Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-09-24T20:35:00Z No. of bitstreams: 2 Santos, Claudia Gomes de Oliveira - Dissertação - 2013.pdf: 1950939 bytes, checksum: 050c57553672656134c6b1264cb562a6 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2014-09-24T20:42:50Z (GMT) No. of bitstreams: 2 Santos, Claudia Gomes de Oliveira - Dissertação - 2013.pdf: 1950939 bytes, checksum: 050c57553672656134c6b1264cb562a6 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-09-24T20:42:50Z (GMT). No. of bitstreams: 2 Santos, Claudia Gomes de Oliveira - Dissertação - 2013.pdf: 1950939 bytes, checksum: 050c57553672656134c6b1264cb562a6 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-07-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The Boundary Element Method (BEM) has been successfully employed in the analysis of various engineering problems. The BEM consists in a mathematical modeling, for a numerical solution of a system of integral equations, and in their cores may appear singularities. This paper presents the Classical and Hypersingular formulation of the Boundary Element Method for dimensional elastostatic problems with smooth boundary geometry. The improper integrals arising from the singularities of the core in the hypersingular formulation are treated by Hadamard finite parts. In the discretization process two types of interpolation are used, one traditional and the other special. Traditional interpolation is used in all bondary elements that have no point , special interpolation ensures the continuity of the tangential derivative of displacements on the element that contains the point . To accomplish this, a theoretical mathematics study of related topics was performed. The hypersingular formulation developed in this work was implemented through the Intel Visual Fortran compiler. Some problems were analyzed and the obtained results were compared with those of analytical solution or through the Finite Element Method. The results achieved were satisfactory validating the proposed formulation / O Método dos Elementos de Contorno (MEC) vem sendo empregado com sucesso na análise de diversos problemas de engenharia. O MEC consisti em uma modelagem matemática, para resolução numérica de um sistema de equações integrais, e que em seus núcleos podem aparecer singularidades. Nesse trabalho apresenta a formulação Clássica e Hipersingular do Método dos Elementos de Contorno para problemas de elastostática bidimensional com geometria de contornos não suaves. As integrais impróprias que surgem da singularidade do núcleo na formulação hipersingular são tratados por partes finitas de Hadamard. No processo de discretização utiliza-se de dois tipos de interpolação, uma tradicional e outra especial. A interpolação tradicional é utilizada em todos os elementos de contorno que não tem o ponto , a interpolação especial garante a continuidade da derivada tangencial dos deslocamentos no elemento que contém o ponto . Para a realização deste, foi realizado um estudo teórico-matemático dos tópicos afins. Implementou-se a formulação hipersingular desenvolvidas no trabalho através do compilador Intel Visual FORTRAN. Foram analisados alguns problemas e os resultados obtidos comparados àqueles de solução analítica ou através do Método dos Elementos Finitos. Os resultados alcançados mostraram-se satisfatórios validando a formulação proposta.

published_or_final_version / abstract / toc / Computer Science and Information Systems / Master / Master of Philosophy

This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element methods are used. Error and stability analysis is presented for some of the methods. Numerical examples suggest that all three methods exhibit very similar convergence properties, consistent with available theoretical results.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 127-134).

Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. / South Africa is involved in huge mining operations deep in the earth's crust. Stresses induced by these mining operations may cause seismic events or rockbursts to occur, which could damage infrastructure and put miners' lives at risk. The effect of different mining layouts are modelled and used by engineers to make design decisions. The frequency at which models are updated and integrated with the decision making process is not optimal. These large mining layouts can not be modelled adequately using domain methods, but they are particularly well suited for the boundary element method (BEM). This work focuses on the theory and background needed for creating a linear elastic static stress boundary element solver suited to South African mining layouts. It starts with linear elastic theory and subsequently describes the physical continuum, governing equations and the fundamental solutions which are an integral part of the BEM. Kelvin's solution cannot be applied to crack-like excavations, therefore the displacement discontinuity kernels, which are very well suited to model fractures, are derived. The derivation is approached from both the direct and indirect BEM's perspectives. The problem is cast as a boundary integral equation which can be solved using the BEM. Some of the different specializations of the BEM are discussed. The major drawback of the BEM is that it produces a dense influence matrix which quickly becomes intractable on desktop computers. Generally a mining layout requires a large amount of boundary elements, even for coarse discretization, therefore different techniques of representing the influence matrix are discussed, which, combined with an iterative solver like GMRES or Bi-CG, allows solving linear elastic static stress models.

