TY - THES A1 - Unger, Jörg F. T1 - Neural networks in a multiscale approach for concrete N2 - From a macroscopic point of view, failure within concrete structures is characterized by the initiation and propagation of cracks. In the first part of the thesis, a methodology for macroscopic crack growth simulations for concrete structures using a cohesive discrete crack approach based on the extended finite element method is introduced. Particular attention is turned to the investigation of criteria for crack initiation and crack growth. A drawback of the macroscopic simulation is that the real physical phenomena leading to the nonlinear behavior are only modeled phenomenologically. For concrete, the nonlinear behavior is characterized by the initiation of microcracks which coalesce into macroscopic cracks. In order to obtain a higher resolution of this failure zones, a mesoscale model for concrete is developed that models particles, mortar matrix and the interfacial transition zone (ITZ) explicitly. The essential features are a representation of particles using a prescribed grading curve, a material formulation based on a cohesive approach for the ITZ and a combined model with damage and plasticity for the mortar matrix. Compared to numerical simulations, the response of real structures exhibits a stochastic scatter. This is e.g. due to the intrinsic heterogeneities of the structure. For mesoscale models, these intrinsic heterogeneities are simulated by using a random distribution of particles and by a simulation of spatially variable material parameters using random fields. There are two major problems related to numerical simulations on the mesoscale. First of all, the material parameters for the constitutive description of the materials are often difficult to measure directly. In order to estimate material parameters from macroscopic experiments, a parameter identification procedure based on Bayesian neural networks is developed which is universally applicable to any parameter identification problem in numerical simulations based on experimental results. This approach offers information about the most probable set of material parameters based on experimental data and information about the accuracy of the estimate. Consequently, this approach can be used a priori to determine a set of experiments to be carried out in order to fit the parameters of a numerical model to experimental data. The second problem is the computational effort required for mesoscale simulations of a full macroscopic structure. For this purpose, a coupling between mesoscale and macroscale model is developed. Representative mesoscale simulations are used to train a metamodel that is finally used as a constitutive model in a macroscopic simulation. Special focus is placed on the ability of appropriately simulating unloading. N2 - Makroskopisch betrachtet kann das Versagen von Beton durch die Entstehung und das Wachstum von Rissen beschrieben werden. Im ersten Teil der Arbeit wird eine Methode zur Simulation der makroskopischen Rissentwicklung von Beton unter Verwendung von kohäsiven diskreten Rissen basierend auf der erweiterten Finiten Elemente Methode vorgestellt. Besondere Bedeutung liegt dabei auf der Untersuchung von Kriterien zur Rissentstehung und zum Risswachstum. Ein Nachteil von makroskopischen Simulationen liegt in der nur phänomenologischen Berücksichtigung der tatsächlichen Vorgänge. Nichtlineares Verhalten von Beton ist durch die Entstehung von Mikrorissen gekennzeichnet, die bei weiterer Belastung zu makroskopischen Rissen zusammenwachsen. Um die Versagenszone realitätsnah abbilden zu können, wurde ein Mesoskalenmodell von Beton entwickelt, welches Zuschläge, Matrix und Übergangszone zwischen beiden Materialien (ITZ) direkt abbildet. Hauptmerkmal sind die Simulation der Zuschläge nach einer Sieblinie, eine kohäsive Materialformulierung der ITZ und ein kombiniertes Model aus Schädigung und Plastizität für das Matrixmaterial. Im Gegensatz zu numerischen Simulationen ist die Systemantwort reeller Strukturen eine unscharfe Größe. Dies liegt u.a. an Heterogenitäten innerhalb der Struktur, die im Rahmen der Arbeit durch eine zufällige Verteilung der Zuschläge und über räumlich variierende Materialparameter unter Verwendung von Zufallsfeldern simuliert werden. Zwei Hauptprobleme sind bei den Mesoskalensimulationen aufgetreten. Einerseits sind Materialparameter auf der Mesoskala oft schwer zu bestimmen. Deswegen wurde eine Methode basierend auf Bayes neuronalen Netzen entwickelt, die eine Parameteridentifikation unter Verwendung von makroskopischen Versuchen erlaubt. Diese Methode ist aber universell anwendbar auf alle Parameteridentifikationsprobleme in numerischen Simulationen basierend auf experimentellen Daten. Der Ansatz liefert sowohl Informationen über den wahrscheinlichsten Parametersatz des Models zur numerischen Simulation eines Experiments als auch eine Einschätzung der Genauigkeit dieses Schätzers. Die Methode kann auch verwendet werden, um a priori einen Satz von Experimenten auszuwählen der notwendig ist, um die Parameter eines numerischen Modells zu bestimmen. Ein zweites Problem ist der numerische Aufwand von Mesoskalensimulationen für makroskopische Strukturen. Aus diesem Grund wurde eine Kopplungsstrategie zwischen Meso- und Makromodell entwickelt, bei dem repräsentative Simulationen auf der Mesoebene verwendet werden, um ein Metamodell zu generieren, welches dann die Materialformulierung in einer makroskopischen Simulation darstellt. Ein Fokus liegt dabei auf der korrekten Abbildung von Entlastungen. T2 - Neuronale Netze in einem Multiskalenansatz für Beton T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2009,1 KW - Beton KW - Mehrskalenmodell KW - Mehrskalenanalyse KW - Neuronales Netz KW - Monte-Carlo-Simulation KW - Simulation KW - Monte-Carlo-Integration KW - Kontinuierliche Simul KW - Bayes neuronale Netze KW - Parameteridentification KW - Bayesian neural networks KW - parameter identification Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20090626-14763 ER - TY - THES A1 - Eckardt, Stefan T1 - Adaptive heterogeneous multiscale models for the nonlinear simulation of concrete N2 - The nonlinear behavior of concrete can be attributed to the propagation of microcracks within the heterogeneous internal material structure. In this thesis, a mesoscale model is developed which allows for the explicit simulation of these microcracks. Consequently, the actual physical phenomena causing the complex nonlinear macroscopic behavior of concrete can be represented using rather simple material formulations. On the mesoscale, the numerical model explicitly resolves the components of the internal material structure. For concrete, a three-phase model consisting of aggregates, mortar matrix and interfacial transition zone is proposed. Based on prescribed grading curves, an efficient algorithm for the generation of three-dimensional aggregate distributions using ellipsoids is presented. In the numerical model, tensile failure of the mortar matrix is described using a continuum damage approach. In order to reduce spurious mesh sensitivities, introduced by the softening behavior of the matrix material, nonlocal integral-type material formulations are applied. The propagation of cracks at the interface between aggregates and mortar matrix is represented in a discrete way using a cohesive crack approach. The iterative solution procedure is stabilized using a new path following constraint within the framework of load-displacement-constraint methods which allows for an efficient representation of snap-back phenomena. In several examples, the influence of the randomly generated heterogeneous material structure on the stochastic scatter of the results is analyzed. Furthermore, the ability of mesoscale models to represent size effects is investigated. Mesoscale simulations require the discretization of the internal material structure. Compared to simulations on the macroscale, the numerical effort and the memory demand increases dramatically. Due to the complexity of the numerical model, mesoscale simulations are, in general, limited to small specimens. In this thesis, an adaptive heterogeneous multiscale approach is presented which allows for the incorporation of mesoscale models within nonlinear simulations of concrete structures. In heterogeneous multiscale models, only critical regions, i.e. regions in which damage develops, are resolved on the mesoscale, whereas undamaged or sparsely damage regions are modeled on the macroscale. A crucial point in simulations with heterogeneous multiscale models is the coupling of sub-domains discretized on different length scales. The sub-domains differ not only in the size of the finite elements but also in the constitutive description. In this thesis, different methods for the coupling of non-matching discretizations - constraint equations, the mortar method and the arlequin method - are investigated and the application to heterogeneous multiscale models is presented. Another important point is the detection of critical regions. An adaptive solution procedure allowing the transfer of macroscale sub-domains to the mesoscale is proposed. In this context, several indicators which trigger the model adaptation are introduced. Finally, the application of the proposed adaptive heterogeneous multiscale approach in nonlinear simulations of concrete structures is presented. N2 - Das nichtlineare Materialverhalten von Beton ist durch die Entwicklung von Mikrorissen innerhalb der heterogenen Materialstruktur gekennzeichnet. In dieser Arbeit wird ein Mesoskalenmodell entwickelt, welches die einzelnen Bestandteile der Materialstruktur explizit auflöst und somit die Simulation dieser Mikrorisse erlaubt. Dadurch können die wirklichen physikalischen Vorgänge, welche das komplexe nichtlineare Verhalten von Beton verursachen, durch relativ einfache Materialformulierungen abgebildet werden. Für Beton wird auf der Mesoskala ein 3-Phasenmodell vorgeschlagen, bestehend aus groben Zuschlägen, Mörtelmatrix und Übergangszone zwischen Zuschlag und Matrix. In diesem Zusammenhang wird ein effizienter Algorithmus vorgestellt, welcher ausgehend von einer gegebenen Sieblinie dreidimensionale Kornstrukturen mittels Ellipsoiden simuliert. Im Mesoskalenmodell wird das Zugversagen der Mörtelmatrix durch einen Kontinuumsansatz beschrieben. Um Netzabhängigkeiten, welche durch das Entfestigungsverhalten des Materials hervorgerufen werden, zu reduzieren, kommen nichtlokale Materialformulierungen zum Einsatz. Risse innerhalb der Übergangszone zwischen Zuschlag und Matrix werden, basierend auf einem kohäsiven Modell, mittels eines diskreten Rissansatzes abgebildet. Die Verwendung einer neuen Nebenbedingung innerhalb der Last-Verschiebungs-Zwangsmethode führt zu einer Stabilisierung des iterativen Lösungverfahrens, so dass eine effiziente Simulation von Snap-back Phänomenen möglich wird. Anhand von Beispielen wird gezeigt, dass Mesoskalenmodelle die stochastische Streuung von Ergebnissen und Maßstabseffekte abbilden können. Da auf der Mesoskala die Diskretisierung der inneren Materialstruktur erforderlich ist, steigt im Vergleich zu Simulationen auf der Makroskala der numerische Aufwand erheblich. Aufgrund der Komplexität des numerischen Modells sind Mesoskalensimulationen in der Regel auf kleine Probekörper beschränkt. In dieser Arbeit wird ein adaptiver heterogener Mehrskalenansatz vorgestellt, welcher die Verwendung von Mesoskalenmodellen in nichtlinearen Simulationen von Betonstrukturen erlaubt. In heterogenen Mehrskalenmodellen werden nur kritische Bereiche auf der Mesoskala aufgelöst, während ungeschädigte Bereiche auf der Makroskala abgebildet werden. Ein wichtiger Aspekt in Simulationen mit heterogenen Mehrskalenmodellen ist die Kopplung der auf unterschiedlichen Längenskalen diskretisierten Teilgebiete. Diese unterscheiden sich nicht nur in der Größe der finiten Elemente sondern auch in der Beschreibung des Materials. Verschiedene Methoden zur Kopplung nicht übereinstimmender Vernetzungen - Kopplungsgleichungen, die Mortar-Methode und die Arlequin-Methode - werden untersucht und ihre Anwendung in heterogenen