For a successful design of an engineering system it is essential to pay careful attention to its dynamic response. This is particularly true, in the case of nonlinear systems, since they can exhibit very complex dynamic behaviour, including multiple co-existing stable solutions and chaotic motions, characterized by large sensitivity to initial conditions. In some systems nonlinear characteristics are desired and designed for, but in other cases they are unwanted and can cause fatigue and failure. A type of dynamical system which is highly nonlinear is discontinuous or non-smooth systems. In this work, systems with impacts are primarily investigated, and this is a typical example of a discontinuous system. To enhance or optimize the performance of dynamical systems, some kind of control can be implemented. This thesis concerns implementation of low-cost control strategies for discontinuous systems. Low-cost control means that a minimum amount of energy is used when performing the control actions, which is a desirable situation regardless of the application. The disadvantage of such a method is that the performance might be limited as compared with a control strategy with no restrictions on energy consumption. In this work, the control objective is to enforce a continuous or discontinuous grazing bifurcation of the system, whichever is desirable. In Paper A, the dynamic response and bifurcation behaviour of an impactoscillator with dry friction is investigated. For a one-degree-of-freedom model of the system, analytical solutions are found in separate regions of state space. These are then used to perform a perturbation analysis around a grazing trajectory. Through the analysis, a condition on the parameters of the system is derived, which assures a continuous grazing bifurcation. It is also shown that the result has bearing on the dynamic response of a two-degree-of-freedom model of the system. A low-cost active control strategy for a class of impact oscillators is proposed in Paper B. The idea of the control method is to introduce small adjustments in the position of the impact surface, at discrete moments in time, to assure a continuous bifurcation. A proof is given for what control parameters assures the stabilization. In Paper C, the proposed low-cost control method is implemented in a quarter-car model of a vehicle suspension, in order to minimize impact velocities with the bumpstop in case of high amplitude excitation. It is shown that the control method is effective for harmonic road excitation. / QC 20101118

The purpose of this study is to contribute to a deeper understanding about how placement discontinuities of children in foster care affect their learning. The aim is to find out more about their learning and what role school plays in their life. A life-world perspective is used and theories mainly developed by Alfred Schütz (2002) build the theoretical framework. The empirical research is mainly based on narratives of a pair of twins at 19 years of age, who agreed to share their life stories and experiences of their time in school. Meetings were arranged separately with Alex, the boy, and Helena, the girl, both eager to participate. They felt that their stories could contribute to knowledge. The stories show that placement discontinuities in their early childhood made memories and their perspective of time blurry. They both suffered severe neglect in two of their foster care placements. School offered them a safe place throughout their adolescent years. However, despite this, they are critical to the teachers who saw that they suffered neglect at home but never acted upon that knowledge. Hence their first-hand experiences suggest that teachers, considered important in earlier research studies, are not as important as friend made or the daily routines that provide certain security in an otherwise uncertain life. The social services didn’t listen or support them. Alex and Helena felt that they had to take care of themselves. Their stories show that both of them are goal-oriented and that they highly value a good education. This is evident since they have always taken responsibility to complete set homework and to make school a functional place where they have also learned to know themselves. Furthermore, it is obvious that the twins have played a tremendous role for each other when their life-world time after time has changed. Alex and Helena’s stories and experiences can give the social services a deeper understanding of what lies behind the statistics. A teacher, who listens, shows support and has ambitious expectations regarding the children’s academic performance, has been confirmed in previous research to be of significant importance. In addition, the study shows that teachers should learn more about children in foster care. A life-world perspective and life-world theories can contribute to an alternative point of view regarding learning in life-world discontinuities. Learning can be reflected on by using Schütz theory about “strangers” as a way of understanding learning in a wider range, especially when there are discontinues in the life-world. The reflections made in this study point out the possibility that schools, as organizations, seem to have independent cultures that can be transferred between one another. In fact there seems to be certain variables that are the same for schools in general and hence it is of significant value to recognize school as a regional life-world. The expectations of how you act as a student and among friends are important for the sense of belonging. It is possible that Alex and Helena succeeded in school partly because some of the things they learned about the first school could be transferred to their new school. The study contributes with two new concepts; “livsvärldsbrott”- life-world-disruption and “livsvärldsbevarande”- life-world-preservation.

