published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

A finite element formulation for the shear-deformable analysis of beams, plates and shells, based on a strain energy expression defined in terms of total and flexural displacement components, is presented. The effects of transverse shear deformation are considered while the normal strain is neglected. The finite element representation requires independent descriptions of total and flexural displacement components. The flexural strain energy term involves second derivatives of flexural displacement component and thereby necessitates slope-compatible shape functions. This requirement is relaxed by adopting the 'discrete Kirchhoff' hypothesis for the flexural displacement component. An element of triangular shape is formulated for the analysis of laminated composite plates and shallow shells. Numerically exact integration is employed in the calculation of element stiffness matrix and corresponding load vectors. The resulting finite element possesses twelve degrees of freedom at each corner node of the triangle. Numerical results obtained for an extensive range of thickness and planform aspect ratios, laminate configurations, mesh sizes, edge conditions, types of loading and geometry of the structure demonstrate the efficacy of the finite element formulation. The element is applicable to a full range of thicknesss ratios. The present formulation is employed for dynamic and stability analysis of beams, as a precursor to the inclusion of these effects in the analysis of plates and shells.

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Equal channel angular pressing ECAP is a process whereby simple shear is applied to a billet during multiple passages through an angled channel of constant cross section. The process is capable of generating very large plastic strains that significantly refines the microstructure without altering the external dimensions of the billet. A number of properties are influenced by grain refinement with the generation of a submicron grain structure SMG by ECAP resulting in improved strength and hardness and enhanced superplasticity. In this thesis, both an AA7075 alloy and AA7075 Al-base metal matrix composite MMC reinforced with 5 wt. percent of 50 nm diameter SiC particles was produced by a powder metallurgy route followed by hot extrusion. The materials were subsequently deformed by ECAP at 350 C to a true effective strain of 4.6 in an attempt to refine the microstructure and further distribute the SiC reinforcement phase in the composite. The high temperature microstructural stability of both the as-deformed alloy and composite was investigated to elucidate the effect of the reinforcement phase on continuous and discontinuous grain coarsening. It was found that ECAP generated a fine equiaxed grain size of ~ 2.3 !m and ~1.8 !m in the alloy and composite, respectively. The composite was more refined after ECAP since the SiC particles allow the matrix to undergo more grain refinement during deformation. ECAP was found to be a reasonable method for further distributing SiC clusters in this composite which is important for optimizing the reinforcement phase in terms of ambient temperature strengthening and enhanced grain stability at elevated temperature. Both the alloy and composite were annealed at times up to 5h at 500 C to assess grain stability. During annealing, the grain structure of both materials evolved in a continuous manner unlike the discontinuous process of recrystallization. Such a process is similar to continuous recrystallization observed in a range of heavily deformed Al alloys. Substantial grain boundary interactions with MgZn2 precipitates and oxide particles were found in the alloy, with precipitate, oxide and SiC particles found in the composite. The strong pinning force exerted by these particles minimised grain growth in both materials with the composite exhibiting a finer less than 2.5 !m grain size than the alloy less than 3.5 !m after extended annealing. This enhanced grain stability was attributed to the high volume fraction SiC particles which resulted in a large value of the dispersion parameter f/d which results in significant boundary pinning during annealing. Grain stability was also analysed in terms of a recently-proposed mean field model of annealing where it was predicted that the composite should not undergo discontinuous coarsening, as observed experimentally.

The problem of cavity expansion in unsaturated soils is investigated. A unified constitutive model for unsaturated soils is presented in a critical state framework using the concepts of effective stress and bounding surface plasticity theory. Consideration is given to the effects of suction and particle crushing in the definition of the critical state. A simple isotropic elastic rule is adopted. A loading surface and bounding surface of the same shape are defined using simple and versatile functions. A limiting isotropic compression line exists, towards which the stress trajectories of all isotropic compression load paths approach. A non-associated flow rule is assumed for all soil types. Isotropic hardening/softening occurs due to changes in plastic volumetric strains as well as suction for some unsaturated soils, enabling account of the phenomenon of volumetric collapse upon wetting. Results of isotropic compression tests, oedometric compression tests and drained and undrained triaxial compression tests performed on Kurnell (quartz) sand in saturated and unsaturated states and subjected to stresses sufficient to cause particle crushing are presented and used to calibrate the model. The model is also calibrated using results reported in the literature for triaxial tests performed on saturated and unsaturated speswhite kaolin and three load paths. For both soils the model leads to a much improved fit between simulation and experiment compared to that for models based on conventional plasticity theory. The model is implemented into a cavity expansion analysis using the similarity technique, extended for application to unsaturated soils. Cylindrical and spherical cavities are considered, as are drained and undrained conditions. Cavity expansion results for the bounding surface model and conventional plasticity models are compared for saturated conditions. Substantial differences highlight the importance of adopting a model that accurately describes stress-strain behaviour. Cavity expansion results for the bounding surface model and saturated and unsaturated conditions are also compared. Substantial differences, particularly in the limit pressure, highlight the major influence of suction and the importance of accounting for this when using cavity expansion theory to interpret results of the cone penetration and pressuremeter tests.

Even though the elastic deformations that occur during the impact of colliding bodies may be small in comparison to their actual dimensions, they play an important role in mechanical collisions. During the time the bodies are in contact, elastic, friction, and inertia properties combine to produce a complex variation of sliding and sticking throughout the contact surface. Detailed analysis of this interaction is quite tedious, but would seem to be necessary for accurately predicting the impulse and velocity changes that occur during contact. However, a considerably-simplified model captures the essential characteristics of the elastic-friction interaction during contact, leading to predictions of impulse and velocity changes that agree well with those of more detailed analyses of a number of different collisions. The model's simplicity enables an examination of parameters that affect a general class of collisions. For planar collisions, the model contains five dimensionless parameters; the effects of four of these on the rebound velocity are examined here. In addition, comparisons are made with a previously-used, somewhat simpler model, which neglects the tangential compliance in the region of contact. / Graduation date: 1993

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (leaves 109-116).

Thesis (Ph. D.)--University of Rhode Island, 2005. / Typescript. Includes bibliographical references (leaves 126-134).

Thesis--M. Sc.(Eng.), University of Hong Kong. / Errata slip inserted. Mimeographed.