bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Dynamics of Washing Machines
Authors: Wagner F. , Pfeiffer F.
Published: March 2011

The mechanical model of a washing machine as an elastic multibody system is presented in this paper. According to the complexity of the machine parts the results of a finite element mode shape analysis are used to describe the elastic behavior. A procedure is presented to expand the Ritz seperation method for incorporating additional terms in the equations of motion resulting from shell or beam elements as well as from attached masses.
Zweibeiniges Technisches Gehen
Authors: Markus Baldinger , Bremer H.
Published: March 2011

Der Bewegungsapparat ist das Instrument, mat dem der Mensch auf die Umwelt zugeht, um einerseits auf sie einzuwirken, andererseits sich selbst in ihr darzustellen. Wie wichtig uns Menschen dieser Bewegungsapparat ist wird uns erst bewußt, wenn durch besondere Umstände (Unfälle oder Krankheiten) diese Bewegungsmöglichkeiten eingeschränkt werden. Daher versuchen Techniker und Ingenieure seit Generationen, die Fähigkeiten dieser komplexen Bewegung durch eine geeignete mathematische Apparatur darzustellen und das Steuerungssystem durch eine entsprechende Regelungsstruktur zu ersetzen. In dieser Arbeit ward dieser Bewegungsablauf durch eine angemessene mathematische Beschreibung dargestellt, und die anschließenden Ergebnisse präsentiert.
Effet du gauchissement et des charges sur les instabilités des poutres à parois minces et à sections ouvertes
Authors: Kamal El. , Mohri F. , Roth J. C.
Published: March 2011

On s'intéresse au phénomène de déversement de poutres à parois minces et à sections ouvertes. Cette instabilité fait intervenir le comportement des poutres en flexion torsion avec gauchissement. Beaucoup de paramétres interviennent dans l'étude. On se limite à exposer l'incidence des conditions aux limites vis à vis du gauchissement et l'effet d'application des charges. Les solutions numériques par éléments finis utilisant les poutres spatiales avec gauchissement sont comparées aux solutions analytiques proposées dans ie règlement européen (EC3).
Bifurcation of a Shaft under Magnetic Load
Authors: Kurnik W.
Published: March 2011

The aim of the paper is to examine interaction between two different instability effects in flexible shafts ‐ rotation in presence of material friction and transverse force of magnetic nature. Such problems arise for instance in multipole induction electric motors and in active vibration control of high‐speed shafts utilising magnetic actuation. A simple magnetomechanical model of the rotor displaying both divergence and flutter instability effects is assumed treating two‐sided magnetic actuators as sources of deflection‐dependent generally nonlinear force of possibly positive or negative sign. The stability region of the trivial equilibrium as well as the near‐critical limit cycles are studied to explain the interaction of both instability effects and the role of the magnetic load.
Stabilitätsuntersuchung von MDOF‐Systemen mit Totzeiten
Authors: Wagner N. , Ruge P.
Published: March 2011

Untersucht wird die Stabilität von mechanischen Systemen mit zwei verschiedenen Totzeiten für die Zustandsgrößen; z.B. eine Totzeit τ1 für die Verschiebungen und die zweite Totzeit τ2 für die Geschwindigkeiten. Gegenüber ]3[ erfolgt eine Verallgemeinerung auf MDOF‐Systeme. Die diskrete Beschreibung des kontinuierlichen Prozesses führt auf ein System von Differenzengleichungen, das mit Hilfe eines Ansatzes auf ein nichtlineares Eigenwertproblem abgebildet wird. Die darin enthaltene Matrixexponentialfunktion wird durch eine Padé‐Entwicklung in ein Matrizenpolynom umgewandelt.
Zur Stabilität der Gleichgewichtslagen eines Doppelpendels mit geradlinig geführtem Endpunkt
Authors: Berger A.
Published: March 2011

Während das Auffinden von stationären Punkten eines Potentials auf einer Teilmannigfaltigkeit eines euklidischen Raumes keine Schwierigkeiten bereitet (Lagrange'sche Multiplikatorenregel), ist eine Bestimmung der Stabilität die‐ser Punkte in der Regel nicht ohne weiteres möglich. Da aber derartige Fragestellungen in der Form von Potentialen unter (parametrisierten) Nebenbedingungen bei zahlreichen Anwendungen eine Rolle spielen, wäre die Verfügbarkeit eines (einfachen) Verfahrens wünschenswert, welches über die Stabilität entsprechender Gleichgewichtslagen zu entscheiden gestattet. Wie im folgenden ausgeführt, liefert eine einfache, geometrisch interpretierbare Bedingung ein solches Verfahren. Dessen Nutzen wird am Beispiel eines Doppelpendels mit geführtem Endpunkt demonstriert.
Abstandsberechnung zwischen Flächen höherer Ordnung und konvexen Polyedern
Authors: Buschmann A. , Frik M.
Published: March 2011

Für die Bahnplanung uon Robotern ist die schnelle Erkennung von Kollisionen und die Bestimmung der Abstände der Robotersegmente der Umgebung wesentlich. Bei einer detailgetreuen Modellierung sind auch Abstände zwischen gekrümmten Flächen, die hier durch superquadratische Ellipsoide modelliert weden, und konvexen Polyedern zu bestimmen. Der vorgestellte Algorithmus stellt eine Kombination des Verfahrens von BOBROW für konvexe Polyeder und einem eigenen Verfahren für superquadratische Ellipsoide dar.
Moment Interactions of Rigid Bodies
Authors: Grekova E.
Published: March 2011