No description available.

In the mammalian auditory system, specifically in the cochlea of the inner ear, the Basilar Membrane (BM) and hair cells are responsible for transducing incoming acoustic waves into electrical signals. These acoustic signals are carried as traveling waves by the BM and propagate from the base of the cochlea toward its apex where the helicotrema is located. An impressive feature of the mammalian auditory system is to prevent the propagated waves from reflecting which allows mammals to hear sounds without any reflection or overlap. This extraordinary characteristic of the inner ear is the main inspiration for this work. In the present study, the dynamic behavior of a beam structure with one or more attached spring-damper (SD) systems as passive absorbers is studied when excited by a harmonic force. The location of the spring-damper system divides the beam into two dynamic regions: one which exhibits non-reflecting traveling waves and the other with standing waves. In this work, the separation of traveling and standing waves is studied analytically, numerically, and experimentally. To the best of the author's knowledge, this is the first time in the literature that traveling and standing wave separation in a beam is realized experimentally using a single-point excitation and a spring-damper. Experimental results are used to validate the models of the system. Moreover, a parametric study is performed to gain a better understanding of the effect of different parameters on the quality of the generated waves in the structure. Furthermore, the effect of attaching the second spring-damper to the system is presented. Adding the secondary SD system results in increasing the excitation frequency range so that wave separation can be achieved. The results of this work can be used in various applications such as vibration suppression, energy absorption, particle transportation, and in exploring possible explanations for the BM and helicotrema functions in the cochlea. / Doctor of Philosophy / In the inner ear of the mammalian auditory system, the sound waves travel inside the cochlea where they are converted to electrical signals sent to the brain. A fascinating characteristic of the mammalian auditory system is that the sound waves traveling in the cochlea do not reflect when they reach its apex where the helicotrema is located. Therefore, we are able to hear sounds without any reflection or overlap. This work is inspired by the biological behavior of the inner ear and studies the dynamic behavior of a simple structure such as a beam with one (or two) attached spring-damper(s). In this work, the attached spring-damper system(s) prevents the waves traveling from the source to the beam's boundary from reflecting. This is similar to what happens in the inner ear. The location of the spring-damper divides the beam into two dynamic regions, one which exhibits non-reflecting traveling waves and the other with standing waves. The wave separation and parameters affecting the wave quality and its reflective or non-reflective features are studied analytically, numerically, and experimentally. To the best of the author's knowledge, the experiments carried out to generate the aforementioned wave types coexisting with each other on the beam are one of a kind. Furthermore, the results of this study showed a very good agreement between the experimental and theoretical results. The outcomes of this work can potentially be used in exploring possible explanations for the function of the cochlea and helicotrema and various applications such as particle transportation and suppression of unwanted vibrations.

