A numerical method has been developed for computing the steady state flow about arbitrary shaped three dimensional bodies on or below the free surface using a Boundary Integral Element Method ( Panel Method). The method uses a singularity distribution over the body surface and the free surface. The method can solve for the potential distribution as well as the source density distribution. In this study a constant source distribution is assumed on each panel. The free surface boundary condition is linearized about the uniform undisturbed flow (Kelvin Free Surface condition). Upstream waves are prevented by the use of an one-sided upstream 4-point finite difference operator for the free surface condition. Wave elevations are computed using the linearized free surface condition. In this study two different bodies were considered: a submerged spheroid and a sphere. The wave resistance was computed for different Froude numbers and compares well with existing results. The study has also analyzed the effect of the number of panels on the body surface, the length of the free surface paneling behind the body and the aspect ratio of the free surface panels. / Master of Science

Based on the expression specifying the deformation of a multi-component object, a component-based condensation method is developed. This further reduces the size of the matrix to be inverted from the total number of unknown displacements to the number of unknown displacements with changing boundary condition. To speed up the construction of matrices, a maximal matrix technology is proposed. By categorizing the changes in boundary conditions, three fast update strategies on matrix inverse are introduced. Based on the maximal matrix technology and the matrix inverse update strategy, eight easily-formed characteristic matrices are defined to enhance the computation speed further. / In this thesis, an algorithm is developed for simulating the deformation of multiple objects with different material properties using the boundary element method. By tessellating the surface of a geometric model into elements, classifying all the element nodes into different groups with different attributes, and partitioning the stiffness matrix into several sub-matrices according to these attributes, a compact expression about the unknown variables is deduced. In this expression, the dimension of the system matrix has been effectively reduced compared with the traditional method. This expression shows that the deformation of a multi-component object can be simulated in a way similar to that of a single-component object. / Research on the real-time deformation of elastic models has captured wide attention and gained considerable achievement in the past two decades. Most related works focus on developing efficient ways to simulate the behavior of a single-component elastic object. However, objects are usually made up of multiple components with different material properties in practice. It is thus essential to develop efficient techniques for modeling objects which are composed of more than one material. / To make the proposed accelerated algorithm more applicable, a method for simulating the deformation of multi-component models with non-matching interfaces is developed. By applying the interpolation and extrapolation methods, the displacement data can be transferred between non-conforming interfaces. With the application of the energy conservation principle, a relationship between the internal forces on different surfaces can also be established. Together with the force equilibrium conditions and displacement compatibility conditions over the common faces of objects, the deformation of models composed of multi-material components with non-matching interfaces can be simulated. During the application of the linear interpolation method, when the mesh densities on the interfaces of the neighboring components are not the same, unexpected phenomena arise in the simulation process because of this disparity. A traction super-imposition method is adopted to enforce the force constraints on the interface. Experiments showed that this approach produces the correct results. / Zhou, Aifang. / "August 2007." / Adviser: Keh Chuen Hui. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1299. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 144-155). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

This thesis reports onreview and research work carried out on the numerical analysis of elastomers. The two numerical techniques investigated for this purpose are the finite and boundary element methods. The finite element method is studied so that existing theory is used to develop a finite element code both to review the finite element method as applied to the stress analysis of elastomers and to provide a comparison of results and numerical approach with the boundary element method. The research work supported on in this thesis covers the application of the boundary element method to the stress analysis of elastomers. To this end a simplified regularization approach is discussed for the removal of strong and hypersingularities generated in the system on non-linear boundary integral equations. The necessary programming details for the implementation of the boundary element method are discussed based on the code developed for this research. Both the finite and boundary element codes developed for this research use the Mooney-Rivlin material model as the strain energy based constitutive stress strain function. For validation purposes four test cases are investigated. These are the uni-axial patch test, pressurized thick wall cylinder, centrifugal loading of a rotating disk and the J-Integral evaluation for a centrally cracked plate. For the patch test and pressurized cylinder, both plane stress and strain have been investigated. For the centrifugal loading and centrally cracked plate test cases only plane stress has been investigated. For each test case the equivalent results for an equivalent FEM program mesh have been presented. The test results included in this thesis prove that the FE and BE derivations detailed in this work are correct. Specifically the simplified domain integral singular and hyper-singular regularization approach was shown to lead to accurate results for the test cases detailed. Various algorithm findings specific to the BEM implementation of the theory are also discussed.

A time-domain model was developed to predict the fluid/structure interaction of a three-dimensional deformable body in a fluid domain subject to long-crested finite amplitude waves. These nonlinear waves induce transient motion in the body. In turn, the interaction of the body with the waves modifies the wave field, causing additional motion in the body. A time-domain simulation was required to describe these nonlinear motions of the body and the wave field. An implicit three-dimensional time-domain boundary element model of the fluid domain was developed and then coupled iteratively with a finite element model of the deformable body. Large body hydrodynamics and ideal fluid flow are assumed and the diffraction/radiation problem solved. Either linear waves or finite amplitude waves can be treated in the model. Thus the full nonlinear kinematic and dynamic free surface boundary conditions are solved in an iterative fashion. To implicitly include time in the governing field equations, Volterra's method was used. The approach is similar to that of the typical boundary element method for a fluid domain where the boundary element integral is derived from the governing field equation. The difference is that in Volterra's method the boundary element integral is derived from the time derivative of the governing field equation. The transient membrane motions are treated by discretizing the spatial domain with curved isoparametric elements. Newton-Raphson iterations are used to account for the geometric nonlinearities and the equations of motion are solved using an implicit numerical method. Examples are included to demonstrate the validity of the boundary element model of the fluid domain. The conditions in a wave channel were numerically modeled and compared to sinusoidal waves. The interaction of a submerged rigid horizontal cylinder with water waves was modeled and results compared to experimental and numerical results. The capability of the model to predict the interaction of highly deformable bodies and water waves was tested by comparing the numerical model to large-scale physical model experiment of a membrane cylinder placed horizontally in a wave channel. / Graduation date: 1992

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (leaves 130-134).

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Bibliography: leaves 91-95. / x, 155 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis contains methods of solution for a number of different problems within the area of the elasticity of anisotropic materials. The first problem concerns the calculation of stresses and strains within a concentric arrangement of cylindrical shells, where each shell has a differing set of anisotropic properties. This has immediate application to the design of yacht masts, and the particular example of the "Moth" yacht mast is considered. The second problem considered is the uncoupled thermo-elastic problem, where a boundary element method is derived for solving the class of boundary value problems governing plane thermo-elastic deformations of isotropic and anisotropic materials. The final class of problems deals with mixed boundary value problems in which the stresses become singular at some points, for instance in elastic problems containing cracks. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1998

Thesis (Ph.D.)--University of Western Australia, 2006.

Diss. Karlstad : Karlstads universitet, 2007.