TY - JOUR A1 - Banihani, Suleiman A1 - Rabczuk, Timon A1 - Almomani, Thakir T1 - POD for real-time simulation of hyperelastic soft biological tissue using the point collocation method of finite spheres JF - Mathematical Problems in Engineering N2 - The point collocation method of finite spheres (PCMFS) is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD) model order reduction (MOR) technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced. KW - Chirurgie KW - Finite-Elemente-Methode Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170413-31203 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 - Ghasemi, Hamid T1 - Stochastic optimization of fiber reinforced composites considering uncertainties N2 - Briefly, the two basic questions that this research is supposed to answer are: 1. Howmuch fiber is needed and how fibers should be distributed through a fiber reinforced composite (FRC) structure in order to obtain the optimal and reliable structural response? 2. How do uncertainties influence the optimization results and reliability of the structure? Giving answer to the above questions a double stage sequential optimization algorithm for finding the optimal content of short fiber reinforcements and their distribution in the composite structure, considering uncertain design parameters, is presented. In the first stage, the optimal amount of short fibers in a FRC structure with uniformly distributed fibers is conducted in the framework of a Reliability Based Design Optimization (RBDO) problem. Presented model considers material, structural and modeling uncertainties. In the second stage, the fiber distribution optimization (with the aim to further increase in structural reliability) is performed by defining a fiber distribution function through a Non-Uniform Rational BSpline (NURBS) surface. The advantages of using the NURBS surface as a fiber distribution function include: using the same data set for the optimization and analysis; high convergence rate due to the smoothness of the NURBS; mesh independency of the optimal layout; no need for any post processing technique and its non-heuristic nature. The output of stage 1 (the optimal fiber content for homogeneously distributed fibers) is considered as the input of stage 2. The output of stage 2 is the Reliability Index (b ) of the structure with the optimal fiber content and distribution. First order reliability method (in order to approximate the limit state function) as well as different material models including Rule of Mixtures, Mori-Tanaka, energy-based approach and stochastic multi-scales are implemented in different examples. The proposed combined model is able to capture the role of available uncertainties in FRC structures through a computationally efficient algorithm using all sequential, NURBS and sensitivity based techniques. The methodology is successfully implemented for interfacial shear stress optimization in sandwich beams and also for optimization of the internal cooling channels in a ceramic matrix composite. Finally, after some changes and modifications by combining Isogeometric Analysis, level set and point wise density mapping techniques, the computational framework is extended for topology optimization of piezoelectric / flexoelectric materials. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2016,1 KW - Optimization KW - Fiber Reinforced Composite KW - Finite Element Method KW - Isogeometric Analysis KW - Flexoelectricity KW - Finite-Elemente-Methode KW - Optimierung Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20161117-27042 ER - TY - THES A1 - Habtemariam, Abinet Kifle T1 - Numerical Demolition Analysis of a Slender Guyed Antenna Mast N2 - The main purpose of the thesis is to ensure the safe demolition of old guyed antenna masts that are located in different parts of Germany. The major problem in demolition of this masts is the falling down of the masts in unexpected direction because of buckling problem. The objective of this thesis is development of a numerical models using finite element method (FEM) and assuring a controlled collapse by coming up with different time setups for the detonation of explosives which are responsible for cutting down the cables. The result of this thesis will avoid unexpected outcomes during the demolition processes and prevent risk of collapsing of the mast over near by structures. KW - Abbruch KW - Finite-Elemente-Methode KW - Optimierung KW - Demolition KW - Guyed antenna masts KW - Explicit finite element method KW - Optimization Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210723-44609 ER - TY - THES A1 - Hanna, John T1 - Computational Fracture Modeling and Design of Encapsulation-Based Self-Healing Concrete Using XFEM and Cohesive Surface Technique N2 - Encapsulation-based self-healing concrete (SHC) is the most promising technique for providing a self-healing mechanism to concrete. This is due to its capacity to heal fractures effectively without human interventions, extending the operational life and lowering maintenance costs. The healing mechanism is created by