La stabilité des exploitations à ciel ouvert (mines ou carrières) excavées dans des massifs rocheux dépend de leur géométrie, des caractéristiques géométriques de la fracturation (orientation et espacement) du massif et des caractéristiques mécaniques du massif et des discontinuités. L'évaluation du risque d'instabilité rocheuse dépend de la quantité et la qualité des informations disponibles sur le massif rocheux et des méthodes d'analyse mises en œuvre pour évaluer le comportement mécanique de l'assemblage de blocs rocheux. Différents sites de talus naturels, d'excavation routière et de carrières et mines à ciel ouvert présentés dans le mémoire montrent que les informations connues peuvent beaucoup varier d'un site à l'autre. Les étapes de collecte et de synthèse des données, puis de modélisation afin d'analyser la stabilité d'une pente rocheuse conduisent à des incertitudes. Le mémoire traite plus particulièrement de l'influence des incertitudes géométriques et différentes méthodes de regroupement des fractures en familles sont explorées. La combinaison du travail proposé par différents auteurs conduit à une nouvelle méthode nommée PSMY. Cette méthode ainsi que la méthode spectrale ont été programmées sous l'environnement Mathematica et les résultats sont comparés à des regroupements "manuels" réalisé avec le logiciel DIPS. Les méthodes de regroupement sont présentées selon le pourcentage d'orientations classé par la méthode. L’orientation et l’espacement des familles de fractures sont ajustées à des lois statistiques. Les paramètres statistiques sont comparés en fonction de la méthode regroupement. Ces paramètres influencent la construction d'un modèle géométrique du massif rocheux appelé DFN (Discrete Fracture Network). L'influence des regroupements sur l'analyse de stabilité est étudiée à partir de modélisation stochastiques à l'équilibre limite utilisant les logiciels SWEDGE et RESOBLOK. Ces logiciels ne prennent pas en compte les mêmes incertitudes et en sortie ils fournissent des indicateurs de stabilité différents. Une analyse de sensibilité des indicateurs (nombre de blocs instables, volume moyen du bloc instable, volume total instable) aux méthodes de regroupement et aux orientations de talus est réalisée. Une analyse de variance permet de préciser l'influence de ces deux facteurs. Une évaluation de l’état de stabilité global du massif, en fonction de la cohésion et de l'angle de frottement est proposée. L'influence de la méthode de modélisation est évoquée en comparant des calculs tridimensionnels à l'équilibre limite et des modélisations bidimensionnel et tridimensionnels en éléments discrets rigides ou déformables. Un couplage entre le logiciel RESOBLOK (équilibre limite) et LMGC90 (éléments discrets) permet de comparer les analyses pour une même géométrie. Pour le cas de la déviation d'Ax-les-Thermes et certaines configurations géométriques instables l’influence des paramètres de modèles sur stabilité du talus est testée. Plusieurs variantes sont comparées. La simulation d’une excavation en 3D multi phases est réalisée et l’indice de mobilisation est étudié pour comparer les divers types de contacts dans LMGC90 par rapport à l’éventuel glissement des blocs dans les étapes successives / The stability of open-cast operations (mines or quarries), excavated in rock mass depends on their geometry, the geometrical characteristics of the rock mass fractures (orientation and spacing) and the mechanical characteristics of the rock mass and the discontinuities. The assessment of the rock instability risk depends on the quantity and quality of the available information on the rock mass and the analysis methods used for the evaluation of the mechanical behavior of the rock block collection. Different sites of natural rock slopes, of road cuts, and of open-cast mines and quarries, described in the present document, show that the known information can vary a lot from one site to the other. The steps of data gathering and analysis, then the modelling step used to analyze the stability of the rock slope, lead to uncertainties. The present work deals in particular with the influence of the geometrical uncertainties, and the different clustering methods, to define families of fractures, are examined. The combination of works suggested by several authors leads to a new method called PSMY. This method, together with the spectral method, was coded in the Mathematica platform, and the obtained results are compared with "hand-made" clusters, done with the DIPS software. The clustering methods are presented according to the ratio of classified orientations. The orientation and spacing of fracture families are fitted by statistical law. The statistical parameters are compared according to the clustering method used. These parameters have an influence on the construction of the rock mass geometrical model, called DFN (Discrete Fracture Network). The