This dissertation presents a sampling-based method that can be used for uncertainty quantification and deterministic or probabilistic optimization. The objective is to simultaneously address several difficulties faced by classical techniques based on response values and their gradients. In particular, this research addresses issues with discontinuous and binary (pass or fail) responses, and multiple failure modes. All methods in this research are developed with the aim of addressing problems that have limited data due to high cost of computation or experiment, e.g. vehicle crashworthiness, fluid-structure interaction etc.The core idea of this research is to construct an explicit boundary separating allowable and unallowable behaviors, based on classification information of responses instead of their actual values. As a result, the proposed method is naturally suited to handle discontinuities and binary states. A machine learning technique referred to as support vector machines (SVMs) is used to construct the explicit boundaries. SVM boundaries can be highly nonlinear, which allows one to use a single SVM for representing multiple failure modes.One of the major concerns in the design and uncertainty quantification communities is to reduce computational costs. To address this issue, several adaptive sampling methods have been developed as part of this dissertation. Specific sampling methods have been developed for reliability assessment, deterministic optimization, and reliability-based design optimization. Adaptive sampling allows the construction of accurate SVMs with limited samples. However, like any approximation method, construction of SVM is subject to errors. A new method to quantify the prediction error of SVMs, based on probabilistic support vector machines (PSVMs) is also developed. It is used to provide a relatively conservative probability of failure to mitigate some of the adverse effects of an inaccurate SVM. In the context of reliability assessment, the proposed method is presented for uncertainties represented by random variables as well as spatially varying random fields.In order to validate the developed methods, analytical problems with known solutions are used. In addition, the approach is applied to some application problems, such as structural impact and tolerance optimization, to demonstrate its strengths in the context of discontinuous responses and multiple failure modes.

O desenvolvimento de métodos que permitam reproduzir numericamente o comportamento el de sistemas estruturais reais tem desa ado cientistas e pesquisadores a abordarem questões que vão além das condições de integridade do sistema. Neste sentido, uma série de novos parâmetros devem ser considerados durante um processo de otimização estrutural, zelando pela con abilidade em níveis aceitáveis enquanto que os custos esperados de falhas sejam minimizados. Aparentemente, os objetivos segurança e economia competem entre si, nesse contexto, a otimização do risco estrutural surge como uma formulação que permite equacionar este problema através do chamado custo esperado total. Nesta Tese, apresenta-se o desenvolvimento de uma técnica precisa para satisfazer os termos que compõem a função custo esperado total, isto é, uma técnica capaz de estimar a con abilidade de sistemas estruturais redundantes pela identi cação dos múltiplos modos de falha de uma maneira mais precisa que os métodos convencionais aproximados e de simulação. Além disso, análises inelásticas de estruturas de aço incluindo as não linearidades físicas e geométricas são consideradas utilizando o MCDG, além de leis constitutivas para prever o comportamento inelástico. Em posse destas informações, o algoritmo calcula o risco como sendo a probabilidade de falha multiplicada pela consequência econômica resultante desta falha. Ao risco são acrescentados os demais custos associados ao sistema estrutural, os quais não dependem dos parâmetros aleatórios do sistema e por isso denominados custos xos. Como produto, tem-se o custo esperado total, o qual corresponde a função objetivo do problema de otimização estrutural. Aplicações numéricas demonstram a precisão e e ciência da metodologia na avaliação da probabilidade de falha de problemas envolvendo funções de estado limite altamente não lineares com múltiplas regiões de falhas, assim como os efeitos causados pelas não linearidades físicas e geométricas nas análises probabil ísticas e na otimização do risco das estruturas. Os resultados demonstraram que, em relação às incertezas e consequências monetárias da falha, a estrutura ótima pode ser encontrada apenas pela formulação da otimização do risco, onde a con guração da estrutura e os limites de segurança são otimizados simultaneamente. A otimização do risco resulta numa estrutura ótima em termos mecânicos, custo esperado total e segurança. / The development of methods that allow to numerically reproduce the actual behavior of real structural systems has challenged scientists and researchers and urged them to address issues that extend beyond the integrity of a system. Therefore, a series of new parameters must be taken into account during the structural optimization process, looking for acceptable reliability levels while minimizing the expected failure costs. Apparently, safety and economy compete with each other, and in this context, structural risk optimization arises as a formulation that allows equating this problem through the so-called total expected cost. In this Thesis, an accurate technique is developed to satisfy the minimization of the total expected cost function i:e:; a technique that allows estimating the reliability of redundant structural systems by the identi cation of multiple failure modes in a more precise way than conventional approximation and simulation methods. Besides, inelastic analysis of steel trusses including both geometric and physical nonlinearities are considered using the generalized displacement control method, in addition to constitutive laws to predict the