Orientador: Paulo Sollero / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-10T03:16:07Z (GMT). No. of bitstreams: 1 Paiva_SeilaVastiFariade_M.pdf: 1387945 bytes, checksum: 04ad3c76f01698f24ef5fd7ebfb49264 (MD5) Previous issue date: 2006 / Resumo: Nesta dissertação é apresentada uma análise de problemas da mecânica da fratura elástica linear em estruturas bimateriais anisotrópicas. Utilizando o método dos elementos de contorno é possível calcular os fatores de intensidade de tensão em problemas planos (2D) devido à presença de trincas interfaciais entre as lâminas que compõem o material. A estrutura pode estar submetida à carregamento em modo I ou modo misto. O problema é modelado usando-se a técnica de sub-regiões para descrever cada um dos diferentes subdomínios, representado por cada material. Na interface das sub-regiões, em que o domínio é dividido, são impostas condições de equilíbrio de forças e continuidade de deslocamentos, exceto na região que corresponde à trinca. O comportamento singular apresentado pelo campo de tensões próximo à ponta da trinca é modelado com elementos de ponto a um quarto com singularidade de forças de superfície. São apresentados exemplos numéricos de problemas com carregamentos no plano. Foi também apresentada a análise de convergência de malhas, mostrando uma pequena dependência da discretização mesmo quando malhas pouco refinadas foram usadas. Alguns dos exemplos têm correspondentes na literatura, os quais foram utilizados para comparação com os resultados obtidos. Observou-se uma boa concordância na comparação dos resultados / Abstract: This thesis presents an analysis of problems of linear elastic fracture mechanics in anisotropic bimaterial structures. Using the boundary element method, it is possible to evaluate stress intensity factors in plane problems (2D) due to the presence of interfacial cracks between the laminae that constitute the material, when the structure is submitted to a mode I or in mixed mode loading. The problem is modeled using the subregion technique to describe each one of the different subdomains, represented by each material. On the interface of subregions, which the domain is divided, conditions of tractions equilibrium and displacements continuity are imposed, except in the corresponding crack region. The singular behavior presented by the stress field near the crack tip is modeled by traction singular quarter point element. Numerical examples of problems with in-plane loading are presented. Mesh convergence analyses are also presented, showing little dependence on the discretization even when coarse meshes were used. Some of these examples have correspondents in literature, that were used for comparisons with the obtained results. A good agreement in the comparisons of results was observed. / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Orientador: Leandro Palermo Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-25T11:44:30Z (GMT). No. of bitstreams: 1 Reis_LuizAntonio_M.pdf: 3239468 bytes, checksum: 6e32be621db949f69c865def857a4bc9 (MD5) Previous issue date: 2014 / Resumo: O presente trabalho está divido em quatro partes. Na primeira parte, utilizando o método dos elementos de contorno (MEC), se fez a análise de problemas bidimensionais com aproximação linear. Foi considerada a possibilidade de se aplicar a técnica de sub-regiões para se levar em conta a diversidade de materiais, bem como a suavização do contorno por mínimos quadrados para evitar a possíveis perturbações. Foi considerado a possibilidade de colocação de uma linha de carga no domínio. Na segunda parte, utilizando o método dos elementos finitos (MEF), se fez a análise linear de pórticos planos. Para este estudo foram utilizadas barras com dois nós e esses com três graus de liberdade. Na terceira parte, a análise elástica linear de meios contínuos (Estado Plano de Tensão Generalizado) enrijecidos com elementos lineares (barras) é estudada fazendo-se um acoplamento entre elementos modelados com o MEC e com o MEF. As fibras são modeladas pelo MEF com elementos lineares de três graus de liberdade por nó e quatro nós por barra. Os elementos planos são modelados pelo MEC com elementos isoparamétricos lineares no perímetro. É permitido o uso de sub-regiões com objetivo de generalizar o tratamento do meio elástico. Na quarta parte, utilizando o acoplamento MEF/MEF, se fez a análise linear de pórticos planos sobre base elástica. O acoplamento se dá entre as barras do pórtico e as barras introduzidas como enriquecedor no problema elástico bidimensional. Tendo em conta estes aspectos da formulação desenvolvida, alguns exemplos são apresentados para avaliação de seu desempenho nos problemas de engenharia / Abstract: This paper is divided into four parts . In the first part , using the boundary element method (BEM) , we did the analysis of two-dimensional problems with linear approximation . We considered the possibility of applying the technique of sub - regions to take into account different materials, as well as smoothing the