TY - JOUR A1 - Amani, Jafar A1 - Saboor Bagherzadeh, Amir A1 - Rabczuk, Timon T1 - Error estimate and adaptive refinement in mixed discrete least squares meshless method JF - Mathematical Problems in Engineering N2 - The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method. KW - Elastizität KW - Fehlerabschätzung KW - MDLSM method Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170413-31181 ER - TY - CHAP A1 - Pham, Hoang Anh ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - ADAPTIVE EXCITATION FOR SELECTIVE SENSITIVITY-BASED STRUCTURAL IDENTIFICATION N2 - Major problems of applying selective sensitivity to system identification are requirement of precise knowledge about the system parameters and realization of the required system of forces. This work presents a procedure which is able to deriving selectively sensitive excitation by iterative experiments. The first step is to determine the selectively sensitive displacement and selectively sensitive force patterns. These values are obtained by introducing the prior information of system parameters into an optimization which minimizes the sensitivities of the structure response with respect to the unselected parameters while keeping the sensitivities with respect to the selected parameters as a constant. In a second step the force pattern is used to derive dynamic loads on the tested structure and measurements are carried out. An automatic control ensures the required excitation forces. In a third step, measured outputs are employed to update the prior information. The strategy is to minimize the difference between a predicted displacement response, formulated as function of the unknown parameters and the measured displacements, and the selectively sensitive displacement calculated in the first step. With the updated values of the parameters a re-analysis of selective sensitivity is performed and the experiment is repeated until the displacement response of the model and the actual structure are conformed. As an illustration a simply supported beam made of steel, vibrated by harmonic excitation is investigated, thereby demonstrating that the adaptive excitation can be obtained efficiently. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-30015 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html 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 - Häfner, Stefan T1 - Grid-based procedures for the mechanical analysis of heterogeneous solids N2 - The importance of modern simulation methods in the mechanical analysis of heterogeneous solids is presented in detail. Thereby the problem is noted that even for small bodies the required high-resolution analysis reaches the limits of today's computational power, in terms of memory demand as well as acceptable computational effort. A further problem is that frequently the accuracy of geometrical modelling of heterogeneous bodies is inadequate. The present work introduces a systematic combination and adaption of grid-based methods for achieving an essentially higher resolution in the numerical analysis of heterogeneous solids. Grid-based methods are as well primely suited for developing efficient and numerically stable algorithms for flexible geometrical modeling. A key aspect is the uniform data management for a grid, which can be utilized to reduce the effort and complexity of almost all concerned methods. A new finite element program, called Mulgrido, was just developed to realize this concept consistently and to test the proposed methods. Several disadvantages which generally result from grid discretizations are selectively corrected by modified methods. The present work is structured into a geometrical model, a mechanical model and a numerical model. The geometrical model includes digital image-based modeling and in particular several methods for the theory-based generation of inclusion-matrix models. Essential contributions refer to variable shape, size distribution, separation checks and placement procedures of inclusions. The mechanical model prepares the fundamentals of continuum mechanics, homogenization and damage modeling for the following numerical methods. The first topic of the numerical model introduces to a special version of B-spline finite elements. These finite elements are entirely variable in the order k of B-splines. For homogeneous bodies this means that the approximation quality can arbitrarily be scaled. In addition, the multiphase finite element concept in combination with transition zones along material interfaces yields a valuable solution for heterogeneous bodies. As the formulation is element-based, the storage of a global stiffness matrix is superseded such that the memory demand can essentially be reduced. This is possible in combination with iterative solver methods which represent the second topic of the numerical model. Here, the focus lies on multigrid methods where the number of required operations to solve a linear equation system only increases linearly with problem size. Moreover, for badly conditioned problems quite an essential improvement is achieved by preconditioning. The third part of the numerical model discusses certain aspects of damage simulation which are closely related to the proposed grid discretization. The strong efficiency of the linear analysis can be maintained for damage simulation. This is achieved by a damage-controlled sequentially linear iteration scheme. Finally a study on the effective material behavior of heterogeneous bodies is presented. Especially the influence of inclusion shapes is examined. By means of altogether more than one hundred thousand random geometrical arrangements, the effective material behavior is statistically analyzed and assessed. N2 - Die wichtige Bedeutung moderner Simulationsverfahren in der