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The Element-free Galerkin Method has become a very popular tool for the simulation of mechanical problems with moving boundaries. The internally applied Moving Least Squares approximation uses in general Gaussian or cubic weighting functions and has compact support. Due to the approximative character of this method the obtained shape functions do not fulfill the interpolation condition, which causes additional numerical effort for the imposition of the essential boundary conditions. The application of a singular weighting function, which leads to singular coefficient matrices at the nodes, can solve this problem, but requires a very careful placement of the integration points. Special procedures for the handling of such singular matrices were proposed in literature, which require additional numerical effort. In this paper a non-singular weighting function is presented, which leads to an exact fulfillment of the interpolation condition. This weighting function leads to regular values of the weights and the coefficient matrices in the whole interpolation domain even at the nodes. Furthermore this function gives much more stable results for varying size of the influence radius and for strongly distorted nodal arrangements than classical weighting function types. Nevertheless, for practical applications the results are similar as these obtained with the regularized weighting type presented by the authors in previous publications. Finally a new concept will be presented, which enables an efficient analysis of systems with strongly varying node density. In this concept the nodal influence domains are adapted depending on the nodal configuration by interpolating the influence radius for each direction from the distances to the natural neighbor nodes. This approach requires a Voronoi diagram of the domain, which is available in this study since Delaunay triangles are used as integration background cells. In the numerical examples it will be shown, that this method leads to a more uniform and reduced number of influencing nodes for systems with varying node density than the classical circular influence domains, which means that the small additional numerical effort for interpolating the influence radius leads to remarkable reduction of the total numerical cost in a linear analysis while obtaining similar results. For nonlinear calculations this advantage would be even more significant.
In this paper we consider three different methods for generating monogenic functions. The first one is related to Fueter's well known approach to the generation of monogenic quaternion-valued functions by means of holomorphic functions, the second one is based on the solution of hypercomplex differential equations and finally the third one is a direct series approach, based on the use of special homogeneous polynomials. We illustrate the theory by generating three different exponential functions and discuss some of their properties. Formula que se usa em preprints e artigos da nossa UI&D (acho demasiado completo): Partially supported by the R\&D unit \emph{Matem\'atica a Aplica\c\~es} (UIMA) of the University of Aveiro, through the Portuguese Foundation for Science and Technology (FCT), co-financed by the European Community fund FEDER.
In engineering science the modeling and numerical analysis of complex systems and relations plays an important role. In order to realize such an investigation, for example a stochastic analysis, in a reasonable computational time, approximation procedure have been developed. A very famous approach is the response surface method, where the relation between input and output quantities is represented for example by global polynomials or local interpolation schemes as Moving Least Squares (MLS). In recent years artificial neural networks (ANN) have been applied as well for such purposes. Recently an adaptive response surface approach for reliability analyses was proposed, which is very efficient concerning the number of expensive limit state function evaluations. Due to the applied simplex interpolation the procedure is limited to small dimensions. In this paper this approach is extended for larger dimensions using combined ANN and MLS response surfaces for evaluating the adaptation criterion with only one set of joined limit state points. As adaptation criterion a combination by using the maximum difference in the conditional probabilities of failure and the maximum difference in the approximated radii is applied. Compared to response surfaces on directional samples or to plain directional sampling the failure probability can be estimated with a much smaller number of limit state points.
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.
Am Beispiel eines 3-feldrigen Durchlaufträgers wird die Versagenswahrscheinlichkeit von wechselnd belasteten Stahlbetonbalken bezüglich des Grenzzustandes der Adaption (Einspielen, shakedown) untersucht. Die Adaptionsanalyse erfolgt unter Berücksichtigung der beanspruchungschabhängigen Degradation der Biegesteifigkeit infolge Rissbildung. Die damit verbundene mechanische Problemstellung kann auf die Adaptionsanalyse linear elastisch - ideal plastischer Balkentragwerke mit unbekannter aber begrenzter Biegesteifigkeit zurückgeführt werden. Die Versagenswahrscheinlichkeit wird unter Berücksichtigung stochastischer Tragwerks- und Belastungsgrößen berechnet. Tragwerkseigenschaften und ständige Lasten gelten als zeitunabhängige Zufallsgrößen. Zeitlich veränderliche Lasten werden als nutzungsdauerbezogene Extremwerte POISSONscher Rechteck-Pulsprozesse unter Berücksichtigung zeitlicher Überlagerungseffekte modelliert, so dass die Versagenswahrscheinlichkeit ebenfalls eine nutzungsdauerbezogene Größe ist. Die mechanischen Problemstellungen werden numerisch mit der mathematischen Optimierung gelöst. Die Versagenswahrscheinlichkeit wird auf statistischem Weg mit der Monte-Carlo-Methode geschätzt.
