Dissertations / Theses on the topic 'Indirect boundary element method'
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Rahman, Abdul Ghaffar Abdul. "An investigation of the regular indirect boundary element method." Thesis, University of Sheffield, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320149.
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Lindkvist, Gaute. "Indirect boundary element methods for modelling bubbles under three dimensional deformation." Thesis, Deaprtment of Engineering Systems and Management, 2009. http://hdl.handle.net/1826/3098.
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The nonlinear behaviour of gas and vapour bubbles is a complex phenomenon
which plays a signi cant role in many natural and man-made processes.
For example, bubbles excited by an acoustic eld play important roles in
lithotripsy, drug delivery, ultrasonic imaging, surface cleaning and give rise
to the phenomenon of sonoluminescence (light emission from a bubble excited
by sound). In such contexts, the oscillation of even a single bubble is not
yet fully understood, let alone the behaviour of multiple bubbles interacting
with each other. An essential part of understanding such problems is un-
derstanding the complex and sometimes unpredictable coupling between the
oscillation of the bubble volume and the bubble shape, a problem requiring
experimental research, theoretical work and numerical studies.
In this Thesis we focus on numerical simulation of a single gas bubble
oscillating in a free liquid. Previously, such numerical simulations have al-
most exclusively assumed axisymmetry and small amplitude oscillations. To
avoid these assumptions we build upon and extend previous boundary ele-
ment methods used for three dimensional simulations of other bubble prob-
lems. We use high order elements and parallel processing to yield an indirect
boundary element method capable of capturing ne surface e ects on three
dimensional bubbles subjected to surface tension, over extended periods of
time.
We validate the method against the classical Rayleigh-Plesset equation
for spherical oscillation problems before validating the indirect boundary el-
ement method and the method used by Shaw (2006), against each other, on
several small amplitude axisymmetric oscillation problems. We then proceed
to study near-resonant non-axisymmetric shape oscillations of order 2 and 4
and the e ect these oscillations have on higher order modes, with a level of
detail we believe has not been achieved in a non-axisymmetric study before.
We also con rm some predictions made by Pozrikidis' on resonant interac-
tions between the second order modes and the volume mode in addition.
Finally we study the spherical instability of a bubble trapped in a uniform
acoustic eld, demonstrating, as expected, that instabilities show up in all
resonant shape modes, including non-axisymmetric ones.
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Lee, Jimin. "Earthquake site effect modeling in sedimentary basins using a 3-D indirect boundary element-fast multipole method." Diss., Online access via UMI:, 2007.
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Fan, Xijun. "Numerical study on some rheological problems of fibre suspensions." Thesis, The University of Sydney, 2006. http://hdl.handle.net/2123/1096.
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This thesis deals with numerical investigations on some rheological problems of fibre suspensions: the fibre level simulation of non-dilute fibre suspensions in shear flow; the numerical simulation of complex fibre suspension flows and simulating the particle motion in viscoelastic flows. These are challenging problems in rheology. Two numerical approaches were developed for simulating non-dilute fibre suspensions from the fibre level. The first is based on a model that accounts for full hydrodynamic interactions between fibres, which are approximately calculated as a superposition of the long-range and short-range hydrodynamic interactions. The long-range one is approximated by using slender body theory and includes infinite particle interactions. The short-range one is approximated in terms of the normal lubrication forces between close neighbouring fibres. The second is based on a model that accounts only for short-range interactions, which comprise the lubrication forces and normal contact and friction forces. These two methods were applied to simulate the microstructure evolution and rheological properties of non-dilute fibre suspensions. The Brownian configuration method was combined with the highly stable finite element method to simulate the complex flow of fibre suspensions. The method is stable and robust, and can provide both micro and macro information. It does not require any closure approximations in calculating the fibre stress tensor and is more efficient and variance reduction, compared to CONNFFESSITT, for example. The flow of fibre suspensions past a sphere in a tube and the shear induced fibre migration were successfully simulated using this method The completed double layer boundary element method was extended to viscoelastic flow cases. A point-wise solver was developed to solve the constitutive equation point by point and the fixed least square method was employed to interpolate and differentiate data locally. The method avoids volume meshing and only requires the boundary mesh on particle surfaces and data points in the flow domain. A sphere settling in the Oldroyd-B fluid and a prolate spheroid rotating in shear flow of the Oldroyd-B fluid were simulated. Based on the simulated orbit of a prolate spheroid in shear flow, a constitutive model for the weakly viscoelastic fibre suspensions was proposed and its predictions were compared with some available experimental results. All simulated results are in general agreement with experimental and other numerical results reported in literature. This indicates that these numerical methods are useful tools in rheological research.
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Fan, Xijun. "Numerical study on some rheological problems of fibre suspensions." School of Aerospace, Mechanical & Mechatronic Engineering, 2006. http://hdl.handle.net/2123/1096.
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Doctor of philosophy (Ph D)This thesis deals with numerical investigations on some rheological problems of fibre suspensions: the fibre level simulation of non-dilute fibre suspensions in shear flow; the numerical simulation of complex fibre suspension flows and simulating the particle motion in viscoelastic flows. These are challenging problems in rheology. Two numerical approaches were developed for simulating non-dilute fibre suspensions from the fibre level. The first is based on a model that accounts for full hydrodynamic interactions between fibres, which are approximately calculated as a superposition of the long-range and short-range hydrodynamic interactions. The long-range one is approximated by using slender body theory and includes infinite particle interactions. The short-range one is approximated in terms of the normal lubrication forces between close neighbouring fibres. The second is based on a model that accounts only for short-range interactions, which comprise the lubrication forces and normal contact and friction forces. These two methods were applied to simulate the microstructure evolution and rheological properties of non-dilute fibre suspensions. The Brownian configuration method was combined with the highly stable finite element method to simulate the complex flow of fibre suspensions. The method is stable and robust, and can provide both micro and macro information. It does not require any closure approximations in calculating the fibre stress tensor and is more efficient and variance reduction, compared to CONNFFESSITT, for example. The flow of fibre suspensions past a sphere in a tube and the shear induced fibre migration were successfully simulated using this method The completed double layer boundary element method was extended to viscoelastic flow cases. A point-wise solver was developed to solve the constitutive equation point by point and the fixed least square method was employed to interpolate and differentiate data locally. The method avoids volume meshing and only requires the boundary mesh on particle surfaces and data points in the flow domain. A sphere settling in the Oldroyd-B fluid and a prolate spheroid rotating in shear flow of the Oldroyd-B fluid were simulated. Based on the simulated orbit of a prolate spheroid in shear flow, a constitutive model for the weakly viscoelastic fibre suspensions was proposed and its predictions were compared with some available experimental results. All simulated results are in general agreement with experimental and other numerical results reported in literature. This indicates that these numerical methods are useful tools in rheological research.
