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Even though the attractive properties of fibre-reinforced polymer composites have led to them becoming essential materials for a wide variety of high performance applications, they pose several drawbacks such as low compressive strength, low delamination resistance and high sensitivity to defects. These drawbacks have led designers to adopt a damage tolerance approach, whereby damage growth is deemed as failure. However, this approach has resulted in heavy composite structures with conservative configurations, which has somewhat negated the significant weight saving potential that composites offer over traditional materials. A step change in the approach by which damage growth is tolerated could provide designers with the freedom to develop novel composite structures. Despite an improvement in the understanding of composites failure, particularly in unidirectional laminates, compressive failure of multidirectional composites is still not fully understood. Therefore, the initial objective of this research project was to investigate the compressive failure processes multidirectional composites, leading to development of material-based approaches (i.e. introduction of a secondary material to the parent composite) which could offer compressive crack arrest/redirection. Such an approach would facilitate the adoption of a damage growth approach for composites design. An extensive experimental, fractographic, theoretical and numerical study on the compressive failure of multidirectional composites was conducted, resulting in the main failure mechanisms being identified and the sequence of events that lead to global fracture being deduced. The influence of the layup, specimen geometry (such as compact, plain and sandwich panel compression) and the proportion of shear loading on the compressive performance of multidirectional laminates were characterised. These observations were then used to validate numerical models, thus yielding more physically based predictions. In the process of formulating novel crack arrest/diversion solutions in composite structures, various concepts ranging from hybridisation to carbon nanotubes and piezoelectric actuators, were investigated. However, after consideration of the relative maturity of these technologies and the time constraints, the latter two approaches were not pursued. Given the absence of an explanation of the hybrid effects observed in composites in the literature, an extensive study was carried out to investigate the effect of hybridisation on the compressive performance of multidirectional composite laminates. For this study, two systems of unidirectional pre-preg tapes with the same epoxy resin but different carbon fibre types and tow sizes were employed. It was identified in this study that hybridisation of selective ply interfaces influenced the location and severity of the fracture mechanisms. Finally, in a complementary study on delamination fracture toughness of hybrid composites, a significant improvement was observed in the delamination resistance (doubling in Mixed Mode I/II toughness) compared to the monolithic composites, indicating that the behaviour of the hybrid interfaces was critical for the compressive performance of the hybrid laminates.

In this work the self-sustaining processes are investigated within a Couette flow de- veloping a method able to apply directly the stress jumps predicted by the vortex wave interaction theory. The challenge of the approach is to implement a technique able to directly implement the stress jumps and to implement a procedure able to deform the mesh to the flow variations. The derivation of the vortex wave interaction theory is also discussed and the numerical formulations of the governing equations are discretized through a spectral/hp element method. The method turns out to agree with the other approaches already utilised in literature and the results repro- duce a constraint of the mathematically inviscid flow suggesting that the flow is weakly dependent on the viscosity. The characteristics of the obtained flow are then discussed. These Navier-Stokes solutions are then perturbed by a sinusoidal wall forcing to study the robustness of the self-sustained mechanism by varying the amplitude of the forcing. The results show the possibility to control the behaviour of the flow and the effectiveness of the considered forcing to induce a drag reduction. Overcoming a certain amplitude threshold, a breakdown of the flow occurs in which the vortex core splits into multiple cores. Also after the breakdown the vortex wave interaction theory has been able to generate a self-sustained multiple core flow.

Offshore wind is set to contribute a significant portion of the UK's renewable energy production. In order to achieve this, installation costs must be reduced and energy density optimised, but this must be balanced with the increase in maintenance costs resulting from fatigue due to wake impact. The aim of this thesis is to investigate the effects of horizontal axis wind turbine wake impact on a downstream rotor. A force-free wake implementation of the unsteady vortex lattice method has been developed in order to simulate the flow around the downstream rotor, including the effects of an upstream rotor wake, uncorrelated wind field and the dynamic inflow response of the turbine wake. In addition, a series of wind tunnel experiments were undertaken to characterise the wake of a horizontal axis wind turbine and measure time histories of the turbine thrust and blade root bending moments in uniform and turbulent inflow and upstream rotor wake impact. Comparisons are made between the model and wind tunnel experiments for a range of flow cases: uniform inflow, turbulent inflow and operation in an upstream rotor wake at varying degrees of lateral offset. The upstream flow field is modelled on a Cartesian grid, following the assumption of frozen turbulence. For both the turbulent flow and upstream rotor wake, a simplified model is used as a starting point and then refined to better model the effect of turbulence. Ambient turbulence is found to have minimal impact on the mean response of the rotor, suggesting that a linearised approach can be taken in the numerical modelling of turbulence effects. The simple model better predicts the low frequency response, but does not capture the per revolution frequencies identified by the refined model, which also better predicts the admittance. The response of the rotor to an aligned upstream rotor wake is found to be dominated by the wake turbulence, although the proposed model does not reproduce the measured response. However, for laterally offset upstream rotor wakes the mean velocity deficit is the dominant factor and the model captures the response, including the shift to higher bending moment cycles which will contribute to increased fatigue.