inelastic behavior. Based on this information, the algorithm calculates risk as the failure probability multiplied by the economic losses resulting from such failure. The other costs associated to the structual system are added to the actual risk and since they do not depend on system's random parameters, they are referred as xed costs. As result, one obtains the total expected cost, which corresponds to the objective function of the structural optimization problem. Numerical applications shows the accuracy and e ciency of the methodology in the evaluation of the failure probability of problems represented by high nonlinear limit state functions with multiple failure regions. It is also included the e ects of geometric and physical nonlinearities originated in the probabilistic analysis and risk optimization of truss structures. Results show that, in consideration of uncertainty and the monetary consequences of failure, the optimum structure can only be found by a risk optimization formulation, where structural con guration and safety margins are optimized simultaneously. Risk optimization yields a structure which is optimum in terms of mechanics and in terms of the compromise between cost and safety.

O desenvolvimento de métodos que permitam reproduzir numericamente o comportamento el de sistemas estruturais reais tem desa ado cientistas e pesquisadores a abordarem questões que vão além das condições de integridade do sistema. Neste sentido, uma série de novos parâmetros devem ser considerados durante um processo de otimização estrutural, zelando pela con abilidade em níveis aceitáveis enquanto que os custos esperados de falhas sejam minimizados. Aparentemente, os objetivos segurança e economia competem entre si, nesse contexto, a otimização do risco estrutural surge como uma formulação que permite equacionar este problema através do chamado custo esperado total. Nesta Tese, apresenta-se o desenvolvimento de uma técnica precisa para satisfazer os termos que compõem a função custo esperado total, isto é, uma técnica capaz de estimar a con abilidade de sistemas estruturais redundantes pela identi cação dos múltiplos modos de falha de uma maneira mais precisa que os métodos convencionais aproximados e de simulação. Além disso, análises inelásticas de estruturas de aço incluindo as não linearidades físicas e geométricas são consideradas utilizando o MCDG, além de leis constitutivas para prever o comportamento inelástico. Em posse destas informações, o algoritmo calcula o risco como sendo a probabilidade de falha multiplicada pela consequência econômica resultante desta falha. Ao risco são acrescentados os demais custos associados ao sistema estrutural, os quais não dependem dos parâmetros aleatórios do sistema e por isso denominados custos xos. Como produto, tem-se o custo esperado total, o qual corresponde a função objetivo do problema de otimização estrutural. Aplicações numéricas demonstram a precisão e e ciência da metodologia na avaliação da probabilidade de falha de problemas envolvendo funções de estado limite altamente não lineares com múltiplas regiões de falhas, assim como os efeitos causados pelas não linearidades físicas e geométricas nas análises probabil ísticas e na otimização do risco das estruturas. Os resultados demonstraram que, em relação às incertezas e consequências monetárias da falha, a estrutura ótima pode ser encontrada apenas pela formulação da otimização do risco, onde a con guração da estrutura e os limites de segurança são otimizados simultaneamente. A otimização do risco resulta numa estrutura ótima em termos mecânicos, custo esperado total e segurança. / The development of methods that allow to numerically reproduce the actual behavior of real structural systems has challenged scientists and researchers and urged them to address issues that extend beyond the integrity of a system. Therefore, a series of new parameters must be taken into account during the structural optimization process, looking for acceptable reliability levels while minimizing the expected failure costs. Apparently, safety and economy compete with each other, and in this context, structural risk optimization arises as a formulation that allows equating this problem through the so-called total expected cost. In this Thesis, an accurate technique is developed to satisfy the minimization of the total expected cost function i:e:; a technique that allows estimating the reliability of redundant structural systems by the identi cation of multiple failure modes in a more precise way than conventional approximation and simulation methods. Besides, inelastic analysis of steel trusses including both geometric and physical nonlinearities are considered using the generalized displacement control method, in addition to constitutive laws to predict the inelastic behavior. Based on this information, the algorithm calculates risk as the failure probability multiplied by the economic losses resulting from such failure. The other costs associated to the structual system are added to the actual risk and since they do not depend on system's random parameters, they are referred as xed costs. As result, one obtains the total expected cost, which corresponds to the objective function of the structural optimization problem. Numerical applications shows the accuracy and e ciency of the methodology in the evaluation of the failure probability of problems represented by high nonlinear limit state functions with multiple failure regions. It is also included the e ects of geometric and physical nonlinearities originated in the probabilistic analysis and risk optimization of truss structures. Results show that, in consideration of uncertainty and the monetary consequences of failure, the optimum structure can only be found by a risk optimization formulation, where structural con guration and safety margins are optimized simultaneously. Risk optimization yields a structure which is optimum in terms of mechanics and in terms of the compromise between cost and safety.

