The ongoing drive for lighter and more efficient structural components by the commercial engineering industry has resulted in the rapid adoption of the finite element method (FE) for design analysis. Satisfied with the success of finite elements in reducing prototyping costs and overall production times, the industry has begun to look at other areas where the finite element method can save time, and in particular, improve designs. First, the mathematical methods of optimisation, on which the methods of structural design improvement are based, are presented. This includes the methods of: topology, influence functions, basis vectors, geometric splines and direct sensitivity methods. Each method is demonstrated with the solution of a sample structural improvement problem for various objectives (frequency, stress and weight reduction, for example). The practical application of the individual methods has been tested by solving three structural engineering problems sourced from the automotive engineering industry: the redesign of two different front suspension control arms, and the cost-reduction of an automatic brake tubing system. All three problems were solved successfully, resulting in improved designs. Each method has been evaluated with respect the practical application, popularity of the method and also any problems using the method. The solutions presented in each section were all solved using the FE design improvement software ReSHAPE from Advea Engineering Pty. Ltd.

Thesis (M.S.)--West Virginia University, 2007. / Title from document title page. Document formatted into pages; contains xii, 86 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 80-82).

The intrinsic flexibility of unstructured meshes is compelling for numerical ocean modeling. Complex topographic features, such as coastlines, islands and narrow straits, can faithfully be represented by locally increasing the mesh resolution and because there is no constraint on the mesh topology. In that respect, the finite element method is particularly promising. Not only does it allow for naturally handling unstructured meshes but it also offers additional flexibility in the choice of interpolation and is sustained by a rich and rigorous mathematical framework. This doctoral research was carried out under the auspices of the SLIM (Second-generation Louvain-la-Neuve Ice-ocean Model) project, the objective of which is to develop an ocean general circulation model using the finite element method. This PhD dissertation deals with one-, two- and three-dimensional finite element ocean modeling. We chiefly focus on the accurate representation of some selected oceanic processes and we devote much effort toward using a consistent finite element method to solve the underlying equations. We first concentrate on the finite element solution to a one-dimensional benchmark for the propagation of Poincaré waves with particular emphasis on the discontinuous Galerkin method and a physical justification for computing the numerical fluxes. We then compare three finite element formulations (vorticity - streamfunction, velocity - pressure and free-surface) for the solution to geophysical fluid flow instabilities problems. The prominent -- and remaining -- part of this work deals with three-dimensional ocean modeling on moving meshes. It covers the selection of the right elements for the vertical velocity and tracers through achieving strict tracer conservation and local consistency between the elevation, continuity and tracer equations. The ensuing three-dimensional model is successfully validated against a realistic tidal flow around a shallow-water island. New physical insights are proposed as to the physical processes encountered in such flows.

Thesis (Ph.D.)--State University of New York at Buffalo, 2006. / Includes bibliographical references. Also available online from ProQuest (http://proquest.umi.com/).

Thesis (Ph. D. in Civil Engineering)--Vanderbilt University, May 2007. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 119-124).

Elliptic partial differential equations that are used to model physical phenomena give rise to large sparse linear systems. Such systems can be symmetric positive definite and can be solved by the preconditioned conjugate gradients method. In this thesis, we develop support graph preconditioners for symmetric positive definite matrices that arise from the finite element discretization of elliptic partial differential equations. An object oriented code is developed for the construction, integration and application of these preconditioners. Experimental results show that the advantages of support graph preconditioners are retained in the proposed extension to the finite element matrices.

The solution of the secondary coupled-vector potential formulation of Maxwell??s equations governing the controlled-source electromagnetic (CSEM) response of an arbitrary, threedimensionalconductivitymodelmust be calculatednumerically.The finite elementmethod is attractive, because it allows the model to be discretized into an unstructured mesh, permitting the specification of realistic irregular conductor geometries, and permitting the mesh to be refined locally, where finer resolution is needed. The calculated results for a series ofsimple test problems, ranging from one-dimensionalscalar differentialequations to three-dimensional coupled vector equations match the known analytic solutions well, with error values several orders of magnitude smaller than the calculated values. The electromagnetic fields of a fully three-dimensional CSEM model, recovered from the potentials using the moving least squares interpolation numerical differentiation algorithm, compares well with published numerical modeling results, particularly when local refinement is applied. Multiple buried conductors in a conductive host interact via mutual induction and current flow through the host due to the dissipation of charge accumulated on the conductor boundary. The effect of this interaction varies with host conductivity, transmitter frequency, and conductor geometry, orientation, and conductivity. For three test models containingtwo highly conductive plate-like targets, oriented in various geometries (parallel, perpendicular, and horizontal), mutual coupling ranges as high as twenty times the total magnetic field. The effect of varying host conductivity is significant, especially at high frequencies. Numerical modeling also shows that the vorticity of the currents density induced in a vertically oriented plate-like conductor rotates from vertical at high frequencies, to horizontal at low frequencies, a phenomenon confirmed by comparison with time domain field data collected in Brazos County, Texas. Furthermore, the effect of the presence of a simple horst on the CSEM response of a homogeneous conductive earth is significant, even when the height of the horst is only a fraction of the skin depth of the model. When the transmitter is placedon topofthe horst, the currents inducedtherein account for nearly all of the total magnetic field of the model, indicating that topography, like mutual coupling must be accounted for when interpreting CSEM data.

