This research investigates composite tubes developed with hybrid preform manufacturing techniques of braiding and filament winding (FW). A quadriaxial braid-wound (QBW) preform [(±45°/0°/90°)2/(±45°/0°)] and a triaxial braided (TB60) preform [(±60°/0°)3] were developed. Quasi-isotropic (QI) fibre orientations were selected for both the lay-ups for comparison of mechanical properties. The large diameter of the tubes led to incomplete surface coverage with (±45°/0°)3 braided preforms (TB45). Circumferential distribution of multiple layers improved the coverage by reducing through the thickness resin pockets. Also addition of hoop winding improved the coverage and consolidated the braided preform. The use of braiding together with FW resulted in an improved fibre volume fraction. Also predicting surface coverage was a fundamental interest for a triaxial braided preform. An equation was proposed for cover factor estimation and was verified by using image analysis. Resin infusion of the preforms was carried out and composite tubes were fabricated. During resin infusion of braided preforms wrinkles were formed. A brief study on wrinkle formation was carried out and the reasons of wrinkle formation for braided tubes were identified based on existing literature. Longitudinal tensioning in conjunction with optimization of fibre amount in a layup and over-winding on braid was established to minimize wrinkle formation. This was primarily due to compaction of braided layers with hoop winding. Hence braid-winding has the additional advantage of manufacturing wrinkle free composite tubes. Finally composite tubes were tested under tension and torsion loads. One of the major findings was the effect of hoop winding on transverse deformation of the braid-wound tubes. As axial fibre percentage for QBW tube was less than that of TB45, the tensile strength was compromised. However presence of hoop winding resulted in lower transverse strain contributing to higher tensile modulus of QBW tubes along with lower Poisson's ratio. Although shear modulus of TB60 tube was exceptionally high for its fibre orientation, for QBW tubes, shear modulus was not significantly higher than that of other tubes. An aluminium tube was also tested for comparing the elastic properties of the QI tubes with those of an isotropic material. QBW tubes specific modulus was higher than that of the aluminium. The shear modulus of the QI and aluminium tubes was estimated by applying the theory for isotropic materials. In comparison to aluminium, for QBW tube the differences between estimated and actual shear modulus was higher. However QBW tube properties were in closer relation to those of the aluminium tube than TB60 tubes. Hence a QBW hybrid layup technique has the potential for manufacturing composite tubes without losing comparative composite material properties.

Herein we consider material tensors that pertain to thin sheets or thin films, which we model as two-dimensional objects. We assume that the thin sheet in question carries a crystallographic texture characterized by an orientation distribution function defined on the rotation group SO(3), which is almost transversely-isotropic about the sheet normal so that mechanical and physical properties of the thin sheet have weak planar-anisotropy. We present a procedure by which a special orthonormal basis can be determined in each tensor subspace invariant under the action of the orthogonal group O(2). We call members of such special bases irreducible basis tensors under O(2). For the class of thin sheets in question, we derive a representation formula in which each tensor in any given tensor subspace Z is written as the sum of a transversely-isotropic term and a linear combination of orthonormal irreducible basis tensors in Z, where the coefficients are given explicitly in terms of texture coefficients and undetermined material parameters. In addition to the general representation formula, we present also the specialized form for subspaces of tensor products of second-order symmetric tensors, a type commonly found in mechanics of materials.

In this thesis we study projective perspective on planar euclidean geometry. First we take an euclidean construction and transform it into the projective language. Then we discover and show principles of this transformation. We show equivalence between complex points I, J and some euclidean structures. Moreover we study conics, triangles, polygons and circles. We build this thesis on examples. 1

This thesis is based on three papers on selected topics in Asymptotic Geometric Analysis. The first paper is about the volume of high-dimensional random polytopes; in particular, on polytopes generated by Gaussian random vectors. We consider the question of how many random vertices (or facets) should be sampled in order for such a polytope to capture significant volume. Various criteria for what exactly it means to capture significant volume are discussed. We also study similar problems for random polytopes generated by points on the Euclidean sphere. The second paper is about volume distribution in convex bodies. The first main result is about convex bodies that are (i) symmetric with respect to each of the coordinate hyperplanes and (ii) in isotropic position. We prove that most linear functionals acting on such bodies exhibit super-Gaussian tail-decay. Using known facts about the mean-width of such bodies, we then deduce strong lower bounds for the volume of certain caps. We also prove a converse statement. Namely, if an arbitrary isotropic convex body (not necessarily satisfying the symmetry assumption (i)) exhibits similar cap-behavior, then one can bound its mean-width. The third paper is about random polytopes generated by sampling points according to multiple log-concave probability measures. We prove related estimates for random determinants and give applications to several geometric inequalities; these include estimates on the volume-radius of random zonotopes and Hadamard's inequality for random matrices. / Mathematics

The aim of this study was to investigate drying characteristics (temperature gradient, rate of drying and temperature change, drying time, diffusivity values, shrinkage) of isotropic and anisotropic foods by observing the changes in temperatures at four different locations and moisture contents and to build an appropriate model for simulation of temperature and moisture distribution using finite element method. The lean meat samples (anisotropic) with three fiber configurations (v / flow normal to fiber, drying along the fiber, h1 / flow normal to fiber, h2 / flow along to fiber) and minced meat (isotropic) were dried at two different temperatures (48

In this thesis, after a general introduction, we first review some differential geometry to provide the mathematical background needed to derive the key equations in cosmology. Then we consider the Robertson-Walker geometry and its relationship to cosmography, i.e., how one makes measurements in cosmology. We finally connect the Robertson-Walker geometry to Einstein's field equation to obtain so-called cosmological Friedmann-Lemaître models. These models are subsequently studied by means of potential diagrams.