O desenvolvimento de métodos que permitam reproduzir numericamente o comportamento el de sistemas estruturais reais tem desa ado cientistas e pesquisadores a abordarem questões que vão além das condições de integridade do sistema. Neste sentido, uma série de novos parâmetros devem ser considerados durante um processo de otimização estrutural, zelando pela con abilidade em níveis aceitáveis enquanto que os custos esperados de falhas sejam minimizados. Aparentemente, os objetivos segurança e economia competem entre si, nesse contexto, a otimização do risco estrutural surge como uma formulação que permite equacionar este problema através do chamado custo esperado total. Nesta Tese, apresenta-se o desenvolvimento de uma técnica precisa para satisfazer os termos que compõem a função custo esperado total, isto é, uma técnica capaz de estimar a con abilidade de sistemas estruturais redundantes pela identi cação dos múltiplos modos de falha de uma maneira mais precisa que os métodos convencionais aproximados e de simulação. Além disso, análises inelásticas de estruturas de aço incluindo as não linearidades físicas e geométricas são consideradas utilizando o MCDG, além de leis constitutivas para prever o comportamento inelástico. Em posse destas informações, o algoritmo calcula o risco como sendo a probabilidade de falha multiplicada pela consequência econômica resultante desta falha. Ao risco são acrescentados os demais custos associados ao sistema estrutural, os quais não dependem dos parâmetros aleatórios do sistema e por isso denominados custos xos. Como produto, tem-se o custo esperado total, o qual corresponde a função objetivo do problema de otimização estrutural. Aplicações numéricas demonstram a precisão e e ciência da metodologia na avaliação da probabilidade de falha de problemas envolvendo funções de estado limite altamente não lineares com múltiplas regiões de falhas, assim como os efeitos causados pelas não linearidades físicas e geométricas nas análises probabil ísticas e na otimização do risco das estruturas. Os resultados demonstraram que, em relação às incertezas e consequências monetárias da falha, a estrutura ótima pode ser encontrada apenas pela formulação da otimização do risco, onde a con guração da estrutura e os limites de segurança são otimizados simultaneamente. A otimização do risco resulta numa estrutura ótima em termos mecânicos, custo esperado total e segurança. / The development of methods that allow to numerically reproduce the actual behavior of real structural systems has challenged scientists and researchers and urged them to address issues that extend beyond the integrity of a system. Therefore, a series of new parameters must be taken into account during the structural optimization process, looking for acceptable reliability levels while minimizing the expected failure costs. Apparently, safety and economy compete with each other, and in this context, structural risk optimization arises as a formulation that allows equating this problem through the so-called total expected cost. In this Thesis, an accurate technique is developed to satisfy the minimization of the total expected cost function i:e:; a technique that allows estimating the reliability of redundant structural systems by the identi cation of multiple failure modes in a more precise way than conventional approximation and simulation methods. Besides, inelastic analysis of steel trusses including both geometric and physical nonlinearities are considered using the generalized displacement control method, in addition to constitutive laws to predict the inelastic behavior. Based on this information, the algorithm calculates risk as the failure probability multiplied by the economic losses resulting from such failure. The other costs associated to the structual system are added to the actual risk and since they do not depend on system's random parameters, they are referred as xed costs. As result, one obtains the total expected cost, which corresponds to the objective function of the structural optimization problem. Numerical applications shows the accuracy and e ciency of the methodology in the evaluation of the failure probability of problems represented by high nonlinear limit state functions with multiple failure regions. It is also included the e ects of geometric and physical nonlinearities originated in the probabilistic analysis and risk optimization of truss structures. Results show that, in consideration of uncertainty and the monetary consequences of failure, the optimum structure can only be found by a risk optimization formulation, where structural con guration and safety margins are optimized simultaneously. Risk optimization yields a structure which is optimum in terms of mechanics and in terms of the compromise between cost and safety.