Mehrskalenmodellen wird gezeigt. Ein weiterer wichtiger Aspekt ist die Bestimmung kritischer Regionen. Eine adaptive Lösungsstrategie wird entwickelt, welche die Umwandlung von Makroskalengebieten auf die Mesoskala erlaubt. In diesem Zusammenhang werden Indikatoren vorgestellt, die eine Modellanpassung auslösen. Anhand nichtlinearer Simulationen von Betonstrukturen wird die Anwendung des vorgestellten adaptiven heterogenen Mehrskalenansatzes demonstriert. T2 - Adaptive heterogene Mehrskalenmodelle zur nichtlinearen Simulation von Beton T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2010,1 KW - Beton KW - Mehrskalenanalyse KW - Finite-Elemente-Methode KW - Nichtlineare Finite-Elemente-Methode KW - Schadensmechanik KW - Mehrskalenmodell KW - Adaptives Verfahren KW - concrete KW - multiscale method KW - finite element method KW - continuum damage mechanics KW - adaptive simulation Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20100317-15023 ER - TY - THES A1 - Luther, Torsten T1 - Adaptation of atomistic and continuum methods for multiscale simulation of quasi-brittle intergranular damage N2 - The numerical simulation of damage using phenomenological models on the macroscale was state of the art for many decades. However, such models are not able to capture the complex nature of damage, which simultaneously proceeds on multiple length scales. Furthermore, these phenomenological models usually contain damage parameters, which are physically not interpretable. Consequently, a reasonable experimental determination of these parameters is often impossible. In the last twenty years, the ongoing advance in computational capacities provided new opportunities for more and more detailed studies of the microstructural damage behavior. Today, multiphase models with several million degrees of freedom enable for the numerical simulation of micro-damage phenomena in naturally heterogeneous materials. Therewith, the application of multiscale concepts for the numerical investigation of the complex nature of damage can be realized. The presented thesis contributes to a hierarchical multiscale strategy for the simulation of brittle intergranular damage in polycrystalline materials, for example aluminum. The numerical investigation of physical damage phenomena on an atomistic microscale and the integration of these physically based information into damage models on the continuum meso- and macroscale is intended. Therefore, numerical methods for the damage analysis on the micro- and mesoscale including the scale transfer are presented and the transition to the macroscale is discussed. The investigation of brittle intergranular damage on the microscale is realized by the application of the nonlocal Quasicontinuum method, which fully describes the material behavior by atomistic potential functions, but reduces the number of atomic degrees of freedom by introducing kinematic couplings. Since this promising method is applied only by a limited group of researchers for special problems, necessary improvements have been realized in an own parallelized implementation of the 3D nonlocal Quasicontinuum method. The aim of this implementation was to develop and combine robust and efficient algorithms for a general use of the Quasicontinuum method, and therewith to allow for the atomistic damage analysis in arbitrary grain boundary configurations. The implementation is applied in analyses of brittle intergranular damage in ideal and nonideal grain boundary models of FCC aluminum, considering arbitrary misorientations. From the microscale simulations traction separation laws are derived, which describe grain boundary decohesion on the mesoscale. Traction separation laws are part of cohesive zone models to simulate the brittle interface decohesion in heterogeneous polycrystal structures. 2D and 3D mesoscale models are presented, which are able to reproduce crack initiation and propagation along cohesive interfaces in polycrystals. An improved Voronoi algorithm is developed in 2D to generate polycrystal material structures based on arbitrary distribution functions of grain size. The new model is more flexible in representing realistic grain size distributions. Further improvements of the 2D model are realized by the implementation and application of an orthotropic material model with Hill plasticity criterion to grains. The 2D and 3D polycrystal models are applied to analyze crack initiation and propagation in statically loaded samples of aluminum on the mesoscale without the necessity of initial damage definition. N2 - Strukturmechanische Ermüdungs- und Lebensdaueranalysen basieren meist auf der Anwendung phänomenologischer Modelle der Schädigungs- und Bruchmechanik zur numerischen Simulationen des makroskopischen Schädigungsverhaltens. Ausgehend von einer definierten Anfangsschädigung sind diese Modelle nicht in der Lage, die tatsächlichen Vorgänge der Rissinitiierung und unterschiedlichen Rissausbreitung zu erfassen. Eine physikalische Interpretation der phänomenologisch eingeführten Schädigungsparameter ist oftmals nicht möglich und deren experimentelle Bestimmung schwierig. Die Berücksichtigung des mikrostrukturellen Aufbaus von Materialien in numerischen Modellen der Schädigungs- und Bruchmechanik bietet neue Möglichkeiten, die für die Rissinitiierung und Rissausbreitung ursächlichen physikalischen Phänomene abzubilden. Zunehmende Erkenntnisse über gleichzeitig auftretende Mikro- und Makroschädigungsvorgänge resultieren in verbesserten numerischen Modellen, mit denen aufwändige und kostenintensive Experimente in der Materialentwicklung zum Teil ersetzt werden können. In Kenntnis einer Vielfalt von unterschiedlichen Schädigungsphänomenen in technischen Materialien fokussiert die vorliegende Dissertation auf die Entwicklung und Verbesserung numerischer Methoden der Atomistik und der Kontinuumsmechanik zur Mehrskalenuntersuchung quasi-spröder Korngrenzenschädigung in polykristallinen Werkstoffen, z.B. Aluminium. Die kombinierte Anwendung dieser Methoden ist Teil eines hierarchischen Mehrskalenansatzes zur Integration des