In this research project, the Boundary Element Method (BEM) is developed and formulated for the solution of two-dimensional convection-diffusion-reaction problems. A combined approach with the dual reciprocity boundary element method (DRBEM) has been applied to solve steady-state problems with variable velocity and transient problems with constant and variable velocity fields. Further, the radial integration boundary element method (RIBEM) is utilised to handle non-homogeneous problems with variable source term. For all cases, a boundary-only formulation is produced. Initially, the steady-state case with constant velocity is considered, by employing constant boundary elements and a fundamental solution of the adjoint equation. This fundamental solution leads to a singular integral equation. The conservation laws, usually applied to avoid this integration, do not hold when a chemical reaction is taking place. Then, the integrals are successfully computed using Telles' technique. The application of the BEM for this particular equation is discussed in detail in this work. Next, the steady-state problem for variable velocity fields is presented and investigated. The velocity field is divided into an average value plus a perturbation. The perturbation is taken to the right-hand-side of the equation generating a non-homogeneous term. This nonhomogeneous equation is treated by utilising the DRM approach resulting in a boundary-only equation. Then, an integral equation formulation for the transient problem with constant velocity is derived, based on the DRM approach utilising the fundamental solution of the steady-state case. Therefore, the convective terms will be encompassed by the fundamental solution and lie within the boundary integral after application of Greens's second identity, leaving on the right-hand-side of the equation a domain integral involving the time-derivative only. The proposed DRM method needs the time-derivative to be expanded as a series of functions that will allow the domain integral to be moved to the boundary. The expansion required by the DRM uses functions which take into account the geometry and physics of the problem, if velocity-dependent terms are used. After that, a novel DRBEM model for transient convection-diffusion-reaction problems with variable velocity field is investigated and validated. The fundamental solution for the corresponding steady-state problem is adopted in this formulation. The variable velocity is decomposed into an average which is included into the fundamental solution of the corresponding equation with constant coefficients, and a perturbation which is treated using the DRM approximation. The mathematical formulation permits the numerical solution to be represented in terms of boundary-only integrals. Finally, a new formulation for non-homogeneous convection-diffusion-reaction problems with variable source term is achieved using RIBEM. The RIM is adopted to convert the domain integrals into boundary-only integrals. The proposed technique shows very good solution behaviour and accuracy in all cases studied. The convergence of the methods has been examined by implementing different error norm indicators and increasing the number of boundary elements in all cases. Numerical test cases are presented throughout this research work. Their results are sufficiently encouraging to recommend the use of the techniques developed for solution of general convection-diffusion-reaction problems. All the simulated solutions for several examples showed very good agreement with available analytical solutions, with no numerical problems of oscillation and damping of sharp fronts.

Orientador: Paulo Sollero / Tese (doutorado) - Universidade Estadual de Campinas. Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-06T09:16:06Z (GMT). No. of bitstreams: 1 Noritomi_PedroYoshito_D.pdf: 4114284 bytes, checksum: 806cfb9e9589c5cd848086ed60178957 (MD5) Previous issue date: 2005 / Resumo: Este trabalho mostra o desenvolvimento de uma metodologia para análise de problemas de bioengenharia, aplicando modelagem numérica elastostática de tensões e deformações, baseada no método dos elementos de contorno com formulação 3D para meios transversalmente isotrópicos lineares, incluindo a capacidade de simulação do comportamento de remodelagem óssea superficial. A implementação do núcleo transversalmente isotrópico sobre a estrutura básica de análise por elementos de contorno 3D utilizou a solução fundamental proposta por Pan & Chou e revisada por Loloi, tendo exigido o cálculo adicional das soluções fundamentais de força de superfície a partir da derivação das soluções fundamentais de deslocamento. O modelo de remodelagem óssea superficial baseou-se na hipótese de estímulo biológico por campo de deformação, partindo de um modelo 2D, adaptado para o espaço 3D com o uso de deformações principais como grandezas de referência. As implementações foram testadas através de análises numéricas de problemas com solução analítica e validações com resultados de aplicações comerciais baseadas em elementos finitos, para problemas padrão de engenharia, bem como comparações com resultados da literatura para problemas de bioengenharia. A análise dos resultados mostrará que, tanto a metodologia quanto as implementações são funcionais, oferecendo uma base sólida para desenvolvimento e teste de novas soluções de bioengenharia / Abstract: This work shows the development of a methodology to analyse bioengineering problems using elastostatic stress-strain numerical modeling based on a 3D transversely isotropic linear boundary element formulation including surface bone remodeling simulation capabilities. The transversely isotropic kernel implementation on the basic 3D boundary element analysis program used the fundamental solution purposed by Pan & Chou and revised by Loloi, with additional fundamental solutions for traction calculation made with the displacement fundamental solution derivatives. The surface bone remodeling model was based on a 2D strain field biological stimulus, extended to the 3D space by using the principal strain as reference values. The implementations were tested through numerical analysis of problems with analytical solution and validation with commercial finite elements applications for standard engineering problems, as well as comparison with literature data for bioengineering problems. The analysis of results will show that both, the methodology and the implementations are fully functional, offering a solid start for development and test of new bioengineering solutions / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

The automotive industry has witnessed a trend in the recent years of reducing the bulk weight of the vehicle in order to achieve improved ride dynamics and economical fuel consumption. Unfortunately, reducing the bulk weight often compromises the noise, vibra- tion, and harshness (NVH) characteristics of the vehicle. In general, the automotive body panels are made out of thin sheet metals (steel and aluminium) that have a very low bend- ing stiffness. Hence, it becomes important to find countermeasures that will increase the structural stiffness of these thin body panels without affecting their bulk weight. One such countermeasure is to introduce the geometrical indentations on various body panels. The geometrical indentation explained in this thesis is in the shape of elliptical dome, which supports the increase of the structural stiffness whilst keeping the bulk weight constant. The primary reason to choose elliptical domes as the applied geometrical indentation is due to a significant amount of interest shown by Jaguar Land Rover. Moreover, the elliptical domes, because of the nature of its design, can cover a larger surface area with minimal depth, thereby, eliminating the possibility of sharp and pointy indentations. This thesis presents a comprehensive study of the structural-acoustic behaviour of the automotive-type panels with dome-shaped indentations. The ultimate aim of this research is to establish a set of design guidelines in order to produce automotive-type panels with optimised dome-shaped indentations. In order to do so, a new design optimisation strategy is proposed that results in the optimal placement of the required dome-shaped indenta- tions. The optimisation problem addressed in this thesis is unlike a general mathematical problem, and requires specific methodologies for its solution. Therefore, the use of genetic algorithm is observed as the most suitable method in order to tackle this type of design optimisation problem. During the development of the optimisation procedure, the preliminary results show a consistency in the design patterns. This led to the motivation to investigate a few intuitively designed panels, which are inspired by the initial, trial, optimisation results. Therefore, four intuitively designed panels are investigated for their structural-acoustic characteristics. The study of the intuitively designed panels provided essential physical insight into the design optimisation problem, which ultimately defined the guidelines in order to develop the proposed optimisation procedure. This type of optimisation procedure is completely new in the domain of structural-acoustic optimisation. The efficiency of the underlying work lies in the separate investigation of both the structural and the acoustic properties of the panels with various dome-shaped indentations, and then utilising the insights gained in order to develop a specific optimisation algorithm to stream-line the dome-shaped panel design procedure.