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To evaluate and test control systems designed for heavy duty hydraulic excava-tor, it is important to simulate the force acting on the bucket during its excavation process. The study of soil-tool interaction contributes to the prediction and simula-tion of resistive forces experienced at the tool during digging. Even though many different finite element (FE) models have been developed in the past to study soil-tool interaction process, there is still needs to study the effects of soil-tool friction coefficient. The main objective of this thesis is to utilize finite element model to simulate the soil-tool interaction process, with the focus on the application of excavation, to study the effects of soil-tool friction coefficient on soil failure zone, soil resistive force, and stress distribution on the cutting tool by utilizing finite element model to simulate the soil-tool interaction process. / October 2016

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Chan Kit Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 90-93). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Model Elliptic Boundary-Value Problems --- p.2 / Chapter 1.2 --- Applications of the Model Boundary-Value Problem --- p.4 / Chapter 1.2.1 --- Curl-Curl Formulation --- p.4 / Chapter 1.2.2 --- Vector Potential Formulation --- p.6 / Chapter 1.2.3 --- Darwin Model and Quasistatic Model --- p.7 / Chapter 1.3 --- Spurious Solutions --- p.8 / Chapter 2 --- Finite Element Formulation --- p.11 / Chapter 2.1 --- Preliminaries --- p.11 / Chapter 2.2 --- Weak Formulation --- p.14 / Chapter 2.2.1 --- Galerkin Method --- p.17 / Chapter 2.2.2 --- The Rayleigh-Ritz Method --- p.19 / Chapter 2.3 --- H1(Ω) Conforming Finite Element Method --- p.23 / Chapter 2.3.1 --- The Dirichlet Problem --- p.24 / Chapter 2.3.2 --- The Neumann Problem --- p.27 / Chapter 3 --- Numerical Implementations --- p.29 / Chapter 3.1 --- Introduction --- p.29 / Chapter 3.2 --- Implementation of Boundary Conditions --- p.32 / Chapter 3.3 --- Numerical Integration Formula --- p.39 / Chapter 3.4 --- Discrete L2-norms --- p.40 / Chapter 3.5 --- Solution of Linear System of Equations --- p.42 / Chapter 3.6 --- Automatic Mesh Generation --- p.43 / Chapter 3.6.1 --- The Cubic Domain Ω --- p.44 / Chapter 3.6.2 --- The Spherical Shell Domain Ωs --- p.44 / Chapter 4 --- Numerical Experiments --- p.50 / Chapter 4.1 --- Numerical Experiments for Dirichlet Problem --- p.50 / Chapter 4.1.1 --- Original Formulation --- p.50 / Chapter 4.1.2 --- Experiments --- p.52 / Chapter 4.1.3 --- Penalty Factor Effect --- p.56 / Chapter 4.2 --- Numerical Experiment for Neumann Problem --- p.61 / Chapter 4.2.1 --- Original Formulation --- p.61 / Chapter 4.2.2 --- Experiments --- p.62 / Chapter 4.2.3 --- Penalty Factor Effect --- p.66 / Chapter 4.2.4 --- Comparison with the Dirichlet Problem --- p.70 / Chapter 4.3 --- Numerical Experiment of Dirichlet Problem with Boundary Condition E = E --- p.71 / Chapter 4.3.1 --- Original Formulation --- p.71 / Chapter 4.3.2 --- Experiments --- p.73 / Chapter 4.3.3 --- Penalty Factor Effect --- p.76 / Chapter 4.4 --- Numerical Experiment on Spherical Shell Domain --- p.81 / Chapter 4.4.1 --- The Spherical Shell Domain --- p.81 / Chapter 4.4.2 --- Dirichlet Problem --- p.82 / Chapter 4.5 --- Some Numerical Phenomena --- p.86 / Chapter 4.5.1 --- GMRES Convergence Accelerator --- p.86 / Chapter 4.5.2 --- Sparsity Improvement --- p.88 / Bibliography --- p.90 / List of Tables --- p.94

