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Interval analysis extends the concept of computing with real numbers to computing with real intervals. As a consequence, some interesting properties appear, such as the delivery of guaranteed results or confirmed global values. The former property is given in the sense that unknown numerical values are in known to lie in a computed interval. The latter property states that the global minimum value, for example, of a given function is also known to be contained in a interval (or a finite set of intervals). Depending upon the amount computation effort invested in the calculation, we can often find tight bounds on these enclosing intervals. The downside of interval analysis, however, is the mathematically correct, but often very pessimistic size of the interval result. This is in particularly due to the so-called dependency effect, where a single variable is used multiple times in one calculation. Applying interval analysis to structural analysis problems, the dependency has a great influence on the quality of numerical results. In this paper, a brief background of interval analysis is presented and shown how it can be applied to the solution of structural analysis problems. A discussion of possible improvements as well as an outlook to parallel computing is also given.
Der Begriff der Zuverlässigkeit spielt eine zentrale Rolle bei der Bewertung von Verkehrsnetzen. Aus der Sicht der Nutzer des öffentlichen Personennahverkehrs (ÖPNV) ist eines der wichtigsten Kriterien zur Beurteilung der Qualität des Liniennetzes, ob es möglich ist, mit einer großen Sicherheit das Reiseziel in einer vorgegebenen Zeit zu erreichen. Im Vortrag soll dieser Zuverlässigkeitsbegriff mathematisch gefasst werden. Dabei wird zunächst auf den üblichen Begriff der Zuverlässigkeit eines Netzes im Sinne paarweiser Zusammenhangswahrscheinlichkeiten eingegangen. Dieser Begriff wird erweitert durch die Betrachtung der Zuverlässigkeit unter Einbeziehung einer maximal zulässigen Reisezeit. In vergangenen Arbeiten hat sich die Ring-Radius-Struktur als bewährtes Modell für die theoretische Beschreibung von Verkehrsnetzen erwiesen. Diese Überlegungen sollen nun durch Einbeziehung realer Verkehrsnetzstrukturen erweitert werden. Als konkretes Beispiel dient das Straßenbahnnetz von Krakau. Hier soll insbesondere untersucht werden, welche Auswirkungen ein geplanter Ausbau des Netzes auf die Zuverlässigkeit haben wird. This paper is involved with CIVITAS-CARAVEL project: "Clean and better transport in cites". The project has received research funding from the Community's Sixth Framework Programme. The paper reflects only the author's views and the Community is not liable for any use that may be made of the information contained therein.
Architektur wird vorwiegend über die den Raum begrenzenden Oberflächen wahrgenommen. Das Oberflächenmaterial kann daher mit seinen sinnlichen Eigenschaften die Entwurfsintention unterstützen, zugleich muss es aber auch zahlreiche technische, ökonomische und ökologische Anforderungen erfüllen. Materialwahl in der Architektur bedeutet somit das Abwägen einer Vielzahl von Parametern, die sich sowohl inhaltlich als auch hinsichtlich ihrer Relevanz stark unterscheiden. Die Entscheidung für ein Material kann dabei durch verschiedene analoge und digitale Ansätze unterstützt werden. Die vorhandenen Systeme sind jedoch allesamt begrenzt: in den von ihnen berücksichtigten Aspekten, den möglichen Suchwegen oder ihren Inhalten. Keines der in dieser Arbeit untersuchten Systeme berücksichtigt zudem die unterschiedliche Wichtigkeit oder gegenseitige Abhängigkeiten und Unschärfen der in die Materialwahl einfließenden Kriterien. Die vorliegende Arbeit formuliert daher eine Gesamtstrategie zur besseren Unterstützung der Entscheidung für ein Oberflächenmaterial. Im Wesentlichen wird dabei eine Methode vorgestellt, wie die inhaltlich höchst unterschiedlichen Kriterien, welche Einfluss auf die Materialwahl ausüben, mit ihrer jeweiligen Relevanz gegeneinander in Ansatz gebracht werden können, um eine umfassende Bewertung der Materialalternativen zu ermöglichen. In einem zweiten Schritt wird mit Multidimensional Scaling eine Technik der Informationsvisualisierung benutzt, die eine zusätzliche Unterstützung durch weitere Analysemöglichkeiten und andere Suchwege eröffnet. Das vorgeschlagene Verfahren ist in einem Software-Prototyp umgesetzt. Die Arbeit leistet damit einen Beitrag, die Auswahl eines geeigneten Materials in der Architektur zu erleichtern, diese Entscheidung plausibel begründen zu können und den Weg der Entscheidungsfindung nachvollziehbar werden zu lassen.