influence of the clusters on the stability analysis is studied from the stochastic models based on the limit equilibrium analysis, in the SWEDGE and RESOBLOK software. These programs do not take into account the same uncertainties, and as a result, they give different stability indicators. A sensitivity analysis of these indicators (number of unstable blocks, average volume of unstable blocks, and total volume of unstable blocks) versus the clustering methods used, and the orientation of the slopes, is carried out. A variance analysis allows an evaluation of the influence of these factors. The assessment of the global stability condition of the rock mass, depending on the cohesion and the friction angle, is proposed. The influence of the modeling method is analyzed by comparing 3D calculations using the limit equilibrium calculations, and 2D and 3D models using discrete rigid and deformable blocks. A coupling between RESOBLOK (limit equilibrium) and LMGC90 (discrete elements) allows the comparison of results on the same original geometry. For the case of Ax-les-Thermes road-cut, and for various unstable geometries, the influence of the model parameters is tested. Several cases are compared. The 3D simulation of an excavation, at different steps, is performed, and the mobilization index is studied, in order to compare several types of contacts, within the LMGC model, in relation to the possible sliding of blocks, at those different steps

Résumé : Le vieillissement des ouvrages en béton est une préoccupation majeure affectant la pérennité et l’efficacité des structures. Le maître d’ouvrage se doit de maintenir les fonctions d’usage de la structure tout en gardant une gestion économique efficace. L’objectif final de ces travaux de recherche est, donc de pouvoir renseigner sur l’état global de fissuration de la structure afin d’aider le maître d’ouvrage à respecter ses engagements. Dans cette optique, cette thèse développe une nouvelle technique aidant à la quantification de l’état des ouvrages massifs en béton. Elle s’appuie, pour cela, sur la méthode non-destructive de résistivité électrique en surface, connue pour sa sensibilité face à des facteurs révélateurs d’une altération. Toutefois, à cause de sa dépendance entre la profondeur d’investigation et la résolution, la méthode ne peut pas garantir de l’état global d’un ouvrage. De ce fait, il a été décidé d’utiliser la résistivité électrique via des forages préexistants dans la structure (diagraphie électrique). L’outil utilisé est une sonde en dispositif normal réservée jusqu’à présent pour la prospection pétrolière et hydrogéologique. En plus d’une prospection en profondeur via le forage, cette sonde peut acquérir des informations sur un rayon de 3.2m autour du forage. Cependant, à mesure que le volume de béton sondé augmente, la résolution décroit. La difficulté est donc de pouvoir exploiter les capacités de prospection de la sonde tout en sachant que la résolution faillit. Il s’agit de contourner le problème en maîtrisant les concepts de la diagraphie et son nouveau milieu d’application. Cette thèse est basée sur une première approche numérique permettant d’apporter des corrections sur les données de terrain et de déterminer la sensibilité de l’outil face à de l’endommagement d’ouverture plurimillimétrique à centimétrique. Ceci est validé par des mesures réalisées sur une écluse de la Voie Maritime du Saint-Laurent. Une étude numérique de la réponse de l’outil en fonction des paramètres de fissure tels que l’ouverture, le contraste entre la résistivité de la discontinuité et du béton, et l’extension est réalisée. Elle permet de construire une base de données afin de développer une méthode pour la caractérisation de l’endommagement. Cette méthode s’appuie sur ces réponses diagraphiques pour retrouver les paramètres de fissure recherchés (problème inverse). Nous procédons tout d’abord par une analyse préliminaire se basant sur un croisement des informations apportées par les différentes électrodes de la sonde puis nous optimisons les résultats par la méthode de recuit simulé. La méthode, ainsi développée est ensuite appliquée à un deuxième ouvrage pour en déterminer l’état interne. Ces travaux détectent plusieurs zones endommagées et caractérisent l’une d’elles par une ouverture centimétrique et une extension comprise entre 1.6m et 3.2m. Ces travaux prometteurs, attestent d’un premier diagnostic interne des ouvrages massifs en béton, un enjeu qui restait sans réponses satisfaisantes jusqu’à maintenant. // Abstract : The aging of concrete structures is a major problem affecting their sustainability and their efficiency. The owner must maintain the structure serviceability and provide cost-effective management. The goal of this work is to provide detailed information about the state of cracking inside the structure in order to assist the owner to meet its commitments. In this context, this