mechanischen Analyse heterogener Festkörper wird eingangs ausführlich dargestellt. Dabei wird als Problem festgestellt, dass die erforderliche hochauflösende Analyse bereits für relativ kleine Körper an die Grenzen heutiger Rechenleistung stößt, sowohl bezüglich Speicherbedarf als auch akzeptablen Rechenaufwands. Ein weiteres Problem stellt die häufig unzureichend genaue geometrische Modellierung der Zusammensetzung heterogener Körper dar. Die vorliegende Arbeit führt eine systematische Kombination und Anpassung von gitterbasierten Methoden ein, um dadurch eine wesentlich höhere Auflösung in der numerischen Analyse heterogener Körper zu erzielen. Gitterverfahren eignen sich ebenfalls ausgezeichnet, um effiziente und numerisch stabile Algorithmen zur flexiblen geometrischen Modellierung zu entwickeln. Ein Schlüsselaspekt stellt ein gleichmäßiges Datenmanagement für Gitter dar, welches dafür eingesetzt werden kann, um den Aufwand und die Komplexität von nahezu allen beteiligten Methoden zu reduzieren. Ein neues Finite-Elemente Programm, namens Mulgrido, wurde eigens dafür entwickelt, um das vorgeschlagene Konzept konsistent zu realisieren und zu untersuchen. Einige Nachteile, die sich klassischerweise aus Gitterdiskretisierungen ergeben, werden gezielt durch modifizierte Verfahren korrigiert. Die gegenwärtige Arbeit gliedert sich in ein geometrisches Modell, ein mechanisches Modell und ein numerisches Modell. Das geometrische Modell beinhaltet neben Methoden der digitalen Bildverarbeitung, insbesondere sämtliche Verfahren zur künstlichen Generierung von Einschluss-Matrix Geometrien. Wesentliche Beiträge werden bezüglich variabler Form, Größenverteilung, Überschneidungsabfragen und Platzierung von Einschlüssen geleistet. Das mechanische Modell bereitet durch Grundlagen der Kontinuumsmechanik, der Homogenisierung und der Schädigungsmodellierung auf eine numerische Umsetzung vor. Als erstes Thema des numerischen Modells wird eine besondere Umsetzung von B-Spline Finiten Elementen vorgestellt. Diese Finite Elemente können generisch für eine beliebige Ordnung k der B-Splines erzeugt werden. Für homogene Körper verfügen diese somit über beliebig skalierbare Approximationseigenschaften. Mittels des Konzepts mehrphasiger Finite Elemente in Kombination mit Übergangszonen entlang von Materialgrenzen gelingt eine hochwertige Erweiterung für heterogene Körper. Durch die Formulierung auf Elementebene, kann die Speicherung der globalen Steifigkeitsmatrix und somit wesentlicher Speicherplatz eingespart werden. Dies ist möglich in Kombination mit iterativen Lösungsverfahren, die das zweite Thema des numerischen Modells darstellen. Dabei liegt der Fokus auf Mehrgitterverfahren. Diese zeichnen sich dadurch aus, dass die Anzahl der erforderlichen Operationen um ein lineares Gleichungssystem zu lösen, nur linear mit der Problemgröße ansteigt. Durch Vorkonditionierung wird für schlecht konditionierte Probleme eine ganz wesentliche Verbesserung erreicht. Als drittes Thema des numerischen Modells werden Aspekte der Schädigungssimulation diskutiert, die in engem Zusammenhang mit der Gitterdiskretisierung stehen. Die hohe Effizienz der linearen Analyse kann durch ein schädigungskontrolliertes, schrittweise lineares Iterationsschema für die Schädigungsanalyse aufrecht erhalten werden. Abschließend wird eine Studie über das effektive Materialverhalten heterogener Körper vorgestellt. Insbesondere wird der Einfluss der Form von Einschlüssen untersucht. Mittels insgesamt weit über hunderttausend zufälliger geometrischer Anordnungen wird das effektive Materialverhalten statistisch analysiert und bewertet. T2 - Gitterbasierte Verfahren zur mechanischen Analyse heterogener Festkörper KW - B-Spline KW - Finite-Elemente-Methode KW - Mehrgitterverfahren KW - Homogenisieren KW - Schädigung KW - Festkörpermechanik KW - Numerische Mathematik KW - B-Spline Finite Elemente KW - Homogenisierung KW - mehrphasig KW - Lösungsverfahren KW - Modellierung KW - B-spline KW - finite element KW - multigrid KW - multiphase KW - effective properties Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20070830-9185 ER - TY - THES A1 - Budarapu, Pattabhi Ramaiah T1 - Adaptive multiscale methods for fracture T1 - Adaptive Multiskalen-Methoden zur Modellierung von Materialversagen N2 - One major research focus in the Material Science and Engineering Community in the past decade has been to obtain a more fundamental understanding on the phenomenon 'material failure'. Such an understanding is critical for engineers and scientists developing new materials with higher strength and toughness, developing robust designs against failure, or for those concerned with an accurate estimate of a component's design life. Defects like cracks and dislocations evolve at nano scales and influence the macroscopic properties such as strength, toughness and ductility of a material. In engineering applications, the global response of the system is often governed by the behaviour at the smaller length scales. Hence, the sub-scale behaviour must be computed accurately for good predictions of the full scale behaviour. Molecular Dynamics (MD) simulations promise to reveal the fundamental mechanics of material failure by modeling the atom to atom interactions. Since the atomistic dimensions are of the order of Angstroms ( A), approximately 85 billion atoms are required to model a 1 micro- m^3 volume of Copper. Therefore, pure atomistic models are prohibitively expensive with everyday engineering computations involving macroscopic cracks and shear bands, which are much larger than the atomistic length and time scales. To reduce the computational effort, multiscale methods are required, which are able to couple a continuum description of the structure with an atomistic description. In