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Hevin, Grégoire. "Utilisation des ondes de surface pour l'auscultation des structures en génie civil : application à la caractérisation des fissures de surface." Université Joseph Fourier (Grenoble), 1998. http://www.theses.fr/1998GRE10161.
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Dans le domaine du genie civil, la demande en matiere de controle non destructif est croissante. Les ondes de surface, et de rayleigh en particulier, presentent differentes proprietes interessantes pour l'auscultation de la surface des structures en beton. L'objectif de ce travail est de proposer et d'evaluer une methode de caracterisation des fissures de surface par les ondes de rayleigh. La diffraction des ondes de rayleigh par une fissure de surface est modelisee par la methode indirecte d'elements de frontiere (ibem pour indirect boundary element method). Les resultats permettent une analyse fine des differents phenomenes de diffraction et l'elaboration d'une methode spectrale de determination de la profondeur des fissures. Des dispositifs et procedures de traitement prenant en compte les effets de la source et des capteurs permettent de l'appliquer experimentalement. La comparaison des donnees numeriques et experimentales sur des fissures artificielles de differentes profondeurs valide la methode. Elle est alors appliquee a des cas particuliers (fissures remplies d'eau, fissures presentant des contacts entre les deux levres) et comparee a une methode temporelle utilisant les ondes de volume. Les resultats montrent clairement la complementarite des deux methodes pour un faible surcout de mise en oeuvre. Leur application a des cas de fissuration reelle sur ouvrage d'art confirme leur complementarite pour de veritables conditions d'auscultation.
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Wen, Pi Hua. "Indirect boundary element formulations for dynamic fracture mechanics." Thesis, University of Portsmouth, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282554.
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Healey, Martin. "The mortar boundary element method." Thesis, Brunel University, 2010. http://bura.brunel.ac.uk/handle/2438/4355.
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This thesis is primarily concerned with the mortar boundary element method (mortar BEM). The mortar finite element method (mortar FEM) is a well established numerical scheme for the solution of partial differential equations. In simple terms the technique involves the splitting up of the domain of definition into separate parts. The problem may now be solved independently on these separate parts, however there must be some sort of matching condition between the separate parts. Our aim is to develop and analyse this technique to the boundary element method (BEM). The first step in our journey towards the mortar BEM is to investigate the BEM with Lagrangian multipliers. When approximating the solution of Neumann problems on open surfaces by the Galerkin BEM the appropriate boundary condition (along the boundary curve of the surface) can easily be included in the definition of the spaces used. However, we introduce a boundary element Galerkin BEM where we use a Lagrangian multiplier to incorporate the appropriate boundary condition in a weak sense. This is the first step in enabling us to understand the necessary matching conditions for a mortar type decomposition. We next formulate the mortar BEM for hypersingular integral equations representing the elliptic boundary value problem of the Laplace equation in three dimensions (with Neumann boundary condition). We prove almost quasi-optimal convergence of the scheme in broken Sobolev norms of order 1/2. Sub-domain decompositions can be geometrically non-conforming and meshes must be quasi-uniform only on sub-domains. We present numerical results which confirm and underline the theory presented concerning the BEM with Lagrangian multipliers and the mortar BEM. Finally we discuss the application of the mortaring technique to the hypersingular integral equation representing the equations of linear elasticity. Based on the assumption of ellipticity of the appearing bilinear form on a constrained space we prove the almost quasi-optimal convergence of the scheme.
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Ademoyero, Oreoluwa Oyinlade. "A parallel Galerkin boundary element method." Thesis, University of Hertfordshire, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.410144.
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Elzein, Abbas. "Plate stability by boundary element method." Thesis, University of Southampton, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.255672.
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Gonçalves, Paulo Cesar 1969. "Estudo de alternativas para aplicação do metodo dos elementos de contorno para elasticidade." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/257768.
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Orientador: Leandro Palermo JuniorDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo
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Resumo: O método dos elementos de contorno foi usado no estudo de problemas de estados planos. O objetivo deste trabalho é a introdução do operador diferencial tangente no núcleo das equações integrais de forças de superfície, como uma alternativa para a aplicação do método dos elementos de contorno. A singularidade forte do tipo 2 1 r , presente no núcleo da equação integral de contorno, foi reduzida a uma singularidade de ordem r 1 com o uso do operador diferencial tangente. A formulação trabalhou com elementos de contorno contínuos e descontínuos. Na determinação de deslocamentos e tensões para pontos próximos do contorno, trabalhou-se apenas com núcleos com uma singularidade de ordem r 1. A técnica da regularização indireta, quando se evitam expressões analíticas, foi aplicada na equação integral de deslocamentos. Quando o ponto de colocação foi levado ao contorno, a singularidade, presente nas equações integrais de contorno, foi tratada pelo valor principal de Cauchy para elementos lineares na obtenção de tensões internas e no contorno. A formulação do método dos elementos de contorno dual usou a equação integral de forças de superfície, com a aplicação do operador diferencial tangente, no tratamento de problemas com trinca em análises da mecânica da fratura elástico-linear. Os fatores de intensidade de tensão são obtidos através do método da extrapolação de deslocamentos
Abstract: The Boundary Element Method was used to study plane state problem. The aim of this study is an application of the tangential differential operator in the kernels of boundary integrals equations for tractions, as an alternative for the applications of Boundary Element Method. Strong singularity of order 2 1 r , present in the kernels of boundary integrals equations was reduced to a weakly singularity of order r 1 when the tangential differential operator was used. The formulation worked with continuous and discontinuous boundary elements. On determination of displacements and stresses for boundary near points, the equation worked only with kernels contained singularity of order r 1. The indirect regularization technique, with avoided analytic expressions, was applied on the boundary integral equations for displacements. When the collocation points was led to boundary, the singularity, present on the boundary integrals equations, was treated by the Cauchy principal value sense for linear boundary elements. The formulation of the dual boundary elements methods used a boundary integral equation for traction, with the application of the tangential differential operator, to treat plane problems with cracks of the linear elastic fracture mechanics. The stress intensity factors are obtained with the displacement extrapolation method
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Mestre em Engenharia Civil
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Bird, Gareth Edward. "The coupled dual boundary element-scaled boundary finite element method for efficient fracture mechanics." Thesis, Durham University, 2012. http://etheses.dur.ac.uk/6996/.
