The objective of this thesis is to broaden current knowledge of the strength and buckling/collapse of shells, with special reference to steel silo structures on discrete supports, and thus to provide design guidance of practical value for future silo design and construction and to develop new research aspects for further investigation. A linear elastic solution of the cylindrical shell bending equations is presented for local loadings, with special attention to local longitudinal distributed loadings. Algebraic expressions for the displacements and stresses induced by a rectangular patch of longitudinal load on a simply supported cylindrical shell are derived using double Fourier series. The solution of this problem is general, and therefore can be applied to cylindrical shells under local I loadings in any direction and with different boundary conditions. Linear elastic analyses of discretely supported perfect cylinders under axial compression are presented using the finite element method. The pre-buckling meridional membrane stress distribution above the support centreline is examined in detail, and is followed by investigations of the linear bifurcation behaviour of the cylinders. The effects on the stress distribution and the buckling strength of different loading patterns and different geometric configurations are extensively examined. Geometrically nonlinear elastic buckling analyses are also performed using large deflection theory. Both perfect and imperfect cylinders are studied with various geometric configurations and under different loading conditions. The nonlinear elastic buckling behaviour, the buckling strength and the buckling configuration are thoroughly investigated for discretely supported cylinders Further studies extend the work into the plastic range. Discretely supported cylinders obeying the von Mises yield criterion are analysed. Limit analyses of perfect cylinders are first conducted using small deflection theory. Geometrically nonlinear elastic-plastic collapse analyses of both perfect and imperfect cylinders are performed next. Studies of different loading conditions and parametric studies of varying geometries and material strengths are presented in both types of analysis. The nonlinear elastic-plastic behaviour of discretely supported cylinders is thus explored. A complete silo which consists of a cylindrical shell, a conical roof hopper and a conical discharge hopper is briefly examined, with the aim of exploring the applicability of the established cylinder model in the elastic buckling analysis of silo structures. Finally, the conclusions drawn from this research are summarised and recommendations are also made for further research on locally supported shells.

The present thesis proposes an innovative technique of applying enrichment to the Boundary Element Method to allow accurate analysis of 2D crack problems. An overview of fracture mechanics is given, with particular emphasis given to numerical methods and the techniques used to extract the highly important stress intensity factors - a measure of the singularity of a crack tip. The Boundary Element Method framework is described and later, the implementation of the new technique of enrichment is defined in detail. Finally, several crack problems are used to verify the accuracy of the method where the results are shown to compare very favourably with other well-established numerical methods.

Recent requirements in the field of non-destructive testing are techniques that quantify micro-structural damage in a wide variety of materials during their manufacture and life cycle for ensuring both their quality and durability. Traditional evaluation techniques such as acoustic pulse echo, impact echo, resonance, ultrasonic transmission, electromagnetic and visual inspection methods are not sufficiently sensitive to the presence and development of domains of incipient and progressive damage. The research presented in this thesis details work undertaken by the author while working at the University of Exeter and is concerned with the development and validation of innovative methods to inspect micro-damage. Various non-linear acoustic measurement techniques, such as detecting defects by measuring the generation of harmonic and inter-modulation products, pulse inversion and resonant frequency deviation has been investigated. In addition to the experimental work new transducers and instrumentation has been developed and used in experimental validation tests on a variety of objects and differing materials. It has been found that the non-linear acoustic testing method provides a practical means by which low levels of progressive damage can be detected and quantified with sensitivities far in excess of that provide by conventional ultrasonic testing methods.