We present the development of a nonlinear reduced-order formulation for the simulation of geometrically-nonlinear responses of flexible aircraft and other aeroelastic systems. The theoretical foundation of the formulation will be presented first, based on a modal projection of the intrinsic description for beams, coupled with a 2-D unsteady aerodynamic description. We will then investigate the preservation of conservation laws in the proposed method and develop the numerical details in a practical implementation of the method in MATLAB. In this work we also developed a method of obtaining coeffcients of the nonlinear modal beam equations by means of a condensation process, based on the direct application of Guyan reduction of a high-fidelity 3D FE model. Structural and aeroelastic simulations will be presented to verify the implementation of the method against theory and published results, as well as demonstrating the numerical properties of the approach. Static trim, stability analysis and open-loop nonlinear flight simulations using the framework will be demonstrated on a highly-flexible flying wing and compared with published results, as well as carrying out control design and closed-loop nonlinear simulations to demonstrate the capabilities of the proposed reduced-order method.

The dynamics of the turbulent three-dimensional wake generated by an axisymmetric bluff body with blunt trailing edge are experimentally and theoretically investigated at a diameter based Reynolds number of 188,000. A detailed analysis of the base pressure measurements shows that the large scale structures of the turbulent three-dimensional wake retain the structure of the laminar instabilities observed in the transitional regimes, in a statistical sense. These persisting instabilities at the turbulent regime, are associated with spatial and temporal symmetry breaking, giving rise to spatial reflectional symmetry and quasi-periodic vortex shedding. The influence of turbulence recovers the lost temporal and spatial symmetries in the long-time average. It is shown that the turbulent spatial dynamics are reproduced by a simple stochastic model the deterministic part of which accounts for the spatial symmetry breaking and gives rise to steady large scale structures through a supercritical pitchfork bifurcation, and the stochastic part modelling in a phenomenological sense the turbulent fluctuations acting on the large scale structures. The axisymmetric body wake is further investigated when axisymmetric slot-jet zero-net-mass-flux forcing is applied on the rear base. Landau-like models that capture the weakly nonlinear interaction between the global vortex shedding mode and axisymmetric forcing are derived from the phase-averaged Navier-Stokes equations. The Landau-like models describe accurately the forced response by means of measured base pressure of the global vortex shedding mode. With the present analysis it is demonstrated that the concept of weakly nonlinear global modes can be extended to a fully turbulent flow, far from the critical bifurcation Reynolds number, and a general framework for the description of systems with broken symmetries---giving rise to global dynamics---and turbulent dynamics is provided. The novel results presented here advance the understanding of the dynamics of three-dimensional turbulent wakes and pave the way for turbulence prediction and control.

The thesis explores the generation of anisotropic and boundary conforming Voronoi regions and Delaunay triangulations, high-order mesh quality and the development of mesh enhancement techniques which incorporate quality measures to preserve mesh validity longer. In the first part an analogy with crystal growth is proposed to handle mesh anisotropy and boundary conformity in Voronoi diagrams and Delaunay mesh generation. A Voronoi partition of a domain corresponds to the steady-state configuration of many crystals growing from their seed points. Mesh anisotropy is incorporated and the shape of the boundary of an isolated crystal is guided by re-interpreting a user-defined Riemann metric in terms of the velocity of the crystal boundary. A straightforward implementation of conformity to boundaries is achieved by treating the boundary of the computational domain as the boundary of a stationary crystal. The second part attempts to answer the question: what is a good highorder element? A review of a priori mesh quality measures suitable for high-order elements is presented. A systematic analysis of the quality measures for interior and boundary elements is then carried out utilising a number of test cases that consist of a set of carefully selected elements with various degrees of distortion. Their ability to identify severe geometrical distortion is discussed. The effect of boundary curvature on the performance of quality measures is also investigated. The last part proposes improvements to a conventional mesh deformation method based on the equations of elasticity to maintain highorder mesh validity and enhance mesh quality. This is accomplished by incorporating additional terms, that can be interpreted as body forces and thermal stresses in the elastic analogy. Different test cases are designed to prolong mesh validity, and their performance is reported. A proposal of how to formulate these terms to incorporate anisotropy is also presented.

The mechanics of airflow in the large airways during inspiration affects important physiological functions such as ventilation, olfaction, heat exchange and mass transfer. The behaviour of the airflow is important not only for healthcare applications including diagnosis, intervention planning and assessment, but for inhalation toxicology. This research aims to further the understanding of human nasal physiology through computational modelling. Specifically, the effects of transient inhalation conditions on flow dynamics and transport were characterised and the changes in flow behaviour in response to certain pathologies quantified. The key findings can be summarised as follows: Firstly, the time scales for airflow in the large airways have been identified and the initial flow patterns revealed. Three phases in the temporal behaviour of the flow were identified (flow initiation, quasi-equilibrium and decay). The duration of each phase differs depending on the quantity of interest. Flow in the nose was characterised as transitional, whilst in parts of the descending airways it is turbulent, particularly in the faster moving regions around the jets which may occur in the pharynx, larynx and at the superior end of the trachea. The bulk of the flow is biased to fill only certain regions of the airways, whilst other regions carry little flow, due to features upstream. Analysis of cross-sectional images provided by medical imaging does not necessarily provide a representative view of the area available to the flow. Various scalar species were employed to represent the fate of nanoparticles and gaseous species within the airways. Only species with high diffusion rates exhibited significant absorption at the airway walls. Airway pathologies often cause changes to the geometry of the airway. One such pathology, the goitre, was found to curve the trachea and in some cases cause constriction. Both these geometric changes were found to increase the pressure loss and energy required to drive flow through the trachea. Furthermore, the flow in pathological cases was more disturbed. High resolution simulations have been used to address these topics and the scales simulated have been analysed in terms of the smallest features possible in the flow to determine their fidelity.

