The non-linear analysis of structures is a very wide field (Chapter l) and this thesis has concentrated more on some areas than others; trusses rather than frames; iterative methods and acceleration techniques rather than direct methods (Chapters 2 and 3), Nevertheless frames receive some attention and comparisons are given in both store (Chapter 4) and time (Chapter 5) between the Jacobi iterative methods and the Gauss direct method with a view to highlighting the advantages of iteration. The analysis of structural behaviour is considered at working load and at collapse (Chapter 6), Also variations in the collapse load behaviour are considered as the loading is varied within limits of the nominal loadings Numerical examples are given to illustrate the underlying theory (Chapter 7). Finally an outline is given (Chapter 8) of a way to help the iterative methods forward: direct methods are in difficulty with time and store; iterative methods are in difficulty with time. To improve the iterative methods it is proposed that one's intuitive structural knowledge - together with relevant analogies and existing numerical solutions - be brought in as part of the data for future problems.

introducedin order to overcome problems stemming from the complex nature of the total potential energy function. Important features of the formulation include an accurate mathematical representation of the deformed state of the structure and the use of direct potential energy minimisation on a local, member by member basis. Chapter 5 describes a computer implementation of the proposed technique and presents the results of a number of evaluative tests. The construction and testing of a skeletal dome of sixteen foot span is described in chapter 6 and a comparison of the observed behaviour of the dome with that predicted by theoretical analyses is presented. Concluding remarks and suggested improvements and extensions are contained in chapter 7.

The shear strength of masonry is the function of many factors, but current research indicates that bond quality is the primary factor. The bond strength is a key parameter representing structural integrity and water-tightness of the masonry system. However, masonry is characterized by low bond strength, and is quite a complex material to analyse due to its inherent variations. The quality of the bond is reliant on, the weather, the quality of the workmanship and the quality of materials used. Therefore, this study investigated ways of improving the bond performance of mortar joints by the use of admixtures as well as examining the efficacy of Acoustic Emission (AE) techniques in monitoring fracture mechanisms. Laboratory based Acoustic Emission (AE) monitory techniques were used on masonry triplets under static and repeated shear loading, in order to investigate the shear bond strength characteristics, and to identify a mortar that will exhibit the long-term properties needed for a masonry structure to be subjected to cyclic loading, such as masonry arch bridges. The FE micro-modelling method was used to predict the shear behaviour of the triplet. Moreover, Photo-elastic analyses were used to investigate the stress distributions within the triplets under shear stress, in order to check the output from FE analyses. The investigation showed that the addition of SBR to mortar improves its performance under both static and cyclic loading when compared to the control sample, all in contrast to the addition of Latex 114 admixture which had the opposite effect. Additionally, the AE technique was found to be useful tool in providing valuable data about the full fracture behaviour during static and cyclic loading. The FE analyses proved to be capable of predicting shear strength to a reasonable degree of accuracy. The Photo-elastic technique was found to be a reliable and simple method of checking the stress profile output from the FE analyses.

Structural Heath Monitoring (SHM) is the term applied to the process of periodically monitoring the state of a structural system with the aim of diagnosing damage in the structure. Over the course of the past several decades there has been ongoing interest in approaches to the problem of SHM. This attention has been sustained by the belief that SHM will allow substantial economic and life-safety benefits to be realised across a wide range of applications. Several numerical and laboratory implementations have been successfully demonstrated. However, despite this research effort, real-world applications of SHM as originally envisaged are somewhat rare. Numerous technical barriers to the broader application of SHM methods have been identified, namely: severe restrictions on the availability of damaged-state data in real-world scenarios; difficulties associated with the numerical modelling of physical systems; and limited understanding of the physical effect of system inputs (including environmental and operational loads). This thesis focuses on the roles of law-based and data-based modelling in current applications of. First, established approaches to model-based SHM are introduced, with the aid of an exemplar ‘wingbox' structure. The study highlights the degree of difficulty associated with applying model-updating-based methods and with producing numerical models capable of accurately predicting changes in structural response due to damage. These difficulties motivate the investigation of non-deterministic, predictive modelling of structural responses taking into account both experimental and modelling uncertainties. Secondly, a data-based approach to multiple-site damage location is introduced, which may allow the quantity of experimental data required for classifier training to be drastically reduced. A conclusion of the above research is the identification of hybrid approaches, in which a forward-mode law-based model informs a data-based damage identification scheme, as an area for future work