embedding capsules containing the healing agent inside the concrete. The healing agent will be released once the capsules are fractured and the healing occurs in the vicinity of the damaged part. The healing efficiency of the SHC is still not clear and depends on several factors; in the case of microcapsules SHC the fracture of microcapsules is the most important aspect to release the healing agents and hence heal the cracks. This study contributes to verifying the healing efficiency of SHC and the fracture mechanism of the microcapsules. Extended finite element method (XFEM) is a flexible, and powerful discrete crack method that allows crack propagation without the requirement for re-meshing and has been shown high accuracy for modeling fracture in concrete. In this thesis, a computational fracture modeling approach of Encapsulation-based SHC is proposed based on the XFEM and cohesive surface technique (CS) to study the healing efficiency and the potential of fracture and debonding of the microcapsules or the solidified healing agents from the concrete matrix as well. The concrete matrix and a microcapsule shell both are modeled by the XFEM and combined together by CS. The effects of the healed-crack length, the interfacial fracture properties, and microcapsule size on the load carrying capability and fracture pattern of the SHC have been studied. The obtained results are compared to those obtained from the zero thickness cohesive element approach to demonstrate the significant accuracy and the validity of the proposed simulation. The present fracture simulation is developed to study the influence of the capsular clustering on the fracture mechanism by varying the contact surface area of the CS between the microcapsule shell and the concrete matrix. The proposed fracture simulation is expanded to 3D simulations to validate the 2D computational simulations and to estimate the accuracy difference ratio between 2D and 3D simulations. In addition, a proposed design method is developed to design the size of the microcapsules consideration of a sufficient volume of healing agent to heal the expected crack width. This method is based on the configuration of the unit cell (UC), Representative Volume Element (RVE), Periodic Boundary Conditions (PBC), and associated them to the volume fraction (Vf) and the crack width as variables. The proposed microcapsule design is verified through computational fracture simulations. KW - Beton KW - Bruchverhalten KW - Finite-Elemente-Methode KW - Self-healing concrete KW - Computational fracture modeling KW - Capsular clustering; Design of microcapsules KW - XFEM KW - Cohesive surface technique KW - Mikrokapsel KW - Selbstheilendem Beton KW - Computermodellierung des Bruchverhaltens KW - Entwurf von Mikrokapseln KW - Kapselclustern KW - Erweiterte Finite-Elemente-Methode KW - Kohäsionsflächenverfahren Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20221124-47467 ER - TY - THES A1 - Hossain, Md Naim T1 - Isogeometric analysis based on Geometry Independent Field approximaTion (GIFT) and Polynomial Splines over Hierarchical T-meshes N2 - This thesis addresses an adaptive higher-order method based on a Geometry Independent Field approximatTion(GIFT) of polynomial/rationals plines over hierarchical T-meshes(PHT/RHT-splines). In isogeometric analysis, basis functions used for constructing geometric models in computer-aided design(CAD) are also employed to discretize the partial differential equations(PDEs) for numerical analysis. Non-uniform rational B-Splines(NURBS) are the most commonly used basis functions in CAD. However, they may not be ideal for numerical analysis where local refinement is required. The alternative method GIFT deploys different splines for geometry and numerical analysis. NURBS are utilized for the geometry representation, while for the field solution, PHT/RHT-splines are used. PHT-splines not only inherit the useful properties of B-splines and NURBS, but also possess the capabilities of local refinement and hierarchical structure. The smooth basis function properties of PHT-splines make them suitable for analysis purposes. While most problems considered in isogeometric analysis can be solved efficiently when the solution is smooth, many non-trivial problems have rough solutions. For example, this can be caused by the presence of re-entrant corners in the domain. For such problems, a tensor-product basis (as in the case of NURBS) is less suitable for resolving the singularities that appear since refinement propagates throughout the computational domain. Hierarchical bases and local refinement (as in the case of PHT-splines) allow for a more efficient way to resolve these singularities by adding more degrees of freedom where they are necessary. In order to drive the adaptive refinement, an efficient recovery-based error estimator is proposed in this thesis. The estimator produces a recovery solution which is a more accurate approximation than the computed numerical solution. Several two- and three-dimensional numerical investigations with PHT-splines of higher