ON THE NAVIER-STOKES EQUATION WITH FREE CONVECTION IN STRIP DOMAINS AND 3D TRIANGULAR CHANNELS
(2006)
The Navier-Stokes equations and related ones can be treated very elegantly with the quaternionic operator calculus developed in a series of works by K. Guerlebeck, W. Sproeossig and others. This study will be extended in this paper. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one basically needs to evaluate two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. With special variants of quaternionic holomorphic multiperiodic functions we obtain explicit formulas for three dimensional parallel plate channels, rectangular block domains and regular triangular channels. The explicit knowledge of the integral kernels makes it then possible to evaluate the operator equations in order to determine the solutions of the boundary value problem explicitly.
In this paper we evaluate 2D models for soil-water characteristic curve (SWCC), that incorporate the hysteretic nature of the relationship between volumetric water content Θ and suction Ψ. The models are based on nonlinear least squares estimation of the experimental data for sand. To estimate the dependent variable Θ the proposed models include two independent variables, suction and sensors reading position (depth d in the column test). The variable d represents not only the position where suction and water content are measured but also the initial suction distribution before each of the hydraulic loading test phases. Due to this the proposed 2D regression models acquire the advantage that they: (a) can be applied for prediction of Θ for any position along the column and (b) give the functional form for the scanning curves.
The quaternionic operator calculus can be applied very elegantly to solve many important boundary value problems arising in fluid dynamics and electrodynamics in an analytic way. In order to set up fully explicit solutions. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one has to evaluate two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. Recently the theory of quaternionic holomorphic multiperiodic functions and automorphic forms provided new impulses to set up explicit representation formulas for large classes of hyperbolic polyhedron type domains. These include block shaped domains, wedge shaped domains (with or without additional rectangular restrictions) and circular symmetric finite and infinite cylinders as particular subcases. In this talk we want to give an overview over the recent developments in this direction.
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.
The management of resources is an essential task in each construction company. Today, ERP systems and e-Business systems are available to assist construction companies to efficiently organise the allocation of their personnel and equipment within the company, but they cannot provide the company with the idle resources for every single task that has to be performed during a construction project. Therefore, companies should have an alternative solution to better exploit expensive resources and compensate their fixed costs, but also have them available at the right time for their own business activities. This paper outlines the approach taken by the EU funded project “e-Sharing” (IST-2001-33325) to support resource management between construction companies. It will describe requirements for the management of construction resources, its core features, and the integration approach. Therefore, we will outline the approach of an integrated resource type model supporting the management and classification of construction equipment, construction tasks and qualification profiles. The development is based on a cross-domain analysis and evaluation of existing models. ...
The planning of projects in building engineering is a complex process which is characterized by a dynamical composition and many modifications during the definition and execution time of processes. For a computer-aided and network-based cooperation a formal description of the planning process is necessary. In the research project “Relational Process Modelling in Cooperative Building Planning” a process model is described by three parts: an organizational structure with participants, a building structure with states and a process structure with activities. This research project is part of the priority program 1103 “Network-Based Cooperative Planning Processes in Structural Engineering” promoted by the German Research Foundation (DFG). Planning processes in civil engineering can be described by workflow graphs. The process structure describes the logical planning process and can be formally defined by a bipartite graph. This structure consists of activities, transitions and relationships between activities and transitions. In order to minimize errors at execution time of a planning process a consistent and structurally correct process model must be guaranteed. This contribution considers the concept and the algorithms for checking the consistency and the correctness of the process structure.
Integrated Engineering Workflow focused on the Structural Engineering in the Industrial Environment
(2004)
The engineering and construction industry has been slow to exploit the full potential of information technology. The industry is highly fragmented, price sensitive, risk-adverse, and profit margins are small. Each project is unique with a small amount of technological innovation opportunities to capitalise on from one project to the next. Technological innovations that have been taking place are just simulating the old traditional paper workflow. Engineering information in digital form is being conveyed using traditional paper representations, which have to be interpreted by humans before the information can be used in other applications, thereby creating ‘islands of information’. It can be seen that poorly implemented IT strategies are duplicating paperwork, rather than reducing or eliminating it (Crowley et al., 2000). This paper will introduce the Integrated Engineering Workflow (IEW) concept to re-organise a structural discipline working on multi-disciplinary projects so as to maximise the advantages offered by new information technology.
Applications for civil engineering tasks usually contain graphical user interfaces for the engineering processes. Persistent objects of the applications are stored to data bases. The influence of the interaction between a graphical user interface and a data base for the development of an civil engineering application is investigated in this paper. A graphic application for the linear elastic analysis of plane frames, which was previously developed with standard tools of the Java platform, is compared to a redesigned implementation using a generalized data base for persistent objects. The investigation leads to the following results : - A strict distinction between persistent and transient objects influences the class structure of an application, in particular the class structure of a graphical user interface. - The structure of an application depends on the logic for updating of references to persistent and transient graphical objects after an application is read from a file. - The complexity of the reference management can usually be handled better by just in time referencing associated with String - identifiers rather than by automated referencing associated with Name - identifiers.
