published_or_final_version / abstract / Civil Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

A poroelastic finite element formulation originally derived for modeling porous absorbing material in air is adapted to the problem of acoustic scattering from a poroelastic seafloor with a one-dimensional randomly rough interface. The developed formulation is verified through calculation of the plane wave reflection coefficient for the case of a flat surface and comparison with the well known analytical solution. The scattering strengths are then obtained for two different sets of material properties and roughness parameters using a Monte Carlo approach. These numerical results are compared with those given by three analytic scattering models---perturbation theory, the Kirchhoff approximation, and the small-slope approximation---and from those calculated using two finite element formulations where the sediment is modeled as an acoustic fluid. / text

The considerable progress in the research and development of thin-walled beam structures responds to their growing use in engineering construction and to their increased need for efficiency in strength and cost. The result is a structure that exhibits large shear strains and important non uniform warping under different loadings, such as non uniform torsion, shear bending and distortion... A unified approach is formulated in this thesis for 3D thin walled beam structures with arbitrary profile geometries, loading cases and boundary conditions. A single warping function, defined by a linear combination of longitudinal displacements at cross sectional nodes (derived from Prokic work), is enhanced and adapted in order to qualitatively and quantitatively reflect and capture the nature of a widest possible range of behaviors. Constraints are prescribed at the kinematics level in order to enable the study of arbitrary cross sections for general loading. This approach, differing from most published theories, has the advantage of enabling the study of arbitrary cross sections (closed/opened or mixed) without any restrictions or distinctions related to the geometry of the profile. It generates automatic data and characteristic computations from a kinematical discretization prescribed by the profile geometry. The amount of shear bending, torsional and distortional warping and the magnitude of the shear correction factor is computed for arbitrary profile geometries with this single formulation. The proposed formulation is compared to existing theories with respect to the main assumptions and restrictions. The variation of the location of the torsional center, distortional centers and distortional rotational ratio of a profile is discussed in terms of their dependency on the loading cases and on the boundary conditions. A 3D beam finite element model is developed and validated with several numerical applications. The displacements, rotations, amount of warping, normal and shear stresses are compared with reference solutions for general loading cases involving stretching, bending, torsion and/or distortion. Some examples concern the case of beam assemblies with different shaped profiles where the connection type determines the nature of the warping transmission. Other analyses –for which the straightness assumption of Timoshenko theory is relaxed– investigate shear deformation effects on the deflection of short and thin beams by varying the aspect ratio of the beam. Further applications identify the cross sectional distortion and highlight the importance of the distortion on the stresses when compared to bending and torsion even in simple loading cases. Finally, a non linear finite element based on the updated lagrangian formulation is developed by including torsional warping degrees of freedom. An incremental iterative method using the arc length and the Newton-Raphson methods is used to solve the non linear problem. Examples are given to study the flexural, torsional, flexural torsional and lateral torsional buckling problems for which a coupling between the variables describing the flexural and the torsional degrees of freedom occurs. The finite element results are compared to analytical solutions based on different warping functions and commonly used in linear stability for elastic structures having insufficient lateral or torsional stiffnesses that cause an out of plane buckling.

The challenge for lithography today is to continue the reduction of feature size whilst facing severe theoretical and practical limitations. In 2006 Rajesh Menon and Hank Smith proposed a new lithography system named absorbance modulation optical lithography (AMOL) [Menon 2006]. AMOL proposed replacing the normal metal mask of a lithography system with an absorbance modulation layer (AML), made from a photochromic material. This allows, through the competition between two incident wavelengths, the creation of an adaptive absorbance mask. The AML allows intimate contact to an underlying resist and hence the optical near-field may be used to create sub-diffraction limited exposures. The aim of this thesis is to model AMOL and demonstrate the abilities and the limits of the system, particularly focusing on sub-diffraction limited imaging. This thesis describes the construction of a vector electromagnetic simulation to explore the idea and performance of AMOL, and an exploration of the ability of AMOL to propagate sub-diffraction limited images into a photoresist. A finite element method (FEM) model was constructed to simulate the formation of apertures in the AML and light transmission through the system. Three major areas of interest were explored in this thesis; the effect of polarisation on imaging, using a plasmonic reflector layers (PRLs) to improve the depth of focus (DOF), and introducing a superlens to AMOL. Investigations of polarisation demonstrated strong preference for a transverse magnetic (TM) polarised exposing wavelength for near-field exposures. Associated with polarisation, and supporting work with absorbance gratings, the importance of the material parameters of the AML in allowing sub-diffraction limited exposures was discussed. It was also noted that, in common with all near-field systems, the depth of focus (DOF) was poor, worse than comparable metal systems. This thesis also demonstrates that the introduction of a PRL can improve the DOF and process latitude for resist thicknesses up to 60 nm and, although performance was reduced when using a silver PRL, the substantial improvements to the DOF and process latitude make a PRL valuable for an AMOL system. This thesis also models the superlens to an AMOL system, which theoretically allows propagation of the image in the near-field. It is demonstrated that the superlens can project an AMOL image into an underlying resist, but that this image is degraded, especially for thick and non-ideal superlenses. The superlens does have a second useful effect, as it can act as a dichroic filter; decreasing the intensity ratio in the resist by a factor of ten, overcoming issues of resist sensitivity. The superlens can allow image projection and filtering with AMOL, however improvements to the available superlens materials or changes to the AML will be needed to avoid image deterioration. This thesis has developed the first full-vector model of an absorbance modulation optical lithography (AMOL) system. This model has been used to increase the understanding of the complex effects that go into the creation of sub-diffraction limited features with AMOL. In particular the model has been used to investigate polarisation, PRLs and superlenses in AMOL. This thesis demonstrates the ability of AMOL to create narrow apertures and sub-diffraction limited exposures in a photoresist, and describes the limitations of AMOL, including material parameters and DOF. AMOL is a new and interesting lithography technique; this thesis simulates the abilities and challenges of sub-diffraction lithography using an AMOL system.