contour by least squares to avoid possible disturbances . We considered the possibility of placing a load line in the field. In the second part, the linear analysis for plane frames was carried out with the finite element method (FEM). Bars with two nodes and three degrees of freedom were used in this study . In the third part, the linear elastic analysis of continuous media (Generalized Plane Stress problems) stiffened with one-dimensional elements (bars) is studied through between elements of the BEM and the FEM. The fibers are modeled by FEM with three degrees of freedom linear elements and using four-nodes. The plane domain is modeled with the BEM and using isoparametric elements. The use of sub - regions in order to generalize the treatment of the elastic medium is allowed. In the fourth part , using the FEM / FEM coupling , a linear analysis of plane frames on elastic foundation is carried out. Some examples are presented to evaluate the formulation behavior engineering problems / Mestrado / Estruturas / Mestre em Engenharia Civil

Orientadores: Éder Lima de Albuquerque, Paulo Sollero / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-22T09:21:57Z (GMT). No. of bitstreams: 1 Doval_PauloCesarMarques_D.pdf: 6139026 bytes, checksum: 105e98efc86e87888cfa20e7b32d931d (MD5) Previous issue date: 2013 / Resumo: Este trabalho apresenta um método de elementos de contorno para a análise de estabilidade de placas de materiais compósitos laminados. A formulação do método proposto não necessita de discretização do domínio, nem de soluções particulares para a solução do problema. Isto torna a formulação proposta diferente das formulações de elementos de contorno existentes, aplicadas à análise de estabilidade estrutural. O método é aplicado a um problema importante em engenharia computacional, que é a estabilidade de placas de materiais isotrópicos e de compósitos laminados. O desempenho é avaliado através de comparação com os resultados de elementos finitos e resultados analíticos, mostrando boa concordância com os mesmos. No entanto, a vantagem em relação ao método dos elementos finitos, especificamente, em análise de estabilidade de placas de materiais compósito laminados, é que se torna um problema de autovalor com um número reduzido de graus de liberdade, uma vez que somente o contorno e poucos pontos internos são necessários na discretização do problema / Abstract: This work presents a boundary element method to the analysis of buckling plates. Neither domain discretization, nor particular solutions are necessary in the proposed formulation. This becomes the proposed formulation different from the existent boundary element formulations applied to structural stability analysis. The method is applied to an important problem in computational engineering that is the stability of perforated and non perforated plates of composite laminate materials. The performance is assessed through comparison with finite element results. The proposed formulation agrees quite well with finite element. However, the stability analysis is a much smaller eigenvalue problem if boundary elements are used instead of finite elements, provided that only the boundary and fewer internal points are necessary in the discretization / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

This dissertation develops and implements an effective numerical scheme, the inclusion-based boundary element method (iBEM), to investigate the mechanical and multi-physical properties of the composites containing arbitrarily shaped particles. Besides the linear elasticity and transient heat conduction problems shown in the dissertation, it can be extended to other problems, such as potential flows and Stokes flows. Through the combination of conventional boundary element method (BEM) and the Eshelby's equivalent inclusion method (EIM), the local field is obtained through superposition of the domain integral of eigen-fields and boundary integral equations. Firstly, the boundary value problems of a composite containing various fully bonding phases of subdomains is introduced. Due to the continuity of displacement (potential) and traction (flux) at the interfaces between different material phases, the interfacial continuity equations are established, which can be solved with the multi-region BEM conventionally. Thanks to Eshelby's celebrated contribution, the material difference in inhomogeneity problems is simulated by an eigenstrain on the inclusion domain but with the same material properties as the matrix. Therefore, the boundary value problems with inhomogeneities can be transformed as domain integral of Green's function with the eigenstrain over the inclusion, where can be determined by the equivalent stress conditions in EIM. Hence, the algorithm of iBEM is formulated and established on the basis of boundary conditions and equivalent stress equations instead of various continuity constraint equations, which saves efforts in computational resources and pre/post-process. The domain integral of Green's function is