Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 100-110).

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.

The present work presents a number of contributions to the areas of numerical integration, singular integrals, and boundary element methods. The first contribution is an elemental distortion technique, based on the Duffy transformation, used to improve efficiency for the numerical integration of near hypersingular integrals. Results show that this method can reduce quadrature expense by up to 75 percent over the standard Duffy transformation. The second contribution is an improvement to integration of weakly singular integrals by using regularization to smooth weakly singular integrals. Errors show that the method may reduce errors by several orders of magnitude for the same quadrature order. The final work investigated the use of regularization applied to hypersingular integrals in the context of the boundary element method in three dimensions. This work showed that by using the simple solutions technique, the BEM is reduced to a weakly singular form which directly supports numerical integration. Results support that the method is more efficient than the state-of-the-art.

Laminated composite plates have become an important and proven structural material in aerospace and ocean vehicles. However, because of the inherent orthotropy of laminated composite materials the analysis of these structures is complex and usually cannot be adequately performed using classical methods. In this dissertation the formulation of the fully coupled fluid-structure interaction of a laminated composite plate and its surrounding fluid medium is presented. The solution technique involves the finite element method for modeling the structural response and the boundary element method for modeling the acoustic field. The model incorporates the Mindlin plate theory which includes five degrees of freedom. An improved integration technique is demonstrated which significantly reduces the approximation error. Storage requirements are reduced by grouping complex numbers. Finally the fully coupled fluid-structure interaction involving laminated composite plates is modeled using the combined FEM-BEM approach demonstrating the usefulness and the significance of the method. / Ph. D.

Nonlinear free-surface flows generated by the motion of a surface-piercing body in an ideal fluid are studied. A numerical scheme employing a mixed Eulerian-Lagrangian approach and involving time stepping is used to simulate the flow. At each time step, the boundary value problem is solved using the Complex Boundary Element Method. The numerical performance of the method is studied by considering cases where the exact solution is known. Computational results for the impulsive wavemaker problem and the wedge entry problem for wedges of half-angles up to 15 degrees are presented. The obtained results are found to be in good agreement with existing analytical and numerical solutions. / Master of Science

A variation of the boundary element method is developed to determine the distribution of frictional heat and the ensuing surface or subsurface temperature rise caused by frictional heating between sliding solids. The theoretical model consists of two semi-infinite substrates each coated with a film of arbitrary thickness and thermal properties. A three dimensional transient analysis is developed which involves the thermal coupling of the two sliding solids at the true contact areas. The boundary element solution is based on a moving Green's function which naturally incorporates the combined conduction and convection effects due to sliding. Results are presented to display some of the important numerical characteristics of the boundary element solution method. Results are also presented that show the sensitivity of surface temperature rise to contact area evolvement, geometry and subdivision. The effects of surface film thickness and thermal properties on surface temperature rise are presented for a range of Peelet numbers. Lastly, a comparison of theoretical predictions and experimental measurements for surface temperature rise of a graphite epoxy ball loaded against a rotating sapphire disk is presented. / Master of Science

Numerical methods and specifically the finite element method have improved significantly since their introduction in the 60's. These advances were mainly in: 1) introducing higher-order elements, 2) developing effective solution schemes, 3) developing sophisticated means of modeling the constitutive behavior of geotechnical materials, and 4) introducing iteration techniques to model material non-linearity. This thesis, on the other hand, deals with the topic of modeling the boundary conditions of the finite element problem. Typically, the boundary conditions will be approximated by specifying displacement constraints. such as restraining the bottom boundary of the finite element mesh against displacements in the horizontal and vertical directions (x- and y-directions). Where bedrock or dense residual soils underlie the soft foundation soil at a relatively shallow depth, this is a good assumption. However. when soft soil is encountered for large depths, the assumption of zero movement constraints for a mesh boundary at a shallower depth than the actual bedrock will result in a serious underestimation of stresses and displacements. By coupling boundary elements to the finite elements and using them to model the infinite extent of the foundation soil, a more realistic answer is obtained. Employing the coupled boundary element - finite element method, four cases were analyzed and the results compared to values of the pure finite element method. The results show that the coupled method indeed yielded higher stress- and displacement-values, indicating that the pure finite element method underestimates stresses and displacements when modeling very deep soils. / Master of Science

Soil-structure interaction problems involve the solution of boundary value problems consisting of two domains: A near field finite domain representing the structure and adjacent soil, and a semi-infinite far-field domain representing the soil distant from the structure. Currently, the most used numerical method for solving such problems, the finite element method, considers only the near field, and neglects the effects of the far field. Depending on the domain size considered, this results in significant errors in the computed displacements and stress compared to closed form solutions. This research develops a numerical method in which both the near and far-field are considered. In this numerical procedure, the far field is assumed to be a homogenous elastic half-plane is modeled using boundary elements based on the Melan fundamental solution. A technique, called the substructure method, for coupling the boundary element method with finite element method is developed. Unlike other coupling techniques, the substructure method preserves the bandedness and symmetry of the system of equations resulting from the finite element method. The substructure method is implemented into a computer for program BEFEC for solving linear elastic and elasto-plastic plane strain problems. The proposed coupling technique is also incorporated into an existing finite element program SOILSTRUCT to perform soil-structure interaction analysis on U-frame lock structures. A series of analyses performed on the elastic strip footing problem indicate that significant errors occur in the predicted displacements and stresses when the effects of the the far field are ignored. These errors are unaffected by the boundary conditions assumed or the type of finite element used. The analyses demonstrated that the displacements and stresses obtained using the coupled BEM-FEM solution agree well with closed form solutions. Results of the soil-structure interaction analyses performed on U-frame lock structures indicates that neglecting the effects of the far field domain results in a significant underprediciton of the vertical displacements. These analyses also showed that there are significant differences in the computed shear stress and lateral pressures when the effects of the far field are considered. Results of the bearing capacity analyses of strip footing on elasto-plastic soils indicate that when the effects of the far field are taken into consideration, initial yield takes place at a higher load level. This in turn results is smaller plastic deformations as compared to the case when the far field is ignored. These analyses also shown that taking into consideration the far field results in significant differences in the computed stresses. These differences are diminished when the effects of self-weight are taken into consideration. The analyses performed on the Rankine earth pressure problem indicate that while the far field does not significantly affect the computed Rankine forces or lateral pressure distribution, much larger wall movements are required to reach both the active or passive States. / Ph. D.