We consider the problem of gravitationally interacting rigid bodies. We obtain formulae for the potential energy of their interaction and the gravitational moment. The first approximation for the problem of two gravitationally interacting bodies is the problem of a rigid body in a newton field of forces. We consider this problem for a body with rotational symmetry fixed in the centre of mass. There found regimes of regular precession and their stability is investigated. Another considered problem is the motion of an infinite system of rigid bodies fixed by their centres of masses in the points of a cubical lattice. It is assumed that every body interacts gravitationally with its six neighbours. It is shown that the regime of rotation around one of lattice axes is unstable.
Closed‐loop analysis of an articulated railcar train
Authors: Heinzl Ph. , Plöchl M. , Mack W. , Lugner P.
Published: March 2011

An articulated railcar train is modelled by a plane three‐body linkage mechanism guided at two points along a given trajectory with a prescribed velocity of the front point. The closed‐loop system is analyzed using a symbolic‐numerical method leading to ordinary differential equations in minimal coordinates.
Evolution of Wear Patterns on Railway Wheels
Authors: Küsel M. , Brommundt E.
Published: March 2011

Railway wheels suffer wear, irregular wear patterns develop on their surfaces. Travel comfort and safety are reduced and expensive profiling of the wheels becomes necessary.

A common explanation is that initial out‐of‐roundnesses increase because of the oscillations they cause. We develop a model to study these mechanisms. Particularly we take into account the evolution of out‐of‐roundnesses in axial and azimuthal direction on the wheel treads and outline the structure of the governing equations.
Dynamic Control of a Biped Walking Robot
Authors: Loffler K. , Gienger M. , Pfeiffer F.
Published: March 2011

The project of a two‐legged walking robot is presented. For this system a nonlinear control scheme is proposed that is based on the method of feedback linearization. In order to allow for a “dynamically” stable motion, the reference trajectories are computed so that the system remains controllable throughout the entire gait cycle. In simulations the robot is controlled in a running motion, including phases without ground contact. The simulation results show the good performance of the control strategy in a purely dynamic motion.
Assembly Modes of Linkages
Authors: Peisach E.
Published: March 2011

This paper deals with the problem of so called “assembly modes” of linkages of both planar and spatial structure. This problem has not been adequately elucidated in the literature. New type of assembly modes named “non‐standard assembly mode” is discovered.
Random Walkers Cellular Automata for Diffusion Processes
Authors: Vamoş Calin , Suciu Nicolae , Vereecken Harry , Jaekel Uwe , Schwarze Holger
Published: March 2011

Smooth concentration fields and balance equations for systems of random walkers are obtained by using the coarsegrained space‐time averaging method from ]5[ and averages over the statistical ensemble. This yields a new cellular automaton numerical model for diffusion processes. The number of particles and the averaging space‐time scale needed to approximate the concentration, with a given precision, are obtained. Applications were made for systems with small concentrations and diffusion in random fields.
Klassifikation serieller, paralleler und hybrider Manipulatoren
Authors: Verhoeven R. , Hiller M.
Published: March 2011

Es wird ein abstraktes mathematisches Modell vorgestellt, das auf alle Manipulatoren mit holonomen Zwangsbedingungen anwendbar ist. Es führt auf zwei Typen von Singularitäten, die typischerweise bei parallelen bzw. seriellen Robotern auftreten, diese aber nicht erschöpfend charakterisieren. Eine solche Charakterisierung wid hingegen möglich durch die Unterscheidung zweier Redundanztypen.
Thermally induced interlaminar stress concentrations at laminate corners
Authors: Becker W. , Jin P. P. , Lindemann J.
Published: March 2011

Subject of consideration is the stress field in the vicinity of a free rectangular corner of a cross‐ply laminate with symmetrical layup under thermal loading. A closed‐form analytical solution is developed for the near corner stress field and is shown to be in good agreement with comparative 3‐dimensional finite element analyses.
Stress Fields Around an Anisotropic Point Defect in a Quasi‐Continuum
Authors: Dobovcarek I.
Published: March 2011

An anisotropic point defect which is embedded in a homogeneous, isotropic, non‐locally elastic crystal is simulated with the help of the Dirac delta function and a general, constant, at the point of action spatially independent, second order tensor, describing anisotropies of the defect. In such form the defect retains intrinsic local structure. On the other hand, the surrounding medium exhibits a long range order of interaction in the classical form of non‐local elasticity. The resulting equations for displacement fields, stresses, and strains aw discussed using the theory of eigenstrains.
Description of two‐phase materials using Discrete Atom Method
Authors: Kolling S. , Gross D.
Published: March 2011

In metallic alloys, especially Ni‐base superalloys, a certain microstructure, formed by second‐phase coherent precipitates can be observed experimentally. To understand the morphological evolution of the precipitate's shape, a lot of theoretical and numerical work has been done during the past few years. Apart from finite and boundary element investigations founding on continuum mechanics descriptions, one alternative to simulate equilibrium morphologies is to use the Discrete Atom Method (DAM), based on a combination of statistical mechanics and linear elasticity. As an example, the equilibrium and stability of a misfitting isotropic second phase particle is treated by this method, taking into account elastic strain and interfacial energy.
3D Equilibrium Shapes of Misfitting Precipitates in Anisotropic Materials
Authors: Mueller R. , Gross D.
Published: March 2011