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A novel numerical method is presented for applications to general fracture mechanics problems in engineering. The coupled dual boundary element-scaled boundary finite element method (DBE-SBFEM) incorporates the numerical accuracy of the SBFEM and the geometric versatility of the DBEM. Background theory, detailed derivations and literature reviews accompany the extensions made to the methods constituents necessary for their coupling as part of the present work. The coupled DBE-SBFEM, its constituent components and their application to linear elastic fracture mechanics are critically assessed and presented with numerical examples to demonstrate both method convergence and improvements over previous work. Further, a proof of concept demonstrates an alternative formation of the DBEM that both negates the need for hyper-singular integration and lends itself to a wider variety of imposed boundary conditions. Conclusions to this work are drawn and further recommendations for research in this area are made.
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Vu, Thu Hang. "Enhancing the scaled boundary finite element method." University of Western Australia. School of Civil and Resource Engineering, 2006. http://theses.library.uwa.edu.au/adt-WU2006.0068.
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[Truncated abstract] The scaled boundary finite element method is a novel computational method developed by Wolf and Song which reduces partial differential equations to a set of ordinary linear differential equations. The method, which is semi-analytical, is suitable for solving linear elliptic, parabolic and hyperbolic partial differential equations. The method has proved to be very efficient in solving various types of problems, including problems of potential flow and diffusion. The method out performs the finite element method when solving unbounded domain problems and problems involving stress singularities and discontinuities. The scaled boundary finite element method involves solution of a quadratic eigenproblem, the computational expense of which increases rapidly as the number of degrees of freedom increases. Consequently, to a greater extent than the finite element method, it is desirable to obtain solutions at a specified level of accuracy while using the minimum number of degrees of freedom necessary. In previous work, no systematic study had been performed so far into the use of elements of higher order, and no consideration made of p adaptivity. . . The primal problem is solved normally using the basic scaled boundary finite element method. The dual problem is solved by the new technique using the fundamental solution. A guaranteed upper error bound based on the Cauchy-Schwarz inequality is derived. A iv goal-oriented p-hierarchical adaptive procedure is proposed and implemented efficiently in the scaled boundary finite element method.
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Ritchie, Jeremey Alexander. "The Boundary Element Method in lubrication analysis." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329039.
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Gordon, R. S. "Boundary element method for axisymmetric thermoelastic analysis." Thesis, Cranfield University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302881.
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Aggarwal, Aditya Mohan. "B-Spline Boundary Element Method for Ships." ScholarWorks@UNO, 2008. http://scholarworks.uno.edu/td/853.
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The development of a three dimensional B-Spline based method, which is suitable for the steady-state potential flow analysis of free surface piercing bodies in hydrodynamics, is presented. The method requires the B-Spline or Non Uniform Rational B-Spline (NURBS) representation of the body as an input. In order to solve for the unknown potential, the source surface, both for the body as well as the free surface, is represented by NURBS surfaces. The method does not require the body surface to be discritized into flat panels. Therefore, instead of a mere panel approximation, the exact body geometry is utilized for the computation. The technique does not use a free surface Green's function, which already satisfies the linear free surface boundary conditions, but uses a separate source patch for the free surface. By eliminating the use of a free surface Green's function, the method can be extended to considering non-linear free surface conditions, thus providing the possibility for wave resistance calculations. The method is first applied to the double body flow problem around a sphere and a Wigley hull. Some comparisons are made with exact solutions to validate the accuracy of the method. Results of linear free surface conditions are then presented.
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Huang, Xiyong. "Probabilistic fracture mechanics by boundary element method." Thesis, Imperial College London, 2010. http://hdl.handle.net/10044/1/6192.
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In this work, a new boundary element method is presented for the Probabilistic Fracture Mechanics analysis. The method developed allows the probabilistic analysis of cracked structure accomplished by the dual boundary element method (DBEM), in which the traction integral equation is used on one of the crack faces as opposed to the usual displacement integral equation. The stress intensity factors and their first order derivatives are evaluated for mode-I and mixed-mode fracture problems. A new boundary element formulation is derived and implemented to evaluate the design variables sensitivities. This method involves the solution of matrix systems formed by the direct differentiation of the discretised dual boundary element equations with respect to the each random parameter. The derivatives of fracture parameters with respect to design variables are calculated using implicit differentiation method (IDM) in DBEM for mode-I and mixed-mode fracture problems. The gradient of performance function is determined analytically and the total derivative method (TDM) is used in probabilistic fatigue crack growth problems. The randomness in the geometry, material property and the applied stress are considered in 2-D fracture problems; while initial crack size, final crack size, material property and applied stress are considered in fatigue crack growth. Uncertainties in other aspects of the problem can be included. First-Order Reliability Method (FORM) is used for predicting the reliability of cracked structures. The Hasofer Lind Rackwitz Fiessler algorithm is used to find the most probable point, referred as reliability index. Finally, the validation and applications of the stochastic boundary element coupled with FORM are presented. Numerical calculations are shown to be in good agreement either with the analytical solution or Monte Carlo Simulation.
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Bapat, Milind S. "New Developments in Fast Boundary Element Method." University of Cincinnati / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1331296947.
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Irfanoglu, Bulent. "Boundary Element-finite Element Acoustic Analysis Of Coupled Domains." Phd thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605360/index.pdf.
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This thesis studies interactions between coupled acoustic domain(s) and enclosing rigid or elastic boundary. Boundary element-finite element (BE-FE) sound-structure interaction models are developed by coupling frequency domain BE acoustic and FE structural models using linear inviscid acoustic and elasticity theories.
Flexibility in analyses is provided by discontinuous triangular and quadrilateral elements in the BE method (BEM), and a rectangular plate and a triangular shell element in the FE method (FEM).
An analytical formulation is developed for an extended fundamental sound-structure interaction problem that involves locally reacting sound absorptive treatment on interior elastic boundary. This new formulation is built upon existing analytical solutions for a configuration known as the cavity-backed-plate problem. Results from developed analytical formulation are compared against those from independent BE-FE analyses.
Analytical and BE-FE analysis results for a selection of cavity-plate(s) interaction cases are given.
Single- and multi-domain BE analyses of cavity-Helmholtz resonator interaction are provided as an alternative to modal method of acoustoelasticity.
A discrete-form of the existing BE acoustic particle velocity formulation is presented and demonstrated on a basic case study. Both the existing and the discretized BE acoustic particle velocity formulations could be utilized in acoustic studies.
A selection of case studies involving fundamental configurations are studied both analytically and computationally (by BE or BE-FE methods). These studies could provide a basis for benchmark case development in the field of acoustics.
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Labaki, Josué 1982. "Uma implementação do metodo dos elementos de contorno indireto baseada em uma solução viscoelastodinamica estacionaria não-singular." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263996.
