bluuebunny/crossref_metadata_2025 huggingface dataset:
Stress and free vibration analysis of functionally graded beams using static Green's functions
Authors: Carl Oliver , Villamil Pedro , Zhang Chuanzeng
Published: December 2011

In this paper static Green's functions for functionally graded Euler‐Bernoulli and Timoshenko beams are presented. All material properties are arbitrary functions along the beam thickness direction. The closed‐form solutions of static Green's functions are derived from a fourth‐order partial differential equation presented in [2]. In combination with Betti's reciprocal theorem the Green's functions are applied to calculate internal forces and stress analysis of functionally graded beams (FGBs) under static loadings. For symmetrical material properties along the beam thickness direction and symmetric cross‐sections, the resulting stress distributions are also symmetric. For unsymmetrical material properties the neutral axis and the center of gravity axis are located at different positions. Free vibrations of functionally graded Timoshenko beams are also analyzed [3]. Analytical solutions of eigenfunctions and eigenfrequencies in closed‐forms are obtained based on reference [2]. Alternatively it is also possible to use static Green's functions and Fredholm's integral equations to obtain approximate eigenfunctions and eigenfrequencies by an iterative procedure as shown in [1]. Applying the Sensitivity Analysis with Green's Functions (SAGF) [1] to derive closed‐form analytical solutions of functionally graded beams, it is possible to modify the derived static Green's functions and include terms taking cracks into account, which are modeled by translational or rotational springs. Furthermore the SAGF approach in combination with the superposition principle can be used to take stiffness jumps into account and to extend static Green's functions of simple beams to that of discontinuous beams by adding new supports. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stabilized mixed triangular finite elements at large deformations using area bubble functions
Authors: Caylak Ismail , Mahnken Rolf , Widany Kai‐Uwe
Published: December 2011

In this paper stabilized mixed triangular finite elements are presented in order to avoid volume locking and to damp stress oscillations. Geometrically non‐linear elastic problems are addressed. The mixed method of incompatible modes and the mixed method of enhanced strains are considered as special cases. As a key idea, volume and area bubble functions are used for the method of incompatible modes and the enhanced strain method [1], thus giving both the interpretation of a mixed finite element method with stabilization terms. Concerning non‐linear problems these are non‐linearly dependent on the current deformation state, however, linearly dependent stabilization terms are used [1]. The approach becomes most attractive for the numerical implementation, since the use of quantities related to the previous Newton iteration step is completely avoided. The variational formulation for the standard two‐field method, the method of incompatible modes and the enhanced strain method in finite deformation problems is derived for a hyper elastic Neo‐Hookean material. In the representative example Cook's membrane problem illustrates the good performance of the presented approaches compared to existing finite element formulations. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Efficient Series Solutions for Shear Forces of Vibrating Thin Rectangular Plates on Elastic Foundation with Thermal Loads
Authors: Holl Helmut J. , Liu Wenqi
Published: December 2011

Simply supported rectangular Kirchhoff‐plates with two‐parametric Pasternak‐type foundation are studied under the action of a transient temperature moment, which is span‐wise constant. In extension to a previous study it can be shown, that an excellent convergence of the series solutions of the static problem can be achieved by means of Kummer's transformation and Cesaro's generalized C1‐Summation. The convergence improvement of the other types of the solutions can be performed analogously. The dynamic solution for the deflection and shear forces is computed using the derived efficient solution for the quasi‐static case with fast convergent Fourier series. Modal expansion is applied for the computation of the vibrations about this quasi‐static part. The results of he analytical solution for defined parameters of the foundation are shown for some characteristic points of the plate and compared to the FE computation results . (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Hilbert‐Huang transform based identification method for general linear time‐varying systems and weakly nonlinear systems
Authors: Hu Han , Proppe Carsten
Published: December 2011

This paper proposes an identification method for general linear time‐varying (LTV) MDOF systems and weakly nonlinear systems based on the Hilbert‐Huang Transform (HHT)[1]. The proposed method uses Empirical mode decomposition (EMD) to decompose the response signals of systems into intrinsic mode functions (IMFs) and residues, and then analyzes the IMFs and the residues by Hilbert transform (HT) to obtain the analytical IMFs and analytical residues. After that, the above signals are synthesized to form new response signals and new analytical response signals. Finally, the new synthesized signals are used to identify the stiffness and damping coefficients of the systems. Three types of variation: smooth, abrupt and periodical variations are considered in the numerical simulations of LTV chainlike[2] and nonchainlike systems as well as weakly nonlinear systems such as Duffing oscillators and Van der Pol oscillators with white noise added in the system responses to demonstrate the effectiveness, accuracy and robustness of the proposed method. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Effects of Damping Mechanisms in Free and Forced Vibrations of Some Structural Members
Authors: Pham Thanh Chung , Wauer Jörg , Seemann Wolfgang
Published: December 2011

For continuous vibrating systems, such as bars and beams, end‐mounted in the environment, knowledge about the mass, damping and stiffness properties of the resonating environment is important for analyzing free and forced vibrations of such structural members which are also damped themselves. To finally get an identification of the clamping parameters, examinations of both vibrating structural members for various restraint conditions and dynamic interaction with viscoelastic halfspaces, etc., are required. As a first step, longitudinal bar vibrations are studied in detail. The method of separation of variables combined with the reformatted orthogonality relation, and numerical integration is applied for calculating the free and forced oscillations. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Shear strength of webs with holes
Authors: Schröder Kai‐Uwe
Published: December 2011