In general relativity, angular momentum of the gravitational field in some volume bounded by an axially symmetric sphere is well-defined as a boundary integral. The definition relies on the symmetry generating vector field, a Killing field, of the boundary. When no such symmetry exists, one defines angular momentum using an approximate Killing field. Contained in the literature are various approximations that capture certain properties of metric preserving vector fields. We explore the continuity of an angular momentum definition that employs an approximate Killing field that is an eigenvector of a particular second-order differential operator. We find that the eigenvector varies continuously in Hilbert space under smooth perturbations of a smooth boundary geometry. Furthermore, we find that not only is the approximate Killing field continuous but that the eigenvalue problem which defines it is stable in the sense that all of its eigenvalues and eigenvectors are continuous in Hilbert space. We conclude that the stability follows because the eigenvalue problem is strongly elliptic. Additionally, we provide a practical introduction to the mathematical theory of strongly elliptic operators and generalize the above stability results for a large class of such operators. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

by Leung Hoi-Chau. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 70-71). / Abstracts in English and Chinese. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Previous Works --- p.2 / Chapter 2.1. --- Facial animations and facial surgery simulations / Chapter 2.2. --- Facial Action Coding System (FACS) / Chapter 2.3. --- The Boundary Element Method (BEM) in Computer Graphics / Chapter Chapter 3. --- The Facial Expression System --- p.7 / Chapter 3.1. --- Input to the system / Chapter 3.1.1. --- Orientation requirements for the input mesh / Chapter 3.1.2. --- Topology requirements for the input mesh / Chapter 3.1.3. --- Type of the polygons of the facial mesh / Chapter 3.2. --- Facial Modeling and Feature Recognition / Chapter 3.3. --- User Control / Chapter 3.4. --- Output of the system / Chapter Chapter 4. --- Boundary Element Method (BEM) --- p.12 / Chapter 4.1. --- Numerical integration of the kernels / Chapter 4.1.1. --- P and Q are different / Chapter 4.1.2. --- P and Q are identical / Chapter 4.1.2.1. --- Evaluation of the Singular Traction Kernel / Chapter 4.1.2.2. --- Evaluation of the Singular Displacement Kernel / Chapter 4.2. --- Assemble the stiffness matrix / Chapter Chapter 5. --- Facial Modeling --- p.18 / Chapter 5.1. --- Offset of facial mesh / Chapter 5.2. --- Thickening of Face Contour / Chapter Chapter 6. --- Facial Feature Recognition --- p.22 / Chapter 6.1. --- Extract all contour edges from the facial mesh / Chapter 6.2. --- Separate different holes from the contour edges / Chapter 6.3. --- Locating the bounding boxes of different holes / Chapter 6.4. --- Determine the facial features / Chapter 6.4.1. --- Eye positions / Chapter 6.4.2. --- Mouth position and Face / Chapter 6.4.3. --- Nose position / Chapter 6.4.4. --- Skull position / Chapter Chapter 7. --- Boundary Conditions in the system --- p.28 / Chapter 7.1. --- Facial Muscles / Chapter 7.2. --- Skull Bone / Chapter 7.3. --- Facial Muscle recognition / Chapter 7.3.1. --- Locating muscle-definers / Chapter 7.3.2. --- Locating muscles / Chapter 7.4. --- Skull Bone Recognition / Chapter 7.5. --- Refine the bounding regions of the facial features / Chapter 7.6. --- Add/Remove facial muscles / Chapter Chapter 8. --- Muscles Movement --- p.40 / Chapter 8.1. --- Muscle contraction / Chapter 8.2. --- Muscle relaxation / Chapter 8.3. --- The Muscle sliders / Chapter Chapter 9. --- Pre-computation --- p.44 / Chapter 9.1. --- Changing the Boundary Values / Chapter Chapter 10 --- . Implementation --- p.46 / Chapter 10.1. --- Data Structure for the facial mesh / Chapter 10.2. --- Implementation of the BEM engine / Chapter 10.3. --- Facial modeling and the facial recognition / Chapter Chapter 11 --- . Results --- p.48 / Chapter 11.1. --- Example 1 (low polygon man face) / Chapter 11.2. --- Example 2 (girl face) / Chapter 11.3. --- Example 3 (man face) / Chapter 11.4. --- System evaluation / Chapter Chapter 12 --- . Conclusions --- p.67 / References --- p.70