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Orientador: Euclides de Mesquita NetoDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
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Resumo: Estados auxiliares são soluções analíticas ou numéricas para operadores matemáticos, sujeitas às condições de contorno de um determinado problema da física matemática. Embora a solução de tais estados tenha aplicação prática limitada a problemas elementares, pode ser utilizada para resolver problemas reais de engenharia através de formulações como o Método dos Elementos de Contorno (MEC). Neste trabalho, usa-se a linguagem Fortran para implementar uma formulação indireta do MEC, utilizando um estado auxiliar viscoelastodinâmico não-singular, com o objetivo de analisar problemas de domínios limitados ou ilimitados, sujeitos a carregamentos estacionários, discretizados somente no contorno por elementos retangulares, constantes e descontínuos. Valida-se minuciosamente uma implementação para este estado auxiliar, e para isso desenvolve-se um estudo sobre quais são, como utilizar e quais as limitações das fontes de validação disponíveis para este tipo de problema. Ao fim, compara se alguns resultados obtidos com o programa em Fortran frente às respostas clássicas da bibliografia para problemas dinâmicos de barra, viga e domínios ilimitados.
Abstract: Auxiliary states are numerical or analytical solutions for mathematical operators, subjected to the boundary conditions of a given problem. Although the solution of these states has its utility limited to elementary problems, it can be used to solve a more real sort of engineering problems through formulations such as the Boundary Element Method (BEM). This work describes an implementation of BEM's Indirect formulation, based on a non-singular, viscoelastodynamic auxiliary state, aiming the analysis of both limited- and unlimited-domain problems, subjected to stationary loadings. The problem is modeled by means of constant, discontinuous, rectangular boundary elements. The present implementation for the viscoelastodynamic auxiliary state is carefully validated. For this purpose, this work also describes a study on validation sources for this kind of states, including their uses and limitations. The final program, written in the Fortran programming language, is used to analyze classic elementary engineering problems, such as bars and beams, and also the case of unlimited domains.
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Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica
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Harbrecht, Helmut, and Reinhold Schneider. "Biorthogonal wavelet bases for the boundary element method." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601308.
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As shown by Dahmen, Harbrecht and Schneider, the fully discrete wavelet Galerkin scheme for boundary integral equations scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. The supposition is a wavelet basis with a sufficiently large number of vanishing moments. In this paper we present several constructions of appropriate wavelet bases on manifolds based on the biorthogonal spline wavelets of A. Cohen, I. Daubechies and J.-C. Feauveau. By numerical experiments we demonstrate that it is worthwhile to spent effort on their construction to increase the performance of the wavelet Galerkin scheme considerably.
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de, Leon Simon. "The boundary element method for linear acoustic systems." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=18709.
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A technique based on the transient boundary element method for the numerical simulation of three-dimensional linear acoustic systems is presented. Using surface meshes generated by \texttt{Distmesh} \cite{persson:2004}, pressure is extracted from points within the enclosed volume of the mesh by integration of retarded potentials across the boundary. As a result, mesh junction calculations and topology-related inaccuracies within the volume are avoided. For simulations of struck instruments, membrane motion is modeled using two-dimensional digital waveguide techniques adapted for an unstructured triangular topology and coupled with the internal pressure field. The method is also used to extract response characteristics of an open, unflanged pipe and the results are compared to a one-dimensional waveguide model. Finally, possible future work using the freely available software developed for this project is discussed.Une technique de simulation numérique des systèmes acoustiques linéaires tridimensionnels basée sur la méthode d'éléments de frontière transitoires est présentée. La librairie Matlab \texttt{Distmesh} \cite{persson:2004} a été employée pour générer des maillages représentant la surface de tels objets. La pression en tout point du volume est obtenue par intégration des potentiels tout au long du maillage. Ainsi les calculs aux noeuds du maillage de même que les inexactitudes de topologies connexes dans le volume sont évités. Dans le cadre de la simulation d'instruments percussifs, le mouvement de la membrane est modélisé au moyen de guides d'ondes bidimensionnels particulièrement bien adaptés à une topologie triangulaire non-structurée. L'effet de couplage dû aux pressions internes est aussi pris en compte. D'autre part, la réponse caractéristique d'un tube droit, ouvert aux deux bouts obtenue par cette méthode est comparée aux résultats d'une méthode basée sur les guides d'ondes monodimensionnels. Enfin, de possibles applications du logiciel developpé pendant ce projet (et librement disponible) sont présentées.
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朱展強 and Chin-keung Chu. "Parallel computation for time domain boundary element method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31220678.
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雷哲翔 and Zhexiang Lei. "Time domain boundary element method & its applications." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31233703.
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Sari, Murat. "Seismic wave modelling using the boundary element method." Thesis, University of South Wales, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325902.
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Costa, J. A. Jr. "The boundary element method applied to plate problems." Thesis, University of Southampton, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.370335.
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Carneiro, Helder Fernando De Franca Mendes. "Fluid flow analysis using the boundary element method." Thesis, Cranfield University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.333131.
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Hargreaves, J. A. "Time domain boundary element method for room acoustics." Thesis, University of Salford, 2007. http://usir.salford.ac.uk/16604/.
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This thesis is about improving the suitability of the time domain Boundary Element Method (BEM) for predicting the scattering from surface treatments used to improve the acoustics of rooms. The discretised integral equations are typically solved by marching on in time from initial silence; however, this being iterative has potential for divergence. Such instability and high computational cost have prohibited the time domain BEM from widespread use. The underlying integral equation is known to not possess unique solutions at certain frequencies, physically interpreted as cavity resonances, and these manifest as resonant poles, all excited and potentially divergent due to numerical error. This has been addressed by others using the combined field integral equation; an approach built upon in this thesis. Accuracy and stability may also be compromised by poor discretisation and integration accuracy. The latter is investigated on real-world surfaces, demonstrating that the popular Gaussian integration schemes are not suitable in some circumstances. Instead a contour integration scheme capable of resolving the integrands‟ singular nature is developed. Schroeder diffusers are Room Acoustic treatments which comprise wells separated by thin fins. The algorithm is extended to model such surfaces, applying the combined field integral equation to the body and an open surface model to the fins. It is shown that this improves stability over an all open surface model. A new model for compliant surfaces is developed, comparable to the surface impedance model used in the frequency domain. This is implemented for surfaces with welled and absorbing sections, permitting modelling of a Schroeder diffuser as a box with surface impedances that simulate the delayed reflections caused by the wells. A Binary Amplitude Diffuser - a partially absorbing diffuser - is also modelled. These new models achieve good accuracy but not universal stability and avenues of future research are proposed to address the latter issue.