The design of building projects involves several types of resources such as architects, structural engineers, mechanical engineers, electrical engineers, and draftsmen, among others. For design firms to stay in business in this very competitive market, they need to manage their resources in a way that improves productivity and cost effectiveness. This task, however, is not simple and requires thorough analysis of process-level operations, resource use, and productivity. Typically, these operational aspects are the responsibility of the design office manager who assigns available resources to the different design projects to save time and lower design expenses. It is noted that limited studies have been carried out in the literature to model overall organizational operations and behavioral aspects, particularly in firms specialized in the design of building projects. In an effort to simplify the modeling process, a simplified modeling and simulation tool is used in this research. A simulation model representing an actual design office was developed assuming that the office performs designs for small, medium, and large size building projects. The developed model was used to simulate several alternatives and examine various resource assignment strategies. The simulation was conducted over ten years and the resulting productivity and income was measured.
This paper presents a specific modeling technique that is focused on preparing planning processes in civil engineering. Planning processes in civil engineering are characterized by some peculiarities so that the sequence of planning tasks needs to be determined for each planning project. Neither the use of optimized partial processes nor the use of lower detailed and optimized processes guarantee an optimal overall planning process. The modeling technique considers these peculiarities. In a first step, it is focused on the logic of the planning process. Algorithms based on the graph theory determine that logic. This approach ensures consistency and logical correctness of the description of a planning process at the early beginning in its preparation phase. Sets of data – the products of engineers like technical drawings, technical models, reports, or specifications – form the core of the presented modeling technique. The production of these sets of data requires time and money. This is expressed by a specific weighting of each set of data in the presented modeling technique. The introduction of these weights allows an efficient progress measurement and controlling of a planning project. For this purpose, a link between the modeling technique used in the preparation phase and the execution phase is necessary so that target and actual values are available for controlling purposes. The present paper covers the description of this link. An example is given to illustrate the use of the modeling technique for planning processes in civil engineering projects.
Available construction time-cost trade-off analysis models can be used to generate trade-offs between these two important objectives, however, their application is limited in large-scale construction projects due to their impractical computational requirements. This paper presents the development of a scalable and multi-objective genetic algorithm that provides the capability of simultaneously optimizing construction time and cost large-scale construction projects. The genetic algorithm was implemented in a distributed computing environment that utilizes a recent standard for parallel and distributed programming called the message passing interface (MPI). The performance of the model is evaluated using a set of measures of performance and the results demonstrate the capability of the present model in significantly reducing the computational time required to optimize large-scale construction projects.
The growing competition pressure in the building industry increases the demands on the design and construction processes in respect to economical, technical and time aspects. These demands require efficient improvements of the value-added chain, which can be realized mainly with the usage of innovative information- and communication-technologies. To support the collaboration of all participants involved in a certain building project the Workflow-Management-System “BauKom-Online” has been developed. In the focus of the system is to support the coordination of the participants and their information exchange. Such a software-method is well suited to ensure a high quality planning process. The modelling of business-processes enables a better self-comprehension of the participants work and helps to enhance the project performance. The system architecture of BauKom-Online contains two basic components: the processmodelling tool and the workflow-engine. The process-model contains of activities and states of the planning and construction processes and their relations. These connected processes compose the workflow. Such a process-model for engineering purposes has to satisfy several needs, e.g., the consideration of planning and building alternatives, dynamic changes of the model during execution of the project and the linkage to further technical objects like costs, building structure, specifications and documentmanagement. Furthermore, the scheduling of the project can be done within the process-model and can be visualized as a Gantt-diagram. ...
As a result of the pilot-project “Grundwasser-Online” the supervision and the active controlling of large monitoring- and catchment-areas are realised by a co-operative integration of all related institutions, a synchronisation-process to combine all distributed data into one central server database, and a high-level eGovernment-Service to provide evaluated information over the internet. Based on this software system the local authorities are able to supervise the groundwater-levels and to find adequate decisions, which finally result in official permissions for the usage of groundwater-reservoirs by the water supply companies.
The methods currently used for scheduling building processes have some major advantages as well as disadvantages. The main advantages are the arrangement of the tasks of a project in a clear, easily readable form and the calculation of valuable information like critical paths. The main disadvantage on the other hand is the inflexibility of the model caused by the modeling paradigms. Small changes of the modeled information strongly influence the whole model and lead to the need to change many more details in the plan. In this article an approach is introduced allowing the creation of more flexible schedules. It aims towards a more robust model that lowers the need to change more than a few information while being able to calculate the important propositions of the known models and leading to further valuable conclusions.
Let the information of a civil engineering application be decomposed into objects of a given set of classes. Then the set of objects forms the data base of the application. The objects contain attributes and methods. Properties of the objects are stored in the attributes. Algorithms which the objects perform are implemented in the methods of the objects. If objects are modified by a user, the consistency of data in the base is destroyed. The data base must be modified in an update to restore its consistency. The sequence of the update operations is not arbitrary, but is governed by dependence between the objects. The situation can be described mathematically with graph theory. The available algorithms for the determination of the update sequence are not suitable when the data base is large. A new update algorithm for large data bases has been developed and is presented in this paper.