order and continuity prove that the proposed method is capable of obtaining results with higher accuracy, better convergence, fewer degrees of freedom and less computational cost than NURBS for smooth solution problems. The adaptive GIFT method utilizing PHT-splines with the recovery-based error estimator is used for solutions with discontinuities or singularities where adaptive local refinement in particular domains of interest achieves higher accuracy with fewer degrees of freedom. This method also proves that it can handle complicated multi-patch domains for two- and three-dimensional problems outperforming uniform refinement in terms of degrees of freedom and computational cost. T2 - Die isogeometrische Analysis basierend auf der geometrieunabhängigen Feldnäherung (GIFT)und polynomialen Splines über hierarchischen T-Netzen KW - Finite-Elemente-Methode KW - Isogeometrc Analysis KW - Geometry Independent Field Approximation KW - Polynomial Splines over Hierarchical T-meshes KW - Recovery Based Error Estimator Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20191129-40376 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 - Jia, Yue T1 - Methods based on B-splines for model representation, numerical analysis and image registration N2 - The thesis consists of inter-connected parts for modeling and analysis using newly developed isogeometric methods. The main parts are reproducing kernel triangular B-splines, extended isogeometric analysis for solving weakly discontinuous problems, collocation methods using superconvergent points, and B-spline basis in image registration applications. Each topic is oriented towards application of isogeometric analysis basis functions to ease the process of integrating the modeling and analysis phases of simulation. First, we develop reproducing a kernel triangular B-spline-based FEM for solving PDEs. We review the triangular B-splines and their properties. By definition, the triangular basis function is very flexible in modeling complicated domains. However, instability results when it is applied for analysis. We modify the triangular B-spline by a reproducing kernel technique, calculating a correction term for the triangular kernel function from the chosen surrounding basis. The improved triangular basis is capable to obtain the results with higher accuracy and almost optimal convergence rates. Second, we propose an extended isogeometric analysis for dealing with weakly discontinuous problems such as material interfaces. The original IGA is combined with XFEM-like enrichments which are continuous functions themselves but with discontinuous derivatives. Consequently, the resulting solution space can approximate solutions with weak discontinuities. The method is also applied to curved material interfaces, where the inverse mapping and the curved triangular elements are considered. Third, we develop an IGA collocation method using superconvergent points. The collocation methods are efficient because no numerical integration is needed. In particular when higher polynomial basis applied, the method has a lower computational cost than Galerkin methods. However, the positions of the collocation points are crucial for the accuracy of the method, as they affect the convergent rate significantly. The proposed IGA collocation method uses superconvergent points instead of the traditional Greville abscissae points. The numerical results show the proposed method can have better accuracy and optimal convergence rates, while the traditional IGA collocation has optimal convergence only for even polynomial degrees. Lastly, we propose a novel dynamic multilevel technique for handling image registration. It is application of the B-spline functions in image processing. The procedure considered aims to align a target image from a reference image by a spatial transformation. The method starts with an energy function which is the same as a FEM-based image registration. However, we simplify the solving procedure, working on the energy function directly. We dynamically solve for control points which are coefficients of B-spline basis functions. The new approach is more simple and fast. Moreover, it is also enhanced by a multilevel technique in order to prevent instabilities. The numerical testing consists of two artificial images, four real bio-medical MRI brain and CT heart images, and they show our registration method is accurate, fast and efficient, especially for large deformation problems. KW - Finite-Elemente-Methode KW - isogeometric methods Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20151210-24849 ER - TY - THES A1 - Keßler, Andrea T1 - Matrix-free voxel-based finite element method for materials with heterogeneous microstructures T1 - Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komplizierter Mikrostruktur N2 - Modern image detection techniques such as micro computer tomography (μCT), magnetic resonance imaging (MRI) and scanning electron microscopy (SEM) provide us with high resolution images of the microstructure of materials in a non-invasive and convenient way. They