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BRUNO, HUGO BASTOS DE SA. "SHAPE OPTIMIZATION WITH SYMMETRIC GALERKIN BOUNDARY ELEMENT METHOD." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=31397@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Esse trabalho propõe uma implementação numérica para otimização de forma em problemas bi-dimensionais de elasticidade. O objetivo principal é propor uma metodologia eficiente e robusta para solução de problemas de otimização de forma considerando a minimização de concentração de tensões. Na implementação proposta, a análise estrutural é realizada pelo Método dos Elementos de Contorno Simétrico de Galerkin (MECSG), evitando-se assim a dispendiosa etapa de geração da malha. A avaliação das tensões no contorno é obtida por meio de um método preciso, ideal para problemas com concentrações de tensões. Outro aspecto relevante na implementação é a adequada partição das equações do MECSG de forma a reduzir, consideravelmente, o esforço computacional associado à etapa da análise estrutural. O problema de otimização é resolvido utilizando-se um método de otimização moderno, conhecido como Programação Cônica de Segunda Orderm (PCSO). Especificamente, busca-se a reposta do problema de otimização não linear por meio da solução de uma sequência de subproblemas de PCSO.
In this work a numerical implementation of shape optimization in two-dimensional linear elasticity problems is proposed. The main goal is to propose a robust and efficient methodology for the solution of shape optimization problems regarding the minimization of stress concentration effects. In the proposed implementation, the structural analysis is performed by the Symmetric Galerkin Boundary Element Method (SGBEM), thus disposing of the mesh generation burden. The boundary stress evaluation is carried out by an accurate approach which is ideally suited for problems with stress concentrations. Another relevant feature of the proposed implementation is a suitable partition of the SGBEM equations which aims at reducing the computational effort associated with the structural analysis stage. The solution for the optimization problem is obtained by means of a modern numerical optimization method, the so-called Second Order Conic Programming (SOCP). Specifically, the solution for the non-linear optimization is sought by solving a sequence of SOCP subproblems.
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COSSIO, MARCO ULISES DE LA QUINTANA. "SENSIVITY ANALYSIS WITH THE HYBRID BOUNDARY ELEMENT METHOD." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1998. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=1405@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOREste trabalho apresenta um estudo do cálculo de sensibilidades necessário para a análise de problemas inversos e de otimização, usando o método híbrido dos elementos de contorno. Com esta finalidade, é desenvolvida uma formulação que permite obter as sensibilidades à mudança de forma, por diferenciação implícita das integrais de contorno, de uma estrutura já discretizada. Demonstra-se que as sensibilidades das matrizes obtidas desta formulação apresentam propriedades espectrais definidas, que são derivadas da formulação básica do método híbrido dos elementos de contorno. Todo o desenvolvimento é feito para um problema da elastostática tridimensional, embora sejam apresentadas apenas aplicações de problemas bidimensionais e de potencial, como casos particulares. As singularidades que surgem na integração no cálculo das sensibilidades são facilmente solucionáveis a partir das integrais da formulação básica do método híbrido dos elementos de contorno. As implementações numéricas são feitas utilizando a linguagem de programação Maple V release 3. Para ambos os casos, de potencial e elasticidade bidimensional, são usados elementos lineares para a representação do contorno. São apresentadas comparações entre os resultados analíticos obtidos através desta formulação com os resultados obtidos usando a técnica de diferenças finitas (centradas), com o objetivo de demonstrar a eficiência e precisão da metodologia aqui desenvolvida.
The present work describes a formulation for computing design sensitivities required in inverse problems and shape optimization of solid objects, in the frame of the hybrid boundary element method. The so-called direct differentiation method is applied in order to calculate the gradients, i.e. the implicit diferentiation of the discretized boundary is performed, resulting in a general and efficient analysis technique for shape design sensitivity analysis of all structural quantities. It is demonstrated that the resulting sensitivities matrices present some useful spectral properties, which are related to the matrix spectral properties of the basic hybrid formulation. This formulation is valid for tridimensional solids, although only potential and bidimensional applications are considered as particular cases. The singularities that appear in the resulting boundary integrals are exactly the same which have already been dealt with in the basic formulation. The analytical and numerical procedures were performed by using the mathematical package Maple V release 3. Linear boundary elements were used for both potential and elasticity problems. Numerical results obtained by the present procedure are compared to finite differences results to demonstrate the effectiveness of the present formulation.
Este trabajo presenta un estudio del cálculo de sensibilidades, que tiene gran importancia en el análisis de problemas inversos y de optimización, usando el método híbrido de los elementos de contorno. Con esta finalidad, se desarrolla una formulación que permite obtener las sensibilidades al cambio de forma de una extructura ya discretizada, por diferenciación implícita de las integrales de contorno. Se demuestra que las sensibilidades de las matrices obtenidas por esta formulación presentan propriedades espectrales definidas, que son derivadas de la formulación básica del método híbrido de los elementos de contorno. El desarrollo de la formulación se realiza para un problema de elastostática tridimensional, aunque se presentan apenas las aplicaciones de problemas bidimensionales y de potencial, como casos particulares. Las singularidades que surgen en la integración en el cálculo de las sensibilidades pueden ser fácilmente resueltas a partir de las integrales de la formulación básica del método híbrido de los elementos de contorno. La implementación numérica utiliza el lenguaje de programación Maple V release 3. Para los casos de potencial y elasticidad bidimensional, se utilizan elementos lineales para la representación del contorno. Se comparan los resultados analíticos obtenidos a través de esta formulación con los resultados obtenidos usando la técnica de diferencias finitas (centradas), con el objetivo de demostrar la eficiencia y precisión de la metodología aqui desarrollada.
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Cherukunnath, Neeraj Narayanan. "Analysis of laminated plates using boundary element method." Thesis, University of Southampton, 2003. https://eprints.soton.ac.uk/45936/.
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Formulations and implementations of the Boundary Element Method (BEM) for bending, membrane stress, buckling and post-buckling analyses of laminated plates are presented. Symmetrically laminated plates are assumed for which the bending-stretching coupling is absent. From the generalized Rayleigh-Green identity corresponding to the plate-bending problem, boundary integral equations are derived using the appropriate fundamental solution. Integral equations are transformed into a system of equations in matrix form by introducing boundary element interpolation models. Linear and quadratic discontinuous boundary elements are employed combined with special schemes for the approximation of jump terms at corners. Singular integrals over elements containing the source point are evaluated from closed-form expressions derived through analytical integration. Using the stress function concept, it is shown that the membrane stress analysis due to arbitrary in-plane loading is mathematically equivalent to plate bending problem. Based on this similarity a new boundary element formulation is developed for the prediction of membrane stresses in a laminated plate. The same fundamental solution, which was used for plate bending problem, is used with the replacement of flexural coefficients with extensional compliance coefficients. A new formulation for the buckling analysis, which is similar to that for the plate bending problem, leads to integral equations with an irreducible domain integral depending on the plate deflection. Boundary modelling is combined with deflection modelling over the plate so that three integral equations are approximated as a discrete system of equations forming an eigenvalue problem from which the critical load is evaluated. This approach removes the need for integral equations involving the domain curvatures yielding directly the buckling mode of the plate. Formulations of membrane stress and bending analyses are expanded by including the nonlinear terms arising from large deflections and combined for the development of an incremental algorithm predicting the post-buckling behaviour of laminate plate. The C codes implementing the solution algorithms are applied to several benchmark problems involving orthotropic and general anisotropic plates and BEM predictions are compared with solutions available from the literature or obtainable through a general-purpose finite element package.