Spontaneous imbibition plays a very important role in the displacement mechanism of non-wetting fluid in naturally fractured reservoirs. We developed a new 2D two-phase finite element numerical model, as available commercial simulators cannot be used to model small-scale experiments with different boundary conditions as well as complex boundary conditions such as fractures and vugs. Starting with the basic equation of fluid flow, we derived the non-linear diffusion saturation equation. This equation cannot be put in weighted-integral weak variational form and hence Rayleigh-Ritz finite element method (FEM) cannot be applied. Traditionally, the way around it is to use higher order interpolation functions and use Galerkin FEM or reduce the differentiability requirement and use Mixed FEM formulation. Other FEM methods can also be used, but iterative nature of those methods makes them unsuitable for solving large-scale field problems. But if we truncate the non-linear terms and decouple the dependent variables, from the spatial as well as the temporal domains of the primary variable to solve them analytically, the non-linear FEM problem reduces to a simple weighted integral form, which can be put into its corresponding weak form. The advantage of using Rayleigh-Ritz method is that it has immediate effect on the computation time required to solve a particular problem apart from incorporating complex boundary conditions. We compared our numerical models with the analytical solution of this diffusion equation. We validated the FDM numerical model using X-Ray Tomography (CT) experimental data from the single-phase spontaneous imbibition experiment, where two simultaneously varying parameters of weight gain and CT water saturation were used and then went ahead and compared the results of FEM model to that of FDM model. A two-phase field size example was taken and results from a commercial simulator were compared to the FEM model to bring out the limitations of this approach.

In the past two decades depth-sensing indentation has becomea widely used technique to measure the mechanical properties ofmaterials. This technique is particularly suitable for thecharacterisation of materials at sub-micro or nano scale thoughthere is a tendency to extend its application to the micro ormacro scale. The load-penetration depth curve of depth-sensingindentation is a characteristic of a material and can be usedfor analysing various mechanical properties in addition tohardness. This thesis deals with the mechanicalcharacterisation of bulk materials, thin films and coatings,gradient materials, and composites using depth-sensingindentation. Finite element method has been resorted to as atool to understand the indentation behaviour of materials. The piling-up or sinking-in behaviour of materials plays animportant role in the accurate determination of materialsproperties using depth-sensing indentation. Finite elementsimulations show that the piling-up or sinking-in behaviour isdetermined by the material parameters, namelyE/σyratio and strain hardening exponent orexperimental parameterhe/hmaxratio, and the contact friction. Anempirical model has been proposed to relate the contact area ofindentation to theE/σyratio and thehe/hmaxratio and used to predict thepiling-up orsinking-in of materials. The existence of friction is found toenhance the sinking-in tendency of materials. A generalrelationship between the hardness and the indentationrepresentative stress valid for both soft and hard materialshas been obtained. A possible method to estimate the plasticproperties of bulk materials has been suggested. Measuring the coating-only properties requires theindentation to be done within a critical penetration depthbeyond which substrate effect comes in. The ratio of thecritical penetration depth to the coating thickness determinedby nanoindentation is independent of coating thickness andabout 0.2 for gold / nickel, 0.4 for aluminium / BK7 glass, and0.2 for diamond-like-carbon / M2 steel and alumina / nickel.Finite element simulations show that this ratio is dependent onthe combination of the coating and the substrate and moresensitive to differences in the elastic properties than in theplastic properties of the coating/substrate system. Thedeformation behaviour of coatings, such as, piling-up of thesoft coatings and cracking of the hard coatings, has also beeninvestigated using atomic force microscope. The constraint factors, 2.24 for WC phase and 2.7 for WC-Cocemented carbides, are determined through nanoindentation andfinite element simulations. A modified hardness model of WC-Cocemented carbides has been proposed, which gives a betterestimation than the Lee and Gurland hardness model. Finiteelement method has also been used to investigate theindentation behaviour of WC-Co gradient coatings. Keywords:depth-sensing indentation, nanoindentation,finite element method, atomic force microscope, mechanicalproperties, hardness, deformation, dislocations, cracks,piling-up, sinking-in, indentation size effect, thin coatings,composite, gradient materials, WC-Co, diamond-like-carbon,alumina, gold, aluminium, nickel, BK7 glass, M2 steel.