We explore the capability of lattice Boltzmann equation (LBE) method for complex fluid flows involving turbulence, mixing, and reaction. In the first study, LBE schemes for binary scalar mixing and multi-component reacting flow with reactions are developed. Simulations of initially non-premixed mixtures yield scalar probability distribution functions that are in good agreement with numerical data obtained from Navier-Stokes (NS) equation based computation. One-dimensional chemically-reacting flow simulation of a premixed mixture yields a flame speed that is consistent with experimentally determined value. The second study involves direct numerical simulation (DNS) and large-eddy simulation (LES) of decaying homogenous isotropic turbulence (HIT) with and without frame rotation. Three categories of simulations are performed: (i) LBE-DNS in both inertial and rotating frames; (ii) LBE-LES in inertial frame; (iii) Comparison of the LBE-LES vs. NS-LES. The LBE-DNS results of the decay exponents for kinetic energy k and dissipation rate ε, and the low wave-number scaling of the energy spectrum agree well with established classical results. The LBE-DNS also captures rotating turbulence physics. The LBE-LES accurately captures low-wave number scaling, energy decay and large scale structures. The comparisons indicate that the LBE-LES simulations preserve flow structures somewhat more accurately than the NS-LES counterpart. In the third study, we numerically investigate the near-field mixing features in low aspect-ratio (AR) rectangular turbulent jets (RTJ) using the LBE method. We use D3Q19 multiple-relaxation-time (MRT) LBE incorporating a subgrid Smagorinsky model for LES. Simulations of four jets which characterized by AR, exit velocity, and Reynolds number are performed. The investigated near-field behaviors include: (1) Decay of mean streamwise velocity (MSV) and inverse MSV; (2) Spanwise and lateral profiles of MSV; (3) Half-velocity width development and MSV contours; and (4) Streamwise turbulence intensity distribution and spanwise profiles of streamwise turbulence intensity. The computations are compared against experimental data and the agreement is good. We capture both unique features of RTJ: the saddle-back spanwise profile of MSV and axis-switching of long axis from spanwise to lateral direction. Overall, this work serves to establish the feasibility of the LBE method as a viable tool for computing mixing, combustion, and turbulence.

Complex wrinkle patterns have been observed in various thin film systems, typically with integrated hard and soft materials for various technological applications as well as in nature. The underlying mechanism of wrinkling has been generally understood as a stress-driven instability. On an elastic substrate, equilibrium and energetics set the critical condition and select the wrinkle wavelength and amplitude. On a viscous substrate, wrinkles grow over time and kinetics select the dominant wavelength. More generally, on a viscoelastic substrate, both energetics and kinetics play important roles in determining the critical condition, the growth rate, and wrinkle patterns. The dynamics of wrinkling, while analogous to other phase ordering phenomena, is rich and distinct under the effects of a variety of stress conditions and nonlocal film-substrate interactions. In this study, a new mathematical model is developed for wrinkling of isotropic and anisotropic elastic films on viscoelastic substrates. Analytic solutions are obtained by a linear perturbation analysis and a nonlinear energy minimization method, which predict the kinetics of wrinkle growth at the initial stage and the equilibrium states at the long-time limit, respectively. In between, a power-law coarsening of the wrinkle wavelength is predicted by a scaling analysis. Numerical simulations confirm the analytical predictions and show diverse wrinkle patterns under various stress conditions. For isotropic elastic films, a transition from parallel wrinkles to zigzag patterns is predicted under anisotropic biaxial stresses. For cubic crystal films, the anisotropic elastic property leads to formation of orthogonal wrinkle patterns under equi-biaxial stresses. In general, the competition between the stress anisotropy and the material anisotropy controls the evolution of wrinkle patterns. Based on the mathematical model, two potential applications of the wrinkling phenomenon are explored, one for surface patterning and the other for estimating viscoelastic properties of thin polymer films. The theoretical and numerical results from this study are compared with experimental observations that are available in literature and through collaborations with experimental groups. The last chapter of this dissertation considers ratcheting-induced wrinkling for an elastic film on an elastoplastic substrate under cyclic temperatures, demonstrating an analogy between plastic ratcheting and viscous creep. / text

Sophisticated electromagnetic pulse sequences that control spin dynamics have been developed in Nuclear Magnetic Resonance (NMR) over the last few decades. However, due to more and more demanding criteria, such as unknown parameters, larger bandwidths, higher signal to noise ratio (SNR), less power consumption, etc., new pulse sequences are constantly needed. This thesis presents new pulse sequences for several important applications of NMR. / Engineering and Applied Sciences

This work is devoted to the numerical analysis of saturated porous media, taking into accountthe damage phenomenon on the solid skeleton. The porous media is taken into poroelasticframework, in full-saturated condition, based on the Biot's Theory. A scalar damage model isassumed for this analysis. An implicit Boundary element Method (BEM) formulation, basedon time-independent fundamental solutions, is developed and implemented to couple thefluid flow and the elasto-damage problems. The integration over boundary elements isevaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case oftriangular domain cells is followed to carry out the relevant domain integrals. The non-linearsystem is solved by a Newton-Raphson procedure. Numerical examples are presented, inorder to validate the implemented formulation and to illustrate its efficiency.