Neste trabalho, são desenvolvidas novas técnicas aproximadas de análise de confiabilidade para grelhas de concreto armado levando-se em consideração as probabilidades de falha de vários modos importantes. Realiza-se um acoplamento entre os métodos de Monte Carlo, elementos finitos e procedimentos de otimização para considerar esses modos de falha importantes e classificá-los. Esse acoplamento também permite a redução do número de chamadas ao modelo de elementos finitos. Os cenários de falha são caracterizados como o encurtamento excessivo do concreto e o alongamento do aço. Estes cenários determinam a capacidade última da estrutura, e podem ser representados por um coeficiente escalar que multiplica todas as ações presentes na estrutura. Para a determinação desses estados estruturais últimos, um procedimento incremental-iterativo é utilizado. A análise de confiabilidade é realizada em diferentes conjuntos de realizações aleatórias das variáveis de projeto. O conjunto de respostas estruturais e de realizações permite a determinação dos coeficientes da superfície de respostas da estrutura. O acoplamento realizado permite também o tratamento com estruturas de concreto com elevado número de modos de falha. Aplicam-se as técnicas em exemplos de grelhas de concreto armado / In this work, new local approaches of reliability analysis applied to reinforced concrete grid structures are developed, taking into account several critical cross-section failure probabilities. Monte Carlo simulations are coupled with finite element analyses and optimization techniques with techniques to take into account the failure in the most important cross-sections, in order to classify the severity of failure modes. The failure scenario is depicted when either a concrete fiber or a steel bar reaches the predefined conventional limit. This scenario gives the structural ultimate capacity, which can be represented by a scalar coefficient multiplying all the loads acting on the structure. To achieve the failure scenario, an incremental and iterative procedure is used. To carry out the reliability analysis, the mechanical analysis has to be performed for different sets of random variable realizations of the mechanical, material and geometrical properties. The set of ultimate coefficients obtained from several mechanical analyses defines the response surface. The coupling between Monte Carlo simulations and response surface techniques applied in this work aims to reduce significantly the number of the finite element model calls, and hence to deal with real, or high-scale, reinforced concrete grids where large number of failure components can be found. The proposed procedure is then applied to reinforced concrete grids in order to show some more complex reinforced concrete examples

Neste trabalho, são desenvolvidas novas técnicas aproximadas de análise de confiabilidade para grelhas de concreto armado levando-se em consideração as probabilidades de falha de vários modos importantes. Realiza-se um acoplamento entre os métodos de Monte Carlo, elementos finitos e procedimentos de otimização para considerar esses modos de falha importantes e classificá-los. Esse acoplamento também permite a redução do número de chamadas ao modelo de elementos finitos. Os cenários de falha são caracterizados como o encurtamento excessivo do concreto e o alongamento do aço. Estes cenários determinam a capacidade última da estrutura, e podem ser representados por um coeficiente escalar que multiplica todas as ações presentes na estrutura. Para a determinação desses estados estruturais últimos, um procedimento incremental-iterativo é utilizado. A análise de confiabilidade é realizada em diferentes conjuntos de realizações aleatórias das variáveis de projeto. O conjunto de respostas estruturais e de realizações permite a determinação dos coeficientes da superfície de respostas da estrutura. O acoplamento realizado permite também o tratamento com estruturas de concreto com elevado número de modos de falha. Aplicam-se as técnicas em exemplos de grelhas de concreto armado / In this work, new local approaches of reliability analysis applied to reinforced concrete grid structures are developed, taking into account several critical cross-section failure probabilities. Monte Carlo simulations are coupled with finite element analyses and optimization techniques with techniques to take into account the failure in the most important cross-sections, in order to classify the severity of failure modes. The failure scenario is depicted when either a concrete fiber or a steel bar reaches the predefined conventional limit. This scenario gives the structural ultimate capacity, which can be represented by a scalar coefficient multiplying all the loads acting on the structure. To achieve the failure scenario, an incremental and iterative procedure is used. To carry out the reliability analysis, the mechanical analysis has to be performed for different sets of random variable realizations of the mechanical, material and geometrical properties. The set of ultimate coefficients obtained from several mechanical analyses defines the response surface. The coupling between Monte Carlo simulations and response surface techniques applied in this work aims to reduce significantly the number of the finite element model calls, and hence to deal with real, or high-scale, reinforced concrete grids where large number of failure components can be found. The proposed procedure is then applied to reinforced concrete grids in order to show some more complex reinforced concrete examples