In high temperature application materials, such as Ni‐base alloys, the microstructure is very important for the overall behaviour. A model for predicting the equilibrium microstructure is presented. The model takes interfacial and elastic energy into account. Together with a Boundary Element Method a numerical procedure is presented allowing a realistic simulation in 9D. The simulation displays relevant factors for certain microstructures. For example the influence of particle size and the ratio of the elastic properties of the precipitate and the matrix: is discussed.
Ein viskoelastisches Schädigungsmodell zur Berechnung von Elastomeren mit Berücksichtigung von Temperatureinfluß
Authors: Nasdala L. , Kaliske M. , Rothert H.
Published: March 2011

Es wird eine viskoelastische Schädigungsformulierung auf der Basis des generalisierten Maxwell‐Modells für die Berechnung von Elastomerstrukturen bei verschiedenen Temperaturen vorgestellt. Urn zu berücksichtigen, daß eine Deformation im Druckbereich eine größere Steifigkeitsreduktion hervorruft als eine entsprechende Zugbeanspruchung, werden spezielle Druckfunktionen eingeführt. Zur Illustration einer praxisrelevanten Anwendung dient ein Vergleich der Spannungsverteilungen in der Bodenaufstandsfläche eines Neureifens und eines Reifens im Betriebszustand.
Computation of Stresses and Strains in Heterogeneous Bodies by Use of the Discrete Fourier Transform
Authors: Neumann S. , Herrmann K. P. , Muller W. H.
Published: March 2011

Discrete Fourier transforms are used to derive a numerical solution for the stresses and strains in a Representative Volume Element (RVE) which is filled with heterogeneities. The so‐called “equivalent inclusion method” (Mura 1987) is applied to reduce the original problem by determination of an auxiliary strain field. This field is related to the stresses by virtue of a spatially constant auxiliary stiffness tensor. By means of discrete Fourier transforms the resulting Partial Differential Equations (PDE) are mapped onto a linear system of equations which can be solved explicitly. A functional relation for the auxiliary strain field results. It can be solved approximately by means of a Neumann iteration procedure. Two heterogeneity problems of the Kirsch type are considered for which an analytical solution exists against which the accuracy of the numerical method can be checked.
Zu Stabilitätsproblemen bei Mikro‐Makro‐Übergängen
Authors: Schröder J.
Published: March 2011

Die Homogenisierung heterogener elastischer Verbundmaterialien erfordert die Modellierung des Materialverhaltens auf verschiedenen Skalen, der Makro‐ und der Mikroskale. Im Rahmen großer elastischer Deformationen betrachten wir mögliche Stabilitätsprobleme auf der Mikroskale und deren Auswirkung auf die Stabilität des makroskopischen Materialverhaltens. Hierbei sind zwei Verzweigungsarten repräsentativer Mikrostrukturen auf der Mikroskale zu unterscheiden, die sogenannten Blochwellen und die Schubdeformationsmodi.
Exact solution of the displacement boundary‐value problem of elasticity for a spindle
Authors: Zabarankin Michail Yu.
Published: March 2011

The exact solution of the displacement boundary‐value problem of elasticity in general case for an elastic medium containing a rigid spindle‐shaped inclusion is constructed. This solution is initially presented by the algebraic comnation of the dilatation function and an arbitrary harmonic vector. Being an analytical function, the Fourier ansform of the dilatation boundary‐value k‐harmonic is determined from the conjugation problem at three parallel mtours in the complex plane. Obtained problem is reduced to Fredholm integral equation with a quasi‐difference kernel.
Über durch Bipotentiale definierte Materialgesetze
Authors: Ban M. , Weichert D.
Published: March 2011

Eine Verallgemeinerung der Hypothese der normalen Dissipation wurde von de Saxcé durch die Einführung des Bipotentials erreicht. In diesem Beitrag werden einige mathematische Eigenschaften des Bipotentials untersucht.
Ein elasto‐plastisches Rebar‐Modell für die Berechnung von Verbundträgern
Authors: Hohn B. , Kaliske M. , Rothert H.
Published: March 2011

Für die Finite‐Elemente‐Berechnung uon Verbundträgern ist eine möglichst effiziente Simulation der Stahlbetonplatte und insbesondere deren Bewehrung erforderlich. Eine diskrete Modellierung der Bewehrung für Untersuchungen der Gesamtstruktur ist meist unrealistisch, da der damit verbundene numerische Modellierungsaufwand zu groß ist. Aus diesem Grund wird an diesem Artikel vorgeschlagen, die Bewehrungsstäbe in den Elementen durch eine Rebar‐Formulierung abzubilden, die keine zusätzlichen Freiheitsgrade erfordert. Für den Betonstahl wird eine elastoplastische Materialformulierung, die sich aus der Superposition beliebig vieler Prandtl‐Elemente zusammensetzt, verwendet. Mit dieser Methode lassen sich verschiedene Spannungs‐Dehnungs‐Beziehungen des Betonstahls abbilden. Abschließend werden verschiedene Möglichkeiten zur Modellierung der Verbundfuge vorgestellt.
Micromechanical Modeling of the Coated Steel Sheets Thermomechanical Behavior
Authors: Ilali I. , Cherkaoui M.
Published: March 2011

