Thesis (M.Eng.)--Memorial University of Newfoundland, 2005. / Bibliography: leaves 116-121.

We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solidand fluidmechanics.For manyof these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model.Most notably, the use of least-squares principles leads to a variational unconstrained minimization problem where stability conditions such as inf-sup conditions (typically arising in mixed methods using weak form Galerkin finite element formulations) never arise. In addition, the least-squares based finite elementmodelalways yields a discrete system ofequations witha symmetric positive definite coeffcientmatrix.These attributes, amongst manyothers highlightedand detailed in this work, allow the developmentofrobust andeffcient finite elementmodels for problems of practical importance. The research documented herein encompasses least-squares based formulations for incompressible and compressible viscous fluid flow, the bending of thin and thick plates, and for the analysis of shear-deformable shell structures.

<p align="justify">In a context of restoration of historical masonry structures, it is crucial to properly estimate the residual strength and the potential structural failure modes in order to assess the safety of buildings. Due to its mesostructure and the quasi-brittle nature of its constituents, masonry presents preferential damage orientations, strongly localised failure modes and damage-induced anisotropy, which are complex to incorporate in structural computations. Furthermore, masonry structures are generally subjected to complex loading processes including both in-plane and out-of-plane loads which considerably influence the potential failure mechanisms. As a consequence, both the membrane and the flexural behaviours of masonry walls have to be taken into account for a proper estimation of the structural stability.</p> <p align="justify">Macrosopic models used in structural computations are based on phenomenological laws including a set of parameters which characterises the average behaviour of the material. These parameters need to be identified through experimental tests, which can become costly due to the complexity of the behaviour particularly when cracks appear. The existing macroscopic models are consequently restricted to particular assumptions. Other models based on a detailed mesoscopic description are used to estimate the strength of masonry and its behaviour with failure. This is motivated by the fact that the behaviour of each constituent is a priori easier to identify than the global structural response. These mesoscopic models can however rapidly become unaffordable in terms of computational cost for the case of large-scale three-dimensional structures.</p> <p align="justify">In order to keep the accuracy of the mesoscopic modelling with a more affordable computational effort for large-scale structures, a multi-scale framework using computational homogenisation is developed to extract the macroscopic constitutive material response from computations performed on a sample of the mesostructure, thereby allowing to bridge the gap between macroscopic and mesoscopic representations. Coarse graining methodologies for the failure of quasi-brittle heterogeneous materials have started to emerge for in-plane problems but remain largely unexplored for shell descriptions. The purpose of this study is to propose a new periodic homogenisation-based multi-scale approach for quasi-brittle thin shell failure.</p> <p align="justify">For the numerical treatment of damage localisation at the structural scale, an embedded strong discontinuity approach is used to represent the collective behaviour of fine-scale cracks using average cohesive zones including mixed cracking modes and presenting evolving orientation related to fine-scale damage evolutions.</p> <p align="justify">A first originality of this research work is the definition and analysis of a criterion based on the homogenisation of a fine-scale modelling to detect localisation in a shell description and determine its evolving orientation. Secondly, an enhanced continuous-discontinuous scale transition incorporating strong embedded discontinuities driven by the damaging mesostructure is proposed for the case of in-plane loaded structures. Finally, this continuous-discontinuous homogenisation scheme is extended to a shell description in order to model the localised behaviour of out-of-plane loaded structures. These multi-scale approaches for failure are applied on typical masonry wall tests and verified against three-dimensional full fine-scale computations in which all the bricks and the joints are discretised.</p>

Proppants are a specific application of granular materials used in oil/gas well stimulation. Employment of hard and soft particle mixtures is one of the many approaches availed by the industry to improve fracture resistance and the stability of the granular pack in the hydraulic fracture. Current industrial practices of proppant characterization involve long term and expensive conductivity tests. However, the mechanics governing the proppant pack response, in particular the effects due to material, shape and size of particles on the pack porosity, stiffness and particle fragmentation are not understood clearly. The present research embodies analytical and experimental approach to model hard (ceramic) and soft (walnut shell and/or pure aluminum) proppant mixtures by taking into account polydispersity in size, shape and material type of individual particles. The hydraulic fracture condition is represented through confined compression and flowback loads. The particle interactions clearly illustrate changes in pore space as a function of pressure, mixture composition and friction. Single particle compression tests on individual particles are carried out to obtain mechanical properties which are incorporated into the finite element models and are further correlated with the compression/crush response of the mixture. The proppant pack stiffness and particle fragmentation depends strongly on the mixture composition as illustrated in the models and experiments. The flowback models demonstrated that the formation of a stable arch is essential to pack stability. Additional variables that enhance flowback resistance are identified as: addition of softer particles to a pack, softer rock surfaces and higher inter-particle friction. The computational studies also led to the discovery of better, and more efficient pack compositions such as - short and thin pure Al needles/ceramic and the pistachio shells/ceramic mixtures. These analytical results have generated great interest and are engaged in the design of experiments to formulate future proppant pack mixtures at Baker Hughes Pressure Pumping, Tomball, TX.

