Refine
Document Type
- Conference Proceeding (18)
- Doctoral Thesis (7)
- Article (5)
- Bachelor Thesis (3)
- Master's Thesis (2)
- Habilitation (1)
Institute
- Professur Angewandte Mathematik (36) (remove)
Keywords
- Computerunterstütztes Verfahren (18)
- Angewandte Mathematik (14)
- Angewandte Informatik (13)
- Architektur <Informatik> (9)
- Building Information Modeling (8)
- Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications (7)
- CAD (6)
- Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing (3)
- Mathematik (3)
- Modellierung (3)
- Bruchmechanik (2)
- Fourier-Reihe (2)
- Funktionentheorie (2)
- Holomorphe Funktion (2)
- Randwertproblem (2)
- discrete fundamental solution (2)
- Analytische Lösung (1)
- BMOM-Raum (1)
- Basic sets of polynomials (1)
- Bauphysik (1)
- Besov spaces (1)
- Besov-Räume (1)
- Beste Approximation (1)
- Betongelenk (1)
- Bloch space (1)
- Bloch-Raum (1)
- Clifford-Algebra (1)
- Clifford-Analysis (1)
- Darstellungssatz von Goursat (1)
- Data, information and knowledge modeling in civil engineering (1)
- Differenzengleichung (1)
- Differenzenpotentiale (1)
- Dirac-Operator (1)
- Discrete function theory (1)
- Discrete fundamental solution (1)
- Discrete potential theory (1)
- Diskrete Fourier-Transformation (1)
- Diskrete Fundamentallösung (1)
- Diskrete Funktionentheorie (1)
- Diskrete Potentialtheorie (1)
- Extended Finite-Elemente-Methode (1)
- Festkörpermechanik (1)
- Finite Elemente Methode (1)
- Finite-Differenzen-Methode (1)
- Finite-Elemente-Methode (1)
- Flächen zweiter Ordnung (1)
- Fourier (1)
- Function theoretic methods and PDE in engineering sciences (1)
- Funktionenraum (1)
- Graphentheorie (1)
- Greensche Matrix (1)
- Hauptachsentransformation (1)
- Hyperholomorphe-Funktion (1)
- Hyperkomplexe Funktion (1)
- Ingenieurwissenschaften (1)
- Kategorientheorie (1)
- Kegelschnitt (1)
- Kopplungsmethode (1)
- Lamé-Gleichung (1)
- Lamé-equation (1)
- Laplace-Operator (1)
- Laurent (1)
- Laurent-Reihe (1)
- Legendre-Funktion (1)
- Lineare Elastizitätstheorie (1)
- Lösung innerer und äußerer Randwertprobleme (1)
- Mathematical methods for (robotics and) computer vision (1)
- Modellierungsmethode (1)
- Numerical modeling in engineering (1)
- Näherungsverfahren (1)
- OA-Publikationsfonds2021 (1)
- Op spaces (1)
- Op-Räume (1)
- Optimization in engineering applications (1)
- Orthonormalbasis (1)
- Quadrik (1)
- Quaternionenalgebra (1)
- Riss (1)
- Rissausbreitung (1)
- Sortierung von Permutationen (1)
- Stapelproblem (1)
- Taylor (1)
- Taylor-Reihe (1)
- Tower of Hanoi (1)
- Transmission problem (1)
- Transmissionsaufgabe (1)
- Turm von Hanoi (1)
- VMOM Raum (1)
- VMOM space (1)
- Wand (1)
- Wärmeleitung (1)
- Wärmeleitungsgleichung (1)
- Wärmeübertragung (1)
- abstraction (1)
- analytische Lösung (1)
- best approximation (1)
- complete orthonormal system (1)
- continuum mechanic (1)
- coupling (1)
- crack propagation (1)
- difference potentials (1)
- discrete Dirac operator (1)
- discrete Fourier transform (1)
- discrete boundary value problems (1)
- discrete fourier transform (1)
- discrete function theory (1)
- discrete monogenic functions (1)
- diskrete Fourier-Transformation (1)
- diskrete Fundamentallösung (1)
- diskretes Einfach- und Doppelschichtpotential (1)
- eindimensionale Wärmeleitung (1)
- elasticity (1)
- energetic approach (1)
- engineering (1)
- finite difference methods (1)
- formal approaches (1)
- fracture mechanics (1)
- generalized Kolosov-Muskhelishvili formulae (1)
- generalized theorem of Goursat (1)
- geometry (1)
- geschichtete Wände (1)
- harmonic (1)
- heuristic solutions (1)
- heuristische Lösungsverfahren (1)
- laplace operator (1)
- mathematics (1)
- mehrschichtige Wände (1)
- modelling (1)
- monogene Orthogonalreihenentwicklungen (1)
- monogenic orthogonal series expansions Fourier (1)
- p-Laplace equation (1)
- permutations (1)
- pile problem (1)
- quaternion (1)
- rectangular lattice (1)
- solution of inner and outer boundary value problems (1)
- spherical harmonics (1)
- type theory (1)
- verallgemeinerte Kolosov-Muskhelishvili Formeln (1)
Modern distributed engineering applications are based on complex systems consisting of various subsystems that are connected through the Internet. Communication and collaboration within an entire system requires reliable and efficient data exchange between the subsystems. Middleware developed within the web evolution during the past years provides reliable and efficient data exchange for web applications, which can be adopted for solving the data exchange problems in distributed engineering applications. This paper presents a generic approach for reliable and efficient data exchange between engineering devices using existing middleware known from web applications. Different existing middleware is examined with respect to the suitability in engineering applications. In this paper, a suitable middleware is shown and a prototype implementation simulating distributed wind farm control is presented and validated using several performance measurements.