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MITRA, KAUSIK PRADIP. "APPLICATION OF MULTIPOLE EXPANSIONS TO BOUNDARY ELEMENT METHOD." University of Cincinnati / OhioLINK, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1026411773.
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Chu, Chin-keung. "Parallel computation for time domain boundary element method /." Hong Kong : University of Hong Kong, 1999. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20565574.
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Lei, Zhexiang. "Time domain boundary element method & its applications /." [Hong Kong : University of Hong Kong], 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13570365.
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Esterhuizen, Jacob J. B. "The evaluation of embankment stresses by coupled boundary element - finite element method." Thesis, Virginia Tech, 1993. http://hdl.handle.net/10919/42954.
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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
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Hinks, Thomas. "The application of the finite element method and the boundary element method to fatigue and fracture." Thesis, Cranfield University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302734.
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Gibson, Dan V. "The boundary element method applied to electrostatic axisymmetric problems." Thesis, University of Ottawa (Canada), 1989. http://hdl.handle.net/10393/5702.
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Hamilton, S. D. "The boundary element method for flow around submerged bodies." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375241.
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Silieti, Mahmood. "INVERSE BOUNDARY ELEMENT/GENETIC ALGORITHM METHOD FOR RECONSTRUCTION O." Doctoral diss., University of Central Florida, 2004. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3325.
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A methodology is formulated for the solution of the inverse problem concerned with the reconstruction of multi-dimensional heat fluxes for film cooling applications. The motivation for this study is the characterization of complex thermal conditions in industrial applications such as those encountered in film cooled turbomachinery components. The heat conduction problem in the metal endwall/shroud is solved using the boundary element method (bem), and the inverse problem is solved using a genetic algorithm (ga). Thermal conditions are overspecified at exposed surfaces amenable to measurement, while the temperature and surface heat flux distributions are unknown at the film cooling hole/slot walls. The latter are determined in an iterative process by developing two approaches. The first approach, developed for 2d applications, solves an inverse problem whose objective is to adjust the film cooling hole/slot wall temperatures and heat fluxes until the temperature and heat flux at the measurement surfaces are matched in an overall heat conduction solution. The second approach, developed for 2d and 3d applications, is to distribute a set of singularities (sinks) at the vicinity of the cooling slots/holes surface inside a fictitious extension of the physical domain or along cooling hole centerline with a given initial strength distribution. The inverse problem iteratively alters the strength distribution of the singularities (sinks) until the measuring surfaces heat fluxes are matched. The heat flux distributions are determined in a post-processing stage after the inverse problem is solved. The second approach provides a tremendous advantage in solving the inverse problem, particularly in 3d applications, and it is recommended as the method of choice for this class of problems. It can be noted that the ga reconstructed heat flux distributions are robust, yielding accurate results to both exact and error-laden inputs. In all cases in this study, results from experiments are simulated using a full conjugate heat transfer (cht) finite volume models which incorporate the interactions of the external convection in the hot turbulent gas, internal convection within the cooling plena, and the heat conduction in the metal endwall/shroud region. Extensive numerical investigations are undertaken to demonstrate the significant importance of conjugate heat transfer in film cooling applications and to identify the implications of various turbulence models in the prediction of accurate and more realistic surface temperatures and heat fluxes in the cht simulations. These, in turn, are used to provide numerical inputs to the inverse problem. Single and multiple cooling slots, cylindrical cooling holes, and fan-shaped cooling holes are considered in this study. The turbulence closure is modeled using several two-equation approach, the four-equation turbulence model, as well as five and seven moment reynolds stress models. The predicted results, by the different turbulence models, for the cases of adiabatic and conjugate models, are compared to experimental data reported in the open literature. Results show the significant effects of conjugate heat transfer on the temperature field in the film cooling hole region, and the additional heating up of the cooling jet itself. Moreover, results from the detailed numerical studies presented in this study validate the inverse problem approaches and reveal good agreement between the bem/ga reconstructed heat fluxes and the cht simulated heat fluxes along the inaccessible cooling slot/hole wallsPh.D.
Department of Mechanical, Materials and Aerospace Engineering;
Engineering and Computer Science
Mechanical Engineering
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Mellings, Sharon Christine. "Flaw identification using the inverse dual boundary element method." Thesis, University of Portsmouth, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239881.
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Lau, C. S. "Applications of boundary element method to time dependent problems." Thesis, City University London, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355581.
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Lin, Feng. "Application of boundary element method to soil-structure interaction." Thesis, London South Bank University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358360.
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Vlachos, Nickolas Dimitris. "Boundary element method of incompressible flow past deforming geometries." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.297802.
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NUNES, DENILSON RICARDO DE LUCENA. "THE HIBRID BOUNDARY ELEMENT METHOD APPLIED TO TRANSIENT PROBLEMS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2002. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=2494@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOMais de três décadas atrás, Przemieniecki introduziu uma formulação para análise de elementos de barra e treliça baseada em uma expansão em série de freqüências. Recentemente esta formulação foi generalizada para análise de sistemas elásticos submetidos a carregamento qualquer e deslocamentos iniciais. Baseado no método da superposição modal, um sistema acoplado, com equações diferenciais de movimento de alta ordem, é transformado em um sistema desacoplado com equações diferenciais de segunda ordem, que pode ser resolvido por qualquer método conhecido na literatura. A motivação para este desenvolvimento é o Método Híbrido dos Elementos de Contorno, que tem sido desenvolvido para problemas dependentes do tempo e problemas dependentes da freqüência. Esta formulação, assim como a introduzida por Pian para o Método dos Elementos Finitos, obtém uma matriz de rigidez utilizando apenas integrais de contorno, para um domínio de forma qualquer contendo vários graus de liberdade. O uso de termos com freqüências de alta ordem melhora muito a precisão numérica. A análise modal de um problema dinâmico, conforme se apresenta, é aplicável a qualquer formulação de elementos finitos, em geral, desde que a matriz de rigidez generalizada possa ser obtida. Este trabalho é uma tentativa de consolidação da formulação teórica proposta, em que se faz uso de integrais exclusivamente no contorno, com a discussão de diversos casos particulares e a conseqüente avaliação numérica: estruturas restringidas ou não; consideração de deslocamentos e velocidades iniciais, tanto em termos de valores nodais quanto de campos prescritos no domínio (incluindo deslocamentos de corpo rígido); deslocamentos forçados dependentes do tempo; forças de massa dependentes do tempo; cálculo de resultados em pontos internos. Vários exemplos acadêmicos para problemas de potencial bidimensionais ilustram este trabalho.