physikalisch beschriebenen Materialverhaltens der Atomistik in ein ingenieurmäßiges Kontinuumsschädigungsmodell. Ziel der Dissertation ist die Entwicklung einer Methodik, die es erlaubt, den Verlust atomarer Bindungen als physikalische Ursache spröder Schädigung zu simulieren und Ergebnisse aus diesen atomistischen Mikroskalen-Simulationen zur Parametrisierung von kohäsiven Materialmodellen der Kontinuumsmechanik zu nutzen. Diese beschreiben den intergranularen Sprödbruch in heterogenen Polykristallmodellen der Mesoskala. Der Einfluss der Heterogenität wird in nichtlinearen Finite-Elemente-Simulationen durch explizite Abbildung der Kornstruktur im mesoskopischen Polykristallmodell berücksichtigt. Durch den Einsatz des kohäsiven Interface-Gesetzes erlaubt das auf der Mesoskala angewandte Kontinuumsmodell die Simulation spröder Korngrenzenschädigung in statisch belasteten 2D und 3D Modellen ohne die Notwendigkeit der Definition einer Anfangsschädigung, wie dies in klassischen Modellen der linear-elastischen Bruchmechanik notwendig ist. Zur effizienten Realisierung der atomistischen Mikroskalen-Simulationen wird eine Implementation der nichtlokalen 3D Quasikontinuumsmethode angewandt. Diese Methode basiert auf einem atomistischen Ansatz und beschreibt das Materialverhalten auf Grundlage atomarer Bindungskräfte. In Modellgebieten mit gleichmäßigem Verformungsfeld werden kinematische Kopplungen atomarer Freiheitsgrade eingeführt, sodass sich die Zahl unabhängiger Freiheitsgrade stark reduziert. Deren effizienter Einsatz erlaubt Simulationen an größeren Modellen ohne Kopplung mit kontinuumsmechanischen Methoden. Eine verbesserte Vernetzung, ein robuster Optimierungsalgorithmus und die vorgenommene Parallelisierung machen die implementierte nichtlokale 3D Quasikontinuumsmethode zu einem effizienten Werkzeug für die robuste Simulation von physikalischen Schädigungsphänomenen in beliebigen atomistischen Konfigurationen. In quasistatischen Simulationen wird eine deutliche Beschleunigung gegenüber der Methode der Gitterstatik bei vergleichbarer Qualität der Ergebnisse erreicht. T2 - Weiterentwicklung numerischer Methoden der Atomistik und Kontinuumsmechanik zur Multiskalen-Simulation quasi-spröder intergranularer Schädigung T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2010,2 KW - Mechanik KW - Computersimulation KW - Mikro-Scale KW - Meso-Scale KW - Polykristall KW - intergranular damage KW - atomistic simulation methods KW - continuum mechanics KW - quasicontinuum method KW - scale transition Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20101101-15245 ER - TY - THES A1 - Brehm, Maik T1 - Vibration-based model updating: Reduction and quantification of uncertainties N2 - Numerical models and their combination with advanced solution strategies are standard tools for many engineering disciplines to design or redesign structures and to optimize designs with the purpose to improve specific requirements. As the successful application of numerical models depends on their suitability to represent the behavior related to the intended use, they should be validated by experimentally obtained results. If the discrepancy between numerically derived and experimentally obtained results is not acceptable, a model revision or a revision of the experiment need to be considered. Model revision is divided into two classes, the model updating and the basic revision of the numerical model. The presented thesis is related to a special branch of model updating, the vibration-based model updating. Vibration-based model updating is a tool to improve the correlation of the numerical model by adjusting uncertain model input parameters by means of results extracted from vibration tests. Evidently, uncertainties related to the experiment, the numerical model, or the applied numerical solving strategies can influence the correctness of the identified model input parameters. The reduction of uncertainties for two critical problems and the quantification of uncertainties related to the investigation of several nominally identical structures are the main emphases of this thesis. First, the reduction of uncertainties by optimizing reference sensor positions is considered. The presented approach relies on predicted power spectral amplitudes and an initial finite element model as a basis to define the assessment criterion for predefined sensor positions. In combination with geometry-based design variables, which represent the sensor positions, genetic and particle swarm optimization algorithms are applied. The applicability of the proposed approach is demonstrated on a numerical benchmark study of a simply supported beam and a case study of a real test specimen. Furthermore, the theory of determining the predicted power spectral amplitudes is validated with results from vibration tests. Second, the possibility to reduce uncertainties related to an inappropriate assignment for numerically derived and experimentally obtained modes is investigated. In the context of vibration-based model updating, the correct pairing is essential. The most common criterion for indicating corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases and is not reliable for automatic approaches. Hence, an alternative criterion, the energy-based modal assurance criterion, is proposed. This criterion combines the mathematical characteristic of orthogonality with the physical properties of the structure by modal strain energies. A numerical example and a case study with experimental data are presented to show the advantages of the proposed energy-based modal assurance criterion in comparison to the traditional modal assurance criterion. Third, the application of optimization strategies combined with information theory based objective functions is analyzed for the purpose of stochastic model updating. This approach serves as an alternative to the common sensitivity-based stochastic model updating strategies. Their success depends strongly on the defined initial model input parameters. In contrast, approaches based on optimization strategies can be more flexible. It