form the basis for the geometrical models of high-resolution analysis, so called image-based analysis. However especially in 3D, discretizations of these models reach easily the size of 100 Mill. degrees of freedoms and require extensive hardware resources in terms of main memory and computing power to solve the numerical model. Consequently, the focus of this work is to combine and adapt numerical solution methods to reduce the memory demand first and then the computation time and therewith enable an execution of the image-based analysis on modern computer desktops. Hence, the numerical model is a straightforward grid discretization of the voxel-based (pixels with a third dimension) geometry which omits the boundary detection algorithms and allows reduced storage of the finite element data structure and a matrix-free solution algorithm. This in turn reduce the effort of almost all applied grid-based solution techniques and results in memory efficient and numerically stable algorithms for the microstructural models. Two variants of the matrix-free algorithm are presented. The efficient iterative solution method of conjugate gradients is used with matrix-free applicable preconditioners such as the Jacobi and the especially suited multigrid method. The jagged material boundaries of the voxel-based mesh are smoothed through embedded boundary elements which contain different material information at the integration point and are integrated sub-cell wise though without additional boundary detection. The efficiency of the matrix-free methods can be retained. N2 - Moderne bildgebende Verfahren wie Mikro-Computertomographie (μCT), Magnetresonanztomographie (MRT) und Rasterelektronenmikroskopie (SEM) liefern nicht-invasiv hochauflösende Bilder der Mikrostruktur von Materialien. Sie bilden die Grundlage der geometrischen Modelle der hochauflösenden bildbasierten Analysis. Allerdings erreichen vor allem in 3D die Diskretisierungen dieser Modelle leicht die Größe von 100 Mill. Freiheitsgraden und erfordern umfangreiche Hardware-Ressourcen in Bezug auf Hauptspeicher und Rechenleistung, um das numerische Modell zu lösen. Der Fokus dieser Arbeit liegt daher darin, numerische Lösungsmethoden zu kombinieren und anzupassen, um den Speicherplatzbedarf und die Rechenzeit zu reduzieren und damit eine Ausführung der bildbasierten Analyse auf modernen Computer-Desktops zu ermöglichen. Daher ist als numerisches Modell eine einfache Gitterdiskretisierung der voxelbasierten (Pixel mit der Tiefe als dritten Dimension) Geometrie gewählt, die die Oberflächenerstellung weglässt und eine reduzierte Speicherung der finiten Elementen und einen matrixfreien Lösungsalgorithmus ermöglicht. Dies wiederum verringert den Aufwand von fast allen angewandten gitterbasierten Lösungsverfahren und führt zu Speichereffizienz und numerisch stabilen Algorithmen für die Mikrostrukturmodelle. Es werden zwei Varianten der Anpassung der matrixfreien Lösung präsentiert, die Element-für-Element Methode und eine Knoten-Kanten-Variante. Die Methode der konjugierten Gradienten in Kombination mit dem Mehrgitterverfahren als sehr effizienten Vorkonditionierer wird für den matrixfreien Lösungsalgorithmus adaptiert. Der stufige Verlauf der Materialgrenzen durch die voxelbasierte Diskretisierung wird durch Elemente geglättet, die am Integrationspunkt unterschiedliche Materialinformationen enthalten und über Teilzellen integriert werden (embedded boundary elements). Die Effizienz der matrixfreien Verfahren bleibt erhalten. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2018,7 KW - Dissertation KW - Finite-Elemente-Methode KW - Konjugierte-Gradienten-Methode KW - Mehrgitterverfahren KW - conjugate gradient method KW - multigrid method KW - grid-based KW - finite element method KW - matrix-free Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20190116-38448 ER - TY - JOUR A1 - Mortazavi, Bohayra A1 - Pereira, Luiz Felipe C. A1 - Jiang, Jin-Wu A1 - Rabczuk, Timon T1 - Modelling heat conduction in polycrystalline hexagonal boron-nitride films JF - Scientific Reports N2 - We conducted extensive molecular dynamics simulations to investigate the thermal conductivity of polycrystalline hexagonal boron-nitride (h-BN) films. To this aim, we constructed large atomistic models of polycrystalline h-BN sheets with random and uniform grain configuration. By performing equilibrium molecular dynamics (EMD) simulations, we investigated the influence of the average grain size on the thermal conductivity of polycrystalline h-BN films at various temperatures. Using the EMD results, we constructed finite element models of polycrystalline h-BN sheets to probe the thermal conductivity of samples with larger grain sizes. Our multiscale investigations not only provide a general viewpoint regarding the heat conduction in h-BN films but also propose that polycrystalline h-BN sheets present high thermal conductivity comparable to monocrystalline sheets. KW - Wärmeleitfähigkeit KW - Bornitrid KW - Finite-Elemente-Methode Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170425-31534 ER -