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.

De nombreux modèles numériques ont été proposés pour mieux comprendre comment le courant électrique est répartit lors d’une stimulation électrique par implant cochléaire. Ceci permet à terme d’optimiser la géométrie des électrodes et les stratégies de stimulation. Les modèles précédemment proposés modélisent les modèles d'interface électrochimique de façon très basique, et ne prennent généralement compte que de l'intensité du courant sur les électrodes. Par conséquent, il leur est difficile de simuler la dynamique temporelle de la stimulation ou de modéliser la répartition du courant en fonction de différents modes de stimulation contrôlés en tension, tels que le mode de de retour commun (Common Ground), ou de retour multiple (Multi-Mode Grounding). Dans cette thèse, nous avons développé un nouveau modèle surfacique de la cochlée. Le modèle géométrique dépend d'un ensemble de paramètres permettant d'ajuster la forme de la cochlée, en utilisant par exemple des données histologiques, des scans CT, ou encore des maillages de surface. Un modèle paramétrique nous a permis de comparer les courants générés par les modèles d'électrodes actuellement disponibles et par un nouveau type d'électrode - faisceau transmodiolaire. Le modèle peut prendre en compte des courants ou des tensions en entrée à chaque électrode, ce qui permet de simuler le mode de retour commun ou multiple. Afin de valider les résultats de simulation et calibrer les paramètres du modèle, nous avons créé un système permettant d'acquérir des mesures in-situ et in-vitro. Les données enregistrées ont permis de valider le modèle combinant le modèle d'interface électrochimique et le modèle tridimensionnel de cochlée. / Computational models have been widely used to improve the knowledge of the current distribution behavior in cochlear implant stimulations, optimizing electrode designs and stimulation strategies. The existing models employed no or simple electrochemical interface models and took current intensity on the electrodes as input. Therefore they have difficulties in making time domain simulations and simulating the stimulation modes that have voltage constraints, such as the Common Ground and the Multi-Mode Grounding modes. In this PhD work, a new parametric surface mesh model of the cochlea has been developed. The shape of the model is controlled by a set of input parameters which can be tuned to fit the cochlear shape acquired from histological images, CT scans or existing cochlear mesh models. The symmetric boundary element method, which was implemented in OpenMEEG, has been applied on the model to simulate the current distribution of the cochlear implant stimulation. Using the parametric model, comparisons on the current field has been made between the existing electrode layouts and a new transmodiolar electrodes. The new model can take either current or voltage as input for each electrode to simulate the common ground and multi-mode grounding modes. By coupling the surface model with lumped capacitor and constant phase element models, time domain simulation of the stimulation waveform has also been achieved. To validate the simulation results and calibrate the parameters of the model, in-situ and in-vitro measurements have been carried out with self-made devices. The recorded data proved the effectiveness of combining lumped components with the surface model.

In this dissertation, we introduce and analyse a scheme for the fast evaluation of integrals stemming from boundary element methods including discretisations of the classical single and double layer potential operators. Our method is based on the parametrisation of boundary elements in terms of a d-dimensional parameter tuple. We interpret the integral as a real-valued function f depending on d parameters and show that f is smooth in a d-dimensional box. A standard interpolation of f by polynomials leads to a d-dimensional tensor which is given by the values of f at the interpolation points. This tensor may be approximated in a low rank tensor format like the canonical format or the hierarchical format. The tensor approximation has to be done only once and allows us to evaluate interpolants in O(dr(m+1)) operations in the canonical format, or O(dk³ + dk(m + 1)) operations in the hierarchical format, where m denotes the interpolation order and the ranks r, k are small integers. In particular, we apply an efficient black box scheme in the hierarchical tensor format in order to adaptively approximate tensors even in high dimensions d with a prescribed (but heuristic) target accuracy. By means of detailed numerical experiments, we demonstrate that highly accurate integral values can be obtained at very moderate costs.

This report presents the work done within the framework of my master thesis in the program Infrastructure Engineering at KTH Royal Institute of Technology, Stockholm. This project has been proposed and sponsored by the French company Setec TPI, part of the Setec group, located in Paris. The overall goal of this study is to investigate fluid-structure interaction and particularly sloshing in liquid-containing structures subjected to seismic or other dynamic action. After a brief introduction, the report is composed of three main chapters. The first one presents and explains fluid-structure interaction equations. Fluid-structure interaction problems obey a general flow equation and several boundary conditions, given some basic assumptions. The purpose of the two following chapters is to solve the corresponding system of equations. The first approach proposes an analytical solution: the problem is solved for 2D rectangular tanks. Different models are considered and compared in order to analyze and describe sloshing phenomenon. Liquid can be decomposed in two parts: the lower part that moves in unison with the structure is modeled as an impulsive added mass; the upper part that sloshes is modeled as a convective added mass. Each of these two added mass creates hydrodynamic pressures and simple formulas are given in order to compute them. The second approach proposes a numerical solution: the goal is to be able to solve the problem for any kind of geometry. The differential problem is resolved using a singularity method and Gauss functions. It is stated as a boundary integral equation and solved by means of the Boundary Element Method. The linear system obtained is then implemented on Matlab. Scripts and results are presented. Matlab programs are run to solve fluid-structure interaction problems in the case of rectangular tanks: the results concur with the analytical solution which justifies the numerical solution. This report gives a good introduction to sloshing phenomenon and gathers several analytical solutions found in the literature. Besides, it provides a Matlab program able to model effects of sloshing in any liquid-containing structures.

