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A new approach to the non-linear analysis of cross-sections loaded by normal forces and bending moments is presented in the paper. The mechanical model is based on the LAGRANGE principle of minimum of total potential energy. Deformations, stresses and limit load parameters are obtained by solving a non-linear optimisation problem. The mathematical model is independent of the specifics of material. In addition to the stress strain relation and the specific strain energy W(ε) two further functions F(ε) and Φ(ε) are introduced to describe the material behaviour. Thus cracks in concrete, non-linearity of material etc. can be taken into account without basic modification of the numerical algorithm. For polygonal cross-sections the GAUSS' integral theorem is used. Numerical solutions of the non-linear optimisation problems can be found by application of standard software. Thus the analysis of reinforced concrete cross-sections or more general composite cross-sections with non-linear behaviour of material is as simple as in the case of linear elasticity. The application of the method is demonstrated for polygonal cross-sections. Pre-stresses or pre-strains can easily be included in the mathematical model.
We show a close relation between the Schrödinger equation and the conductivity equation to a Vekua equation of a special form. Under quite general conditions we propose an algorithm for explicit construction of pseudoanalytic positive formal powers for the Vekua equation that as a consequence gives us a complete system of solutions for the Schrödinger and the conductivity equations. Besides the construction of complete systems of exact solutions for the above mentioned second order equations and the Dirac equation, we discuss some other applications of pseudoanalytic function theory.
Durch die Betrachtung des Produktions-Prozesses als zentrales Transformationselement wird die Struktur der Bauproduktion realitätsnah gefasst. Die Integration der prozessorientierten Kostendefinition setzt relevante Kostenparameter und Produktionsfaktoren so in Beziehung, dass sie im Einklang mit der realen Kostenstruktur und Kostendynamik einer Baustelle stehen. Die Beziehung zwischen Bauzeit und Kosten wird direkt erfasst und ausgewertet. Der hohen Dynamik der Bauproduktion zwischen kapazitätsbeschränkten Einsatzmitteln und Produktionsprozessen wurde durch das Poolmodell und der Simulation als Berechnungsmethode Rechnung getragen. Eine einfache Modellierung von sich zyklusartig wiederholenden Arbeitsvorgängen (Taktplanung) ist möglich. Die Taktbildung vollzieht sich bei der Simulation durch Kapazitätsbeschränkungen ohne Zutun des Benutzers. Durch eine Optimierungsmethode kann automatisiert nach der kostengünstigsten oder zeitlich schnellsten Produktionsvariante gesucht werden
In the final decades many scientists were occupied intensively with the change of materials during a process and their mathematical descriptions. The extensive and extensive analyses were supported by the advanced computer science. A mathematical description of the phase transformation is a condition for a realistic FE simulation of the state of microstructure. It is possible to simulate the temperature and stress field also in complex construction based on the state of microstructure. In the last years a great number of mathematical models were expanded to describe the transformation between different phases. For the development of the models for transformation kinetics it is practical to subdivide into isothermal and non-isothermal processes according to the thermal conditions. Some models for the description of the transformation with non-isothermal processes represent extensions for isothermal of processes. A part of parameters for the describing equations can be derived from the time-temperature-transformation diagrams in the literature. Furthermore the two possibilities of transformation are considered by different models - diffusion controlled and not diffusion controlled. The material-specific characteristics can be simulated during the transformation for each individual phase in a realistic FE analyses. Also new materials can be simulated after a modification of the parameters in the describing equations for the phase transformation. The effects in the temperature and stress field are a substantial reason for the investigation of the phase transformation during the welding and TIG-dressing processes.
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.
