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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.
The design of safety-critical structures, exposed to cyclic excitations demands for non-degrading or limited-degrading behavior during extreme events. Among others, the structural behavior is mainly determined by the amount of plastic cycles, completed during the excitation. Existing simplified methods often ignore this dependency, or assume/request sufficient cyclic capacity. The paper introduces a new performance based design method that considers explicitly a predefined number of re-plastifications. Hereby approaches from the shakedown theory and signal processing methods are utilized. The paper introduces the theoretical background, explains the steps of the design procedure and demonstrates the applicability with help of an example. This project was supported by German Science Foundation (Deutsche Forschungsgemeinschaft, DFG)
The present paper is part of a comprehensive approach of grid-based modelling. This approach includes geometrical modelling by pixel or voxel models, advanced multiphase B-spline finite elements of variable order and fast iterative solver methods based on the multigrid method. So far, we have only presented these grid-based methods in connection with linear elastic analysis of heterogeneous materials. Damage simulation demands further considerations. The direct stress solution of standard bilinear finite elements is severly defective, especially along material interfaces. Besides achieving objective constitutive modelling, various nonlocal formulations are applied to improve the stress solution. Such a corrective data processing can either refer to input data in terms of Young's modulus or to the attained finite element stress solution, as well as to a combination of both. A damage-controlled sequentially linear analysis is applied in connection with an isotropic damage law. Essentially by a high resolution of the heterogeneous solid, local isotropic damage on the material subscale allows to simulate complex damage topologies such as cracks. Therefore anisotropic degradation of a material sample can be simulated. Based on an effectively secantial global stiffness the analysis is numerically stable. The iteration step size is controlled for an adequate simulation of the damage path. This requires many steps, but in the iterative solution process each new step starts with the solution of the prior step. Therefore this method is quite effective. The present paper provides an introduction of the proposed concept for a stable simulation of damage in heterogeneous solids.
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.
In this paper an adaptive heterogeneous multiscale model, which couples two substructures with different length scales into one numerical model is introduced for the simulation of damage in concrete. In the presented approach the initiation, propagation and coalescence of microcracks is simulated using a mesoscale model, which explicitly represents the heterogeneous material structure of concrete. The mesoscale model is restricted to the damaged parts of the structure, whereas the undamaged regions are simulated on the macroscale. As a result an adaptive enlargement of the mesoscale model during the simulation is necessary. In the first part of the paper the generation of the heterogeneous mesoscopic structure of concrete, the finite element discretization of the mesoscale model, the applied isotropic damage model and the cohesive zone model are briefly introduced. Furthermore the mesoscale simulation of a uniaxial tension test of a concrete prism is presented and own obtained numerical results are compared to experimental results. The second part is focused on the adaptive heterogeneous multiscale approach. Indicators for the model adaptation and for the coupling between the different numerical models will be introduced. The transfer from the macroscale to the mesoscale and the adaptive enlargement of the mesoscale substructure will be presented in detail. A nonlinear simulation of a realistic structure using an adaptive heterogeneous multiscale model is presented at the end of the paper to show the applicability of the proposed approach to large-scale structures.
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.
Summer overheating in buildings is a common problem, especially in office buildings with large glazed facades, high internal loads and low thermal mass. Phase change materials (PCM) that undergo a phase transition in the temperature range of thermal comfort can add thermal mass without increasing the structural load of the building. The investigated PCM were micro-encapsulated and mixed into gypsum plaster. The experiments showed a reduction of indoor-temperature of up to 4 K when using a 3 cm layer of PCM-plaster with micro-encapsulated paraffin. The measurement results could validate a numerical model that is based on a temperature dependent function for heat capacity. Thermal building simulation showed that a 3 cm layer of PCM-plaster can help to fulfil German regulations concerning heat protection of buildings in summer for most office rooms.
In this paper we study the structure of the solutions to higher dimensional Dirac type equations generalizing the known λ-hyperholomorphic functions, where λ is a complex parameter. The structure of the solutions to the system of partial differential equations (D- λ) f=0 show a close connection with Bessel functions of first kind with complex argument. The more general system of partial differential equations that is considered in this paper combines Dirac and Euler operators and emphasizes the role of the Bessel functions. However, contrary to the simplest case, one gets now Bessel functions of any arbitrary complex order.