the key to the algorithm of iBEM, as it bridges the inhomogeneities and the boundary. The closed-form expression of domain integrals for ellipsoidal / elliptical inclusions with polynomial eigenstrain, polygonal and polyhedral inclusions with constant eigenstrain have already existed in the literature. However, it is not applicable to arbitrary particles with varying eigenstrain. This dissertation derives the closed-form domain integrals for polygon and polyhedral inclusions with polynomial eigenstrain source terms, which creates feasibility to solve the local field and effective material properties for composites with arbitrary particles. Although the EIM with polynomial-form eigenstrain has been applied to simulate the material mismatch for ellipsoidal / elliptical inhomogeneities by using the Taylor's of eigenstrain field at the particle center, when it is extended to angular particles, the inaccuracy is significantly reduced due to the rapid and complicated eigenstrain variation in the neighborhood of vertices with the strong singular effects. Therefore, the domain discretization of an angular particle is proposed to tackle the complicated distribution of elastic fields, which keeps the features of exactness (no approximation of interior field) and 𝐂⁰ continuity of eigenstrain. Hereby, the iBEM is proposed to serve as an effective and powerful tool, which takes the advantages of both BEM and EIM. The interaction of inhomogeneities is considered in the process of constructing EIM equations, and boundary effects are taken into account as the contribution to displacement of the eigen-field over inhomogeneities, hence, a complete linear equation system can be established. For the inclusion problems with a prescribed eigenstrain, no domain discretization is required because the exact elastic solution is obtained given the specific dimension of the geometry. Regarding to inhomogeneity problems, 1) the ellipsoidal / elliptical shape is versatile, which could be switched to various of shapes by adjusting the aspect ratio and orientations; 2) though the angular subdomain requires discretization, this method is rapidly convergent and no mesh is needed for the matrix. Therefore, this method enables the simulation of thousands 3𝐷 and 2𝐷 arbitrary shaped particles in a desk-top computer and the effective moduli can be obtained through virtual experiments (i.e, uni-axial loading) or periodic boundary conditions. This method can be easily extended to multi-physical problems, such as transient hear transfer, steady state heat, through changing the fundamental solutions accordingly. Three major packages have been added to the iBEM software, as transient heat transfer, closed-form 2D/3D domain integrals, and domain discretization method. Some case studies demonstrate the capability and applications of this method and software. This main contributions of the PhD studies are as follows: 1) The closed-form domain integrals for polygonal and polyhedral inhomogeneities have been derived based on the gravitational potential theory and transformed coordinates. The solutions are verified with the classic solution of circular and spherical potentials with polynomial source terms (i.e, linear and quadratic) by using many triangular and tetrahedral elements. It enables to solve the inhomogeneity problems with arbitrary particles. 2) Due to the discontinuity on the surfaces and edges of the subdomains and strong singular effects on the vertices, the variation of eigenstrain field is complicated in the neighborhood of edges and vertices. The domain discretization approach is proposed to provide a rapid convergent and effective solution in the infinite space. Different from the Taylor's expansion, the eigenstrain is assigned exactly at the nodes with shape functions instead of at the centroid of the elements, therefore, a 𝐂⁰ continuity is enforced. Here 3-node, 6-node triangular elements and 4-node, 10-node tetrahedral elements are implemented in the code of iBEM, which agree well with FEM but with much fewer of elements. Other types of element are also implementable in the same fashion. 3) The discretization method is applied to investigate the stress singularities of a vertex on an isosceles triangle embedded in an unbounded matrix. Two types of stress singularities are investigated: when the load is applied to the triangular inclusion with the same stiffness as the matrix, the singularity is caused by the irregular load distribution, namely load singularity, and can be exactly evaluated by integral of the potentials on the source with Eshelby's tensor. The second singularity, namely material singularity, is caused by the stiffness mismatch between the triangular inhomogeneity and the matrix under a uniform far field stress, in which the material mismatch is simulated by an eigenstrain. The relationship between the load singularity and material singularity is investigated, and the linkages of these singularities with line distributed force, cracking, and point force are discussed. 