thesis develops a new technology to assess the condition of mass concrete structures. It relies on a non-destructive method based on electrical resistivity measured from surface, known for its sensitivity to factors associated with concrete deterioration. However, because of its dependence between the investigation depth and the resolution, the method cannot assess the overall state of a structure. Therefore, it was decided to use the electrical resistivity through preexisting boreholes in the structure (electrical logging). The tool used is a normal probe, which has been traditionally used for oil and hydrogeological exploration. In addition to the investigation in depth via boreholes, this probe can get information over a radius of 3.2m around the borehole. However, as the probing volume of concrete increases, the resolution decreases. Difficulty is to use the exploration abilities of the tool, knowing that the resolution is limited. This is to get around the problem by mastering logging concepts and its new application environment. This thesis is based on a first numerical approach to make corrections on field data and to determine the tool sensitivity with regard to the multi-millimeter and centimeter crack size damage. This was validated with measurements made on a full-size lock located on the St. Lawrence Seaway. A numerical study of the tool response versus the discontinuities parameters such as the crack aperture, the resistivity contrast between the discontinuity and the concrete, and the extension was done. It allowed building a database used to develop a method for the characterization of the damage. This method is based on the tool responses to find the crack parameters (inverse problem). First, we proceed with a preliminary analysis based on a cross of information provided by the different electrodes of the probe then we optimize the results by the method of simulated annealing. The characterization method is applied to another structure to quantify its internal state. These studies detect several damaged areas and characterize one of them by a centimeter aperture and an extension between 1.6m and 3.2m. This work attest to a first internal diagnosis of massive concrete structures, an issue that remained without satisfactory answers so far.

A formação e propagação de fissuras é um fenômeno observado em diversos materiais utilizados na engenharia, como concreto, metais, cerâmicas e rochas. Tendo em vista a grande influência que fissuras têm no comportamento global da estrutura o objetivo deste trabalho consiste na implementação de um modelo de fissura com descontinuidades fortes incorporadas a fim de analisar o processo de fratura em materiais quase-frágeis. A descontinuidade no campo de deslocamentos (descontinuidade forte) é representada através da introdução de graus de liberdade adicionais no interior do elemento finito, sendo esta abordagem denominada enriquecimento elementar (E-FEM). Nestes modelos a fissura pode se propagar em qualquer direção dentro do elemento finito, evitando a necessidade de redefinição da malha em cada etapa, além de fornecer resultados relativamente independentes da malha de elementos finitos utilizada. Por serem internos a cada elemento finito, os graus de liberdade adicionais podem ser eliminados da solução global por condensação estática. Desta forma as descontinuidades são definidas em nível de elemento e o modelo pode ser facilmente implementado em códigos computacionais existentes. O modelo implementado foi proposto por Dvorkin, Cuitiño e Gioia (1990), o qual pertence à classe de modelos com formulação assimétrica estaticamente e cinematicamente consistente (SKON). Esta formulação é caracterizada por garantir o movimento de corpo rígido entre as partes do elemento além de assegurar a continuidade de tensões na linha de fissura, resultando numa matriz de rigidez assimétrica. Diferentes relações constitutivas podem ser utilizadas para descrever o comportamento das regiões com e sem fissura. Portanto, para a região não fissurada, utilizouse um modelo constitutivo elástico linear e para a região fissurada foi analisada a performance de dois modelos constitutivos distintos: linear e exponencial. A capacidade de representar o comportamento de elementos estruturais fissurados foi ilustrada através de exemplos de tração e flexão comparados com outros modelos de fissura existentes e com resultados experimentais. Em relação aos modelos constitutivos para a linha da fissura, o modelo linear não se mostrou adequado por superestimar as tensões de pico além de apresentar um ramo de amolecimento mais frágil. Já o modelo exponencial mostrou-se bastante eficiente representando de forma correta o comportamento de materiais quase-frágeis. / The formation and propagation of cracks is a phenomenon observed in many materials used in engineering, such as concrete, metals, ceramics and rocks. In view of the