such paradigms, cracks and dislocations are explicitly modeled at the atomistic scale, whilst a self-consistent continuum model elsewhere. Many multiscale methods for fracture are developed for "fictitious" materials based on "simple" potentials such as the Lennard-Jones potential. Moreover, multiscale methods for evolving cracks are rare. Efficient methods to coarse grain the fine scale defects are missing. However, the existing multiscale methods for fracture do not adaptively adjust the fine scale domain as the crack propagates. Most methods, therefore only "enlarge" the fine scale domain and therefore drastically increase computational cost. Adaptive adjustment requires the fine scale domain to be refined and coarsened. One of the major difficulties in multiscale methods for fracture is to up-scale fracture related material information from the fine scale to the coarse scale, in particular for complex crack problems. Most of the existing approaches therefore were applied to examples with comparatively few macroscopic cracks. Key contributions The bridging scale method is enhanced using the phantom node method so that cracks can be modeled at the coarse scale. To ensure self-consistency in the bulk, a virtual atom cluster is devised providing the response of the intact material at the coarse scale. A molecular statics model is employed in the fine scale where crack propagation is modeled by naturally breaking the bonds. The fine scale and coarse scale models are coupled by enforcing the displacement boundary conditions on the ghost atoms. An energy criterion is used to detect the crack tip location. Adaptive refinement and coarsening schemes are developed and implemented during the crack propagation. The results were observed to be in excellent agreement with the pure atomistic simulations. The developed multiscale method is one of the first adaptive multiscale method for fracture. A robust and simple three dimensional coarse graining technique to convert a given atomistic region into an equivalent coarse region, in the context of multiscale fracture has been developed. The developed method is the first of its kind. The developed coarse graining technique can be applied to identify and upscale the defects like: cracks, dislocations and shear bands. The current method has been applied to estimate the equivalent coarse scale models of several complex fracture patterns arrived from the pure atomistic simulations. The upscaled fracture pattern agree well with the actual fracture pattern. The error in the potential energy of the pure atomistic and the coarse grained model was observed to be acceptable. A first novel meshless adaptive multiscale method for fracture has been developed. The phantom node method is replaced by a meshless differential reproducing kernel particle method. The differential reproducing kernel particle method is comparatively more expensive but allows for a more "natural" coupling between the two scales due to the meshless interpolation functions. The higher order continuity is also beneficial. The centro symmetry parameter is used to detect the crack tip location. The developed multiscale method is employed to study the complex crack propagation. Results based on the meshless adaptive multiscale method were observed to be in excellent agreement with the pure atomistic simulations. The developed multiscale methods are applied to study the fracture in practical materials like Graphene and Graphene on Silicon surface. The bond stretching and the bond reorientation were observed to be the net mechanisms of the crack growth in Graphene. The influence of time step on the crack propagation was studied using two different time steps. Pure atomistic simulations of fracture in Graphene on Silicon surface are presented. Details of the three dimensional multiscale method to study the fracture in Graphene on Silicon surface are discussed. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2015,1 KW - Material KW - Strukturmechanik KW - Materialversagen KW - material failure Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20150507-23918 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 - Schwedler, Michael T1 - Integrated structural analysis using isogeometric finite element methods N2 - The gradual digitization in the architecture, engineering, and construction industry over the past fifty years led to an extremely heterogeneous software environment, which today is embodied by the multitude of different digital tools and proprietary data formats used by the many specialists contributing to the design process in a construction project. Though these projects become increasingly complex, the demands on financial efficiency and the completion within a tight schedule grow at the same time. The digital collaboration of project partners has been identified as one key issue in successfully dealing with these challenges. Yet currently, the numerous software applications and their respective individual views on the design process severely impede that collaboration. An approach to establish a unified basis for the digital collaboration, regardless of the existing software heterogeneity, is a comprehensive digital building model contributed to by all projects partners. This type of data management known as building information modeling (BIM) has many benefits, yet its adoption is associated with many difficulties and thus, proceeds only slowly. One aspect in the field of conflicting requirements on such a digital model is the cooperation of architects and structural engineers. Traditionally, these two disciplines use different abstractions of reality for their models that in consequence lead to incompatible digital representations thereof. The onset of isogeometric analysis (IGA) promised to ease