4) A parametric study of accuracy on stress field for uniform, linear and quadratic eigenstrain fields was performed and case studies have been presented to demonstrate the capability of iBEM for virtual experiments of ellipsoidal / elliptical inhomogeneities. Subsequently, combining the domain discretization method, iBEM is also applied to study the local elastic fields of the angular inhomogeneities. The effective material behavior is obtained with either large number of particles or periodic boundary condition (PBC) and some interesting discoveries of microstructure-dependent material behavior are reported with the aid of virtual experiments. 5) The iBEM is extended to multiphysical problems. The temperature and hear flux fields of composite materials containing phase change materials (PCM) for energy efficient buildings is demonstrated. Different from the static EIM, the thermal property mismatch between PCM particle and matrix phase is simulated with a uniformly distributed eigen-temperature gradient field and a fictitious heat source on the particle. With the equivalent heat flux conditions and the specific heat-temperature relationship, the eigen-temperature gradient and fictitious heat source can be solved and temperature field of the bounded domain can be calculated. Verified with FEM and laboratory measurements of the transient heat transfer within a building block containing a PCM capsule. Parametric studies have also been conducted to study the influences of the PCM location and volume fraction on the temperature fields of composites with multiple particles. The virtual experiments demonstrate the energy saving and phase delay by using the PCM-concrete wall panel. In summary, the proposed iBEM algorithm bridges the gap between conventional EIM and BEM for virtual experiments of composites samples. The combination of shape functions and domain integrals of polygonal / polyhedral subdomain enables its application to arbitrary shaped particles. It serves as a powerful tool to conduct virtual experiments for composite materials with various geometry and investigate the effective moduli under uni-axial load of samples with large number of particles or under the periodic boundary condition. In the future, the iBEM will be implemented for time independent and dependent nonlinear behavior of composites, such as elastoplastic, viscoelastic, and dynamic elastic problems. In addition to the current parallel computing scheme, GPU can be employed to speed up particle - particle interactions.

Uma implementação computacional baseada nos conceitos da mecânica do contato e no Método dos Elementos de Contorno é desenvolvida para simular a interação entre discos de corte e maciço rochosos. Simula-se o contato considerando-se inicialmente uma superfície potencial de contato que é atualizada durante um processo de carregamento incremental, podendo conter elementos separados, em contato sem deslizamento ou com deslizamento parcial. A cada passo do carregamento incremental estima-se a configuração do modelo e os dados obtidos neste passo serão utilizados como parâmetros no passo seguinte até que todo o carregamento esteja aplicado. O modelo em estudo consiste em dois discos de corte paralelos atuando sobre uma base sólida com característica elástica linear. São feitas duas simulações com os discos de corte. Na primeira delas, compara-se a penetração dos discos utilizando-se como parâmetro os valores calculados em uma análise por elementos finitos. No segundo caso, estuda-se a distribuição de tensões no maciço quando se altera o espaçamento entre os discos para um mesmo carregamento. Além desta análise, duas outras comparações são feitas utilizando como parâmetros soluções analíticas e numéricas de modelos clássicos da mecânica do contato. São estes: cilindro e pilar em base elástica. / A computational implementation based on contact mechanics and on the Boundary Element Method is developed in order to simulate the interaction between disc cutters and rock mass. The contact simulation considers initially a potential contact area which is updated during an incremental load process, in such way the surface can include elements in separation, stick or partial slip. At each incremental load step the configuration of the model shall be evaluated and the values computed at such step are used as parameter to the next load step until the end of the loading process. The investigated model consists in two parallel cutter discs on a flat elastic foundation. In the first simulation the penetration of the discs are studied and the results are compared against a finite element simulation. In the second simulation, the stress distribution in the rock mass is evaluated considering different spacing between the disc cutters by keeping the same load. In addition, two benchmark problems of contact mechanics, such as the cylinder and the flat punch on a elastic foundation, were modeled in order to validate the proposed algorithm. The obtained results were compared against analytical and numerical solutions.