Micromechanical model is developed to determine be macroscopic thermomechanical behavior of metallic coated sheets. To study the thermoelastoplastic behavior of such heterogeneous materials (in general, substrate + inter‐phase + coating), classical localization and homogenization techniques are used in the framework of continuum mechanics with small perturbations hypothesis. Coatings are considered as a multi‐laminated medium in which every layer or phase exhibits an anisotropic thermoelastoplastic behavior with plane and perfect interfaces. The real heterogeneous material is replaced by a fictitious homogeneous one called Equivalent Homogeneous Material (E.H.M.). To consider the effect of anisotropy, the Hill's yield criterion for anisotropic strain‐hardening materials is used The interface problem is solved by introducing the interfacial operators of solid mechanics. One general “three‐phase” model is proposed and considered in the case of damaged coating by taking into account the coupling between plasticity and damage phenomena. First results show the effects of damaged or undamaged metallic coating on elastoplastic behavior of coated steel sheets.
Designing of components made from porous materials. Lines of stress discontinuity
Authors: Mielniczuk J. , Mostowski R.
Published: March 2011

Using the earlier formulated pasticity theory and the extremum principles for porous materials some properties of stress dicontinuity lines in plane stress and plane strain are described. For a given porosity the geometry of lines (angles) and the critical value of external loading (pressure) can be determined.
The Proof of an Extension of Melan's Theorem at Large Strains
Authors: Schieck B.
Published: March 2011

Melan's statical shakedown theorem, originally for small deformations, is extended for finite strains and rotations. The proof is given large strains and finite rotations and v. Mises yield condition with associated flow rule.
Collapsing cylindrical shock waves in gases with low absorptivities
Authors: Hirschler T.
Published: March 2011

In the self‐similar formulation of the collapse of a cylindrical shock wave in radiating gas the temperature gradient at the shock front is an undetermined quantity. Together with the absorptivity an arbitrary choice of these two variables is the basis of a parametric study. The paramretric study focuses upon gases with low absorptivities and is extended up to the isothermal limit where the absorptivity is equal to zero. In this context it is shown that the heat flux at the shock front is almost negligible. For gases with low absorptivities the assumption of an adiabatic shock front is therefore a sufficient accurate approximation.
Numerical Simulation of Inviscid Shock Interactions on Double‐Wedges
Authors: van Keuk J. , Ballmann J.
Published: March 2011

In supersonic and hypersonic flight double wedge geometries can cause very complex interaction phenomena between different wave types. These interactions can sometimes lead to anomalously high pressure and heat loads on the contour of aerospace planes like the ELAC1 configuration developed in the Collaborative Research Center (SFB 253) in Aachen. For the numerical simulation of such flows one has to use a method that should be both robust and accurate. The algorithm used here is based on the DLR FLOWer‐Code extended by several Upwind‐Splitting Methods for the physically correct description of the inviscid flux vector. Numerical solutions of 2 D inviscid shock interactions on double‐wedge geometries are presented and compared with corresponding results of other authors.
Towards Technical Application of Large Eddy Simulation
Authors: Breuer M.
Published: March 2011

The paper is concerned with the computation of high Reynolds number circular cylinder flow (Re = 3900/140,000) based on the large eddy simulation (LES) technique. Because this flow involves a variety of complex flow features encountered in technical applications, successful simulations for this test case, especially at high Reynolds numbers, can be considered as the first step to real world applications of LES. Based on an efficient finite‐volume LES code, a detailed study on different aspects influencing the quality of LES results was carried out. In the present paper, some of the results are presented and compared with experimental measurements available.
Random Vibration Systems with Weakly Correlated Random Excitation
Authors: Starkloff H.‐J. , Von Scheidt J. , Wunderlich R.
Published: March 2011

In the paper asymptotic expansions for second‐order moments of solutions to ordinary differential equations with weakly correlated random inhomogeneous terms are presented. Such equations arise e.g. in the mathematical modeling of vibration systems with an external random excitation. The given expansions allow an efficient approximative computation of moment functions of the solution process, particularly when the number of degrees of freedom is large.
Adaptive Optimal Stochastic Trajectory Planning in real‐time using neural network approximations
Authors: Aurnhammer A. , Marti K.
Published: March 2011

In Optimal Stochastic Trajectory Planning (OSTP) of industrial robots, the problem can be represented by a variational problem under stochastic disturbances. Using deterministic substitute problems obtained from stochastic optimisation theory, the corresponding deterministic substitute variational problem can be solved approximatively via mathematical programming techniques. However, due to the computationally expensive algorithms involved, these techniques can be used for off‐line calculations only. Hence, neural networks are trained to solve the trajectory‐planning problem in real‐time and to provide suitable solutions for on‐line applications.
Prozeßspezifische Roboteroptimierung
Authors: Burgmair R. , Pfeiffer F.
Published: March 2011

Es werden Zielfunktionen und Nebenbedingungen zur numerischen Optimierung der Lage, Reglerkoeffizienten und der Fügerichtung von Robotern, die Objekte mit großen Auslenkungen montieren, vorgeschlagen. Das nichtlineare Vektoroptimierungsproblem wird mit einem SQP‐Algorithmus gelöst, Optimierungsergebnisse werden gezeigt.
The interaction problem for the locally cooled free convection boundary layer
Authors: Exner A. , Kluwick A.
Published: March 2011