The translaminar fracture toughness of fibre reinforced polymers (FRP) is important for characterising the failure resistance of composite structures. Measuring the translaminar fracture toughness for any possible layup is not feasible. Therefore, it is of interest to relate the translaminar toughness of a laminate to that of its plies. Numerous studies have measured the translaminar fracture toughness of composite laminates and of individual plies. However, any attempts to relate the two have so far been very limited, and restricted to initiation values. This work presents experimental and analytical research on Compact Tension (CT) tests on several T800s/M21 carbon-epoxy laminates with different combinations of 0° , ±45 and 90° plies, and with various ply thicknesses. Post-mortem techniques, such as X-ray, optical and scanning electron microscopy, were used to determine the damage extent in each specimen. Acoustic emission (AE) was also used to sequence the occurrence of the failure mechanisms. Failure mechanisms found in the multidirectional laminates included a combination of the failure mechanisms found on bidirectional laminates ( /90° ) made of its constituent plies. Ply splitting, fibre bridging and fibre pull-out were the main features characterizing the fracture surfaces. Assuming that the damage can be represented as a single crack, the resistance curve (R-curve) for each layup was extracted from these tests. From each laminate R-curve, three distinct fracture toughness values were obtained for each layup: non-linearity onset, initiation and propagation. The R-curves were used to define a trilinear cohesive law for each layup, and the specimens were then successfully simulated using a cohesive approach in a Finite Element (FE) model. On the one hand, there was good agreement supporting the representation of translaminar damage as a cohesive crack. On the other hand, damage was considerably diffuse when the laminate included substantial ply-blocking, thus suggesting that a single equivalent crack may, in some cases, neglect some important aspects of translaminar damage (as well as delamination). Four analytical predictive models were used to predict the translaminar toughness of the laminates from that of the constituent plies. The assumption of translaminar fracture toughness additivity by means of a rule of mixtures correlated best with the experimental results. The experimental results for a mode I crack propagation in a 45° ply were shown to corroborate a simple analytical model which relates the critical energy release rate of a 45° ply to those of 0 and 90 plies. Thickness size effects were investigated by using different 0 ply thicknesses, by means of 0° ply-blocks and using two grades of the same material system. Since it was found that excessive ply-blocking can lead to significantly diffuse damage, a second study with thin-ply TR50s/K51 carbon-epoxy system was conducted, leading to the first translaminar fracture characterisation of a 0° CFRP ply for a range of thicknesses from 0.03 mm to 0.12 mm. The toughness of the 0° plies was confirmed to be significantly dependent on the thickness, even for ranges of thicknesses where delamination does not play a significant role.

Since composite materials have been developed, many types of materials (e.g. carbon fibre, carbon nanotubes (CNTs)) can be embedded in a standard matrix in order to obtain materials with enhanced physical properties. To investigate enhanced properties of nano-composites, not only mechanical properties but also electrical properties should be taken into account. Furthermore, at the nano-scale, covalent forces between atoms play a crucial role in their behaviour. This thesis is focused on eletromechanical effects (i.e. piezoelectricity and flexoelectricity) and the size effect in micro/nano materials. The aim is to implement continuum modelling solutions for nonlocal/gradient elastic problems in which size effect plays a significant role in material behaviour. The FEniCS Project is used to provide a novel tool for automated solutions of partial differential equations (PDE) by the finite element method. In particular, it offers significant flexibility with regards to discretization choices for triangular elements. When implementing a nonlocal/strain gradient elastic framework using FEniCS, a weak form of the gradient elasticity derived from the Principal of Virtual Work (PVW) is required. Due to the fourth order PDE in term of displacements in the gradient elasticity, C1 continuous elements (e.g. Hermitian finite element) are usually required. However, to avoid the use of C1 continuous elements, an equivalent mixed-type finite element formulation is considered. To investigate the material behaviour, strain gradient finite element formulations based on a mixed variational approach are used. Numerical results are compared with analytical solutions or experimental data to confirm the convergence and accuracy of the simulations. To extend the capability of the implementation to allow the modelling of nanocomposites efficiently, Extended Finite Element Method (XFEM) is introduced. By increasing mesh density only around the discontinuities, the resulting program runs faster than if a finer mesh had been used everywhere, with the additional benefit that more accurate results are obtained.