We consider the application of high-order spectral/hp finite element technology to the numerical solution of boundary-value problems arising in the fields of fluid and solid mechanics. For many problems in these areas, high-order finite element procedures offer many theoretical and practical computational advantages over the low-order finite element technologies that have come to dominate much of the academic research and commercial software of the last several decades. Most notably, we may avoid various forms of locking which, without suitable stabilization, often plague low-order least-squares finite element models of incompressible viscous fluids as well as weak-form Galerkin finite element models of elastic and inelastic structures. The research documented in this dissertation includes applications of spectral/hp finite element technology to an analysis of the roles played by the linearization and minimization operators in least-squares finite element models of nonlinear boundary value problems, a novel least-squares finite element model of the incompressible Navier-Stokes equations with improved local mass conservation, weak-form Galerkin finite element models of viscoelastic beams and a high-order seven parameter continuum shell element for the numerical simulation of the fully geometrically nonlinear mechanical response of isotropic, laminated composite and functionally graded elastic shell structures. In addition, we also present a simple and efficient sparse global finite element coefficient matrix assembly operator that may be readily parallelized for use on shared memory systems. We demonstrate, through the numerical simulation of carefully chosen benchmark problems, that the finite element formulations proposed in this study are efficient, reliable and insensitive to all forms of numerical locking and element geometric distortions.

The development of low-frequency sonar systems, using for instance a network of autonomous systems in unmanned vehicles, provides a practical means for bistatic measurements (i.e. when the source and receiver are widely separated) allowing for multiple viewpoints of the target of interest. Time-frequency analysis, in particular Wigner-Ville analysis, takes advantage of the evolution time dependent aspect of the echo spectrum to differentiate a man-made target (e.g. elastic spherical shell) from a natural one of the similar shape (e.g. solid). A key energetic feature of fluid loaded and thin spherical shell is the coincidence pattern, or mid-frequency enhancement echoes (MFE), that result from antisymmetric Lamb-waves propagating around the circumference of the shell. This thesis investigates numerically the bistatic variations of the MFE (with respect to the monostatic configuration) using the Wigner-Ville analysis. The observed time-frequency shifts of the MFE are modeled using a previously derived quantitative ray theory for spherical shell's scattering. Additionally, the advantage of an optimal array beamformer, based on joint time delays and frequency shifts (over a conventional time-delay beamformer) is illustrated for enhancing the detection of the MFE recorded across a bistatic receiver array.

Several problems must be solved in the construction, design, and operation of a nuclear fusion reactor. One of the chief problems in the manufacture of high-powered copper/polymer composite magnets is the difficulty to precisely control the fiber volume fraction. In this thesis, the effect of variations in fiber volume fraction on thermal stresses in copper/cyanate ester composite cylinders is investigated. The cylinder is a composite that uses copper wires that run longitudinally in a cyanate ester resin specifically developed by Composite Technology Development, Inc. This composite cylinder design is commonly used in magnets for nuclear fusion reactors. The application of this research is for magnets that use cylindrical coil geometry such as the Mega Amp Spherical Tokamak (MAST) in the UK. However, most stellarator magnet designs use complex geometries including the National Compact Stellarator Experiment (NCSX), and the Quasi-Poloidal Stellarator (QPS). Even though the actual stresses calculated for the cylindrical geometry may not be directly applicable to these projects, the relationship between fiber volume fraction and stresses will be useful for any geometry. The effect of fiber volume fraction on stresses produced by mechanical, thermal and magnetic loads on cylindrical magnet coils is studied using micromechanics with laminate plate theory (LPT) and finite element analysis (FEA).Based on the findings of this research, variations in volume fraction do significantly affect the stress experienced by the composite cylinder. Over a range of volume fractions from 0.3 to 0.5, the LPT results demonstrate that thermally induced stresses vary approximately 30% while stresses due to pressure vary negligibly. The FEA shows that magnetic stresses vary much less at around only 5%. FEA results seem to confirm the LPT model. It was also concluded that the stress in the insulation layers due to all types of loadings is significant and must be considered when using this system in fusion applications.

Thesis (Ph.D.)--Memorial University of Newfoundland, 2001. / Bibliography: leaves 166-174.

Thesis (M.Eng.)--Memorial University of Newfoundland, 2000. / Restricted until November 2001. Bibliography: leaves 93-99.

In the simulation of deformations of plates it is well known that we have to use a special treatment of the thickness dependence. Therewith we achieve a reduction of dimension from 3D to 2D. For linear elasticity and small deformations several techniques are well established to handle the reduction of dimension and achieve acceptable numerical results. In the case of large deformations of plates with non-linear material behaviour there exist different problems. For example the analytical integration over the thickness of the plate is not possible due to the non-linearities arising from the material law and the large deformations themselves. There are several possibilities to introduce a hypothesis for the treatment of the plate thickness from the strong Kirchhoff assumption on one hand up to some hierarchical approaches on the other hand.