The free convection boundary layer which forms on a heated vertical flat plate of constant temperature is investigated in the vicinity of a localized disturbance of the wall temperature. In a small region the wall is cooled in a prescribed manner. The short strong disturbance results in an interaction problem which is solved numerically. If the disturbances are sufficiently weak, the interaction equations can be linearised allowing for analytical solutions. For strong disturbances, a numerical calculation of the non‐linear interaction problem is performed.
On Optimal Control of Mobile Robots
Authors: Kiriazov Petko
Published: March 2011

There are continuously increasing demands to mobile robots (MR) for faster operation, higher accuracy, and lower energy cost. A unified direct‐search optimization approach is proposed which employs parameterized control laws consistent with the Pontryagin Maximum principle. We define mostly appropriate input‐output pairs and transform the given two‐point boundary‐value problem into a system of shooting equations. The control parameters which are not in the input‐output pairs are used for time/energy optimization. Existence of solutions is guaranteed under a weak and reasonable condition. The approach is applied on a dynamic model of a MR having two independently driven wheels.
A Priori Constraint Elimination
Authors: Ales Krajnc , Darko Beg
Published: March 2011

The problem of steel frames optimal design, when it is written in mathematical programming form, gives a moderate number of unknowns and a huge number of constraints. A typical frame has about 50 unknowns and 20000 constraints. The large number of constraints, which are complex functions of many parameters, represents a problem for most non‐linear programming solvers. In order to reduce the number of constraints, we developed a method, which eliminates a large portion of constraints without their costly evaluation. The method is based on the problem specific constraints organization, where the constraints are organized into sets. It turns out that we can remove individual constraints from a set by simply comparing constraint parameters.
Wavelet filtering of three‐dimensional turbulence
Authors: Farge Marie , Pellegrino Giulio , Schneider Kai
Published: March 2011

We present a new vortex tube extraction method for three‐dimensional turbulent flows. The method is based on an orthogonal wavelet decomposition of the vorticity vector field. The coherent part of the flow is reconstructed from the strongest wavelet coefficients using an universal threshold criterion. As example we present the vortex tube extraction of three‐dimensional homogeneous isotropic turbulence.
Querschnittsoptimierung unter mehrfacher Belastung
Authors: Mikulski L.
Published: March 2011

Mit Hilfe des Maximumprinzips kann gezeigt weden, daß die Optimierung der durchlaufenden Träger, die simultan verschiedene Belastungsfälle aushalten, und dabei die maximale Spannung (Verschiebung) minimal halten, ein Mehrpunktrandwertprobem (MPRWP) ist. Die maximale Spannung (Verschiebung) soll unter verschiedenen Neben‐bedingungen minimal sein J(U) = minU {maxx σx}. Als Steuervariablen wird die Höhe des rechteckigen Querschnitts und auch die Lage der Unterstützungspunkte gewählt. Durch die Einführung des Steuerungsparameter p kann das Zielfunktional auf das Mayerischesproblem zurückgeführt werden. Das erhaltene Mehrpunktrandwertproblem mit Dimension 161 kann mit Hilfe des Dircolprogramm gelöst werden.
Accuracy and implementation of refined second order semi‐analytical design sensitivities
Authors: Vervenne K. , De Boer H. , van Keulen F.
Published: March 2011

Accurate second order design sensitivities of finite element responses play an important role in the optimization process. The semi‐analytical (SA) method is often used to compute these sensitivities. A disadvantage of the SA method is that severe inaccuracies may be observed for shape design variables. To improve the accuracy of the SA method a refined second order method has been proposed and implemented. The improvement has been based on the consistency conditions for rigid body modes and their derivatives. Both analytical and numerical examples indicate a considerable accuracy improvement of the refined method over the standard SA method.
Optimal design in automotive engineering with scattering design variables
Authors: Thomas Vietor
Published: March 2011

The development of a passenger car is a multidisciplinary task. The vehicle has to fulfill demands out of different attributes like vehicle dynamics, driveability, acoustics, thermal and heat management, safety, durability, crash and economics. One main problem is the variability of mechanical quantities responsible for the performance and customer perception of a car. To overcome this, the extension of the conventional deterministic oriented development process to a process which includes stochastic quantities is necessary. In this paper the current deterministic approach is described briefly. It is not possible to perform the extension in a single step. In a first extended version of the process the variability of material parameters is included. In further steps the formulation and solution of stochastic optimization problems for sub‐problems is necessary. Finally the complete approach should fully integrate the variability of stochastic quantities.
Duality based contact shape optimization
Authors: Vondrák V. , Dostál Z. , Rasmussen J.
Published: March 2011

An implementation of semi‐analytic method for the sensitivity analysis in contact shape optimization without friction is described. This method is then applied to the contact shape optimization.
Nonnegative Interpolation with Clough‐Tocher Splines of Cubic Precision
Authors: Bastian Marion , Schmidt Jochen W.
Published: March 2011

In ]4[ the Clough‐Tocher splines of quadratic precision are shown to allow always nonnegative interpolation of scattered data. The aim of the present note is to point out that Clough‐Tocher splines of cubic precision are suitable, too. This result extends to range restricted interpolation if the obstacles are piecewise constant. For piecewise linear and continuous obstacles the Clough‐Tocher splines may fail. However, for this type of restrictions it seems to be possible to derive an always working interpolation algorithm by means of the parametric Clough‐Tocher splines recently introduced in ]1[.
Flatness criteria for subdivision of rational Bézier curves and surfaces
Authors: Dyllong E. , Luther W.
Published: March 2011