L’évolution récente des commutateurs de sélection de longueurs d’onde (WSS -Wavelength Selective Switch) favorise le développement du multiplexeur optique d’insertionextraction reconfigurable (ROADM - Reconfigurable Optical Add/Drop Multiplexers) à plusieurs degrés sans orientation ni coloration, considéré comme un équipement fort prometteur pour les réseaux maillés du futur relativement au multiplexage en longueur d’onde (WDM -Wavelength Division Multiplexing ). Cependant, leur propriété de commutation asymétrique complique la question de l’acheminement et de l’attribution des longueur d’ondes (RWA - Routing andWavelength Assignment). Or la plupart des algorithmes de RWA existants ne tiennent pas compte de cette propriété d’asymétrie. L’interruption des services causée par des défauts d’équipements sur les chemins optiques (résultat provenant de la résolution du problème RWA) a pour conséquence la perte d’une grande quantité de données. Les recherches deviennent ainsi incontournables afin d’assurer la survie fonctionnelle des réseaux optiques, à savoir, le maintien des services, en particulier en cas de pannes d’équipement. La plupart des publications antérieures portaient particulièrement sur l’utilisation d’un système de protection permettant de garantir le reroutage du trafic en cas d’un défaut d’un lien. Cependant, la conception de la protection contre le défaut d’un lien ne s’avère pas toujours suffisante en termes de survie des réseaux WDM à partir de nombreux cas des autres types de pannes devenant courant de nos jours, tels que les bris d’équipements, les pannes de deux ou trois liens, etc. En outre, il y a des défis considérables pour protéger les grands réseaux optiques multidomaines composés de réseaux associés à un domaine simple, interconnectés par des liens interdomaines, où les détails topologiques internes d’un domaine ne sont généralement pas partagés à l’extérieur. La présente thèse a pour objectif de proposer des modèles d’optimisation de grande taille et des solutions aux problèmes mentionnés ci-dessus. Ces modèles-ci permettent de générer des solutions optimales ou quasi-optimales avec des écarts d’optimalité mathématiquement prouvée. Pour ce faire, nous avons recours à la technique de génération de colonnes afin de résoudre les problèmes inhérents à la programmation linéaire de grande envergure. Concernant la question de l’approvisionnement dans les réseaux optiques, nous proposons un nouveau modèle de programmation linéaire en nombres entiers (ILP - Integer Linear Programming) au problème RWA afin de maximiser le nombre de requêtes acceptées (GoS - Grade of Service). Le modèle résultant constitue celui de l’optimisation d’un ILP de grande taille, ce qui permet d’obtenir la solution exacte des instances RWA assez grandes, en supposant que tous les noeuds soient asymétriques et accompagnés d’une matrice de connectivité de commutation donnée. Ensuite, nous modifions le modèle et proposons une solution au problème RWA afin de trouver la meilleure matrice de commutation pour un nombre donné de ports et de connexions de commutation, tout en satisfaisant/maximisant la qualité d’écoulement du trafic GoS. Relativement à la protection des réseaux d’un domaine simple, nous proposons des solutions favorisant la protection contre les pannes multiples. En effet, nous développons la protection d’un réseau d’un domaine simple contre des pannes multiples, en utilisant les p-cycles de protection avec un chemin indépendant des pannes (FIPP - Failure Independent Path Protecting) et de la protection avec un chemin dépendant des pannes (FDPP - Failure Dependent Path-Protecting). Nous proposons ensuite une nouvelle formulation en termes de modèles de flots pour les p-cycles FDPP soumis à des pannes multiples. Le nouveau modèle soulève un problème de taille, qui a un nombre exponentiel de contraintes en raison de certaines contraintes d’élimination de sous-tour. Par conséquent, afin de résoudre efficacement ce problème, on examine : (i) une décomposition hiérarchique du problème auxiliaire dans le modèle de décomposition, (ii) des heuristiques pour gérer efficacement le grand nombre de contraintes. À propos de la protection dans les réseaux multidomaines, nous proposons des systèmes de protection contre les pannes d’un lien. Tout d’abord, un modèle d’optimisation est proposé pour un système de protection centralisée, en supposant que la gestion du réseau soit au courant de tous les détails des topologies physiques des domaines. Nous proposons ensuite un modèle distribué de l’optimisation de la protection dans les réseaux optiques multidomaines, une