can be demonstrated, that the investigated nature inspired optimization strategies in combination with Bhattacharyya distance and Kullback-Leibler divergence are appropriate. The obtained accuracies and the respective computational effort are comparable with sensitivity-based stochastic model updating strategies. The application of model updating procedures to improve the quality and suitability of a numerical model is always related to additional costs. The presented innovative approaches will contribute to reduce and quantify uncertainties within a vibration-based model updating process. Therefore, the increased benefit can compensate the additional effort, which is necessary to apply model updating procedures. N2 - Eine typische Anwendung von numerischen Modellen und den damit verbundenen numerischen Lösungsstrategien ist das Entwerfen oder Ertüchtigen von Strukturen und das Optimieren von Entwürfen zur Verbesserung spezifischer Eigenschaften. Der erfolgreiche Einsatz von numerischen Modellen ist abhängig von der Eignung des Modells bezüglich der vorgesehenen Anwendung. Deshalb ist eine Validierung mit experimentellen Ergebnissen sinnvoll. Zeigt die Validierung inakzeptable Unterschiede zwischen den Ergebnissen des numerischen Modells und des Experiments, sollte das numerische Modell oder das experimentelle Vorgehen verbessert werden. Für die Modellverbesserung gibt es zwei verschiedene Möglichkeiten, zum einen die Kalibrierung des Modells und zum anderen die grundsätzliche Änderung von Modellannahmen. Die vorliegende Dissertation befasst sich mit der Kalibrierung von numerischen Modellen auf der Grundlage von Schwingungsversuchen. Modellkalibrierung ist eine Methode zur Verbesserung der Korrelation zwischen einem numerischen Modell und einer realen Struktur durch Anpassung von Modelleingangsparametern unter Verwendung von experimentell ermittelten Daten. Unsicherheiten bezüglich des numerischen Modells, des Experiments und der angewandten numerischen Lösungsstrategie beeinflussen entscheidend die erzielbare Qualität der identifizierten Modelleingangsparameter. Die Schwerpunkte dieser Dissertation sind die Reduzierung von Unsicherheiten für zwei kritische Probleme und die Quantifizierung von Unsicherheiten extrahiert aus Experimenten nominal gleicher Strukturen. Der erste Schwerpunkt beschäftigt sich mit der Reduzierung von Unsicherheiten durch die Optimierung von Referenzsensorpositionen. Das Bewertungskriterium für vordefinierte Sensorpositionen basiert auf einer theoretischen Abschätzung von Amplituden der Spektraldichtefunktion und einem dazugehörigen Finite Elemente Modell. Die Bestimmung der optimalen Konfiguration erfolgt durch eine Anwendung von Optimierungsmethoden basierend auf genetischen Algorithmen und Schwarmintelligenzen. Die Anwendbarkeit dieser Methoden wurde anhand einer numerischen Studie an einem einfach gelagerten Balken und einem real existierenden komplexen Versuchskörper nachgewiesen. Mit Hilfe einer experimentellen Untersuchung wird die Abschätzung der statistischen Eigenschaften der Antwortspektraldichtefunktionen an diesem Versuchskörper validiert. Im zweiten Schwerpunkt konzentrieren sich die Untersuchungen auf die Reduzierung von Unsicherheiten, hervorgerufen durch ungeeignete Kriterien zur Eigenschwingformzuordnung. Diese Zuordnung ist entscheidend für Modellkalibrierungen basierend auf Schwingungsversuchen. Das am Häufigsten verwendete Kriterium zur Zuordnung ist das modal assurance criterion. In manchen Anwendungsfällen ist dieses Kriterium jedoch kein zuverlässiger Indikator. Das entwickelte alternative Kriterium, das energy-based modal assurance criterion, kombiniert das mathematische Merkmal der Orthogonalität mit den physikalischen Eigenschaften der untersuchten Struktur mit Hilfe von modalen Formänderungsarbeiten. Ein numerisches Beispiel und eine Sensitivitätsstudie mit experimentellen Daten zeigen die Vorteile des vorgeschlagenen energiebasierten Kriteriums im Vergleich zum traditionellen modal assurance criterion. Die Anwendung von Optimierungsstrategien auf stochastische Modellkalibrierungsverfahren wird im dritten Schwerpunkt analysiert. Dabei werden Verschiedenheitsmaße der Informationstheorie zur Definition von Zielfunktionen herangezogen. Dieser Ansatz stellt eine Alternative zu herkömmlichen Verfahren dar, welche auf gradientenbasierten Sensitivitätsmatrizen zwischen Eingangs- und Ausgangsgrößen beruhen. Deren erfolgreicher Einsatz ist abhängig von den Anfangswerten der Eingangsgrößen, wobei die vorgeschlagenen Optimierungsstrategien weniger störanfällig sind. Der Bhattacharyya Abstand und die Kullback-Leibler Divergenz als Zielfunktion, kombiniert mit stochastischen Optimierungsverfahren, erwiesen sich als geeignet. Bei vergleichbarem Rechenaufwand konnten ähnliche Genauigkeiten wie bei den Modellkalibrierungsverfahren, die auf Sensitivitätsmatrizen basieren, erzielt werden. Die Anwendung von Modellkalibrierungsverfahren zur Verbesserung der Eignung eines numerischen Modells für einen bestimmten Zweck ist mit einem Mehraufwand verbunden. Die präsentierten innovativen Verfahren tragen zu einer Reduzierung und Quantifizierung von Unsicherheiten innerhalb eines Modellkalibrierungsprozesses basierend auf Schwingungsversuchen bei. Mit dem zusätzlich generierten Nutzen kann der Mehraufwand, der für eine Modellkalibrierung notwendig ist, nachvollziehbar begründet werden. T2 - Modellkalibrierung basierend auf Schwingungsversuchen: Reduzierung und Quantifizierung von Unsicherheiten T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2011,1 KW - Dynamik KW - Optimierung KW - Modellkalibrierung KW - Modezuordung KW - optimale Sensorpositionierung KW - model updating KW - mode pairing KW - optimal sensor positions KW - dissimilarity measures KW - optimization Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20110926-15553 ER - TY - THES A1 - Schrader, Kai T1 - Hybrid 3D simulation methods for the damage analysis of multiphase composites T1 - Hybride 3D Simulationsmethoden zur Abbildung der Schädigungsvorgänge in Mehrphasen-Verbundwerkstoffen N2 - Modern digital