Many of well‐known algorithms in the context of Computer Aided Geometric Design are based on subdivision techniques. Unfortunately, termination criteria for subdivision mostly require a time‐consuming computation of the maximum deviation between any given curve segment and its linear approximation at each subdivision step. We generalize results by Wang for Bézier curves ]3[ and present an approach which in advance specifies the number of necessary subdivision steps to obtain a piecewise linear approximation within an assumed accuracy for a given rational Bézier curve or surface.
Global convergence of Newton's method to the solution of equations of Reissner's Elastica
Authors: Flajs R. , Saje M. , Zakrajsek E.
Published: March 2011

The sufficient conditions under which the generalized solution of a planar elastic, Reissner's type cantilever beam if solely based on the rotation ]5[ loaded by conservative load, exists and is unique, are presented. Sufficient conditions for the global convergence of Newton's method and damped Newton's method with a short step are derived. The point load is also taken into account. The derived inequalities are sharp.
Eigenvalue Reanalysis and Condensation with General Masters
Authors: Hofferek Birgit , Voss Heinrich
Published: March 2011

In design optimization very often several changes of a structure are necessary to reach predetermined demands, and in each step very large eigenvalue problems have to be solved which are small modifications of each other. For large eigenvalue problems condensation methods are used to reduce the number of degrees of freedom to manageable size. In this note we take advantage of preceding computations by implementing eigenvectors of previous models as general masters into condensation.
Multi‐language approach in automatic generation of numerical procedures
Authors: Korelc J.
Published: March 2011

Practice shows that at the research stage of derivation of a new numerical software different languages and different platforms are the best means for assessment of performances and failures of the numerical model. By the classical approach, re‐coding in different languages would be extremely time consuming and is never done. The paper presents the use of symbolic and algebraic systems for improved quality control of automatically generated numerical procedures. With the symbolic concepts the code is automatically generated for several languages and for several platforms from the same basic symbolic description.
Dependency of the Bypass‐Transition on the Initiating Disturbance
Authors: Heiken S. , Demuth R. , Laurien E.
Published: March 2011

Numerical Simulations are made by integration of the three‐dimensional Navier‐Stokes equations for the early stages of the turbulent spot development in accelerated flat plate boundary layers. Serveral initial finite amplitude disturbances are stretched and develop a steep velocity gradient in the spanwise direction. The structure, visualized by tracer particles, becomes more complex and looks similar to a turbulent spot, shown in experiments by Elder.
Constraint partitioning in dynamic iteration methods
Authors: Arnold M.
Published: March 2011

Dynamic iteration (waveform relaxation) is a well approved approach to the numerical solution of coupled instationary differential equations that is based on a splitting into several subsystems. If the subsystems are coupled by constraints then there is no generic way to assign these constraints to the subsystems. In the present paper we consider three partitioning strategies for constraints that couple two differential‐algebraic systems. An error analysis shows that the stability of the dynamic iteration method depends strongly on the partitioning of the constraints.
Developments in Multirating for Coupled Systems
Authors: Andreas Bartel , Michael Günther
Published: March 2011

In technologically computer‐aided design, the demand for a refined modelling yields the numerical simulation of coupled systems. Often the dynamics of these systems can be described as initial value problems of ordinary differential equations, which are characterised by largely varying time constants. A natural approach is to use multirate integration schemes which integrate the subsystems by their inherent step size. The realisation of the couplings of these subsystems, however done, is the crucial point.

To begin, we give a short survey on multirate behaviour and its possible numerical exploitation in one‐step‐schemes. Based on the conception of generalised multirate, we classify multirate methods by the means, which compute the coupling terms for the internal stages: On one hand, extra/interpolation, on the other hand, the incremental formulation, which yields a genuine one‐step‐method. For the latter approach, we discuss the multirate W‐method as an example and give finally test results for a multirate version of Prothero‐Robinson's equation and the Inverter‐Chain.
Uniform pointwise convergence of finite difference schemes for quasilinear convection‐diffusion problems
Authors: Torsten Linss
Published: March 2011

We study convergence properties of an upwind difference scheme on layer‐adapted grids for the discretization of a class of singularly perturbed quasilinear two‐point boundary value problems. We derive conditions that are sufficient for uniform convergence in the maximum norm, with respect to the perturbation parameter, of the method. These conditions are easy to check and enable one to immediately deduce the rate of uniform convergence.
Advanced Methods to Compute Multiphase Turbulent Reacting Flows
Authors: Heinz S.
Published: March 2011

PDF and FDF methods do not require approximations for chemical reactions, which makes them extremely valuable for reacting flow calculations. The performance of these methods depends significantly on the accuracy of simulating small‐scale mixing processes. It is illustrated, in which way models may be developed that simulate mixing for various phases as a multi‐scale process in dependence on different factors. Further developments towards a system of very accurate and (less expensive) simplified methodologies for reacting flow calculations are pointed out.
A Conforming Exponentially Fitted Finite Element Scheme for the Semiconductor Continuity Equations in 3D
Authors: Angermann L. , Wang S.
Published: March 2011