formulation beaucoup plus réaliste car elle est basée sur l’hypothèse d’une gestion de réseau distribué. Ensuite, nous ajoutons une bande pasiv sante partagée afin de réduire le coût de la protection. Plus précisément, la bande passante de chaque lien intra-domaine est partagée entre les p-cycles FIPP et les p-cycles dans une première étude, puis entre les chemins pour lien/chemin de protection dans une deuxième étude. Enfin, nous recommandons des stratégies parallèles aux solutions de grands réseaux optiques multidomaines. Les résultats de l’étude permettent d’élaborer une conception efficace d’un système de protection pour un très large réseau multidomaine (45 domaines), le plus large examiné dans la littérature, avec un système à la fois centralisé et distribué. / Recent developments in the wavelength selective switch (WSS) technology enable multi-degree reconfigurable optical add/drop multiplexers (ROADM) architectures with colorless and directionless switching, which is regarded as a very promising enabler for future reconfigurable wavelength division multiplexing (WDM) mesh networks. However, its asymmetric switching property complicates the optimal routing and wavelength assignment (RWA) problem, which is NP-hard. Most of the existing RWA algorithms do not consider such property. Disruption of services through equipment failures on the lightpaths (output of RWA problem) is consequential as it involves the lost of large amounts of data. Therefore, substantial research efforts are needed to ensure the functional survivability of optical networks, i.e., the continuation of services even when equipment failures occur. Most previous publications have focused on using a protection scheme to guarantee the traffic connections in the event of single link failures. However, protection design against single link failures turns out not to be always sufficient to keep the WDM networks away from many downtime cases as other kinds of failures, such as node failures, dual link failures, triple link failures, etc., become common nowadays. Furthermore, there are challenges to protect large multi-domain optical networks which are composed of several singledomain networks, interconnected by inter-domain links, where the internal topological details of a domain are usually not shared externally. The objective of this thesis is to propose scalable models and solution methods for the above problems. The models enable to approach large problem instances while producing optimal or near optimal solutions with mathematically proven optimality gaps. For this, we rely on the column generation technique which is suitable to solve large scale linear programming problems. For the provisioning problem in optical networks, we propose a new ILP (Integer Linear Programming) model for RWA problem with the objective of maximizing the Grade of Service (GoS). The resulting model is a large scale optimization ILP model, which allows the exact solution of quite large RWA instances, assuming all nodes are asymmetric and with a given switching connectivity matrix. Next, we modify the model and propose a solution for the RWA problem with the objective of finding the best switching connectivity matrix for a given number of ports and a given number of switching connections, while satisfying/maximizing the GoS. For protection in single domain networks, we propose solutions for the protection against multiple failures. Indeed, we extent the protection of a single domain network against multiple failures, using FIPP and FDPP p-cycles. We propose a new generic flow formulation for FDPP p-cycles subject to multiple failures. Our new model ends up with a complex pricing problem, which has an exponential number of constraints due to some subtour elimination constraints. Consequently, in order to efficiently solve the pricing problem, we consider: (i) a hierarchical decomposition of the original pricing problem; (ii) heuristics in order to go around the large number of constraints in the pricing problem. For protection in multi-domain networks, we propose protection schemes against single link failures. Firstly, we propose an optimization model for a centralized protection scheme, assuming that the network management is aware of all the details of the physical topologies of the domains. We then propose a distributed optimization model for protection in multi-domain optical networks, a much more realistic formulation as it is based on the assumption of a distributed network management. Then, we add bandwidth sharing in order to reduce the cost of protection. Bandwidth of each intra-domain link is shared among FIPP p-cycles and p-cycles in a first study, and then among paths for link/path protection in a second study. Finally, we propose parallel strategies in order to obtain solutions for very large multi-domain optical networks. The result of this last study allows the efficent design of a protection scheme for a very large multi-domain network (45 domains), the largest one by far considered in the literature, both with a centralized and distributed scheme.