More than three decades ago, Przemieniecki introduced a formulation for the free vibration analysis of bar and beam elements based on a power series of frequencies. Recently, this formulation was generalized for the analysis of the dynamic response of elastic systems submitted to arbitrary nodal loads as well as initial displacements. Based on the mode-superposition method, a set of coupled, higher-order differential equations of motion is transformed into a set of uncoupled second order differential equations, which may be integrated by means of standard procedures. Motivation for this theoretical achievement is the hybrid boundary element method, which has been developed for time-dependent as well as frequency-dependent problems. This formulation, as a generalization of Pian`s previous achievements for finite elements, yields a stiffness matrix for which only boundary integrals are required, for arbitrary domain shapes and any number of degrees of freedom. The use of higher-order frequency terms drastically improves numerical accuracy. The introduced modal assessment of the dynamic problem is applicable to any kind of finite element for which a generalized stiffness matrix is available. The present work is an attempt of consolidating this boundary- only theoretical formulation, in which a series of particular cases are conceptually outlined and numerically assessed: Constrained and unconstrained structures; initial displacements and velocities as nodal values as well as prescribed domain fields (including rigid body movement); forced time-dependent displacements; time-dependent body forces; evaluation of results at internal points. Several academic examples for 2D problems of potential illustrate the formulation.
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MOSQUEIRA, DANIEL HUAMAN. "THE HYBRID BOUNDARY ELEMENT METHOD FOR GRADIENT ELASTICITY PROBLEMS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=23938@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Atualmente está bem difundido o uso de novas modelagens matemáticas para o estudo do comportamento de micro e nano sistemas mecânicos e eléctricos. O problema de escala é notável quando o tamanho das moléculas, partículas, grãos ou cristais de um sólido é relativamente considerável em relação ao comprimento do microdispositivo. Nesses casos a teoria clássica dos meios contínuos não descreve apropriadamente a solicitação estrutural e é necessária uma abordagem mais geral através de teorias generalizadas não-clássicas que contém a elasticidade clássica como um caso particular delas, onde os parâmetros constitutivos que representam às partículas são desprezíveis. Quando os efeitos microestruturais são importantes, o comportamento não responde como um material homogêneo se não como um material homogêneo. Cem anos atrás os irmãos Cosserat desenvolveram uma teoria de grãos rígidos imersos dentro de um macromeio elástico; posteriormente Toupin, Mindlin e outros pesquisadores na década de 60 formularam a chamada teoria gradiente de deformações, que recentemente é um objeto de muitas investigações analíticas e experimentais. Na década de oitenta, Aifantis e colaboradores conseguiram desenvolver uma teoria de gradiente de deformações simplificada, baseada em só uma constante elástica adicional não-clássica representativa da energia de deformação volumétrica para caracterizar satisfatoriamente os padrões dos fenômenos não-clássicos. Beskos e colaboradores estenderam o campo de aplicações da proposta inicial de Aifantis e fizeram as primeira implementações de elementos de contorno 2D e 3D para análises de elasticidade gradiente estática, no domínio da frequência e a mecânica da fratura. Desde o tempo de Toupin e Mindlin, procura-se estabelecer uma base variacional da teoria e uma formulação consistente das condições de contorno cinemáticas e de equilíbrio, o que parece ter tido êxito com os recentes trabalhos de Amanatidou e Aravas. Esta tese apresenta a formulação do método híbrido de elementos de contorno e finitos na elasticidade gradiente desenvolvida por Dumont e Huamán decompondo o potencial de Hellinger-Reissner em dois princípios de trabalhos virtuais: o primeiro em deslocamentos virtuais e o segundo em forças virtuais. Com esta finalidade é considerado além dos parâmetros clássicos, o trabalho realizado pelas tensões, deformações, forças e deslocamentos não-clássicos. É apresentado o desenvoltimento das soluções fundamentais singulares e polinomiais atráves das equações diferenciais de sexta ordem obtidas da equação de equilíbrio em termos de deslocamento na elasticidade gradiente. É apresentada também a aplicaçõ do método híbrido de contorno para problemas de tensão axial unidimensional e flexão bidimensional de vigas. Finalmente mostra-se a aplicação numérica do método em elementos finitos, é verificado o patch test de elementos finitos de diferentes ordem e mostra-se também análises de convergência.
The use of new mathematical modeling in the study of micro and Nano electro mechanical systems is currently becoming widespread. The scaling problem is apparent when the length of molecules, particles or grains immersed in the material is relatively important compared with the whole micro device dimension. Under this approach the classical theories of mechanics cannot describe suitably the structural requirement and it is necessary a more general outlook through non classical generalized theories which enclose the classical elasticity as a particular case where the non-classical constitutive parameters are negligible. When the microstructural effects are important, the material does not respond as a homogeneous but as a non-homogeneous one. A hundred years ago Cosserat brothers formulated a new theory of rigid grains which were embedded in an elastic macro medium; later Toupin, Mindlin along others researchers in 1960s developed a gradient strain theory which has been recently the source of many analystics and experimental investigations. In 1980s Ainfantis et al could develop a simplified strain gradient theory with just one additional non classical elastic constant which represents the volumetric elastic strain energy and characterized successfully the whole non classical pattern phenomenon. Beskos et al extended the treatment proposed initially by Aifantis and developed the first numerical applications for 2D and 3D boundary element methods and solved static as dynamic and crack problems. Since the times of Toupin and Mindlin it is looking for to establish a variational theory with a consistent cinematic and equilibrium boundary conditions, which seemed to have had success in the recent works of Amanatiodou and Aravas. This work presents the formulation of the hybrid boundary and finite element methods under the strain gradient scope which were developed by Dumont and Huamán through the versatile decomposition of the Hellinger-Reissner potential in two work principles: the displacements virtual work and the forces virtual work; both principles contain the virtual work performed by the non-classical magnitudes. Following, it is presented the complete development of singular and polynominal fundamental solutions abtained through the sixth order strain gradient differential equilibrium equations in terms of displacements. Next it is shown an application of the method to unidimensional truss element and bidimensional beam. Finally, it is presented a numerical application to strain gradient finite element, it is checked the patch tests to different elements orders and it is also shown a series of convergence analysis.