The modeling of crack propagation in plain and reinforced concrete structures is still a field for many researchers. If a macroscopic description of the cohesive cracking process of concrete is applied, generally the Fictitious Crack Model is utilized, where a force transmission over micro cracks is assumed. In the most applications of this concept the cohesive model represents the relation between the normal crack opening and the normal stress, which is mostly defined as an exponential softening function, independently from the shear stresses in tangential direction. The cohesive forces are then calculated only from the normal stresses. By Carol et al. 1997 an improved model was developed using a coupled relation between the normal and shear damage based on an elasto-plastic constitutive formulation. This model is based on a hyperbolic yield surface depending on the normal and the shear stresses and on the tensile and shear strength. This model also represents the effect of shear traction induced crack opening. Due to the elasto-plastic formulation, where the inelastic crack opening is represented by plastic strains, this model is limited for applications with monotonic loading. In order to enable the application for cases with un- and reloading the existing model is extended in this study using a combined plastic-damage formulation, which enables the modeling of crack opening and crack closure. Furthermore the corresponding algorithmic implementation using a return mapping approach is presented and the model is verified by means of several numerical examples. Finally an investigation concerning the identification of the model parameters by means of neural networks is presented. In this analysis an inverse approximation of the model parameters is performed by using a given set of points of the load displacement curves as input values and the model parameters as output terms. It will be shown, that the elasto-plastic model parameters could be identified well with this approach, but require a huge number of simulations.
Die effektive Kooperation aller beteiligten Fachplaner im Bauplanungsprozess ist die Voraussetzung für wirtschaftliches und qualitativ hochwertiges Bauen. Bauprojektorganisationen bestehen in der Regel aus zahlreichen unabhängigen Planungspartnern, die örtlich verteilt spezifische Planungsaufgaben bearbeiten und die Ergebnisse in Teilproduktmodellen ablegen. Da Planungsprozesse im Bauwesen stark arbeitsteilig ablaufen, sind die Teilproduktmodelle der einzelnen Fachplanungen in hohem Maße voneinander abhängig. Ziel des hier vorgestellten Ansatzes ist die Integration der Teilproduktmodelle der Gebäudeplanung in einem netzwerkbasierten Modellverbund am Beispiel der Brandschutzplanung. Im Beitrag werden die Probleme der Verteiltheit und insbesondere der semantischen Heterogenität der involvierten Teilproduktmodelle betrachtet. Der verteilte Zugriff wird mithilfe mobiler Software-Agenten realisiert. Die Agenten können sich dabei frei im netzwerkbasierten Planungsverbund bewegen und agieren als Vertreter der Fachplaner. Das Problem der semantischen Heterogenität der Teilproduktmodelle wird auf der Basis von Ontologien gelöst. Dazu werden erstens Domänenontologien entwickelt, die Objekte der realen Welt einer abgeschlossenen Domäne, hier des Brandschutzes, abbilden. Zweitens werden Applikationsontologien entwickelt, die die einzelnen proprietären Datenhaltungen (im Sinne von Teilproduktmodellen) der jeweiligen Fachplanungen repräsentieren. Beide Ontologien werden mit einem regelbasierten Ansatz verknüpft. Im vorgestellten Anwendungsfall Brandschutz dient die Domänenontologie als einheitliche Schnittstelle für den Zugriff auf die verteilten Modelle und abstrahiert dabei von deren Datenbankspezifika und proprietären Schemata. Mithilfe von mobilen Agenten und semantischen Technologien kann so eine Plattform zur Verfügung gestellt werden, die erstens die dynamische Integration von Ressourcen in den Planungsverbund erlaubt und zweitens auf deren Basis unabhängig von der Verteiltheit und Heterogenität der eingebundenen Ressourcen ingenieurgerechte Verarbeitungsmethoden realisiert werden können.
In classical complex function theory the geometric mapping property of conformality is closely linked with complex differentiability. In contrast to the planar case, in higher dimensions the set of conformal mappings is only the set of Möbius transformations. Unfortunately, the theory of generalized holomorphic functions (by historical reasons they are called monogenic functions) developed on the basis of Clifford algebras does not cover the set of Möbius transformations in higher dimensions, since Möbius transformations are not monogenic. But on the other side, monogenic functions are hypercomplex differentiable functions and the question arises if from this point of view they can still play a special role for other types of 3D-mappings, for instance, for quasi-conformal ones. On the occasion of the 16th IKM 3D-mapping methods based on the application of Bergman's reproducing kernel approach (BKM) have been discussed. Almost all authors working before that with BKM in the Clifford setting were only concerned with the general algebraic and functional analytic background which allows the explicit determination of the kernel in special situations. The main goal of the abovementioned contribution was the numerical experiment by using a Maple software specially developed for that purpose. Since BKM is only one of a great variety of concrete numerical methods developed for mapping problems, our goal is to present a complete different from BKM approach to 3D-mappings. In fact, it is an extension of ideas of L. V. Kantorovich to the 3-dimensional case by using reduced quaternions and some suitable series of powers of a small parameter. Whereas until now in the Clifford case of BKM the recovering of the mapping function itself and its relation to the monogenic kernel function is still an open problem, this approach avoids such difficulties and leads to an approximation by monogenic polynomials depending on that small parameter.