Structural Health Monitoring (SHM) is the monitoring of any type of structure for the express purpose of determining its condition and future lifespan and if, when and where any reparative action is needed. A focus of the work in this thesis is SHM for long-span bridges and particularly the effects of environmental and operational conditions on a monitoring campaign. There is currently a trend for heavily instrumenting civil structures with large sensor networks that continually collect terabytes of data. However, these large data sets are often redundantly stored and not used for anything. One of the principal aims in the thesis is to exploit such monitoring data for the development of diagnostic tools for structural condition assessment. The first part of the thesis concerns formulating a baseline for the Tamar Bridge that represents the normal undamaged condition of the structure. To do this a large amount of analysis was needed in order to understand how different structural measurements are interrelated and how the bridge responds to normal environmental and operational conditions. Particular attention was paid to measurements that can be sensitive to structural degradation (such as modal properties). Often simple causal relationships were found between monitored variables, and response surface models were formulated that could predict selected variables with good accuracy given measurement of operational and environmental conditions, such as air temperature, traffic loading and wind profile. The predictive models developed are intended to be used as diagnostic tools, for example, a departure from the normal condition of the bridge will bring about a significant increase in prediction error, which may be monitored as a system alarm. The second part of the thesis directly concerns how the influence of environmental and operational variation on features sensitive to damage can be lessened or removed without measurement of these conditions themselves. This is a very important issue in SHM, as often the effects of fluctuating environmental and operational conditions can mask any indication of damage to a structure that may be evident in structural response. In the thesis a solution to the problem based on the econometric theory of cointegration is introduced. Application of this theory is found to be ideally suited to remove unwanted environmental and operational trends from SHM data, and forms an exceedingly promising contribution to the development of SHM technology.

This thesis deals with optimisation using the principles of continuum mechanics. Both shape and mesh optimisation will be covered. A unified approach will be introduced to obtain shape and mesh optimisation for hyperelastic, hyperelastodynamic and hyperelastoplastic settings. The approach makes use of the generated material force method in mesh optimisation and the so-called imposed material force method in shape optimisation. To this end, the appropriate spatial and material continuum mechanic Equations will be developed in hyperelastic, hyperelastodynamic and hyperelastoplastic settings. A summary of the four main parts is as follows. The first part begins with structural optimisation in hyperelastic setting. After introducing the necessary Equations, the effectiveness of the material force method to obtain global optimised solutions for truss structures will be demonstrated. The implementation produces the global optimised undeformed configuration and the global optimised deformed configuration. The shape and mesh optimisation will be tested for two and three dimensional truss structures under small and large deformations. In addition, these formulations will be extended to obtain constrained optimised solutions. The penalty method is used to realise optimised truss structures within certain design criteria. The second part develops a new Arbitrary Lagrangian Eulerian (ALE) hyperelastic setting in rate form. It will deal with two systems of partial differential Equations, namely the spatial and the material momentum Equation. Both are discretised with the finite element method. The spatial Equation will then be linearised by taking the material time derivative while the material Equation will be linearised by taking the spatial time derivative. The solution defines the optimal spatial and material configuration in the context of energy minimisation in hyperelastic setting. The implemented examples will illustrate shape optimisation under the effect of mesh refinement The third part provides the formulation and implementation details of ALE hyperelastodynamic problem classes. This ALE formulation is based on the dual balance of momentum in terms of both spatial and material forces. The balance of spatial momentum results in the usual Equation of motion, whereas the balance of the material momentum indicates deficiencies in the nodal positions, hence providing an objective criterion to optimise the finite element mesh. The main difference with traditional ALE approaches is that the combination of the Lagrangian and Eulerian description is no longer arbitrary. In other words the mesh motion is no longer user defined but completely embedded within the formulation. This presents a discretisation and linearisation for a recently developed variational arbitrary Lagrangian Eulerian framework in hyperelastodynamics setting. The spatial and material variational Equations will be discretised to obtain the weak form of the momentum and continuity Equations. The discretised ALE Hamiltonian Equations of the spatial motion problem introduces the balance of the discretised spatial momentum and the discretised spatial continuity Equation while the corresponding material motion problem defines the balance of the discretised material (or configurational) momentum and the discretised material continuity Equation. We will deal with two systems of partial differential Equations: the scalar continuity Equation and the vector balance of momentum Equation. The momentum and continuity Equations will then be linearised. The time integration of both the spatial and the material Equations is performed with Newmark scheme. A monolithic solution strategy solving both the spatial and the material momentum Equations has been carried out while updating of the spatial and the material densities were attained through solving the spatial and material continuity Equations (mass conservation). The concept of generated material force has been implemented to optimise the mesh and consequently the wave propagation. The solution defines the optimal spatial and material configuration in the context of energy minimisation. The fourth part provides the framework and implementational details of ALE hyperelastoplasticity problem classes. This ALE formulation is based on the dual balance of momentum in terms of spatial forces (the well-known Newtonian forces) as well as material forces (also known as configurational forces). The balance of spatial momentum results in the usual Equation of motion, whereas the balance of the material momentum indicates deficiencies in the nodal positions, hence providing an objective criterion to optimise the shape or the finite element mesh. The earlier developed ALE hyperelastic setting will provide the platform to extend the formulation to include plasticity. The new ALE hyperelastoplasticity setting will be developed at finite strain. In ALE hyperelastoplastic formulation additional Equations are required to update the stresses. The principle of maximum plastic dissipation as well as the consistency conditions in spatial and material setting will introduce the spatial and material plastic parameters and rate form of the stress-strain relations. The solution defines the optimal spatial and material configuration in the context of energy minimisation in hyperelastoplasticity setting. The concepts of imposed and generated material force are implemented to provide improvements over Lagrangian solutions.

