The research work presented here deals with the problems of geometrically nonlinear analysis of thin shell structures. The specific objective was to develop geometrically nonlinear formulations, using Discrete-Kirchhoff Curved Triangular (DKCT) thin shell elements. The DKCT elements, formulated in the natural curvilinear coordinates, based on arbitrary deep shell theory and representing explicit rigid body modes, were successfully applied to linear elastic analysis of composite shells in an earlier research work. A detailed discussion on the developments of classical linear and nonlinear shell theories and the Finite Element applications to linear and nonlinear analysis of shells has been presented. The difficulties of developing converging shell elements due to Kirchhoff's hypothesis have been discussed. The importance of formulating shell elements based on deep shell theory has also been pointed out. The development of shell elements based on Discrete-Kirchhoff's theory has been discussed. The development of a simple 3-noded curved triangular thin shell element with 27 degrees-of-freedom in the tangent and normal displacements and their first-order derivatives, formulated in the natural curvilinear coordinates and based on arbitrary deep shell theory, has been described. This DKCT element has been used to develop geometrically nonlinear formulation for the nonlinear analysis of thin shells. A detailed derivation of the geometrically nonlinear (GNL) formulation, using the DKCT element based on the Total Lagrangian approach and the principles of virtual work has been presented. The techniques of solving the nonlinear equilibrium equations, using the incremental methods has been described. This includes the derivation of the Tangent Stiffness matrix. Various Newton-Raphson solution algorithms and the associated convergence criteria have been discussed in detail. Difficulties of tracing the post buckling behavior using these algorithms and hence the necessity of using alternative techniques have been mentioned. A detailed numerical evaluation of the GNL formulation has been carried out by solving a number of standard problems in the linear buckling and GNL analysis. The results compare well with the standard solutions in linear buckling cases and are in general satisfactory for the GNL analysis in the region of large displacements and small rotations. It is concluded that this simple and economical element will be an ideal choice for the expensive nonlinear analysis of shells. However, it is suggested that the element formulation should include large rotations for the element to perform accurately in the region of large rotations.

Grinding/polishing and indentation induced residual stresses were measured by confocal Cr³⁺ fluorescence microscopy with high spatial resolution (~2 μm),obtaining local stress variation information rather than the mean stress averaged over a large sampling volume as is measured by other techniques. Due to the translucency of alumina materials, a substantial portion of the fluorescence signal comes from beneath the surface of the specimen. A probe response function (PRF) was developed taking account of microscope resolution, refraction, absorption and scattering, to quantitatively describe where the collected signal came from. It described the fluorescence intensity variations against defocus distance very well for a range of materials including sapphire, ruby, polycrystalline alumina and AI₂O₃/SiC nanocomposites. Large variations in the residual stresses on ground and polished surfaces were observed, owing to the surface fracture and pullouts. The broad peaks and narrow peaks separated from the spectra collected near the ground/polished surfaces physically represented the two distinct regions in the ground region: a plastically deformed surface layer and the elastically deformed material underneath. A model for the residual stress field taking into account the pullout was proposed using an array of virtual dislocations. The model agreed with the experimental results well when the PRF was included. Tensile stresses were detected on the ground surfaces of polycrystalline aluminas and 2 vol.% SiC nanocomposite, but not on the polished surfaces of polycrystalline aluminas or ground surfaces of 5 and 10 vol.% SiC nanocomposites. This was explained in terms of difference in the amount of pullouts on the surfaces. The depth of deformation was deeper in the ground polycrystalline alumina compared to the polished condition; the depth of deformation in alumina and the AI₂O>sub>3</sub>/SiC nanocomposites were similar (~1 μm) while the compressive stresses in the nanocomposites were greater owing to the reduction in pullout. The main difference between ground alumina and AI₂O₃/SiC nanocomposites was the brittle fracture behavior rather than the plastic deformation. Line scans and area mapping were carried out on 1 kg loaded Vickers indentations of alumina-based ceramics. Tensile stresses were found at the tips of radial cracks and lateral cracks and compressive stresses were found around the indent impression. The line scan results in the elastic regions agreed qualitatively with Yoffe's model and the quantitative discrepancy was attributed mainly to the cracking that relaxed the stresses. The differences in residual stresses between alumina and AI₂O₃/SiC nanocomposites were small if measured with high spatial resolution but it would be exaggerated with lower resolution.

published_or_final_version / Civil Engineering / Master / Master of Philosophy

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The need for the development of a rigorous analytical model of the lumbar spine to clarify the role of mechanical factors in low-back disorders has long been recognized. In response to this need, a general three dimensional nonlinear finite element program has been developed as part of this work and has been applied to the analysis of a lumbar L(,2-3) joint including the posterior elements. The analysis accounts for both the material and geometric nonlinearities and is based on a representation of the nucleus as an incompressible inviscid fluid and of the annulus as a composite of collagenous fibres embedded in a matrix of ground substance. The facet articulation has been accounted for by treating it as a general moving contact problem. The ligaments have been modelled as a collection of nonlinear axial elements. The geometry of the finite element model is based on in-vitro measurements. / The response of the joint under single compression, single flexion, single extension and also under flexion or extension combined with compression and sagittal shear has been analyzed for both the normal and degenerated states of the nucleus. Validity of the model has then been established by a comparison of those predictions which are also amenable to direct measurements. The states of strain and stress in different components of the lumbar joint have been thoroughly studied under all the foregoing loading conditions. / Those elements of the joint predicted to be vulnerable to mechanical failure or damage under the above types of loading have been identified. These results have been correlated with the lumbar joint injuries reported clinically. Furthermore, some joint injury mechanisms and degeneration processes have been proposed and the supporting clinical evidences have been presented.

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