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.
... WITHOUT RIGHT ANGLE.
(2006)
Currently sculptural design is one of the most discussed themes in architecture. Due to their light weight, easy transportation and assembly, as well as an almost unlimited structural variety, parameterised spatial structures are excellently suited for constructive realisation of free formed claddings. They subdivide the continuous surface into a structure of small sized nodes, straight members and plane glass panels. Thus they provide an opportunity to realise arbitrary double-curved claddings with a high degree of transparency, using industrial semi-finished products (steel sections, flat glass). Digital design strategies and a huge number of similar looking but in detail unique structural members demand a continuous digital project handling. Within a research project, named MYLOMESH, a free-formed spatial structure was designed, constructed, fabricated and assembled. All required steps were carried out based on digital data. Different digital connections (scripts) between varying software tools, which are usually not used in the planning process of buildings, were created. They allow a completely digital workflow. The project, its design, meshing, constructive detailing and the above-mentioned scripts are described in this paper.
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.
PLANUNGSUNTERSTÜTZUNG DURCH DIE ANALYSE RÄUMLICHER PROZESSE MITTELS COMPUTERSIMULATIONEN. Erst wenn man – zumindest im Prinzip – versteht, wie eine Stadt mit ihren komplexen, verwobenen Vorgängen im Wesentlichen funktioniert, ist eine sinnvolle Stadtplanung möglich. Denn jede Planung bedeutet einen Eingriff in den komplexen Organismus einer Stadt. Findet dieser Eingriff ohne Wissen über die Funktionsweise des Organismus statt, können auch die Auswirkungen nicht abgeschätzt werden. Dieser Beitrag stellt dar, wie urbane Prozesse mittels Computersimulationen unter Zuhilfenahme so genannter Multi-Agenten-Systeme und Zellulärer Automaten verstanden werden können. von
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.
At the end of the 1960s, architects at various universities world- wide began to explore the potential of computer technology for their profession. With the decline in prices for PCs in the 1990s and the development of various computer-aided architectural design systems (CAAD), the use of such systems in architectural and planning offices grew continuously. Because today no ar- chitectural office manages without a costly CAAD system and because intensive soſtware training has become an integral part of a university education, the question arises about what influence the various computer systems have had on the design process forming the core of architectural practice. The text at hand devel- ops ten theses about why there has been no success to this day in introducing computers such that new qualitative possibilities for design result. RESTRICTEDNESS
Nähert man sich der Frage nach den Zusammenhängen zwischen Strukturalismus und generativen algorithmischen Planungsmethoden, so ist zunächst zu klären, was man unter Strukturalismus in der Architektur versteht. Allerdings gibt es letztlich keinen verbindlichen terminologischen Rahmen, innerhalb dessen sich eine solche Klärung vollziehen könnte. Strukturalismus in der Architektur wird oftmals auf ein formales Phänomen und damit auf eine Stilfrage reduziert. Der vorliegende Text will sich nicht mit Stilen und Phänomenen strukturalistischer Architektur auseinandersetzen, sondern konzentriert sich auf die Betrachtung strukturalistischer Entwurfsmethoden und stellt Bezüge her zu algorithmischen Verfahren, wobei das Zusammenspiel zwischen regelgeleitetem und intuitivem Vorgehen beim Entwerfen herausgearbeitet wird.
Im vorliegenden Beitrag wird ein Framework für ein verteiltes dynamisches Produktmodell (FREAC) vorgestellt, welches der experimentellen Softwareentwicklung dient. Bei der Entwicklung von FREAC wurde versucht, folgende Eigenschaften umzusetzen, die bei herkömmlichen Systemen weitgehend fehlen: Erstens eine hohe Flexibilität, also eine möglichst hohe Anpassbarkeit für unterschiedliche Fachdisziplinen; Zweitens die Möglichkeit, verschiedene Tools nahtlos miteinander zu verknüpfen; Drittens die verteilte Modellbearbeitung in Echtzeit; Viertens das Abspeichern des gesamten Modell-Bearbeitungsprozesses; Fünftens eine dynamische Erweiterbarkeit sowohl für Softwareentwickler, als auch für die Nutzer der Tools. Die Bezeichnung FREAC umfasst sowohl das Framework zur Entwicklung und Pflege eines Produktmodells (FREAC-Development) als auch die entwickelten Tools selbst (FREAC-Tools).