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Farooq, Aurangzeb. "Modelling surface waves using the hypersingular boundary element method." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/modelling-surface-waves-using-the-hypersingular-boundary-element-method(ddf69c96-26a6-44e3-8c56-18a04ff03a4c).html.
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The theme of the research is on the use of the hypersingular boundary element method for the modelling of surface waves. Surface waves in solids are known to be partially reflected & transmitted and mode converted into body waves at stress discontinuities, which suggests that a formulation continuous in stress and strain might prove beneficial for modelling purposes. Such continuity can be achieved with a subparametric approach where the geometry is approximated using linear elements and the field variables, displacement and traction, are approximated using cubic Hermitian and linear shape functions respectively. The higher order polynomial for approximating displacement is intended to be a more accurate representation of the physics relating to surface wave phenomena, especially at corners, and thus, is expected to capture this behaviour with greater accuracy than the standard isoparametric approach. The subparametric approach affords itself to continuity in stress and strain by imposing a smoothness in the elements, which is not available to the isoparametric approach. As the attention is focused primarily on the modelling of surface waves on the boundary of a medium rather than the interior, the boundary element method lends itself appropriately to this end.A 2D semi analytical integration scheme is employed to evaluate the integrals appearing in the hypersingular boundary integral formulation. The integration scheme is designed to reduce the errors incurred when integrals with singular integrands are evaluated numerically. The scheme involves the application of Taylor expansions to formulate the integrals into two parts. One part is regular and is evaluated numerically and the other part is singular but sufficiently simple to be evaluated analytically. The scheme makes use of the aforementioned subparametric approach and is applied to linear elements for the use in steady state elastodynamic boundary element method problems. The steady state problem is used as it is a simplified problem and is sufficient to permit the investigation of surface vibration at a constant motion. The 2D semi analytical integration scheme presented can be naturally extended to 3D.A particular focus and novelty of the work is the application of different limiting approaches to determine the free terms common to boundary integral methods. The accurate numerical solution of hypersingular boundary integral equations necessitates the precise evaluation of free terms, which are required to counter discontinuous and often unbounded behaviour of hypersingular integrals at a boundary. The common approach for the evaluation of free terms involves integration over a portion of a circular/spherical shaped surface centred at a singularity and allowing the radius of the circle/sphere to tend to zero. This approach is revisited in order to ascertain whether incorrect results are possible as a consequence of shape dependency, which is a recognised issue for hypersingular integrals.Two alternative methods, which are shape invariant, are proposed and investigated for the determination of free terms. The first approach, the point limiting method, involves moving a singularity towards a shrinking integration domain at a faster rate than the domain shrinks. Issues surrounding the choice of approach, shrinkage rates and path dependency are examined. A related and second approach, the boundary limiting method, involves moving an invariant, but shrinking, boundary toward the singularity, again at a faster rate than the shrinkage of the domain. The latter method can be viewed as a vanishing exclusion zone approach but the actual boundary shape is used for the boundary of the exclusion zone. Both these methods are shown to provide consistent answers and can be shown to be directly related to the result obtained by moving a singularity towards a boundary, that is, by comparison with the direct method. Unlike the circular/spherical approach the two methods involve integration over the actual boundary shape and consequently shape dependency is not an issue. A particular highlight of the point limiting approach is the ability to obtain free terms in mixed formulation, which is not available to the circular/spherical approach.There are three numerical problems considered in this research. The first problem considers the longitudinal vibration of a square plate. This is a problem for which a known analytical solution exists and is used to verify the equation formulation and integration scheme adopted for the isoparametric and subparametric formulations. Both formulations are as accurate as each other and produce results that are in keeping with the analytical solution, thus instilling confidence in their predictions.The second problem considers the simulation of surface waves on a square plate. Various boundaries of a square plate have displacement conditions imposed on them as a result of surface wave propagation. The results indicate that the surface wave behaviour is not captured. However, the analytical solution does not make any consideration for the effects from corners; the analytical solution is for a Rayleigh wave propagating upon a planar surface. It does not take into account the wave phenomena encountered at corners. Therefore, these results cannot be used to validate the predictions obtained on the boundary of the problem considered. The purpose of this problem is to illustrate the impact of corners on the surface wave propagation. Sensitivity studies are conducted to illustrate the effect of corners on the computed solution at the boundary.The final problem considers the simulation of surface waves on a circular plate. Various portions of the boundary of the circular plate have displacement conditions imposed on them as a result of surface wave propagation on curved surfaces. The results indicate that the isoparametric and subparametric predictions are similar to one another. However, both displacement profiles predict the presence of other waves. Given the multi faceted nature of the mesh, the computed solution is picking up mode conversion and partial reflection & transmission of surface waves. In reality, this is not expected as the surface of the boundary is smooth. However, due to the discretisation there are many corners in this problem.
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Hazanee, Areena. "Boundary element method for solving inverse heat source problems." Thesis, University of Leeds, 2015. http://etheses.whiterose.ac.uk/10570/.
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In this thesis, the boundary element method (BEM) is applied for solving inverse source problems for the heat equation. Through the employment of the Green’s formula and fundamental solution, the BEM naturally reduces the dimensionality of the problem by one although domain integrals are still present due to the initial condition and the heat source. We mainly consider the identification of time-dependent source for heat equation with several types of conditions such as non-local, non-classical, periodic, fixed point, time-average and integral which are considered as boundary or overdetermination conditions. Moreover, the more challenging cases of finding the space- and time-dependent heat source functions for additive and multiplicative cases are also considered. Under the above additional conditions a unique solution is known to exist, however, the inverse problems are still ill-posed since small errors in the input measurements result in large errors in the output heat source solution. Then some type of regularisation method is required to stabilise the solution. We utilise regularisation methods such as the Tikhonov regularisation with order zero, one, two, or the truncated singular value decomposition (TSVD) together with various choices of the regularisation parameter. The numerical results obtained from several benchmark test examples are presented in order to verify the efficiency of adopted computational methodology. The retrieved numerical solutions are compared with their analytical solutions, if available, or with the corresponding direct numerical solution, otherwise. Accurate and stable numerical solutions have been obtained throughout for all the inverse heat source problems considered.
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Burstow, Mark C. "A combined boundary element and finite element method for elasto-plastic fracture analysis." Thesis, University of Sheffield, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387269.
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Zarco, Mark Albert. "Solution of soil-structure interaction problems by coupled boundary element-finite element method." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/38298.
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Zarco, Mark Albert. "Solution fo soil-structure interaction problems by coupled boundary element-finite element method /." This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06062008-164808/.
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