever wings are investigated using laminated flat beams (plates) and thin-walled beams of rectangular and biconvex cross-sections. Various parameters, such as, the fibre angle, β, the coupling parameter, ψ, the angle of sweep, Λ, the static unbalance, Xα, and the non-dimensional ratio of the fundamental (uncoupled) bending to fundamental torsional frequency, ωh/ωα, are varied and their subsequent effects on aeroelastic stability are investigated. The importance of torsional rigidity GJ on the flutter of composite wings is shown to be substantial in contrast with ψ, which is generally the most important parameter to be considered when the objective is that of increasing the divergence speed. Modal interchanges in the free vibration and flutter of laminated composite wings are shown to be primarily responsible for behaviour not experienced with metallic wings, in particular the effect of wash-in and wash-out on flutter. The most intriguing features of these investigations, however, are those which show that models adequate for the analysis of composite wings may be based on two parameters, the frequency ratio ωh/ωα and the coupling parameter ψ. Some results are confirmed by independent optimisation studies. Finally, a preliminary investigation is carried out into the flutter suppression and gust alleviation of a laminated composite wing by the use of active controls. The results show that by using an active control in an optimum trailing edge position the gust response of a wing can be significantly alleviated without compromising the already optimised flutter speed by the use of aeroelastic tailoring.

In this thesis a theory for the geometrically nonlinear analysis of thin curved beam-type structures is proposed and an associated displacement finite element formulation developed. An exact two-dimensional large rotation theory, which is based on an intrinsic coordinate system, has been developed. Four alternative Lagrangian formulations of the theory have been presented for comparison. A family of two-dimensional thin curved beam elements has been developed by using the constraint technique to include the convective coordinate system. The elements are relatively simple and the minimum number of degrees of freedom necessary has been used. The Total Lagrangian formulation has been shown to be numerically more effective than the Updated Lagrangian formulation. A new Total Lagrangian formulation that includes the effect of curvature change on axial force in the incremental equilibrium equations has been developed. The formulation is based on the geometric strains and has the capability of predicting true axial force values in large rotation and curvature problems. This approach can be used in the general continuum mechanics largz; d3formation formulations. A large rotation theory for three-dimensional beams and Total Lagrangian formulations of the theory, which are based on the Green strains and the geometric strains, have been developed. The theory correctly describes the large rotation elastic response of a thin eccentric curved beam of rectangular cross-section. Material nonlinearity, which is based an the von-Mises yield function and the Prandtl-Reuss flow rule and in which isotropic hardening is assumed, has been included in the formulation. A family of three-diinensional beam elements, that can accurately accommodate the theory, has been developed by the constraint technique. The elements are suitable for use as stiffeners in the analysis of stiffened shell structures. The elements, which have been developed, have been implemented in the LUSAS finite element system. The accuracy of the results obtained has been demonstrated by comparison with*published results.

Series capacitors offer considerable technical and economical advantages in long distance a.c. transmission. In particular, their excellent reliability and minimal maintenance requirements make series compensation the most cost effective method of enhancing the power transfer capability of an existing or proposed interconnection. E.H.V. lines employing series capacitors however, pose difficult problems for the line protection relays, not encountered with plain feeders. One important cause of these problems is the resonance between the series capacitor and the line series inductance, which in turn imposes a sub-synchronous oscillation on the system signals. Also, the rapid changes in the circuit parameters, resulting from the operation of the capacitor protection equipment, namely the spark gaps, introduce some difficulties for the line protection schemes, especially an impedance measuring relay. These spark gaps are installed in parallel with the series capacitors to prevent the development of very high voltages across the capacitor which could cause excessive damage to the equipment. The work presented herein describes a new digital distance relay suitable for series compensated line applications. The errors in the impedance measurement for a phase to earth fault when the spark gaps do not flash over, are discussed and new methods are proposed to compensate for these errors. The new concept of a complex residual compensation factor, as opposed to a real one, is also discussed. A new adaptive filtering is incorporated in the relay in order to minimise the detrimental effect of the subsynchronous oscillation on the relay decision logic. Finally, the relay is thoroughly tested for many different system configurations, to fully evaluate the relay response.