An einem Teil der Topologie architektonischer Räume, dem Volumenadjazenzgraphen (VAG), wird gezeigt wie topologisches Modellieren Anwendungen der Bauplanung integrieren kann. Dazu wird ein Prototyp vorgestellt, der im wesentlichen aus drei Komponenten besteht: Mit dem Anforderungsmanager werden Anforderungen eigegeben, die formal gut handhabbar sind. Mit dem Topologiemanager werden diese Anforderungen mit gezeichneten Räumen kombiniert. Die topologischen Relationen in den Zeichnungen werden mit den entsprechenden Mitteln des GIS berechnet und in eine Datenbank exportiert. Der Anforderungsprüfer vergleicht dann die Anforderungsdaten, die mit Hilfe des Anforderungsmanagers erzeugt wurden, mit den Topologiedaten. Dieser Ansatz soll zeigen, wie topologische Modelle eine Formalisierung semantisch hochstehender Informationen ermöglichen, indem sie als Eigenschaften von Graphen dargestellt werden
The execution of project activities generally requires the use of (renewable) resources like machines, equipment or manpower. The resource allocation problem consists in assigning time intervals to the execution of the project activities while taking into account temporal constraints between activities emanating from technological or organizational requirements and costs incurred by the resource allocation. If the total procurement cost of the different renewable resources has to be minimized we speak of a resource investment problem. If the cost depends on the smoothness of the resource utilization over time the underlying problem is called a resource levelling problem. In this paper we consider a new tree-based enumeration method for solving resource investment and resource levelling problems exploiting some fundamental properties of spanning trees. The enumeration scheme is embedded in a branch-and-bound procedure using a workload-based lower bound and a depth first search. Preliminary computational results show that the proposed procedure is promising for instances with up to 30 activities.
Digital models of buildings are widely used in civil engineering. In these models, geometric information is used as leading information. Engineers are used to have geometric information, and, for instance, it is state of the art to specify a point by its three coordinates. However, the traditional approaches have disadvantages. Geometric information is over-determined. Thus, more geometric information is specified and stored than needed. In addition, engineers already deal with topological information. A denotation of objects in buildings is of topological nature. It has to be answered whether approaches where topological information becomes a leading role would be more efficient in civil engineering. This paper presents such an approach. Topological information is modelled independently of geometric information. It is used for denoting the objects of a building. Geometric information is associated to topological information so that geometric information “weights” a topology.
The concept presented in this paper has already been used in surveying existing buildings. Experiences in the use of this concept showed that the number of geometric information that is required for a complete specification of a building could be reduced by a factor up to 100. Further research will show how this concept can be used in planning processes.
TOOL TO CHECK TOPOLOGY AND GEOMETRY FOR SPATIAL STRUCTURES ON BASIS OF THE EXTENDED MAXWELL'S RULE
(2006)
One of the simplest principle in the design of light-weight structures is to avoid bending. This can be achieved by dissolving girders into members acting purely in axial tension or compression. The employment of cables for the tensioned members leads to even lighter structures which are called cable-strut structures. They constitute a subclass of spatial structures. To give fast information about the general feasibility of an architectural concept employing cable-strut structures is a challenging task due to their sophisticated mechanical behavior. In this regard it is essential to control if the structure is stable and if pre-stress can be applied. This paper presents a tool using the spreadsheet software Microsoft (MS) Excel which can give such information. Therefore it is not necessary to purchase special software and the according time consuming training is much lower. The tool was developed on basis of the extended Maxwell's rule, which besides topology also considers the geometry of the structure. For this the rank of the node equilibrium matrix is crucial. Significance and determination of the rank and the implementation of the corresponding algorithms in MS Excel are described in the following. The presented tool is able to support the structural designer in an early stage of the project in finding a feasible architectural concept for cable-strut structures. As examples for the application of the software tool two special cable-strut structures, so called tensegrity structures, were examined for their mechanical behavior.
Design activity could be treated as state transition computationally. In stepwise processing, in-between form-states are not easily observed. However, in this research time-based concept is introduced and applied in order to bridge the gap. In architecture, folding is one method of form manipulation and architects also want to search for alternatives by this operation. Besides, folding operation has to be defined and parameterized before time factor is involved as a variable of folding. As a result, time-based transformation provides sequential form states and redirects design activity.
The concrete is modeled as a material with damage and plasticity, whereat the viscoplastic and the viscoelastic behaviour depends on the rate of the total strains. Due to the damage behaviour the compliance tensor develops different properties in tension and compression. There have been tested various yield surfaces and flow rules, damage rules respectively to their usability in a concrete model. One three-dimensional yield surface was developed from a failure surface based on the Willam--Warnke five-parameter model by the author. Only one general uni-axial stress-strain-relation is used for the numeric control of the yield surface. From that curve all necessary parameters for different strengths of concrete and different strain rates can be derived by affine transformations. For the flow rule in the compression zone a non associated inelastic potential is used, in the tension zone a Rankine potential. Conditional on the time-dependent formulation, the symmetry of the system equations is maintained in spite of the usage of non-associated potentials for the derivation of the inelastic strains. In case of quasi statical computations a simple viscoplastic law is used that is rested on an approach to Perzyna. The principle of equality of dissipation power in the uni-axial and the three-axial state of stress is used. It is modified by a factor that depends on the actual stress ratio and in comparison with the Kupfer experiments it implicates strains that are more realistic. The implementation of the concrete model is conducted in a mixed hybrid finite element. Examples in the structural level are introduced for verification of the concrete model.
For assessment of old buildings, thermal graphic analysis aided with infra-red camera have been employed in a wide range nowadays. Image processing and evaluation can be economically practicable only if the image evaluation can also be automated to the largest extend. For that reason methods of computer vision are presented in this paper to evaluate thermal images. To detect typical thermal image elements, such as thermal bridges and lintels in thermal images respectively gray value images, methods of digital image processing have been applied, of which numerical procedures are available to transform, modify and encode images. At the same time, image processing can be regarded as a multi-stage process. In order to be able to accomplish the process of image analysis from image formation through perfecting and segmentation to categorization, appropriate functions must be implemented. For this purpose, different measuring procedures and methods for automated detection and evaluation have been tested.