Current research in the field of limit analysis is focussing on the development of numerical tools which are sufficiently efficient and robust to be used in engineering practice. This places demands on the numerical discretisation strategy adopted as well as on the mathematical programming tools applied, which are the key ingredients of a typical computational limit analysis procedure. In this research, the Element-Free Galerkin (EFG) discretisation strategy is used to approximate the displacement and moment fields in plate and slab problems, and second-order cone programming (SOCP) is used to solve the resulting discretised formulations. A numerical procedure using the EFG method and second-order cone programming for the kinematic limit analysis problem was developed first. The moving least squares technique was used in combination with a stabilised conforming nodal integration scheme, both to keep the size of the optimisation problem small and to provide stable and accurate solutions. The formulation was expressed as a problem of minimizing a sum of Euclidean norms, which was then transformed into a form suitable for solution using SOCP. To improve the accuracy of solutions and to speed-up the computational process, an efficient h-adaptive EFG scheme was also developed. The naturally conforming property of meshfree approximations (with no nodal connectivity required) facilitates the implementation of h-adaptivity. The error in the computed displacement field was estimated accurately using the Taylor expansion technique. A stabilised conforming nodal integration scheme was also extended to error estimators, leading to an efficient and truly meshfree adaptive method. To obtain an indication of bounds on the solutions obtained, an equilibrium formulation was also developed. Pure moment fields were approximated using a moving least squares technique. The collocation method was used to enforce the strong form of the equilibrium equations and a stabilised conforming nodal integration scheme was introduced to eliminate numerical instability problems. The von Mises and Nielsen yield criteria were then enforced by introducing second-order cone constraints.

The microstructure and composition of water and KOH activated hardened pastes of commercial neat white Portland cement (WPC) and blends with 30% fly ash (PFA) have been characterised using a multi-technique approach, With particular emphasis on the nature of the C-S-H phase. The neat and fly ash blended pastes were activated with water or a 5M KOH solution and cured for one year at 25'C, one month at 55'C and one month at 85'C. The mean length of the aluminosilicate anion structure of C-S-H (29 Si MAS NMR) increased with age and it was higher in the fly ash blended systems. Formulae were presented for the average structural units in the C-S-H present in the systems analysed by TEM-EDX. SEM micrographs showed that as hydration occurred, the microstructure became denser because outer product C-S-H was formed in the water filled spaces and additional C-S-H resulted from the pozzolanic reaction. The chemical composition of C-S-H could not be determined by SEM-EDX because of intermixing with other phases; TEM-EDX was necessary. Inner product C-S-H morphology was fine and homogeneous and that of outer product C-S-H was fibrillar in the water activated systems and foil-like with alkali activation. Fly ash replacement did not change the morphology of lp and Op C-S-H. Small fully hydrated cement and PFA particles were filled with a less dense lp C-S-H with morphology very similar to the foil-like one. TEM-EDX showed that, in general, the mean Ca/(AI+Si) atomic ratio was lower in the water activated blends than that in the neat cement pastes due to the fly ash reaction. The composition- structure data were discussed in terms of models for the nanostructure of C-S-H. Higher curing temperature accelerated the rate of the cement hydration. The mean length of the aluminosilicate of the C-S-H anions was much higher than that of C-S-H formed at lower temperatures, and it was also higher in the blended pastes than with neat cement. Backscattered electron images showed that the grey level of C-S-H in the systems cured at 55T and 85T was in places quite similar to that of the calcium hydroxide: that is, it was brighter than in pastes cured at lower temperature. SEM also showed that the microstructure of the systems cured at higher temperature exhibited non uniform porosity. Inner product C-S-H with a fine scale, homogeneous morphology, was abundant in all systems cured at 55'C and 85'C. Op C-S-H was generally fibrillar with Nvater, and foil-like with alkali. However, the higher temperature curing did result in coarser fibrillar morphology (water activated systems) than that formed at lower temperatures. The C-S-H gel formed in the commercial WPC-30% PFA blended paste hydrated for one year at 25'C and water leached for twelve weeks was also characterised in this work. A matrix effect was clearly observed by 29 Si MAS NMR. Cross-linking of the aluminosilicate anion structure of C-S-H occurred after leaching the sample for four weeks. Formulae were also presented for the average structural units in the C-S-H present in the unleached and four weeks water leached systems analysed by TEM-EDX. lp C-S-H morphology was fine and homogeneous and Op C-S-H had fibrillar morphology. There were many areas in the microstructure of the leached sample where Op C-S-H with foil-like morphology coexisted with fibrillar Op C-S-H.