Der vorliegende Text beschreibt ein computerbasiertes Verfahren zur Lösung von Layout-problemen in Architektur und Städtebau, welches mit möglichst wenig Problemwissen auskommt und schnell brauchbare Ergebnisse liefert, die durch schrittweises Hinzufügen von Problemwissen interaktiv weiter ausgearbeitet werden können. Für das generative Verfahren wurde eine Evolutions-Strategie verwendet, die mit Mechanismen zur Kollisionserkennung und virtuellen Federn zu einem hybriden Algorithmus kombiniert wurde. Dieser dient erstens der Lösung des Problems der Dichten Packung von Rechtecken sowie zweitens der Herstellung bestimmter topologischer Beziehungen zwischen diesen Rechtecken. Die Bearbeitung beider Probleme wird durch schrittweise Erweiterung grundlegender Verfahren untersucht, wobei die einzelnen Schritte anhand von Performancetests miteinander verglichen werden. Am Ende wird ein iterativer Algorithmus vorgestellt, der einerseits optimale Lösungen garantiert und andererseits diese Lösungen in einer für eine akzeptable Nutzerinteraktion ausreichenden Geschwindigkeit generiert.
Entwerfen Versionieren: Probleme und Lösungsansätze für die Organisation verteilter Entwurfsprozesse
(2011)
Entwerfen ist ein komplexer Vorgang. Soll dieser Vorgang nicht allein, sondern räumlich verteilt mit mehreren Beteiligten gemeinsam stattfinden, so sind digitale Werkzeuge zur Unterstützung dieses Prozesses unumgänglich. Die Verwendung von Werkzeugen für Ent-wurfsprozesse bedeutet jedoch immer auch eine Manipulation des zu unterstützenden Prozesses selbst. Im Falle von Werkzeugen zur Unterstützung der Kollaboration mehrerer Beteiligter stellen die implementierten Koordinationsmechanismen solche prozessbeeinflussenden Faktoren dar. Damit diese Mechanismen, entsprechend der Charakteristika kreativer Prozesse, so flexibel wie möglich gestaltet werden können, liegt die Anforderung auf technischer Ebene darin, ein geeignetes Konzept für eine nachvollziehbare Speicherung (Versionierung) der stattfindenden Entwurfshandlungen zu schaffen. Der vorliegende Artikel beschäftigt sich mit dem Thema der Entwurfsversionierung in computergestützten kollaborativen Arbeitsumgebungen. Vor dem Hintergrund, dass die Versionierung den kreativen Entwurfsprozess möglichst wenig manipulieren soll, werden technische sowie konzeptionelle Probleme der diskutiert und Lösungsansätze für diese vorgestellt.
This work is based on the concept that the structure of a city can be defined by six basic urban patterns. To enable more complex urban planning as a long-term objective I have developed a simulation method for generating these basic patterns and for combining them to form various structures. The generative process starts with the two-dimensional organisation of streets followed by the parceling of the remaining areas. An agent-based diffusion-contact model is the basis of these first two steps. Then, with the help of cellular automata, the sites for building on are defined and a three-dimensional building structure is derived. I illustrate the proposed method by showing how it can be applied to generate possible structures for an urban area in the city of Munich.
Some caad packages offer additional support for the optimization of spatial configurations, but the possibilities for applying optimization are usually limited either by the complexity of the data model or by the constraints of the underlying caad system. Since we missed a system that allows to experiment with optimization techniques for the synthesis of spatial configurations, we developed a collection of methods over the past years. This collection is now combined in the presented open source library for computational planning synthesis, called CPlan. The aim of the library is to provide an easy to use programming framework with a flat learning curve for people with basic programming knowledge. It offers an extensible structure that allows to add new customized parts for various purposes. In this paper the existing functionality of the CPlan library is described.