"It is well known that singularities occur when solving elliptic value problems with non-convex domains or when some part of the data or the coefficients of the PDE are not smooth. Such problems and correspondent singularities often arise in practice, for instance, in fracture mechanics, in the material science with heterogeneities, or when dealing with mixed boundary conditions. A great deal is known about the nature of the singularities, which arise in some of these problems. In this thesis, we consider the scalar transmission problems with straight interfaces and with cross points across coefficients and possibly on a non-convex region ($L$-shaped domain). It is known that only $H^{1+au}$ ($0 < au< 1$) regularity on the solution is obtained and therefore the use of finite element method with the piecewise linear continuous function space does not give optimal accuracy. In this thesis, we introduce a new algorithm which are second order accurate on the (weighted) $L_2$, first order accurate on the (weighted) $H_1$ norm and second order accurate for the Stress Intensive Factor (SIF). The new methods take advantage of Mortar techniques. The main feature of the proposed algorithms is that we use primal singular functions {it without} cutting-off functions. The old algorithms use cutting-off functions as a tool of satisfying boundary conditions. In algorithms proposed in this thesis, use instead Mortar finite element technique to match the boundary and interfaces conditions. In this thesis, we also consider non-matching meshes sizes for different coefficients. We note that a new Mortar Lagrange multiplier is required in order to obtain optimal consistence errors for transmission problems. The proposed algorithms are very appealing over other methods because they are very accurate, do not require complicated numerical quadratures or interpolations, it is simple to design PCGs, and it can be generalized to other PDEs and to higher order methods."

Errata pasted onto front end-paper. Bibliography: leaves 101-104. This thesis employs integral equation methods, or boundary element methods (BEMs), for the solution of three kinds of engineering problems associated with inhomogeneous materials or media: a class of elliptical boundary value problems (BVPs), the boundary value problem of static linear elasticity, and the calculation of the solution of the initial-boundary value problem of non-linear heat conduction for anisotropic media.

This thesis is concerned with a mathematical study of several problems involving infiltration from irrigation channels into an unsaturated homogeneous soil. All the problems considered are two dimensional and are solved numerically by employing boundary integral equation techniques. In the first chapter I introduce some of the literature and ideas surrounding my thesis. Some background information is stated followed by an outline of the thesis and a list of author’s published works that support the material in the thesis. Full descriptions of the fundamental equations used throughout the thesis are provided in chapter 2. Chapter 3 contains the first problem considered in this thesis which is infiltration from various shapes of single and periodic irrigation channels. Specifically strip, semi-circular, rectangular and v shaped channels. The solutions are obtained using the boundary element technique. The solutions are then compared with the results obtained by Batu [14] for single and periodic strip sources. In chapter 4 a boundary integral equation method is adopted for the solution of flow from single and periodic semi-circular channels into a soil containing impermeable inclusions. The impermeable inclusions considered are of rectangular, circular and square shapes. The aim is to observe how the various shapes of inclusions can affect the direction of the flow particularly in the region adjacent to the zone where plant roots would be located. Chapter 5 solves the problem of infiltration from single and periodic semicircular irrigation channels into a soil containing impermeable layers. A modification is made to the boundary integral equation in order to include the impermeable layers with the integration over the layers involving Hadamard finite-part integrals. The objective of the work is to investigate how the number and the depth of the impermeable layers affects the flow. Chapter 6 employs a particular Green’s function in the boundary integral equation. The Green’s function is useful for flow from a single channel since it removes the need to evaluate the boundary integral along the soil surface outside the irrigation channel. A time dependent infiltration problem is considered in chapter 7. The Laplace transform is applied to the governing equations and the boundary integral equation technique is used to solve the resulting partial differential equation. The Laplace transform is then inverted numerically to obtain the time dependent values of the matric flux potential. / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2008

Errata pasted onto front end-paper. / Bibliography: leaves 101-104. / xi, 174 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis employs integral equation methods, or boundary element methods (BEMs), for the solution of three kinds of engineering problems associated with inhomogeneous materials or media: a class of elliptical boundary value problems (BVPs), the boundary value problem of static linear elasticity, and the calculation of the solution of the initial-boundary value problem of non-linear heat conduction for anisotropic media. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 2002

Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

In this study, a heterogeneous flow model is proposed based on a non-overlapping domain decomposition method. The model combines potential flow and incompressible viscous flow. Both flow domains contain a free surface boundary. The heterogeneous domain decomposition method is formulated following the Dirichlet-Neumann method. Both an implicit scheme and an explicit scheme are proposed. The algebraic form of the implicit scheme is of the same form of the Dirichlet--Neumann method, whereas the explicit scheme can be interpreted as the classical staggered scheme using the splitting of the Dirichlet-Neumann method. The explicit scheme is implemented based on two numerical solvers, a Boundary element method (BEM) solver for the potential flow model, and a finite element method (FEM) solver for the Navier-Stokes equations (NSE). The implementation based on the two solvers is validated using numerical examples. / Graduation date: 2013