The paper presents an exponentially fitted tetrahedral finite element method for the decoupled continuity equations in the drift‐diffusion model of semiconductor devices. This finite element method is based on a set of piecewise exponential basis functions constructed on a tetrahedral mesh. Error estimates for the approximate solution and its associated flux are given, where the error bounds depend on some first‐order seminorms of the exact solution, the exact flux and the coefficient function of the convection terms.
Spectral Schemes on Triangular Elements
Authors: Heinrichs W. , Loch B.
Published: March 2011

First we consider the Poisson Problem with homogeneous Dirichlet boundary conditions on a triangle. The mapping between square and triangle is realized by mapping an edge of the square onto a corner of the triangle. Then standard Chebyshev collocation techniques can be applied. Numerical experiments demonstrate the expected high spectral accuracy. Further, it is shown that finite difference preconditioning can be successfully applied in order to construct an efficient iterative solver. Finally, a domain decomposition technique is applied to the patching of rectangular and triangular elements.
Stabilized FEM with shock‐capturing for advection‐diffusion problems
Authors: Knopp T. , Lube G. , Rapin G.
Published: March 2011

Stabilized FEM of streamline‐diffusion type to advection‐diffusion problems may exhibit local oscillations in cross‐wind direction(s). As a remedy, a shock‐capturing variant is considered as an additional consistent (but nonlinear) stabilization. We present some preliminary results of the numerical analysis. The shock‐capturing method has been applied within the numerical solution of the k/e turbulence model of incompressible flow problems for the arising nonlinear advection‐diffusion problems.
The lid‐driven cavity revisited: Stability of two‐dimensional flow
Authors: Albensoeder S. , Kuhlmann H. C. , Rath H. J.
Published: March 2011

The lid‐driven cavity has been studied quite extensively both experimentally and numerically. Today it is the most wide‐spread benchmark problem in CFD. Despite this fact, the linear stability of the steady two‐dimensional flow has hardly been considered, not even for the square cavity. In the present study we revisit this classical problem and calculate the linear stability of the two‐dimensional flow with respect to three‐dimensional perturbations for various aspect ratios. The structure of the critical modes as well as the instability mechanism are addressed.
Stability of hydrothermal‐wave states
Authors: Leypoldt J. , Kuhlmann H. C. , Rath H. J.
Published: March 2011

The half‐zone model is investigated for unit aspect ratio, zero gravity, and Prandtl numbers Pr = 1.5 … 7 by numerical simulations. For thermocapillary Reynolds numbers Re > Rec, the 2D stationary flow is unstable to 3D travelling waves. In the simulations, standing waves can be generated slightly above Rec. It is found, that these states are unstable and decay into either a clock‐or a counter‐clockwise propagating wave. Amplitude equations are used to quantitatively describe the instability of the standing wave states and to estimate the range of Pr within which only travelling waves are stable.
Domain Optimization for the Navier‐Stokes Equations by an Embedding Domain Technique
Authors: Slawig Thomas
Published: March 2011

A class of domain optimization problems for the two‐dimensional stationary Navier‐Stokes equations is studied. An embedding domain technique provides an equivalent formulation of the problem on a fixed domain, a reduction of the computational effort for the solution of the state equations, and moreover a simply computable formula for the derivative of the cost functional with respect to the domain. Existence of a solution to the class of domain optimization problems is proved. Numerical examples show the reliability of the derivative formula.
Coherent Vortex Simulation (CVS) of two‐dimensional turbulence
Authors: Schneider Kai , Farge Marie
Published: March 2011

We present a new turbulence model to compute fully developed turbulent flows. The method is based on the solution of the wavelet filtered Navier‐Stokes equations in vorticity‐velocity formulation using an adaptive wavelet discretization. As application we present a Coherent Vortex Simulation (CVS) of a two‐dimensional mixing layer and compare the results with those obtained with Direct Numerical Simulation (DNS).
Settling velocity of porous particles using the particle‐in‐cell model
Authors: Zlatanovski T.
Published: March 2011

We extend the particle‐in‐cell model to the case of settling porous particles. The particle swarm is assumed to consist of identical unit cells each containing a porous particle surrounded by a fluid shell. The steady axisymmetric creeping flow in this multifield unit cell model is assumed to be governed by the Stokes equation in the fluid shell and the Brinkman equation in the porous particle. Analytical solutions for the case of porous‐sphere‐in‐cell and porous‐spheroid‐in‐cell model are obtained.
Konvektiver Wärmeübergang bei instationärer Anströmung
Authors: Mocikat H. , Pražák J. , Göppert St. , Herwig H.
Published: March 2011

Der Einfluss instationärer Strömungen, z.B. rotierender oder pulsierender Prallstrahlen, auf den Wärmeübergang an einer angeströmten Platte wird mit Hilfe gemessener Temperatur‐und Wärmestromfelder untersucht. Die Bewertung der Strömungsvarianten mit Wärmeübergangs‐Koeffizienten a bzw. Nußelt‐Zahlen Nu ist problematisch, weil α unstetig werden kann und die charakteristische Länge der Nu‐Zahl für verschiedenste Düsenkonstruktionen schlecht vergleichbar ist. Deshalb wird eine neue Auswertung mit Hilfe der Parameter “Leistung des Prallstrahls” sowie einer Effektivitäts‐Kennzahl E vorgestellt.
Upstream travelling waves in the boundary layer of a horizontal mixed convection flow
Authors: Steinruck H.
Published: March 2011

