TY - JOUR A1 - Unger, Jörg F. A1 - Teughels, A. A1 - De Roeck, G. T1 - System identification and damage detection of a prestressed concrete beam JF - Journal of Structural Engineering N2 - System identification and damage detection of a prestressed concrete beam KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2006 SP - 1691 EP - 1698 ER - TY - JOUR A1 - Most, Thomas A1 - Bucher, Christian T1 - Stochastic simulation of cracking in concrete structures using multi-parameter random fields JF - International Journal of Reliability and Safety N2 - Stochastic simulation of cracking in concrete structures using multi-parameter random fields KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2006 SP - 168 EP - 187 ER - TY - JOUR A1 - Kaltenbacher, Barbara A1 - Lahmer, Tom A1 - Mohr, Marcus A1 - Kaltenbacher, Manfred T1 - PDE based determination of piezoelectric material tensors JF - European Journal of Applied Mathematics N2 - PDE based determination of piezoelectric material tensors. KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2006 U6 - http://dx.doi.org/10.25643/bauhaus-universitaet.3595 SP - 383 EP - 416 ER - TY - JOUR A1 - Bucher, Christian A1 - Frangopol, D.M. T1 - Optimization of lifetime maintenance strategies for deteriorting structures considering probabilities of violating safety, condition, and cost thresholds JF - Probabilistic Engineering Mechanics N2 - Optimization of lifetime maintenance strategies for deteriorting structures considering probabilities of violating safety, condition, and cost thresholds KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2006 SP - 1 EP - 8 ER - TY - CHAP A1 - Häfner, Stefan A1 - Kessel, Marco A1 - Könke, Carsten ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - MULTIPHASE B-SPLINE FINITE ELEMENTS OF VARIABLE ORDER IN THE MECHANICAL ANALYSIS OF HETEROGENEOUS SOLIDS N2 - Advanced finite elements are proposed for the mechanical analysis of heterogeneous materials. The approximation quality of these finite elements can be controlled by a variable order of B-spline shape functions. An element-based formulation is developed such that the finite element problem can iteratively be solved without storing a global stiffness matrix. This memory saving allows for an essential increase of problem size. The heterogeneous material is modelled by projection onto a uniform, orthogonal grid of elements. Conventional, strictly grid-based finite element models show severe oscillating defects in the stress solutions at material interfaces. This problem is cured by the extension to multiphase finite elements. This concept enables to define a heterogeneous material distribution within the finite element. This is possible by a variable number of integration points to each of which individual material properties can be assigned. Based on an interpolation of material properties at nodes and further smooth interpolation within the finite elements, a continuous material function is established. With both, continuous B-spline shape function and continuous material function, also the stress solution will be continuous in the domain. The inaccuracy implied by the continuous material field is by far less defective than the prior oscillating behaviour of stresses. One- and two-dimensional numerical examples are presented. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29643 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html ER - TY - CHAP A1 - Häfner, Stefan A1 - Könke, Carsten ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - MULTIGRID PRECONDITIONED CONJUGATE GRADIENT METHOD IN THE MECHANICAL ANALYSIS OF HETEROGENEOUS SOLIDS N2 - A fast solver method called the multigrid preconditioned conjugate gradient method is proposed for the mechanical analysis of heterogeneous materials on the mesoscale. Even small samples of a heterogeneous material such as concrete show a complex geometry of different phases. These materials can be modelled by projection onto a uniform, orthogonal grid of elements. As one major problem the possible resolution of the concrete specimen is generally restricted due to (a) computation times and even more critical (b) memory demand. Iterative solvers can be based on a local element-based formulation while orthogonal grids consist of geometrical identical elements. The element-based formulation is short and transparent, and therefore efficient in implementation. A variation of the material properties in elements or integration points is possible. The multigrid method is a fast iterative solver method, where ideally the computational effort only increases linear with problem size. This is an optimal property which is almost reached in the implementation presented here. In fact no other method is known which scales better than linear. Therefore the multigrid method gains in importance the larger the problem becomes. But for heterogeneous models with very large ratios of Young's moduli the multigrid method considerably slows down by a constant factor. Such large ratios occur in certain heterogeneous solids, as well as in the damage analysis of solids. As solution to this problem the multigrid preconditioned conjugate gradient method is proposed. A benchmark highlights the multigrid preconditioned conjugate gradient method as the method of choice for very large ratio's of Young's modulus. A proposed modified multigrid cycle shows good results, in the application as stand-alone solver or as preconditioner. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29626 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html ER - TY - JOUR A1 - Häfner, Stefan A1 - Eckardt, Stefan A1 - Luther, Torsten A1 - Könke, Carsten T1 - Mesoscale modeling of concrete: Geometry and numerics JF - Computers and Structures N2 - Mesoscale modeling of concrete: Geometry and numerics KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2006 SP - 450 EP - 461 ER - TY - CHAP A1 - Luther, Torsten A1 - Könke, Carsten ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - INVESTIGATION OF CRACK GROWTH IN POLYCRYSTALLINE MESOSTRUCTURES N2 - The design and application of high performance materials demands extensive knowledge of the materials damage behavior, which significantly depends on the meso- and microstructural complexity. Numerical simulations of crack growth on multiple length scales are promising tools to understand the damage phenomena in complex materials. In polycrystalline materials it has been observed that the grain boundary decohesion is one important mechanism that leads to micro crack initiation. Following this observation the paper presents a polycrystal mesoscale model consisting of grains with orthotropic material behavior and cohesive interfaces along grain boundaries, which is able to reproduce the crack initiation and propagation along grain boundaries in polycrystalline materials. With respect to the importance of modeling the geometry of the grain structure an advanced Voronoi algorithm is proposed to generate realistic polycrystalline material structures based on measured grain size distribution. The polycrystal model is applied to investigate the crack initiation and propagation in statically loaded representative volume elements of aluminum on the mesoscale without the necessity of initial damage definition. Future research work is planned to include the mesoscale model into a multiscale model for the damage analysis in polycrystalline materials. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29886 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html 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 - CHAP A1 - Unger, Jörg F. A1 - Könke, Carsten ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - DISCRETE CRACK SIMULATION OF CONCRETE USING THE EXTENDED FINITE ELEMENTMETHOD N2 - The extended finite element method (XFEM) offers an elegant tool to model material discontinuities and cracks within a regular mesh, so that the element edges do not necessarily coincide with the discontinuities. This allows the modeling of propagating cracks without the requirement to adapt the mesh incrementally. Using a regular mesh offers the advantage, that simple refinement strategies based on the quadtree data structure can be used to refine the mesh in regions, that require a high mesh density. An additional benefit of the XFEM is, that the transmission of cohesive forces through a crack can be modeled in a straightforward way without introducing additional interface elements. Finally different criteria for the determination of the crack propagation angle are investigated and applied to numerical tests of cracked concrete specimens, which are compared with experimental results. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-30303 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html ER -