material approaches for the visualization and simulation of heterogeneous materials allow to investigate the behavior of complex multiphase materials with their physical nonlinear material response at various scales. However, these computational techniques require extensive hardware resources with respect to computing power and main memory to solve numerically large-scale discretized models in 3D. Due to a very high number of degrees of freedom, which may rapidly be increased to the two-digit million range, the limited hardware ressources are to be utilized in a most efficient way to enable an execution of the numerical algorithms in minimal computation time. Hence, in the field of computational mechanics, various methods and algorithms can lead to an optimized runtime behavior of nonlinear simulation models, where several approaches are proposed and investigated in this thesis. Today, the numerical simulation of damage effects in heterogeneous materials is performed by the adaption of multiscale methods. A consistent modeling in the three-dimensional space with an appropriate discretization resolution on each scale (based on a hierarchical or concurrent multiscale model), however, still contains computational challenges in respect to the convergence behavior, the scale transition or the solver performance of the weak coupled problems. The computational efficiency and the distribution among available hardware resources (often based on a parallel hardware architecture) can significantly be improved. In the past years, high-performance computing (HPC) and graphics processing unit (GPU) based computation techniques were established for the investigationof scientific objectives. Their application results in the modification of existing and the development of new computational methods for the numerical implementation, which enables to take advantage of massively clustered computer hardware resources. In the field of numerical simulation in material science, e.g. within the investigation of damage effects in multiphase composites, the suitability of such models is often restricted by the number of degrees of freedom (d.o.f.s) in the three-dimensional spatial discretization. This proves to be difficult for the type of implementation method used for the nonlinear simulation procedure and, simultaneously has a great influence on memory demand and computational time. In this thesis, a hybrid discretization technique has been developed for the three-dimensional discretization of a three-phase material, which is respecting the numerical efficiency of nonlinear (damage) simulations of these materials. The increase of the computational efficiency is enabled by the improved scalability of the numerical algorithms. Consequently, substructuring methods for partitioning the hybrid mesh were implemented, tested and adapted to the HPC computing framework using several hundred CPU (central processing units) nodes for building the finite element assembly. A memory-efficient iterative and parallelized equation solver combined with a special preconditioning technique for solving the underlying equation system was modified and adapted to enable combined CPU and GPU based computations. Hence, it is recommended by the author to apply the substructuring method for hybrid meshes, which respects different material phases and their mechanical behavior and which enables to split the structure in elastic and inelastic parts. However, the consideration of the nonlinear material behavior, specified for the corresponding phase, is limited to the inelastic domains only, and by that causes a decreased computing time for the nonlinear procedure. Due to the high numerical effort for such simulations, an alternative approach for the nonlinear finite element analysis, based on the sequential linear analysis, was implemented in respect to scalable HPC. The incremental-iterative procedure in finite element analysis (FEA) during the nonlinear step was then replaced by a sequence of linear FE analysis when damage in critical regions occured, known in literature as saw-tooth approach. As a result, qualitative (smeared) crack initiation in 3D multiphase specimens has efficiently been simulated. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2013,2 KW - high-performance computing KW - finite element method KW - heterogeneous material KW - domain decomposition KW - scalable smeared crack analysis KW - FEM KW - multiphase KW - damage KW - HPC KW - solver Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20131021-20595 ER - TY - THES A1 - Ahmad, Sofyan T1 - Reference Surface-Based System Identification N2 - Environmental and operational variables and their impact on structural responses have been acknowledged as one of the most important challenges for the application of the ambient vibration-based damage identification in structures. The damage detection procedures may yield poor results, if the impacts of loading and environmental conditions of the structures are not considered. The reference-surface-based method, which is proposed in this thesis, is addressed to overcome this problem. In the proposed method, meta-models are used to take into account significant effects of the environmental and operational variables. The usage of the approximation models, allows the proposed method to simply handle multiple non-damaged variable effects simultaneously, which for other methods seems to be very complex. The input of the meta-model are the multiple non-damaged variables while the output is a damage indicator. The reference-surface-based method diminishes the effect of the non-damaged variables to the vibration based damage detection results. Hence, the structure condition that is assessed by using ambient vibration data at any time would be more reliable. Immediate reliable information regarding the structure condition is required to quickly respond to the event, by means to take necessary actions concerning the future use or further investigation of the structures, for instance shortly after extreme events such as earthquakes. The critical part of the proposed damage detection method is the learning phase, where the meta-models are trained by using input-output relation of observation data. Significant problems that may encounter during the learning phase are outlined and some remedies to overcome the problems are suggested. The proposed damage identification method is applied to numerical and experimental models. In addition to the natural frequencies, wavelet energy and stochastic subspace damage indicators are used. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2013,3 KW - System Identification KW - Schadensdetektionsverfahren KW - Referenzfläche Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20140205-21132 ER - TY - THES A1 - Nguyen-Thanh, Nhon T1 - Isogeometric analysis based on rational splines over hierarchical T-mesh and alpha finite element method for structural analysis N2 - This thesis presents two new methods in finite elements and isogeometric analysis for structural analysis. The first method proposes an alternative alpha finite element method using triangular elements. In this method, the piecewise constant strain field of linear triangular finite element method models is enhanced by additional strain terms with an adjustable parameter a, which results in an effectively softer stiffness formulation compared to a linear triangular element. In order to avoid the transverse shear locking of Reissner-Mindlin plates analysis the alpha finite element method is coupled with a discrete shear gap technique for triangular elements to significantly improve the accuracy of the standard triangular finite elements. The basic idea behind this element formulation is to approximate displacements and rotations as in the standard finite element method, but to construct the bending, geometrical and shear strains using node-based smoothing domains. Several numerical examples are presented and show that the alpha FEM gives a good agreement compared to several other methods in the literature. Second method, isogeometric analysis based on rational splines over hierarchical T-meshes (RHT-splines) is proposed. The RHT-splines are a generalization of Non-Uniform Rational B-splines (NURBS) over hierarchical T-meshes, which is a piecewise bicubic polynomial over a hierarchical T-mesh. The RHT-splines basis functions not only inherit all the properties of NURBS such as non-negativity, local support and partition of unity but also more importantly as the capability of joining geometric objects without gaps, preserving higher order continuity everywhere and allow local refinement and adaptivity. In order to drive the adaptive refinement, an efficient recovery-based error estimator is employed. For this problem an imaginary surface is defined. The imaginary surface is basically constructed by RHT-splines basis functions which is used for approximation and interpolation functions as well as the construction of the recovered stress components. Numerical investigations prove that the proposed method is capable to obtain results with higher accuracy and convergence rate than NURBS results. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2013,4 KW - Isogeometric analysis KW - NURBS KW - FEM KW - RHT-splines KW - Isogeometric analysis KW - NURBS KW - FEM KW - RHT-splines Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20131125-20781 SN - 1610-7381 ER - TY - THES A1 - Zhao, Jun-Hua T1 - Multiscale modeling of nanodevices based on carbon nanotubes and polymers T1 - Multiskalige Modellierung von auf Kohlenstoffnanoröhren und Polymeren basierenden Nanobauteilen N2 - This thesis concerns the physical and mechanical interactions on carbon nanotubes and polymers by multiscale modeling. CNTs have attracted considerable interests in view of their unique mechanical, electronic, thermal, optical and structural properties, which enable them to have many potential applications. Carbon nanotube exists in several structure forms, from individual single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) to carbon nanotube bundles and networks. The mechanical properties of SWCNTs and MWCNTs have been extensively studied by continuum modeling and molecular dynamics (MD) simulations in the past decade since the properties could be important in the CNT-based devices. CNT bundles and networks feature outstanding mechanical performance and hierarchical structures and network topologies, which have been taken as a potential saving-energy material. In the synthesis of nanocomposites, the formation of the CNT bundles and networks is a challenge to remain in understanding how to measure and predict the properties of such large systems. Therefore, a mesoscale method such as a coarse-grained (CG) method should be developed to study the nanomechanical characterization of CNT bundles and networks formation. In this thesis, the main contributions can be written as follows: (1) Explicit solutions for the cohesive energy between carbon nanotubes, graphene and substrates are obtained through continuum modeling of the van der Waals interaction between them. (2) The CG potentials of SWCNTs are established by a molecular mechanics model. (3) The binding energy between two parallel and crossing SWCNTs and MWCNTs is obtained by continuum modeling of the van der Waals interaction between them. Crystalline and amorphous polymers are increasingly used in modern industry as tructural materials due to its important mechanical and physical properties. For crystalline polyethylene (PE), despite its importance and the studies of available MD simulations and continuum models, the link between molecular and continuum descriptions of its mechanical properties is still not well established. For amorphous polymers, the chain length and temperature effect on their elastic and elastic-plastic properties has been reported based on the united-atom (UA) and CG MD imulations in our previous work. However, the effect of the CL and temperature on the failure behavior is not understood well yet. Especially, the failure behavior under shear has been scarcely reported in previous work. Therefore, understanding