Dreiaxiale Druckprüfungen können als Einstufenversuche, als Mehrstufenversuche oder als Versuche mit kontinuierlichen Bruchzuständen ausgeführt werden. Bei der Anwendung der Mehrstufentechnik ergeben sich insbesondere Fragestellungen hinsichtlich der richtigen Wahl des Umschaltpunktes und des optimalen Verlaufs des Spannungspfades zwischen den einzelnen Versuchsstufen. Fraglich beim Versuch mit kontinuierlichen Bruchzuständen bleibt, ob im Versuchsverlauf tatsächlich Spannungszustände erfasst werden, welche die Höchstfestigkeit des untersuchten Materials repräsentieren. Die Dissertation greift diese Fragestellungen auf, ermöglicht den Einstieg in die beschriebene Thematik und schafft die Voraussetzungen, die zur Lösung der aufgeführten Problemstellungen notwendig sind. Auf der Grundlage einer umfangreichen Datenbasis gesteinsmechanischer und petrophysikalischer Kennwerte wurde ein numerisches Modell entwickelt, welches das Spannungs-Verformungs-, Festigkeits- und Bruchverhalten eines Sandsteins im direkten Zug- und im einaxialen Druckversuch sowie in dreiaxialen Druckprüfungen zufriedenstellend wiedergibt. Das Festigkeitsverhalten des entwickelten Modells wurde in Mehrstufentests mit unterschiedlichen Spannungspfaden analysiert und mit den entsprechenden Laborbefunden verglichen.

Dreiaxiale Druckprüfungen können als Einstufenversuche, als Mehrstufenversuche oder als Versuche mit kontinuierlichen Bruchzuständen ausgeführt werden. Bei der Anwendung der Mehrstufentechnik ergeben sich insbesondere Fragestellungen hinsichtlich der richtigen Wahl des Umschaltpunktes und des optimalen Verlaufs des Spannungspfades zwischen den einzelnen Versuchsstufen. Fraglich beim Versuch mit kontinuierlichen Bruchzuständen bleibt, ob im Versuchsverlauf tatsächlich Spannungszustände erfasst werden, welche die Höchstfestigkeit des untersuchten Materials repräsentieren. Die Dissertation greift diese Fragestellungen auf, ermöglicht den Einstieg in die beschriebene Thematik und schafft die Voraussetzungen, die zur Lösung der aufgeführten Problemstellungen notwendig sind. Auf der Grundlage einer umfangreichen Datenbasis gesteinsmechanischer und petrophysikalischer Kennwerte wurde ein numerisches Modell entwickelt, welches das Spannungs-Verformungs-, Festigkeits- und Bruchverhalten eines Sandsteins im direkten Zug- und im einaxialen Druckversuch sowie in dreiaxialen Druckprüfungen zufriedenstellend wiedergibt. Das Festigkeitsverhalten des entwickelten Modells wurde in Mehrstufentests mit unterschiedlichen Spannungspfaden analysiert und mit den entsprechenden Laborbefunden verglichen.