The propagation of small disturbances in a mixed convection boundary layer flow over a horizontal plate is considered. Employing an asymptotic analysis with respect to a small buoyancy parameter K = Gr/Re2 a triple deck structure of the perturbed flow field is found. Two effects contribute to the pressure perturbation in the lower deck: The displacement of the outer field and the buoyancy in the main deck. Linearizing the perturbation equations and taking the Fourier transform with respect to time and the coordinate parallel to the wall the dispertion relation is derived. Considering the case that the buoyancy induced pressure dominates the displacement induced pressure upstream travelling waves are found. These waves are confined to the boundary‐layer and exist only in the case of the flow over a cooled plate. Furthermore a stationary downstream growing mode exists which indicates that the solution of the boundary layer equations is not unique.
The Calculation of Velocity of Sound near the Liquid‐Gas Transition
Authors: Avsec J. , Marcic M.
Published: March 2011

The paper features the mathematical model of thermodynamic functions of state in gas‐liquid region for pure refrigerants with the help of classical thermodynamics and statistical thermodynamics. To calculate the thermodynamic properties of real fluid we used models on the base of Lennard‐Jones intermolecular potential.
Coating by Capillary Transport through Porous Media
Authors: Baumbach V. , Dreyer M. , Rath H. J.
Published: March 2011

A coating device which works with the help of a porous medium is considered. The fluid of interest is a surfactant solution which passes a porous medium before it is deposited on a solid substrate. A hydrostatic model for the process is proposed which assumes the validity of DARCY's law as well as an approach for slot coaters developed by Higgins and Scriven (1980). Emphasis will also be placed on the experimental determination of the porous media permeability and porosity. Moreover the model is compared with experimental results.
Neglect of the Fluid Extra Stresses in Volumetrically Coupled Solid‐Fluid Problems
Authors: Diebels S. , Ehlers W. , Markert B.
Published: March 2011

Usually the fluid flow through porous media is described by Darcy 's law or generalizations of it. In this contribution, Darcy 's law is derived from the theory of porous media. To archive this, the fluid extra stress (frictional stress) is neglected in comparision with the momentum exchange (drag force) between the fluid phase and the solid skeleton of a two‐phase model. This common assumption is motivated by the results obtained from a microscopic capillary model in combination with a dimensional analysis of the continuum mechanical model. This analysis shows that the influence of the fluid extra stress decreases with increasing number of capillary tubes per area element.
Mixing in two‐dimensional turbulent reactive flows
Authors: Gerlinger W. , Schneider K. , Bockhorn H.
Published: March 2011

Enhanced transport and mixing of scalars in turbulent flows are of major importance, in particular, when chemical time scales are smaller or of the same order as the the mixing time. We present direct numerical simulation of the mixing of passive and reactive scalars in two‐dimensional flows dominated by coherent vortices These organized structures have a significant impact on the mixing dynamics in turbulence. By means of a Fourier‐pseudospectral method the instationary equations are numerically integrated. To quantify the mixing, we consider statistical properties, i.e. the variance decay and histograms to approximate the probability density functions of the scalars. Also, the influence of a chemical reaction on mixing are investigated.
Structure and Extinction of Laminar Ethanol/Air Spray Flames
Authors: Gutheil E.
Published: March 2011

The paper presents the structure and extinction of both mono‐ and bidisperse ethanol/air spray flames in the counterflow configuration. A similarity transformation for monodisperse spray flames is extended to polydisperse spray flames, and the resulting one‐dimensional formulation accesses the use of detailed chemical reaction mechanisms as well as detailed transport. For the ethanol/air system, 38 species and 331 elementary reactions are used. At high strain, the droplets cross the gas stagnation plane, reverse and return towards their injector. For this situation, the width of the chemical reaction zone of bidisperse and monodisperse sprays with the Sauter mean radius is almost the same. However, the droplet oscillation causes the spray flame of the bidisperse spray to strongly increase the total spray flame thickness. For the injection velocity of the spray studied here, the droplets returning to their injector hit the boundary of the computational domain as strain is increased whereas the monodisperse spray flame extinguishs at a considerably higher value of gas strain rate. Thus, the extinction behavior of the bidisperse spray flame is not represented by the monodisperse spray flame with the Sauter mean radius. The model is also suitable to predict pollutant formation.
Some Recent Findings on Turbulent Diffusion Flames from DNS
Authors: Kai Luo
Published: March 2011

Direct numerical simulation (DNS) is a valuable tool for the study of complex interactions between turbulence and combustion, thanks to its ability to resolve the wide range of time and length scales involved. Its application in the fundamental study of turbulent diffusion flames has been particularly fruitful in recent years, which led to some new findings, improved understanding of known phenomena and the development of new theories and models. This paper is concerned with the effects of heat release from finite‐rate chemistry on compressible turbulence. The present DNS results reveal intricate interactions among combustion, turbulent transport and mixing.
Computing Virtual Mass by Direct Numerical Simulation
Authors: Niemann J. , Laurien E.
Published: March 2011

Bubbles resist acceleration with an apparent added mass. An improved knowledge of this virtual mass is desirable for accurate models of bubbly flows, for instance, in a two‐fluid‐model. A high‐resolution, two‐phase numerical code based on a volume‐of‐fluid method is used to compute the virtual mass of air and vapour bubbles in water. The dependency of virtual mass from void fraction is investigated. A well known analytically obtained equation of this dependency is confirmed and the hitherto undetermined quadratic term, which is of importance for medium and high void fractions, is established. A dependency on bubble size and shape is investigated.