Requires for reliability and durability of structures and their elements with simultaneous material economy have stimulated improvement of constitutive equations for description of elasto-plastic deformation processes. This has led to the development of phenomenological modelling of complex phenomena of irreversible deformation including history-dependent and rate-dependent effects. During the last several decades many works have been devoted to the development of elasto-plastic models, in order to better predict the material behavior under combined variable thermo-mechanical loading. The increase of accuracy of stress analysis and safety factors for complex structures with the help of modern finite-element packages (ABAQUS, ANSYS, COSMOS, LS-DYNA, MSC.MARC, MSC.NASTRAN, PERMAS and other) can be provided only by use of complex and special variants of plasticity theories, which are adequate for the considered loading conditions and based on authentic information about properties of materials. The areas of application of the various theories (models) are as a rule unknown to the users of finite-element packages at the existing variety loading condition sin machine-building designs. At the moment a universal theory of inelasticity is absent and even the most accomplished theories can not guarantee adequate description of deformation processes for arbitrary structure under wide range of loading programs. The classifier of materials, loading conditions, effects (phenomena) and list of basic experiments are developed by the authors. Use of these classifiers for an establishment of hierarchy of models is a first step for introduction of the multimodel analysis into computational practice. The set of the classic and modern inelasticity theories is considered, so that they are applicable for stress analysis of structures under complex loading programs. Among them there are plastic flow theories with linear and nonlinear isotropic and kinematic hardening, multisurface theories, endochronic theory, holonomic theory, rheologic models, theory of elasto-plastic processes, slip theory, physical theories (single crystal and polycrystalline models) and others. The classification of materials provides rearranging by a degree of homogeneous, chemical composition, level of strength and plasticity, behavior under cyclic loading, anisotropy of properties at initial condition, anisotropy of properties during deformation process, structural stability. The classification of loading conditions takes into consideration proportional and non-proportional loading, temperature range, combination of cyclic and monotonous loading, one-axial, two-axial and complex stress state, curvature of strain path, presence of stress concentrators and level of strain gradient. A unified general form of constitutive equations is presented for all used material models based upon the concept of internal state variables. The wide range of mentioned above inelastic material models has been implemented into finite element program PANTOCRATOR developed by authors (see for details www.pantocrator.narod.ru). Application possibility of different material models is considered both for material element and for complex structures subjected to complex non-proportional loading.
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.
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.
The mathematical and technical foundations of optimization have been developed to a large extent. In the design of buildings, however, optimization is rarely applied because of insufficient adaptation of this method to the needs of building design. The use of design optimization requires the consideration of all relevant objectives in an interactive and multidisciplinary process. Disciplines such as structural, light, and thermal engineering, architecture, and economics impose various objectives on the design. A good solution calls for a compromise between these often contradictory objectives. This presentation outlines a method for the application of Multidisciplinary Design Optimization (MDO) as a tool for the designing of buildings. An optimization model is established considering the fact that in building design the non-numerical aspects are of major importance than in other engineering disciplines. A component-based decomposition enables the designer to manage the non-numerical aspects in an interactive design optimization process. A façade example demonstrates a way how the different disciplines interact and how the components integrate the disciplines in one optimization model. In this grid-based façade example, the materials switch between a discrete number of materials and construction types. For light and thermal engineering, architecture, and economics, analysis functions calculate the performance; utility functions serve as an important means for the evaluation since not every increase or decrease of a physical value improves the design. For experimental purposes, a genetic algorithm applied to the exemplary model demonstrates the use of optimization in this design case. A component-based representation first serves to manage non-numerical characteristics such as aesthetics. Furthermore, it complies with usual fabrication methods in building design and with object-oriented data handling in CAD. Therefore, components provide an important basis for an interactive MDO process in building design.
MODELLING THE PLASTIC HINGE IN THE STATICALLY INDETERMINABLE REINFORCED CONCRETE BAR ELEMENTS
(2006)
The paper presents the example numerical model to calculate the reinforced concrete bar structures. Usually applied methods of structure dimensioning do not include the case of plastic hinges occurrence under the limit load of construction. The model represented by A. Borcz is based on the differential equation of deflection line of the beam and it includes the effects of rearrangement of the internal forces and reological effects. The experimental parameters obtained in earlier investigations describe effects resulting from the rise of plastic hinges in the proposed equation.