the discrepancy in design and analysis model representations. Yet, that initial focus quickly shifted towards using these methods as a more powerful basis for numerical simulations. Furthermore, the isogeometric representation alone is not capable of solving the model abstraction problem. It is thus the intention of this work to contribute to an improved digital collaboration of architects and engineers by exploring an integrated analysis approach on the basis of an unified digital model and solid geometry expressed by splines. In the course of this work, an analysis framework is developed that utilizes such models to automatically conduct numerical simulations commonly required in construction projects. In essence, this allows to retrieve structural analysis results from BIM models in a fast and simple manner, thereby facilitating rapid design iterations and profound design feedback. The BIM implementation Industry Foundation Classes (IFC) is reviewed with regard to its capabilities of representing the unified model. The current IFC schema strongly supports the use of redundant model data, a major pitfall in digital collaboration. Additionally, it does not allow to describe the geometry by volumetric splines. As the pursued approach builds upon a unique model for both, architectural and structural design, and furthermore requires solid geometry, necessary schema modifications are suggested. Structural entities are modeled by volumetric NURBS patches, each of which constitutes an individual subdomain that, with regard to the analysis, is incompatible with the remaining full model. The resulting consequences for numerical simulation are elaborated in this work. The individual subdomains have to be weakly coupled, for which the mortar method is used. Different approaches to discretize the interface traction fields are implemented and their respective impact on the analysis results is evaluated. All necessary coupling conditions are automatically derived from the related geometry model. The weak coupling procedure leads to a linear system of equations in saddle point form, which, owed to the volumetric modeling, is large in size and, the associated coefficient matrix has, due to the use of higher degree basis functions, a high bandwidth. The peculiarities of the system require adapted solution methods that generally cause higher numerical costs than the standard procedures for symmetric, positive-definite systems do. Different methods to solve the specific system are investigated and an efficient parallel algorithm is finally proposed. When the structural analysis model is derived from the unified model in the BIM data, it does in general initially not meet the requirements on the discretization that are necessary to obtain sufficiently accurate analysis results. The consequently necessary patch refinements must be controlled automatically to allowfor an entirely automatic analysis procedure. For that purpose, an empirical refinement scheme based on the geometrical and possibly mechanical properties of the specific entities is proposed. The level of refinement may be selectively manipulated by the structural engineer in charge. Furthermore, a Zienkiewicz-Zhu type error estimator is adapted for the use with isogeometric analysis results. It is shown that also this estimator can be used to steer an adaptive refinement procedure. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2016,2 KW - Finite-Elemente-Methode KW - NURBS KW - Isogeometrische Analyse KW - finite element method KW - isogeometric analysis KW - mortar method KW - building information modelling Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170130-27372 ER - TY - THES A1 - Amiri, Fatemeh T1 - Computational modelling of fracture with local maximum entropy approximations N2 - The key objective of this research is to study fracture with a meshfree method, local maximum entropy approximations, and model fracture in thin shell structures with complex geometry and topology. This topic is of high relevance for real-world applications, for example in the automotive industry and in aerospace engineering. The shell structure can be described efficiently by meshless methods which are capable of describing complex shapes as a collection of points instead of a structured mesh. In order to find the appropriate numerical method to achieve this goal, the first part of the work was development of a method based on local maximum entropy (LME) shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method (XFEM) at a comparable computational cost. In addition, we keep the advantages of the LME shape functions,such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes near the crack such as blending or shifting. As extension of this method to three dimensional problems and complex thin shell structures with arbitrary crack growth is cumbersome, we developed a phase field model for fracture using LME. Phase field models provide a powerful tool to tackle moving interface problems, and have been extensively used in physics and materials science. Phase methods are gaining popularity in a wide set of applications in applied science and engineering, recently a second order phase field approximation for brittle fracture has gathered significant interest in computational fracture such that sharp cracks discontinuities are modeled by a diffusive crack. By minimizing the system energy with respect to the mechanical displacements and the phase-field, subject to an irreversibility condition to avoid crack healing, this model can describe crack nucleation, propagation, branching and merging. One of the main advantages of the phase field modeling of fractures is the unified treatment of the interfacial tracking and mechanics, which potentially leads to