Petrov-Galerkin finite element methods based on time-space elements are developed for the time-dependent multi-dimensional linear convection-diffusion equation. The methods introduce two parameters in conjunction with perturbed weighting functions. These parameters are determined locally using truncation error analysis techniques. In the one-dimensional case, the new algorithms are thoroughly analyzed for convergence and stability properties. Numerical schemes that are second order in time, third order in space and stable when the Courant number is less than or equal to one are produced. Extensions of the algorithm to nonlinear Navier-Stokes equations are investigated. In this case, it is found more efficient to use a Petrov-Galerkin method based on a one parameter perturbation and a semi-discrete Petrov-Galerkin formulation with a generalized Newmark algorithm in time. The algorithm is applied to the two-dimensional simulation of natural convection in a horizontal circular cylinder when the Boussinesq approximation is valid. New results are obtained for this problem which show the development of three flow regimes as the Rayleigh number increases. Detailed calculations for the fluid flow and heat transfer in the cylinder for the different regimes as the Rayleigh number increases are presented.

The purpose of the research was to develop a quantitative method which could be used to obtain a clearer understanding of the time-dependent fluid filteration and load-deformation behavior of soft, porous, fluid filled materials (e.g. biological tissues, soil). The focus of the study was on the development of a finite strain theory for multiphasic media and associated computer models capable of predicting the mechanical stresses and the fluid transport processes in porous structures (e.g. across the large blood vessels walls). The finite element (FE) formulation of the nonlinear governing equations of motion was the method of solution for a poroelastic (PE) media. This theory and the FE formulations included the anisotropic, nonlinear material; geometric nonlinearity; compressibility and incompressibility conditions; static and dynamic analysis; and the effect of chemical potential difference across the boundaries (known as swelling effect in biological tissues). The theory takes into account the presence and motion of free water within the biological tissue as the structure undergoes finite straining. Since it is well known that biological tissues are capable of undergoing large deformations, the linear theories are unsatisfactory in describing the mechanical response of these tissues. However, some linear analyses are done in this work to help understand the more involved nonlinear behavior. The PE view allows a quantitative prediction of the mechanical response and specifically the pore pressure fluid flow which may be related to the transport of the macromolecules and other solutes in the biological tissues. A special mechanical analysis was performed on a representative arterial walls in order to investigate the effects of nonlinearity on the fluid flow across the walls. Based on a finite strain poroelastic theory developed in this work; axisymmetric, plane strain FE models were developed to study the quasi-static behavior of large arteries. The accuracy of the FE models was verified by comparison with analytical solutions wherever is possible. These numerical models were used to evaluate variables and parameters, that are difficult or may be impossible to measure experimentally. For instance, pore pressure distribution within the tissue, relative fluid flow; deformation of the wall; and stress distribution across the wall were obtained using the poroelastic FE models. The effect of hypertension on the mechanical response of the arterial wall was studied using the nonlinear finite element models. This study demonstrated that the finite element models are powerful tools for the study of the mechanics of complicated structures such as biological tissue. It is also shown that the nonlinear multiphasic theory, developed in this thesis, is valid for describing the mechanical response of biological tissue structures under mechanical loadings.

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