Subject of the paper is the realisation of a model based efficiency control system for PV generators using a simulation model. A standard 2-diodes model of PV generator is base of the ColSim model, which is implemented in ANSI C code for flexible code exporting. The algorithm is based on discretisized U-I characteristics, which allows the calculation of string topologies witch parallel and serial PV cells and modules. Shadowing effects can be modelled down to cell configuration using polar horizon definitions. The simulation model was ported to a real time environment, to calculate the efficiency of a PV system. Embedded System technology allows the networked operation and the integration of standard I/O devices. Futher work focus on the adaption of shadowing routine, which will be adapted to get the environment conditions from the real operation.
MODEL OF TRAM LINE OPERATION
(2006)
From passenger's perspective punctuality is one of the most important features of trams operations. Unfortunately in most cases this feature is only insufficiently fulfilled. In this paper we present a simulation model for trams operation with special focus on punctuality. The aim is to get a helpful tool for designing time-tables and for analyzing the effects by changing priorities for trams in traffic lights respectively the kind of track separation. A realization of trams operations is assumed to be a sequence of running times between successive stops and times spent by tram at the stops. In this paper the running time is modeled by the sum of its mean value and a zero-mean random variable. With the help of multiple regression we find out that the average running time is a function depending on the length of the sections and the number of intersections. The random component is modeled by a sum of two independent zero-mean random variables. One of these variables describes the disturbance caused by the process of waiting at an intersection and the other the disturbance caused by the process of driving. The time spent at a stop is assumed to be a random variable, too. Its distribution is estimated from given measurements of these stop times for different tram lines in Kraków. Finally a special case of the introduced model is considered and numerical results are presented. 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.
In diesem Beitrag wird eine mobile Software-Komponente zur Vor-Ort-Unterstützung von Bauwerksprüfungen gemäß DIN 1076 „Ingenieurbauwerke im Zuge von Strassen und Wegen, Überwachung und Prüfung“ vorgestellt, welche sich im praktischen Einsatz bei der Hochbahn AG Hamburg befindet. Mit Hilfe dieses Werkzeugs kann die Aktivität am Bauwerk in den gesamten softwaregestützten Geschäftsprozess der auwerksinstandhaltung integriert und somit die Bearbeitungszeit einer Bauwerksprüfung von der Vorbereitung bis zur Prüfbericht-Erstellung reduziert werden. Die Technologie des Mobile Computing wird unter Berücksichtigung spezieller fachlicher Randbedingungen, wie z.B. dem Einsatzort unter freiem Himmel, erläutert und es werden Methoden zur effizienten Datenerfassung mit Stift und Sprache vorgestellt und bewertet. Ferner wird die Einschränkung der Hardware durch die geringere Größe der Endgeräte, die sich durch die Bedingung der Mobilität ergibt, untersucht.
Due to economical, technical or political reasons all over the world about 100 nuclear power plants have been disconnected until today. All these power stations are still waiting for their complete dismantling which, considering one reactor, causes cost of up to one Bil. Euros and lasts up to 15 years. In our contribution we present a resource-constrained project scheduling approach minimizing the total discounted cost of dismantling a nuclear power plant. A project of dismantling a nuclear power plant can be subdivided into a number of disassembling activities. The execution of these activities requires time and scarce resources like manpower, special equipment or storage facilities for the contaminated material arising from the dismantling. Moreover, we have to regard several minimum and maximum time lags (temporal constraints) between the start times of the different activities. Finally, each disassembling activity can be processed in two alternative execution modes, which lead to different disbursements and determine the resource requirements of the considered activity. The optimization problem is to determine a start time and an execution mode for each activity, such that the discounted cost of the project is minimum, and neither the temporal constraints are violated nor the activities' resource requirements exceed the availability of any scarce resource at any point in time. In our contribution we introduce an appropriate multi-mode project scheduling model with minimum and maximum time lags as well as renewable and cumulative resources for the described optimization problem. Furthermore, we show that the considered optimization problem is NP-hard in the strong sense. For small problem instances, optimal solutions can be gained from a relaxation based enumeration approach which is incorporated into a branch and bound algorithm. In order to be able to solve large problem instances, we also propose a truncated version of the devised branch and bound algorithm.