The knowledge of crack path mechanism could improve the safety issues, design and finally reduce the cost of the maintenance or production of structures in aerospace and energy industries. However, the physical mechanism behind the crack path development is not still completely understood although many criteria have been developed to predict the crack path. It is even more challenging to predict the crack trajectory in areas such as multi site damage zones where there are interactions between cracks. A study has been undertaken on sets of cracks with different interaction properties, both numerically, using a finite element (FE) method, and experimentally, using Thermoelastic Stress Analysis (TSA) where the effectiveness of three of the most common criteria was assessed. It was shown that the crack paths are not always repeatable as expected by FE models. It was found that the crack path criteria are capable of an acceptable prediction only in the early stages of the crack growth. Furthermore, the Stress Intensity Factors (SIF) only partially control the crack path and it has been recognised that the T -stress is one the influential parameters of the crack trajectory. Despite the vital role of T-stress, not only in directional stability problems but also in crack growth rate and the shape and size of the plastic zone ahead of the crack tip, little attention has been paid to experimentally determine the T-stress. Therefore, based on both Muskhelishvili's and Williams' approaches, methodologies were developed to determine the SIF and the T -stress from both stress field and displacement data generated artificially and using a finite element method. These methodologies were successfully employed to experimentally determine the SIF and the T -stress for different types of notched and fatigue cracked specimens manufactured from Al 7010 T765 I using TSA and Digital Image Correlation (DIC) technique. It was shown that the Muskhelishvili's approach is equivalent to the Williams' 2 terms stress solution for SIF determination. However, the 2 terms solution is not sufficient to determine the T -stress and, three or more terms are needed both from the stress and displacement fields. Results obtained from the stress field are numerically unstable if more than four terms are used. However, results obtained from the displacement field show more robustness with an increased number of terms.

The non-linear programming algorithms for the minimum weight design of structural frames are presented in this thesis. The first, which is applied to rigidly jointed and pin jointed plane frames subject to deflexion constraints, consists of a search in a feasible design space. Successive trial designs are developed so that the feasibility and the optimality of the designs are improved simultaneously. It is found that this method is restricted lo the design of structures with few unknown variables. The second non-linear programming algorithm is presented .in a general form. This consists of two types of search, one improving feasibility and the other optimality. The method speeds up the 'feasible direction' approach by obtaining a constant weight direction vector that is influenced by dominating constraints. For pin jointed plane and space frames this method is used to obtain a 'minimum weight' design which satisfies restrictions on stresses and deflexions. The matrix force method enables the design requirements to be expressed in a general form and the design problem is automatically formulated within the computer. Examples are given to explain the method and the design criteria are extended to include member buckling. Fundamental theorems are proposed and proved to confirm that structures are inter-related. These theorems are applicable to linear elastic structures and facilitate the prediction of the behaviour of one structure from the results of analysing another, more general, or related structure. It becomes possible to evaluate the significance of each member in the behaviour of a structure and the problem of minimum weight design is extended to include shape. A method is proposed to design structures of optimum shape with stress and deflexion limitations. Finally a detailed investigation is carried out into the design of structures to study the factors that influence their shape.

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It is accepted today that the design of structures should include consideration of their vibrational characteristics. It is thus necessary to obtain structural vibration data by measurement or by use of computer predictions and to evaluate and modify the structures so that satisfactory characteristics are ultimately achieved. The amount of data involved is difficult to handle in all but the simplest cases and so relatively simple computer models become necessary to reduce this amount and to facilitate investigation of the effects of changes of design parameters. Spatial models consist of matrices of mass, stiffness and damping properties expressed in relation to selected coordinates of interest, in particular at points of connection. The lightly damped structures featured in this thesis have the property that their natural frequencies are easily distinguished from each other. The dynamic range of their mobility properties is very large. The earlier parts of this thesis are concerned with identification of modal parameters which represent the vibration behaviour of specific points on a structure. Extension is then made to the relationship of several points which are related by natural mode shapes. It is shown that such modal data can be converted into a spatial model of the structure. Particular attention is paid to the need to measure rotational mobilities and cope with the limitations of transducers. The use of residues to represent the effects of modes beyond the range of measurement is explored. The modelling techniques are initially evaluated on error-free data for ideal systems with finite numbers of modes and beams with unlimited numbers of modes. The latter parts of the thesis are concerned with the application of the foregoing measurement and analysis techniques to physical structures. Good results are obtained for modelling a simple beam assembly and for prediction of the lowest cantilever frequency of a turbine blade based on measurements of its free-free properties.

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