simple, robust, scalable computer codes applicable to complex systems. In other words, this approximation reduces considerably the implementation complexity because the numerical tracking of the fracture is not needed, at the expense of a high computational cost. We present a fourth-order phase field model for fracture based on local maximum entropy (LME) approximations. The higher order continuity of the meshfree LME approximation allows to directly solve the fourth-order phase field equations without splitting the fourth-order differential equation into two second order differential equations. Notably, in contrast to previous discretizations that use at least a quadratic basis, only linear completeness is needed in the LME approximation. We show that the crack surface can be captured more accurately in the fourth-order model than the second-order model. Furthermore, less nodes are needed for the fourth-order model to resolve the crack path. Finally, we demonstrate the performance of the proposed meshfree fourth order phase-field formulation for 5 representative numerical examples. Computational results will be compared to analytical solutions within linear elastic fracture mechanics and experimental data for three-dimensional crack propagation. In the last part of this research, we present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximum-entropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantageous over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected pipes. KW - Fracture mechanics KW - Local maximum entropy approximants KW - PU Enrichment method KW - Phase-field model KW - Thin shell KW - Kirchoff--love theory Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20160719-26310 ER - TY - THES A1 - Nanthakumar, S.S. T1 - Inverse and optimization problems in piezoelectric materials using Extended Finite Element Method and Level sets T1 - Inverse und Optimierungsprobleme für piezoelektrische Materialien mit der Extended Finite Elemente Methode und Level sets N2 - Piezoelectric materials are used in several applications as sensors and actuators where they experience high stress and electric field concentrations as a result of which they may fail due to fracture. Though there are many analytical and experimental works on piezoelectric fracture mechanics. There are very few studies about damage detection, which is an interesting way to prevent the failure of these ceramics. An iterative method to treat the inverse problem of detecting cracks and voids in piezoelectric structures is proposed. Extended finite element method (XFEM) is employed for solving the inverse problem as it allows the use of a single regular mesh for large number of iterations with different flaw geometries. Firstly, minimization of cost function is performed by Multilevel Coordinate Search (MCS) method. The XFEM-MCS methodology is applied to two dimensional electromechanical problems where flaws considered are straight cracks and elliptical voids. Then a numerical method based on combination of classical shape derivative and level set method for front propagation used in structural optimization is utilized to minimize the cost function. The results obtained show that the XFEM-level set methodology is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations. The XFEM-level set methodology is improved to solve the inverse problem of detecting inclusion interfaces in a piezoelectric structure. The material interfaces are implicitly represented by level sets which are identified by applying regularisation using total variation penalty terms. The formulation is presented for three dimensional structures and inclusions made of different materials are detected by using multiple level sets. The results obtained prove that the iterative procedure proposed can determine the location and approximate shape of material subdomains in the presence of higher noise levels. Piezoelectric nanostructures exhibit size dependent properties because of surface elasticity and surface piezoelectricity. Initially a study to understand the influence of surface elasticity on optimization of nano elastic beams is performed. The boundary of the nano structure is implicitly represented by a level set function, which is considered as the design variable in the optimization process. Two objective functions, minimizing the total potential energy of a nanostructure subjected to a material volume constraint and minimizing the least square error compared to a target displacement, are chosen for the numerical examples. The numerical examples demonstrate the importance of size and aspect ratio in determining how surface effects impact the optimized topology of nanobeams. Finally a conventional cantilever energy harvester with a piezoelectric nano layer is analysed. The presence of surface piezoelectricity in nano beams and nano plates leads to increase in electromechanical coupling coefficient. Topology optimization of these piezoelectric structures in an energy harvesting device to further increase energy conversion using appropriately modified XFEM-level set algorithm is performed . KW - Finite-Elemente-Methode KW - Piezoelectricity KW - Inverse problems KW - Optimization problems KW - Nanostructures KW - XFEM KW - level set method KW - Surface effects Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20161128-27095 ER - TY - CHAP A1 - Nguyen-Thanh, Nhon A1 - Rabczuk, Timon ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - A SMOOTHED FINITE ELEMENT METHOD FOR THE STATIC AND FREE VIBRATION ANALYSIS OF SHELLS N2 - A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Architektur KW - Computerunterstütztes Verfahren KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28777 UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html SN - 1611-4086 ER -