influence of cracks in the global behavior of the structure, the aim of this work is the implementation of an embedded strong discontinuity model in order to analyze the fracture process in quasi-brittle materials. The discontinuity in the displacement field (strong discontinuity) is represented by the introduction of additional degrees of freedom within the finite element. This approach is called elemental enrichment (E-FEM). The embedded models allow the propagation of crack in any direction within the finite element, avoiding the need of remeshing and providing objective results (mesh independent). The additional degrees of freedom are introduced into the finite element, then these degrees can be eliminated from the global solution by static condensation and the model can be easily implemented in existent computational codes. The model used here was proposed by Dvorkin, Cuitiño and Gioia (1990), which belongs to the statically and kinematically optimal non-symmetric (SKON) formulation. In this formulation, the kinematics that allows for relative rigid body motion and the enforcement of the traction continuity are introduced at element level, resulting a non-symmetric formulation. Different constitutive relations can be used to describe the behavior of the zones with and without cracks. For the zone without cracks it was used a linear elastic model and for the cracked zone it was analyzed the behavior of two different constitutive models: linear and exponential. The ability of the model to represent the behavior of cracked structural elements was illustrated by bending and tensile tests and the results were compared with numerical and experimental data. Regarding the constitutive models for the fracture zone, it was concluded that the linear model was not suitable because it overestimated the maximum stress and promoted a britller softening. In contrast, the exponential model proved to be very efficient to represent the behavior of quasi-brittle materials.

A análise estrutural das descontinuidades e da tectônica rúptil atuante em um maciço rochoso é uma abordagem essencial em vários campos da geologia aplicada. No presente trabalho utilizou-se de técnicas tradicionais de levantamentos estruturais de detalhe via linha de varredura (scanlines) e técnicas de fotogrametria terrestre digital para a análise das descontinuidades de um maciço rochoso. Os resultados obtidos através de duas técnicas de caracterização foram comparados. Os trabalhos foram desenvolvidos em uma mina de metacalcário incluída no Grupo São Roque, situada próximo à borda leste da Bacia do Paraná, e próxima a grandes estruturas transcorrentes do sudeste do Estado de São Paulo. Foram amostrados taludes com direções ortogonais entre si visando uma amostragem que fosse tridimensionalmente representativa. Quando o levantamento foi efetuado através de técnicas tradicionais lineares, as estruturas preferencialmente amostradas foram aquelas com as direções perpendiculares à direção de amostragem. Inversamente as amostragens por fotogrametria terrestre digital evidenciaram as estruturas paralelas ao plano de levantamento. Os resultados foram bastante semelhantes em termos das atitudes das estruturas planares. O levantamento clássico mostrou-se bastante demorados, porém com análise mais direta, enquanto o levantamento fotogramétrico ofereceu uma abrangência maior, porém com tratamento e análise dos dados mais trabalhosos. Embora seja uma nova tecnologia que pode agilizar os levantamentos, um controle in situ se faz necessário. / Structural analysis of discontinuities in a brittle rock mass is an essential approach in various fields of applied geology. In this study we used traditional techniques of structural detail surveys scanlines and techniques of digital terrestrial photogrammetry for the analysis of discontinuities of rock mass. The results obtained by the two characterization techniques were then compared. The work was carried out in a limestone mine included in the São Roque Group, located near the eastern edge of the Paraná Basin, and near large transcurrent shear zones that occurs in the southeastern State of São Paulo. Slopes were sampled within orthogonal directions to each one in order to take a three-dimensional representative sample. When the survey was carried out using traditional linear techniques the structures preferentially sampled were those with the directions perpendicular to the direction of sampling. Conversely, sampling by digital photogrammetry showed that structures parallel to the survey. The results were quite similar in terms of the attitudes of planar structures. The classic survey proved to be very time consuming, but with more direct analysis, while the photogrammetric survey offered a bigger coverage, but with treatment and analysis more hard-working. Although it is a new technology that can speed up the surveys, an in situ control is necessary.