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 walls

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The point absorber, one of the most popular types of ocean wave energy converter (WEC), usually consists of a rigid body buoy that can be efficiently modeled using existing WEC simulation tools. However, new wave energy technologies have looked to utilize flexible buoy structures to decrease costs, improve power generation, and increase portability. In addition to replacing rigid body designs, the combination of multiple renewable energy sources is another area that shows promising potential for increasing WEC power generation. With these concepts in mind, this work considers a new WEC design that features a flexible-inflatable buoy, an ocean current harvesting turbine, and a buoy shape that has been optimized for simultaneous wave and current energy harvesting. For this device, conventional modeling techniques cannot be used due to the highly nonlinear hydrodynamic interactions that result between the flexible buoy and the ocean waves. As a result, a Fluid-Structure Interaction (FSI) model must be used to determine how the flexibility of the buoy will influence the device's power generation. Currently, high-fidelity FSI modeling approaches are computationally expensive and unsuitable for early design decisions. As a result, this thesis utilizes a mid-fidelity method, the generalized modes modeling approach, to accurately and efficiently model the FSI of a WEC's flexible buoy. The resulting flexible buoy model was then compared to a rigid design to determine the performance differences between a rigid and flexible buoy, with a complex, optimized shape. / Master of Science / The ocean is a vast potential energy resource with a variety of different sources of renewable energy. Of these sources, ocean waves and ocean currents are two potentially massive power reserves present in many coastal areas. To capture energy from these sources, this work discusses the development of a device that can harvest energy from ocean waves and ocean currents simultaneously. In addition to harvesting energy from multiple sources, this device also features a flexible-inflatable buoy, with a shape that has been optimized for this unique application. However, since this device utilizes flexible materials, traditional modeling techniques used for rigid body designs would not be applicable. As a result, this work looks to model the interaction between the flexible buoy and the ocean waves to accurately predict the power generation of this device's wave energy converter.

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

Thesis (MEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Current numerical methods in the eld of hydraulic fracturing are based mainly on continuum methods, such as the Finite Element Method (FEM) and the Boundary Element Method (BEM). These methods are governed by Linear Elastic Fracture Mechanics (LEFM) criteria, which su er from the inherent aw of a non-physical stress representation at the fracture tip. In response to this, a non-local method is proposed, namely the peridynamic theory, to model sleeved hydraulic fracture. A 2D implicit quasi-static ordinary state based peridynamic formulation is implemented on various benchmark problems, to verify the ability to capture constitutive behaviour in a linear elastic solid, as well as, the quanti cation of adverse e ects on the accuracy of the displacement solution, due to the nature of the non-local theory. Benchmark tests consist of a plate in tension, where convergence to the classical displacement solution, non-uniform re nement and varying cell sizes are tested, as well as, a thick walled cylinder with internal pressure, where three di erent loading techniques are tested. The most accurate loading technique is applied to the sleeved fracture model, in order to simulate fracture initiation and propagation. This model is then veri ed and validated by using the Rummel & Winter hydraulic fracturing model and experimental results, respectively. Displacement error minimisation methods are implemented and as a result, the displacement solutions for a plate in tension converges to the analytical solution, while the thick walled cylinder solutions su er from inaccuracies due to an applied load on an irregularly discretized region. The fracture initiation test captures the fracture tip behaviour of the Rummel & Winter model and the fracture propagation test show good correlation with experimental results. This research shows that the peridynamic approach to sleeved hydraulic fracture can yield a realistic representation of fracture initiation and propagation, however, further research is needed in the area of a pressure load application on a solid using the peridynamic approach. / AFRIKAANSE OPSOMMING: Huidige numeriese metodes in die veld van hidrouliese breking is hoofsaaklik gebaseer op kontinuum metodes, soos die Eindige Element Metode (EEM) en die Rand Element Metode (REM). Hierdie metodes word beheer deur Linie^ere Elastiese Breukmeganika (LEB) kriteria, wat ly aan die inherente gebrek van 'n nie- siese voorstelling van die spanning by die fraktuur punt. Om hierdie probleme aan te spreek, word 'n nie-lokale metode voorgestel, naamlik die peridinamiese teorie, om gehulsde hidrouliese breking te modelleer. 'n 2D implisiete kwasi-statiese ordin^ere toestand gebaseerde peridinamika formulering word ge mplimenteer op verskeie norm probleme, om te veri eer of dit oor die vermo e beskik om die konstitutiewe gedrag van 'n linie^ere elastiese soliede materiaal te modeleer, asook die kwanti sering van nadelige e ekte op die verplasings oplossing as gevolg van die natuur van die nie-lokale teorie. Normtoetse bestaan uit 'n plaat in trek spanning, waar konvergensie na die klassieke verplasings oplossing, nie-uniforme verfyning en vari^eerende sel groottes getoets word, asook 'n dikwandige silinder onder interne druk, waar drie verskillende belasting aanwendingstegnieke getoets word. Die mees akkurate belasting aanwendingstegniek word dan gebruik in die gehulsde hidrouliese breking model, om fraktuur aanvangs en uitbreiding na te boots. Die model word dan geveri- eer deur die Rummel & Winter hidrouliese breking model en eksperimentele resultate, onderskeidelik. Fout minimering metodes word toegepas en as 'n resultaat, konvergeer die verplasing oplossing vir die plaat na die analitiese oplossing, terwyl die oplossing van die dikwandige silinder onakuraathede toon as gevolg van 'n toegepaste belasting op 'n onre elmatig gediskretiseerde gebied. Die modellering van die fraktuur inisi ering by die fraktuur punt, stem goed ooreen met die Rummel en Winter voorspelling en die fraktuur uitbreiding stem goed ooreen met eksperimentele resultate. Hierdie navorsing toon dat die peridinamiese benadering tot gehulsde hidrouliese breking wel die fraktuur inisi ering en uitbreiding realisties kan modelleer, maar nog navorsing word wel benodig in die area waar 'n druk belasting op 'n peridinamiese soliede model toegepas word.