The results of a series of 19 full scale tests carried out on pin-ended reinforced concrete columns are reported. The columns tested had either tapered rectangular sections along the length or octagonal cross sections. All columns, except the last 6, were subjected to uniaxial eccentricities at one of the ends (the stronger end), and a nominally concentric load at the other end. For the case of the last six columns the loading applied at the stronger end was biaxially eccentric. For each of these tests, a complete set of measurements, covering the entire range of loading, are reported. The test results are compared with the analytical results produced by the program VAR OIS, and the design strengths predicted by the Limit State Code for Bridges BS5400: Part 4 [8]. The thesis also includes a onarvey of published 'Literature on reinforced concrete columns, covering mainly the period from 1955 to 1981. The available information has been reviewed under three headings : predominantly theoretical research, methods of design, and tests on reinforced concrete columns. Most of the test data available on slender reinforced concrete columns, have been used to verify a computer program VAROOLS, which was originally written for composite columns, and had been verified for that type of application, but is also suitable for slender reinforced concrete columns. The comparisons show that the program predicts the ultimate strength safely in almost all cases. A new method of design for slender reinforced concrete columns with uniform and tapered cross sections is developed and design charts and worked example are presented. The method is shown to be simple and easy to be used and when compared with test results a good agreement was obtained.

This research is concerned with the problem of optimisation of steady state large scale systems using mathematical models. Algorithms for on-line optimisation of interconnected industrial processes are investigated. The research is concerned with two different kinds of algorithms which are based on the structure of the model used and the way of incorporating the real process information in order to compensate for model-reality differences. The first class of algorithms are developed from the price method with global feedback information which is mainly based on the normal Lagrangian function. Two existing algorithms are examined: The double iterative price correction mechanism and the augmented interaction balance method. Both methods use a double iterative coordination strategy and global feedback measurements from the real process. They are based respectively on the normal and the augmented Lagrangian functions. Hence, the first algorithm can only be recommended for application to convex problems. An algorithm, namely the augmented price correction mechanism, has been developed to extend the applicability of the previous price correction mechanism to non-convex problems. It is also applicable to convex problems with the advantage of reducing the number of times that information is required from the real process. The second class of algorithms is known as integrated system optimisation and parameter estimation (ISOPE) • The model used contains uncertain parameters and the algorithm solves the optimisation and parameter estimation tasks repeatedly until no furthur improvement is obtained. Developed ISOPE algorithms are involved in this research to cover the problems with output dependent constraints. Simulation results show superiority of the double iterative algorithm over that of single loop method in considerably reducing the number of times that information is required from the real process and hence saving on-line computing time. It is hoped that this work will provide useful information for implementing and furthur developing on-line steady state optimisation techniques.

The measurement of soil stiffness at very small strains (Gmax) has been carried out under both dynamic and continuous loading in the triaxial apparatus up to high stresses. A new system of LVDTs has been used to measure axial strain locally during continuous loading while dynamic stiffnesses were measured using bender elements. Using the two methods good agreement was found between the stiffnesses at 0.0001% strain for two different materials. Bender elements measure the propagation time of shear waves through a soil sample so that the value of Gnax can be determined. The design of the bender element configuration in the triaxial apparatus has been improved so that the reduction in the electrical noise resulted in a high quality of received signal. Bender elements were also incorporated into high pressure triaxial cells and were used to test very stiff soils for the first time. Theoretical studies and dynamic finite element analyses are presented which have been carried out to develop more objective criteria for the determination of Gmax. Several techniques have been proposed for simple and direct measurement of the arrival time of the shear wave to an accuracy of ±1%. The thesis presents the results of bender element tests examining the variation of Gmax for sands, which is then related to the stiffness at larger strains determined under continuous loading using the new system of LVDTs. Three sands with very different geological origins were tested over a wide range of stresses allowing a general framework for stiffnesses to be established. The interpretation of the results is based on the correct normalisation of the data by which means unique relationships have been derived for each soil. The framework demonstrates that the confining stress and volumetric state relative to the normal compression line are the principal controlling factors of stiffness as they would be for clays. However, the framework distinguishes that for sands the means of arriving at its initial volume stress state are also important, in particular whether this is by overconsolidation or compaction. The thesis also presents results of bender element tests examining the anisotropy of Gmax of both natural and reconstituted clays. The work investigates both the stress induced and inherent components of anisotropy related to an axi-symmetric stress state or cross anisotropy of the soil fabric. The results show that the stress induced anisotropy of soils is generally small for an axi-symmetric stress state while significant inherent anisotropy was found in natural London clay. The same degree of inherent anisotropy has been reproduced by anisotropic straining of reconstituted London clay suggesting that the inherent anisotropy is a variable factor related to the strain history. The rate of change was, however, found to be very small so that. when an isotropic stress regime was applied the Gmax anisotropy persisted long after the plastic strain increments became isotropic. Finally, finite element analyses were carried out using the 3 SKH model (Stallebrass, 1990b) to investigate the influence of Giax on calculated ground movements. The analyses consisted of parametric studies of the stress-strain behaviour of a triaxial sample, the load deflection behaviour of a foundation and the ground movements around a tunnel. Although constrained by the limitations of the model the analyses offer an insight into the behaviour which can be also important for a general understanding of the behaviour of real soils. The studies highlighted that the assessment of the importance of Gmax on the stress strain behaviour should consider all the relevant factors which control the non linearity of soil's response, in particular the recent stress history of the soil and the geometry of the boundary value problem.