the molecular origins of macroscopic fracture behavior such as fracture energy is a fundamental scientific challenge. In this thesis, the main contributions can be written as follows: (1) An analytical molecular mechanics model is developed to obtain the size-dependent elastic properties of crystalline PE. (2) We show that the two molecular mechanics models, the stick-spiral and the beam models, predict considerably different mechanical properties of materials based on energy equivalence. The difference between the two models is independent of the materials. (3) The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers are scrutinized using molecular dynamics simulations. Finally, the influence of polymer wrapped two neighbouring SWNTs’ dispersion on their load transfer is investigated by molecular dynamics (MD) simulations, in which the SWNTs' position, the polymer chain length and the temperature on the interaction force is systematically studied. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2014,1 KW - Mehrskalenmodell KW - Kohlenstoff Nanoröhre KW - Polymere KW - Multiscale modeling KW - Carbon nanotubes KW - Polymers Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20140130-21078 ER - TY - THES A1 - Itam, Zarina T1 - Numerical Simulation of Thermo-Chemo-Hygro-Mechanical Alkali-Silica Reaction Model in Concrete at the Mesoscale and Macroscale N2 - Alkali-silica reaction causes major problems in concrete structures due to the rapidity of its deformation which leads to the serviceability limit of the structure being reached well before its time. Factors that affect ASR vary greatly, including alkali and silica content, relative humidity, temperature and porosity of the cementitious matrix,all these making it a very complex phenomenon to consider explicitly. With this in mind, the finite element technique was used to build models and generate expansive pressures and damage propagation due to ASR under the influence of thermo-hygrochemoelastic loading. Since ASR initializes in the mesoscopic regions of the concrete, the accumulative effects of its expansion escalates onto the macroscale level with the development of web cracking on the concrete surface, hence solution of the damage model as well as simulation of the ASR phenomenon at both the macroscale and mesoscale levels have been performed. The macroscale model realizes the effects of ASR expansion as a whole and shows how it develops under the influence of moisture, thermal and mechanical loading. Results of the macroscale modeling are smeared throughout the structure and are sufficient to show how damage due to ASR expansion orientates. As opposed to the mesoscale model, the heterogeneity of the model shows us how difference in material properties between aggregates and the cementitious matrix facilitates ASR expansion. With both these models, the ASR phenomenon under influence of thermo-chemo-hygro-mechanical loading can be better understood. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2014,2 KW - Strukturmechanik KW - Alkali-silica reaction KW - macroscale KW - mesoscale KW - ASR Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20141218-23352 ER - TY - THES A1 - Mai, Luu T1 - Structural Control Systems in High-speed Railway Bridges N2 - Structural vibration control of high-speed railway bridges using tuned mass dampers, semi-active tuned mass dampers, fluid viscous dampers and magnetorheological dampers to reduce resonant structural vibrations is studied. In this work, the addressed main issues include modeling of the dynamic interaction of the structures, optimization of the parameters of the dampers and comparison of their efficiency. A new approach to optimize multiple tuned mass damper systems on an uncertain model is proposed based on the H-infinity optimization criteria and the DK iteration procedure with norm-bounded uncertainties in frequency domain. The parameters of tuned mass dampers are optimized directly and simultaneously on different modes contributing significantly to the multi-resonant peaks to explore the different possible combinations of parameters. The effectiveness of the present method is also evaluated through comparison with a previous method. In the case of semi-active tuned mass dampers, an optimization algorithm is derived to control the magnetorheological damper in these semi-active damping systems. The use of the proposed algorithm can generate various combinations of control gains and state variables. This can lead to the improvement of the ability of MR dampers to track the desired control forces. An uncertain model to reduce detuning effects is also considered in this work. Next, for fluid viscous dampers, in order to tune the optimal parameters of fluid viscous dampers to the vicinity of the exact values, analytical formulae which can include structural damping are developed based on the perturbation method. The proposed formulae can also be considered as an improvement of the previous analytical formulae, especially for bridge beams with large structural damping. Finally, a new combination of magnetorheological dampers and a double-beam system to improve the performance of the primary structure vibration is proposed. An algorithm to control magnetorheological dampers in this system is developed by using standard linear matrix inequality techniques. Weight functions as a loop shaping procedure are also introduced in the feedback controllers to improve the tracking ability of magnetorheological damping forces. To this end, the effectiveness of magnetorheological dampers controlled by the proposed scheme, along with the effects of the uncertain and time-delay parameters on the models, are evaluated through numerical simulations. Additionally, a comparison of the dampers based on their performance is also considered in this work. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2014,3 KW - High-speed railway bridge KW - Control system KW - Passive damper KW - Semi-active damper KW - Railway bridges Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20141223-23391 SN - 1610-7381 ER -