It's not uncommon that analysis and simulation methods are used mainly to evaluate finished designs and to proof their quality. Whereas the potential of such methods is to lead or control a design process from the beginning on. Therefore, we introduce a design method that move away from a “what-if” forecasting philosophy and increase the focus on backcasting approaches. We use the power of computation by combining sophisticated methods to generate design with analysis methods to close the gap between analysis and synthesis of designs. For the development of a future-oriented computational design support we need to be aware of the human designer’s role. A productive combination of the excellence of human cognition with the power of modern computing technology is needed. We call this approach “cognitive design computing”. The computational part aim to mimic the way a designer’s brain works by combining state-of-the-art optimization and machine learning approaches with available simulation methods. The cognition part respects the complex nature of design problems by the provision of models for human-computation interaction. This means that a design problem is distributed between computer and designer. In the context of the conference slogan “back to command”, we ask how we may imagine the command over a cognitive design computing system. We expect that designers will need to let go control of some parts of the design process to machines, but in exchange they will get a new powerful command on complex computing processes. This means that designers have to explore the potentials of their role as commanders of partially automated design processes. In this contribution we describe an approach for the development of a future cognitive design computing system with the focus on urban design issues. The aim of this system is to enable an urban planner to treat a planning problem as a backcasting problem by defining what performance a design solution should achieve and to automatically query or generate a set of best possible solutions. This kind of computational planning process offers proof that the designer meets the original explicitly defined design requirements. A key way in which digital tools can support designers is by generating design proposals. Evolutionary multi-criteria optimization methods allow us to explore a multi-dimensional design space and provide a basis for the designer to evaluate contradicting requirements: a task urban planners are faced with frequently. We also reflect why designers will give more and more control to machines. Therefore, we investigate first approaches learn how designers use computational design support systems in combination with manual design strategies to deal with urban design problems by employing machine learning methods. By observing how designers work, it is possible to derive more complex artificial solution strategies that can help computers make better suggestions in the future.
In computer-aided design (CAD), industrial products are designed using a virtual 3D model. A CAD model typically consists of curves and surfaces in a parametric representation, in most cases, non-uniform rational B-splines (NURBS). The same representation is also used for the analysis, optimization and presentation of the model. In each phase of this process, different visualizations are required to provide an appropriate user feedback. Designers work with illustrative and realistic renderings, engineers need a
comprehensible visualization of the simulation results, and usability studies or product presentations benefit from using a 3D display. However, the interactive visualization of NURBS models and corresponding physical simulations is a challenging task because of the computational complexity and the limited graphics hardware support.
This thesis proposes four novel rendering approaches that improve the interactive visualization of CAD models and their analysis. The presented algorithms exploit latest graphics hardware capabilities to advance the state-of-the-art in terms of quality, efficiency and performance. In particular, two approaches describe the direct rendering of the parametric representation without precomputed approximations and timeconsuming pre-processing steps. New data structures and algorithms are presented for the efficient partition, classification, tessellation, and rendering of trimmed NURBS surfaces as well as the first direct isosurface ray-casting approach for NURBS-based isogeometric analysis. The other two approaches introduce the versatile concept of programmable order-independent semi-transparency for the illustrative and comprehensible visualization of depth-complex CAD models, and a novel method for the hybrid reprojection of opaque and semi-transparent image information to accelerate stereoscopic rendering. Both approaches are also applicable to standard polygonal geometry which contributes to the computer graphics and virtual reality research communities.
The evaluation is based on real-world NURBS-based models and simulation data. The results show that rendering can be performed directly on the underlying parametric representation with interactive frame rates and subpixel-precise image results. The computational costs of additional visualization effects, such as semi-transparency and stereoscopic rendering, are reduced to maintain interactive frame rates. The benefit of this performance gain was confirmed by quantitative measurements and a pilot user study.
The Finite Element Method (FEM) is widely used in engineering for solving Partial Differential Equations (PDEs) over complex geometries. To this end, it is required to provide the FEM software with a geometric model that is typically constructed in a Computer-Aided Design (CAD) software. However, FEM and CAD use different approaches for the mathematical description of the geometry. Thus, it is required to generate a mesh, which is suitable for FEM, based on the CAD model. Nonetheless, this procedure is not a trivial task and it can be time consuming. This issue becomes more significant for solving shape and topology optimization problems, which consist in evolving the geometry iteratively. Therefore, the computational cost associated to the mesh generation process is increased exponentially for this type of applications.
The main goal of this work is to investigate the integration of CAD and CAE in shape and topology optimization. To this end, numerical tools that close the gap between design and analysis are presented. The specific objectives of this work are listed below:
• Automatize the sensitivity analysis in an isogeometric framework for applications in shape optimization. Applications for linear elasticity are considered.