O trabalho tem como objetivo trazer contribuições à simulação numérica pelo método dos elementos de contorno (MEC) de formação e propagação de descontinuidades no campo de deslocamentos (descontinuidades fortes) em sólidos bidimensionais. A formação de descontinuidades fortes caracteriza o processo de falha material, que pode estar associado ao fraturamento em materiais quase frágeis ou a superfícies de deslizamentos de materiais dúcteis. Apresenta-se uma formulação do MEC baseada na incorporação de interfaces de descontinuidade no interior de células internas, que possibilita propagação arbitrária de descontinuidades usando uma malha de células internas fixa, definida antes da análise. Comparam-se diferentes alternativas provenientes do relaxamento dos requisitos de consistência estática e analisa-se a influência do alinhamento da malha. Apresenta-se também um possível esquema de construção adaptativa de células internas com interface incorporada para capturar a trajetória arbitrária da descontinuidade que se propaga durante o processo de carregamento. Este esquema visa aumentar a robustez e reduzir o esforço computacional. As características geométricas das células internas geradas são estabelecidas em função da orientação da descontinuidade fornecida pelo critério de falha, de maneira a proporcionar melhor eficiência numérica. Os estudos são levados a cabo através da simulação numérica de testes experimentais colhidos da literatura. / This work has the objective of bringing contributions to the numeric simulation using the boundary elements method (BEM) to model the initiation and propagation of strong discontinuities in the displacement field in bidimensional solids. The initiation process of strong discontinuities characterizes the failure process of material, which can be associated with the fracture of quasi-brittle materials and slip lines in ductile materials such as metals. The effect of the displacement jump of a discontinuity interface embedded in an internal cell is provided by an equivalent strain field over the cell. This model allows the study of arbitrary crack growth using a fixed mesh defined before the analysis. The dissipative process in the cell interface is described by an isotropic damage model in the continuum approach of strong discontinues. Alternatives that come from relaxing the static consistencies and the influence of the mesh alignment are analyzed. An adaptative algorithm for internal cells creation is also presented to capture the path of the crack growth during the loading process. This algorithm intends to overcome some convergence problems found in models with predefined meshes and also to reduce the computational efforts. The geometric characteristics of the generated internal cells are defined using the crack orientation, given by the failure criterion, to provide a better numerical efficiency. The results obtained with the proposed formulation are compared with the ones obtained with other numerical methods and also from experiments.

In this thesis, both theoretical and application oriented results are obtained for differential equations with discontinuities of different types: impulsive differential equations, differential equations with piecewise constant argument of generalized type and differential equations with discontinuous right-hand sides. Several qualitative problems such as stability, Hopf bifurcation, center manifold reduction, permanence and persistence are addressed for these equations and also for Lotka-Volterra predator-prey models with variable time of impulses, ratio-dependent predator-prey systems and logistic equation with piecewise constant argument of generalized type. For the first time, by means of Lyapunov functions coupled with the Razumikhin method, sufficient conditions are established for stability of the trivial solution of differential equations with piecewise constant argument of generalized type. Appropriate examples are worked out to illustrate the applicability of the method. Moreover, stability analysis is performed for the logistic equation, which is one of the most widely used population dynamics models. The behaviour of solutions for a 2-dimensional system of differential equations with discontinuous right-hand side, also called a Filippov system, is studied. Discontinuity sets intersect at a vertex, and are of the quasilinear nature. Through the B&amp / #8722 / equivalence of that system to an impulsive differential equation, Hopf bifurcation is investigated. Finally, the obtained results are extended to a 3-dimensional discontinuous system of Filippov type. After the existence of a center manifold is proved for the 3-dimensional system, a theorem on the bifurcation of periodic solutions is provided in the critical case. Illustrative examples and numerical simulations are presented to verify the theoretical results.