While current assessment methods for preventing progressive collapse are mainly associated with blast and impact loading, no systematic framework is currently available for the practical and rational assessment of robustness of multi-storey building structures under localised fire. In this thesis, a robustness assessment framework with various alternative levels of sophistication is presented with the aim of bridging the gap between the topics of structural fire resistance and progressive collapse. The robustness assessment framework developed in this thesis is comprised of four basic components, namely, detailed Temperature-Dependent Approach, simplified Temperature-Dependent Approach, Temperature-Independent Approach, and practical design recommendations. These assessment approaches can satisfy various design requirements in different design stages. To illustrate their application, localised fire induced by burning vehicles in a typical multi-storey steel-composite car park is considered as a main reference scenario. A Robustness Limit State (RLS) is proposed, which is based on the fact that large inelastic deformations of building structures subject to extreme loading are typically concentrated in the joint regions, thus failure of joints in certain locations may lead to floor collapse, and subsequently trigger progressive collapse. Therefore, no floor collapse is allowed in the current RLS. Since joint resistance and ductility play an essential role in mitigating progressive collapse, a component-based joint modelling technique and multiple joint failure criteria for commonly used semi-rigid joints are proposed and thoroughly discussed. The proposed joint modelling strategy is shown to be capable of capturing realistic nonlinear behaviour of joints under both ambient and elevated temperatures. Employing the proposed joint failure criteria, the application of the robustness assessment framework is illustrated for the reference structure, and important conclusions are drawn relating to the accuracy and reliability of each assessment approach. Furthermore, multi-level structural modelling strategies, the significance of structural dynamic effects during fire, factors influencing structural robustness, and future research

The importance of Structural Health Monitoring (SHM) in several industrial fields has been continuously growing in the last few years with the increasing need for the development of systems able to monitor continuously the integrity of complex structures. In order to be competitive with conventional non destructive evaluation techniques, SHM must be able to effectively detect the occurrence of damage in the structure, giving information regarding the damage location. Ultrasonic guided waves offer the possibility of inspecting large areas of structures from a small number of sensor positions. However, inspection of complex structures is difficult as the reflections from different features overlap. Therefore damage detection becomes an extremely challenging problem and robust signal processing is required in order to resolve strongly overlapping echoes. In our work we have considered at first the possibility of employing a deconvolution approach for enhancing the resolution of ultrasonic time traces and the potential and the limitations of this approach for reliable SHM applications have been shown. The effects of noise on the bandwidth of the typical signals in SHM and the effects of frequency dependent phase shifts are the main detrimental issues that strongly reduce the performance of deconvolution in SHM applications. The second part of this thesis is concerned with the evaluation of a subtraction approach for SHM when changes of environmental conditions are taken into account. Temperature changes result in imperfect subtraction even for an undamaged structure, since temperature changes modify the mechanical properties of the material and therefore the velocity of propagation of ultrasonic guided waves. Compensation techniques have previously been used effectively to overcome temperature effects, in order to reduce the residual in the subtraction. In this work the performance of temperature compensation techniques has been evaluated also in the presence of other detrimental effects, such as liquid loading and different temperature responses of materials in adhesive joints. Numerical simulations and experiments have been conducted and it has been shown that temperature compensation techniques can cope in principle with non temperature effects. It is concluded that subtraction approach represents a promising method for reliable Structural Health Monitoring. Nonetheless the feasibility of a subtraction approach for SHM depends on environmental conditions.