• A methodology is developed for providing a direct link between the CAD model and the analysis mesh. In consequence, the sensitivity analysis can be performed in terms of the design variables located in the design model.
• The last objective is to develop an isogeometric method for shape and topological optimization. This method should take advantage of using Non-Uniform Rational B-Splines (NURBS) with higher continuity as basis functions.
Isogeometric Analysis (IGA) is a framework designed to integrate the design and analysis in engineering problems. The fundamental idea of IGA is to use the same basis functions for modeling the geometry, usually NURBS, for the approximation of the solution fields. The advantage of integrating design and analysis is two-fold. First, the analysis stage is more accurate since the system of PDEs is not solved using an approximated geometry, but the exact CAD model. Moreover, providing a direct link between the design and analysis discretizations makes possible the implementation of efficient sensitivity analysis methods. Second, the computational time is significantly reduced because the mesh generation process can be avoided.
Sensitivity analysis is essential for solving optimization problems when gradient-based optimization algorithms are employed. Automatic differentiation can compute exact gradients, automatically by tracking the algebraic operations performed on the design variables. For the automation of the sensitivity analysis, an isogeometric framework is used. Here, the analysis mesh is obtained after carrying out successive refinements, while retaining the coarse geometry for the domain design. An automatic differentiation (AD) toolbox is used to perform the sensitivity analysis. The AD toolbox takes the code for computing the objective and constraint functions as input. Then, using a source code transformation approach, it outputs a code for computing the objective and constraint functions, and their sensitivities as well. The sensitivities obtained from the sensitivity propagation method are compared with analytical sensitivities, which are computed using a full isogeometric approach.
The computational efficiency of AD is comparable to that of analytical sensitivities. However, the memory requirements are larger for AD. Therefore, AD is preferable if the memory requirements are satisfied. Automatic sensitivity analysis demonstrates its practicality since it simplifies the work of engineers and designers.
Complex geometries with sharp edges and/or holes cannot easily be described with NURBS. One solution is the use of unstructured meshes. Simplex-elements (triangles and tetrahedra for two and three dimensions respectively) are particularly useful since they can automatically parameterize a wide variety of domains. In this regard, unstructured Bézier elements, commonly used in CAD, can be employed for the exact modelling of CAD boundary representations. In two dimensions, the domain enclosed by NURBS curves is parameterized with Bézier triangles. To describe exactly the boundary of a two-dimensional CAD model, the continuity of a NURBS boundary representation is reduced to C^0. Then, the control points are used to generate a triangulation such that the boundary of the domain is identical to the initial CAD boundary representation. Thus, a direct link between the design and analysis discretizations is provided and the sensitivities can be propagated to the design domain.
In three dimensions, the initial CAD boundary representation is given as a collection of NURBS surfaces that enclose a volume. Using a mesh generator (Gmsh), a tetrahedral mesh is obtained. The original surface is reconstructed by modifying the location of the control points of the tetrahedral mesh using Bézier tetrahedral elements and a point inversion algorithm. This method offers the possibility of computing the sensitivity analysis using the analysis mesh. Then, the sensitivities can be propagated into the design discretization. To reuse the mesh originally generated, a moving Bézier tetrahedral mesh approach was implemented.
A gradient-based optimization algorithm is employed together with a sensitivity propagation procedure for the shape optimization cases. The proposed shape optimization approaches are used to solve some standard benchmark problems in structural mechanics. The results obtained show that the proposed approach can compute accurate gradients and evolve the geometry towards optimal solutions. In three dimensions, the moving mesh approach results in faster convergence in terms of computational time and avoids remeshing at each optimization step.
For considering topological changes in a CAD-based framework, an isogeometric phase-field based shape and topology optimization is developed. In this case, the diffuse interface of a phase-field variable over a design domain implicitly describes the boundaries of the geometry. The design variables are the local values of the phase-field variable. The descent direction to minimize the objective function is found by using the sensitivities of the objective function with respect to the design variables. The evolution of the phase-field is determined by solving the time dependent Allen-Cahn equation.
Especially for topology optimization problems that require C^1 continuity, such as for flexoelectric structures, the isogeometric phase field method is of great advantage. NURBS can achieve the desired continuity more efficiently than the traditional employed functions. The robustness of the method is demonstrated when applied to different geometries, boundary conditions, and material configurations. The applications illustrate that compared to piezoelectricity, the electrical performance of flexoelectric microbeams is larger under bending. In contrast, the electrical power for a structure under compression becomes larger with piezoelectricity.