The stress state of a piecewise-homogeneous elastic body, which has a semi-infinite crack along the interface, under in-plane and antiplane loads is considered. One of the crack edges is reinforced by a rigid patch plate on a finite interval adjacent to the crack tip. The crack edges are loaded with specified stresses. The body is stretched at infinity by specified stresses. External forces with a given principal vector and moment act on the patch plate. The problem reduces to a Riemann-Hilbert boundary-value matrix problem with a piecewise-constant coefficient for two complex potentials in the plane case and for one in the antiplane case. The complex potentials are found explicitly using a Gaussian hypergeometric function. The stress state of the body close to the ends of the patch plate, one of which is also simultaneously the crack tip, is investigated. Stress intensity factors near the singular points are determined.
DIGITAL SUPPORT OF MATERIAL- AND PRODUCT SELECTION IN THE ARCHITECTURAL DESIGN- AND PLANNING PROCESS
(2006)
Architecture is predominantly perceived over the surfaces limiting the space. The used surface materials thereby should support the design intention and have to fulfil various technical and economical requirements. If the architect wants to select the "right" or the "best" material he has to play with very different and sometimes contradicting criteria and must weight these individually for the special purpose. This selection process is supported only insufficiently by today's digital systems. If it would be possible to illustrate all the various parameters by numerical values, the method of multidimensional scaling will offer a solution for architects to find the material which is best fitting on basis of his individual weighting of criteria. By displaying the result of the architect's multidimensional query in a spatial arrangement multidimensional scaling can support an interactive selection process with additional feedback over the applied search strategy.
Monitoring und Bewertung sind Hauptaufgaben im Management bzw. der Revitalisierung von Bauwerken. Unterschiedliche Verfahren können bei der Akquisition der erforderlichen geometrischen Information, wie z. B. Größe oder Verformung eines Gebäudes, eingesetzt werden. Da das Potenzial der digitalen Fotografie kontinuierlich wächst, stellt die Industriephotogrammetrie heute eine bedeutende Alternative zu den klassischen Verfahren wie Dehnmessstreifen oder anderen taktilen Sensoren dar. Moderne Industriephotogrammetrie erfasst die Bilder mittels digitaler Systeme. Dies bedeutet, dass die Information digitaler Bilder mit Hilfe der digitalen Bildverarbeitung untersucht werden muss, um die Bildkoordinaten der Messpunkte zu erhalten. Eine der Aufgaben der Bildverarbeitung für photogrammetrische Zwecke besteht somit darin, den Mittelpunkt von kreisförmigen Marken zu lokalisieren. Die modernen Operatoren liefern Subpixelgenauigkeit für die Koordinaten des Punktes. Das optische Messverfahren der Industriephotogrammetrie erfordert hinsichtlich der Hardware in erster Linie hochauflösende digitale Kameras. Dabei lassen sich die Kameras in Videokameras, HighSpeed-Kameras, intelligente Kameras sowie so genannte Consumer und Professionelle Kameras unterscheiden. Die geometrische Auflösung digitaler HighEnd-Kameras liegt heute bei über 10 Megapixel. In punkto Datentransfer zum Rechner sind verschiedene Standards am Markt verfügbar, z. B. USB2.0, GigE-Vision, CameraLink oder Firewire. Die Wahl des Standards hängt immer von der spezifischen Aufgabenstellung ab, da keine der Techniken eine führende Position einnimmt. Die moderne Photogrammetrie bietet viele neue Möglichkeiten für das Monitoring und die Bewertung von Bauwerken. Sie kann ein-, zwei-, drei- oder vierdimensionale Informationen liefern, falls erforderlich auch in Echtzeit. Als berührungsloses Messverfahren ist der Einsatz der Photogrammetrie noch möglich, wenn die taktilen Sensoren z. B. aufgrund ihres Platzbedarfes nicht mehr eingesetzt werden können. Hochauflösende Videokameras erlauben es, selbst dynamische Untersuchungen mit großer Präzision durchzuführen.
Die Bruchmechanik hat einen wichtigen Platz im modernen Bauingenieurwesen, um die Ausbreitung von Rissen in Bauteilen und ihre Gefährlichkeit einzuschätzen. Dabei kommen verschiedenste Methoden zum Einsatz. In dieser Arbeit soll die Qualitätsbewertung für einige dieser Methoden untersucht werden. Zu vergleichen sind u. a. die Genauigkeit, die Schnelligkeit, die Komplexität und die Stabilität. In den Vergleich sind die Finite Elemente Methode, die Extended Finite Elemente Methode und eine Kopplungsmethode (analytische Lösung für die Rissspitze und Finite Elemente Lösung für den Rest des Gebietes) einzubeziehen. Als reales Beispiel aus dem Bauingenieurwesen wird ein Betongelenk mit einem vorhandenen Riss betrachtet.
This thesis applies the theory of \psi-hyperholomorphic functions dened in R^3 with values in the set of paravectors, which is identified with the Eucledian space R^3, to tackle some problems in theory and practice: geometric mapping properties, additive decompositions of harmonic functions and applications in the theory of linear elasticity.
In this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical–numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann–Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.