Existing experimental results are studied to determine the factors (including those not previously identified) affecting the strength of grouted connections. The current bond strength formula is evaluated and its limitations noted. Previous analytical work is examined and strengths and weaknesses investigated. A nonlinear finite element analysis is developed using a friction gap element to model the steel/grout bond. This includes a dilation effect when slip occurs and successfully simulates the behaviour of plain pipe connections up to ultimate load. An elastic-plastic, work-hardening, cracking and crushing constitutive model is developed to represent the behaviour of grout material. This is used for a detailed finite element analysis of the load-slip behaviour of individual shear keys of various shapes. The friction-gap element is adapted to give a representation of the shear keys using data derived from the detailed shear key analysis. A confinement factor is used to give higher ultimate shear key loads when the bond opening is small. This accounts for the observed fact that higher key loads are achieved with increased sleeve and pile dimensions due to greater confinement of the grout. Load-slip behaviour and strains up to ultimate load for shear keyed connections are successfully simulated using the friction-gap element. Bond stress distributions show that high normal bond stress concentrations are necessary to balance the bending moments in the grout annulus. Various extreme geometries are analysed and their failure modes determined. The effects of connection length, stiffeners, alternative loading arrangements, scale and shear key geometry are also fully investigated. Results are used to produce a new bond strength formula which takes into account most factors affecting bond strength and is stle to give good results over the full rang of geometries. Experimental tests have been conducted to determine the coefficient of friction between shot-blasted steel and grout for use in the numerical analyses.

The research concerns the influence of piles, installed beneath deep excavations, as a means of reducing movements in the surrounding ground. The work focussed on the use of piles installed as a part of top down basement construction, a technique used in conjunction with deep excavations in urban areas. The investigations sought to explore the effectiveness of bored piles as a means of enhancing the stiffness of the soil beneath the excavation and so reducing the spread of movements to the surrounding ground. Experimental data were obtained from a series of 19 centrifuge model tests undertaken at 100g. The plane strain models consisted of a pre-formed excavation temporarily supported by fluid pressures acting at formation level and against the retaining wall. The fluid support was removed as the test proceeded and successive levels of props were advanced against the retaining wall using pressurised hydraulic cylinders as jacks. Ground movements were measured using a combination of transducers and analysis of digital images from a camera viewing the front of the model seen through the Perspex side of the model container. These systems gave ground surface, formation level and wall displacement profiles as well as overall patterns of movement. The general model behaviour was characterised in a series of datum tests. These established the magnitude of displacements generated with ground support provided by the retaining wall alone in key positions throughout the model. Following this the overall stiffness of the soil below excavation formation level was enhanced by the introduction of either one or two rows of cast in situ piles installed at distances of 3 and 6 pile diameters from the retaining wall during model making. Direct comparison was then made between the various test results. These procedures were repeated in a small number of additional tests in which the retaining wall embedment depth was reduced. The use of piles was found to reduce both horizontal movements and settlement behind the retaining wall. Maximum reductions in settlement behind the retaining wall were found to be about 55%. The influence of piles on settlement was limited to a distance of about two times the excavation depth behind the retaining wall. Maximum reductions in horizontal displacement, near to the retaining wall, were about 70%. The effectiveness of the piles in reducing ground movement diminished with increasing prop stiffness such that when lateral displacement of the retaining wall was effectively prevented maximum movements were reduced by 40% (settlement) and 50% (horizontal). The piles were found to create a general stiffening effect that reduced horizontal movement at the toe of the retaining wall and led to reductions in overall prop load. Additionally the piles provided restraint against heave movements at the excavation formation and therefore also acted in tension. As a result the soil mass around the piles tended to behave as a block. This behaviour was observed for excavations in which both one and two rows of piles were used despite the relatively discrete nature of the elements. With increasing time after completion of the excavation the block behaviour became less well defined although the effect was better maintained when the greater number of piles were used. Finite element analyses of the centrifuge models also predicted reductions in displacement when piles were modelled at excavation formation level although the magnitude of reduction was less than that observed in the centrifuge tests.