U-splines are a novel approach to the construction of a spline basis for representing smooth objects in Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE). A spline is a piecewise-defined function that satisfies continuity constraints between adjacent cells in a mesh. U-splines differ from existing spline constructions, such as Non-Uniform Rational B-splines (NURBS), subdivision surfaces, T-splines, and hierarchical B-splines, in that they can accommodate local variation in cell size, polynomial degree, and smoothness simultaneously over more varied mesh configurations. Mixed cell types (e.g., triangle and tetrahedron and quadrilateral and hexahedral cells in the same mesh) and T-junctions are also supported. The U-spline construction is presented for curves, surfaces, and volumes with higher dimensional generalizations possible. A set of requirements are given to ensure that the U-spline basis is positive, forms a partition of unity, is complete, and is locally linearly independent.

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Frost heave is the expansion of soil upon freezing due to the formation and growth of segregated ice lenses. Because of the large stresses and displacements associated with frost heave, it is an import design consideration for geotechnical structures such as roads, foundations, and buried pipelines, particularly in cold regions. The objective of this research was to characterize frost heave expansion within the context of design and analysis applications. A series of laboratory-scale frost heave experiments were conducted to examine frost heave under one-dimensional freezing. The previously established segregation potential concept (SP) was utilized to characterize both the intrinsic frost heave behavior of two reference soils. A novel modification was proposed to account for the observed variation of SP with freezing rate; it was noted that ignoring this influence would lead under-predictions the heave expansion. The thermal properties of frozen soils were explored. A method for characterizing the anisotropic thermal conductivity was proposed utilizing existing composite models in a multi-level homogenization. Ultimately it was determined that for ice lens-rich soils, a simpler and isotropic expression may provide similar performance, namely the geometric mean approximation. Additionally, a method was proposed to characterize the thermal conductivity of composite materials containing discrete particle phases using numerical simulations of complex phase geometries. This method was used to develop a specified characterization of discrete particle composites. iv A two-dimensional, fully coupled thermal-mechanical and implicitly coupled hydraulic frost heave model was formulated from thermodynamic principles. The model included the proposed form of SP to characterize the mass transport process. The finite element method was used to implement the model and its performance was validated in one-dimension through comparative analysis with the laboratory frost heave tests. Finally, the model was applied to a two-dimensional, full-scale problem involving the frost heave- induced displacement of a chilled natural gas problem. / Thesis / Doctor of Philosophy (PhD) / An experimental investigation was conducted and a numerical model was developed to predict the effects of frost heave in freezing soils. Frost heave is the expansion of soils caused by the formation of a specific type of ice, called ice lenses. This expansion can cause damage and lead to failure in roads, foundations, buried pipelines and other infrastructure exposed to heaving soils. The research developed a model capable of providing engineers with the information necessary to account for, and possibly avoid, these effects when designing such infrastructure. A series of experiments were conducted to produce frost heave in soils in a laboratory. The information gained from these tests was used to both develop and confirm the performance of a frost heave model using established numerical techniques. Finally, the model was used to simulate the upward movement of a buried natural gas pipeline exposed to frost heave in a cold region.

<p> A finite element method, incorporating the Hellinger-Reissner variational principle, has been developed for calculations of stress-strain and pore pressure for undrained and drained soil deformations. The soil is considered as cross-isotropically elastic material to account for the anisotropy of soil behaviour resulting from geological formations. A general expression for pore pressure parameters, taking into account the consolidation condition, has been hypothesized. Experimental investigations of consolidated undrained triaxial tests have been performed to study the validity of this expression.</p> / Thesis / Doctor of Philosophy (PhD)

<p> A stream function finite element model is developed to solve for particle paths within a large ice mass. A steady-state primitive variable finite element model, treating ice as an incompressible non-Newtonian fluid, is used to furnish the necessary input velocities and rotations for the stream function finite element model. Time-integration along the particle paths is used to determine the age of the ice within the ice mass.</p> <p> Two ice masses are studied: the Barnes Ice Cap, Baffin Island, N.W.T., and Mount Logan, Yukon Territory. It is shown that if a realistic approximation of the velocity field of an ice mass can be established, the age of ice determined by time-integration along particle paths corresponds to the age determined by standard methods. Results of simulations using a transient model suggest that the elastic response of large ice masses is negligible.</p> / Thesis / Master of Engineering (MEngr)

AA7075 is a precipitation hardening structural aluminum alloy, which has garnered considerable interest in automotive industry, primarily due its lightweighting capacity compared to many other aluminum alloys from 2xxx and 6xxx series. However, the damage evolution in AA7075 is quite complex due to the presence of different second phase particles in the microstructure and their contribution on damage evolution is largely unknown at large plastic strains. The common second phase particles are η precipitates, θ precipitates and Fe-rich intermetallic particles. The current work presents an extensive multiscale numerical framework, which in conjunction with complementary experiments, is applied to study strain localization, void nucleation, growth, and coalescence in a particle rich matrix. Experimentally, void nucleation is observed to be driven by particle decohesion and particle fracture. Nanoscale molecular dynamics (MD) simulation is carried out to estimate interface properties of the three distinct particle types. The extracted properties are used as input for real particle field 2D and 3D microstructure based finite element (FE) models. The stochastic nature of particle fracture is described using a Weibull distribution, while the effect of grains is incorporated in terms of their Taylor factors. Ductile matrix is described using the well known Gurson Tvergaard Needleman (GTN) void damage model. Complementary experiments included uniaxial tensile tests carried out in-situ in Scanning Electron Microscope (SEM) and X-ray Computed Tomography (XCT), ex-situ high resolution XCT and Electron Back Scattered Diffraction (EBSD) tests. The FE models with three distinct particle stoichiometries and three competing damage mechanisms, show good agreement with experimental observations. Particle fracture marginally dominates particle decohesion. At low plastic strains, void nucleation is initiated by decohesion and fracture of larger Fe-rich particles, which facilitate formation of localized deformation bands. At large plastic strain, elevated stresses within the localized bands facilitate decohesion and fracture of more resistant η and θ precipitates. Due to their inherent larger size and more irregular morphology, θ precipitates contribute to voiding more than η precipitates. Under uniaxial tensile loads, void growth takes place in the middle of the specimen, driven by higher triaxiality stress state in the middle, relative to the surface. Void coalescence occurs along deformation bands driven by higher stresses due accumulated plastic strain within the bands, in a process known as void sheeting. / Thesis / Doctor of Philosophy (PhD)

A finite element solver has been developed for performing analysis and sensitivity analysis with Poisson's equation. An application of Poisson's equation in fluid dynamics is that of poential flow, in which case Posson's equaiton reduces to Laplace's equation. The stiffness matrix and sensitivity of the stiffness matrix are evaluated by direct integrations, as opposed to numerical integration. This allows less computational effort and minimizes the sources of computational errors. The capability of evaluating sensitivity derivatives has been added in orde to perform design sensitivity analysis of non-lifting airfoils. The discrete-direct approach to sensitivity analysis is utilized in the current work. The potential flow equations and the sensitivity equations are computed by using a preconditionaed conjugate gradient method. This method greatly reduces the time required to perfomr analysis, and the subsequent design optimization. Airfoil shape is updated at each design iteratioan by using a Bezier-Berstein surface parameterization. The unstrucured grid is adapted considering the mesh as a system of inteconnected springs. Numerical solutions from the flow solver are compared with analytical results obtained for a Joukowsky airfoil. Sensitivity derivaatives are validated using carefully determined central finite difference values. The developed software is then used to perform inverse design of a NACA 0012 and a multi-element airfoil.

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