The paper is a proposal of calculation of internal forces and dislocations in the reinforced concrete beams before and after cracking. For the ideally elastic bars transfer matrix proposed by Rakowski was applied. The effects associated with cracking were introduced by means of the Borcz's theory in the spectrally way. Numerical example was shown. The presented attitude also enables to calculate dynamic problems and those connected with the stability of the compressed and bending cracked beams and columns.
The paper contains a description of dynamic effects in the silo wall during the outflow of a stored material. The work allows for determining the danger of construction damage due to resonant vibrations and is of practical importance by determining the influence of cyclic pressures and vibro–creeping during prolonged use of a silo. The paper was devised as a result of tests on silo walls in semi-technical scale. The model is generally applicable and allows for identification of parameters in real- size silos as well.
At the 16th IKM Bock, Falcão and Gürlebeck presented examples of the application of some specially developed Maple-Software in hypercomplex analysis. Other papers of those authors continued this work and showed the efficiency of such tools for concrete numerical calculations as well as for numerical experiments, supporting the detection of new relationships and even theorems in a highly technical theoretical work. The mentioned software has been developed mainly for the use on mapping problems in the Euclidean spaces of dimension 3 and 4 by means of Bergman kernel methods (BKM), which are related to monogenic functions as solutions of generalized Cauchy-Riemann equations with respect to the Euclidean metric (Riesz system). The developed procedures concerning generalized powers of totally regular variables and the corresponding homogeneous polynomials basically rely on results and conventions introduced in the paper "Power series representation for monogenic functions in Rm+1 based on a permutational product", Complex Variables, 15, No.3, 181-191 (1990) by H. Malonek. Since 1992 H. Leutwiler, S. L. Eriksson and others developed in a number of papers a modified Clifford analysis and, particularly, a modified quaternionic analysis. The modification mainly consists in considering generalized Cauchy-Riemann equations with respect to a hyperbolic metric in a half space. The aim of this contribution is to show how through a change of the basic combinatorial relations used in the modified quaternionic analysis the aforementioned Maple-software (that has been recently published on CD-Rom as integrated part of the text book "Funktionentheorie in der Ebene und im Raum" by K. Gürlebeck, K. Habetha, and W. Sprössig, in the series "Grundstudium Mathematik" of Birkhäuser Verlag, 2006) can directly be used for numerical calculations in the modified theory.
This paper presents results of applying Fuzzy Inference System for estimation of the number of potential Park and Ride users. Usually it is difficult to evaluate the number of users because it depends on human factor and data in the considered system are uncertain. In such situation the traditional mathematical approaches can not take into consideration rough data. Therefore a fuzzy approach can be applied in this case. A fuzzy methodology is treated as a proper way to describe choice of mode of transport, and especially that uncertainty accompanied of choosing process has rather fuzzy character. The proposed approach is based on the Mamdani Fuzzy Inference System and for calculation there is used Matlab software with Fuzzy Logic Toolbox. Mamdani model requires, as an input data, knowledge of the shape of membership function. These functions can be calibrated taking into consideration results of questionnaires conducted among users of Park and Ride system. Due to lack of representative sample of users, one has decided to use results of experts' questionnaires as a input data for calibration the shape of membership functions. Describing factor will be generalized cost of the trip for different modes of transport. Proposed approach consists of two main stages: modeling of share of public/private transport trips and Multimodal model estimating number of Park and Ride users. Verification of presented methodology is treated as an indirect proof. Proposed approach can be applied for estimation of bi-modal split. Then the results are compared with traditional approaches based on logit functions. Comparable results of proposed fuzzy approach with traditional logit models can be treated as a confirmation of chosen methodology.