In lightweight design the webs of beams which are loaded by bending are often provided with holes. Aim of this article is to present a method to calculate the shear strength of webs with certain holes. The semi‐analytical method is derived with respect to the results of geometrically and physically non‐linear numerical simulations in which the shear strength of the web is calculated. The method consists of a plastic failure approach for rather thick webs and a framework analogy to model the failure of a solid web after onset of buckling. To take the influence of the holes into account the shear strength of the solid web is reduced as a function of geometry parameters. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Buckling of a non‐Euclidean annular plate
Authors: Schwarzbart Michael , Steindl Alois
Published: December 2011

The effect of free edges of a monoatomic graphene sheet leads to excess edge energy due to the reconstruction of dangling bonds. Molecular static calculations show, that individual carbon atoms near the edge are displaced out of plane for relaxed nanoribbons [1]. In this work we are considering the effect of excess edge energy for almost circular graphene patches. To tackle this problem in the framework of continuum mechanics we are modelling the edge effect with a non‐Euclidean plate model. A linear stability analysis of the flat configuration leads to the stability boundary in the parameter plane. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Structural health monitoring of hybrid composite structure with piezoelectric patches
Authors: Zemčík Robert , Kroupa Tomás̆ , Bartos̆ek Jan
Published: December 2011

Structural health monitoring is performed on a hybrid structure specially designed for simple assembly and disassembly or replacement of components. The net‐like structure is composed of composite beams connected with aluminum pads and it is fixed to a frame in selected locations. Modal analysis is performed both experimentally and numerically. The experiment is carried out using impact hammer, accelerometer and spectrum analyzer and the frequency and damping characteristics are thus obtained. The numerical model using finite element method is validated by comparison of the calculated and measured eigenfrequencies and eigenshapes. Furthermore, piezoelectric patches are applied on selected beam. The modal analysis is carried out again using the piezoelectric patches and with some of the composite beams replaced by damaged beam. The variation in modal characteristics between original and damaged configurations is analyzed both experimentally and numerically. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Chaotic nonlinear dynamics of cantilever beams under the action of signs‐variables loads
Authors: Krysko A. V. , Koch M. I. , Yakovleva T. V. , Nackenhorst U. , Krysko V. A.
Published: December 2011

In this study we investigate the nonlinear chaotic dynamics of structures, consisting of three contacting isotropic Euler‐Bernoulli beams under alternating transverse load. The beams are connected to each other via weak contact conditions. Geometric as well as physical nonlinearity and contact interaction between the beams are taken into account. A new method was proposed for the analysis of chaotic phase synchronization for the multilayered construction consisting of three titanium beams by using Morlet wavelets. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Rotation of an axisymmetric particle in a plane flow
Authors: Renner Barbara , Altenbach Holm , Naumenko Konstantin
Published: December 2011

The rotation of an inertialess ellipsoidal particle in a shear flow of a Newtonian fluid has been firstly analyzed by Jeffery [1]. He found that the particle rotates such that the end of its symmetry axis describes a closed periodic orbit. Based on the balance equation of the angular momentum we derived the equation of rotational motion of a cylindrical particle, that is suspended in a plane shear flow field of a viscous fluid, and solved numerically. The rotary inertia is taken into account. The solution is compared with the rotation of a slender particle. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A comparison between elastohydrodynamic and dry hertzian line contacts with regard to their nonlinear vibration behaviour
Authors: Wiegert Benedikt , Hetzler Hartmut , Seemann Wolfgang
Published: December 2011

The nonlinear dynamic behaviour of a simple system employing two different types of contact is compared: elastohydrodynamic line contact and Hertzian line contact with appropriate damping. The elastohydrodynamic problem is solved with finite elements. For the Hertzian line contact problem an analytical solution is known.

It is found that for highly loaded cases Hertzian and elastohydrodynamic contacts lead to very similar frequency response curves. This means that instead of solving the computational expensive elastohydrodynamic problem the Hertzian contact can be used. However, considering weakly loaded contacts the two types of contact show very different behaviour. In particular the natural frequencies are different and the elastohydrodynamic contact exhibits rich nonlinear dynamic behaviour including jump phenomena as well as sub‐ and superharmonic bifurcations. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Hysteresis Behaviour of 51CrV4 and Viscoplastic Modeling Aspects
Authors: Al‐Baldawi Ammar , Schreiber Lothar , Wünsch Olaf
Published: December 2011

In this work we investigate the material behaviour of steel 51CrV4 in classical uniaxial strain controlled tension tests of different strain rates interposed by relaxation steps, in which the equilibrium stress observed is significantly smaller than the stresses seen in slowest strain rate test. Also, some cyclic experiments with different strain rates and amplitudes were done to analyze the hysteresis behaviour of the material. Against this background of experimental data the modeling possibilties of two models are explored: the Lion model and the Chaboche model with kinematic hardening ansatz. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A novel constitutive law for Silicon under contact loading
Authors: Budnitzki Michael , Kuna Meinhard
Published: December 2011

Silicon (Si) remains the most important semiconductor material to date. The understanding of its deformation behavior under contact (indenter‐) loading is crucial to improving technologically relevant abrasive machining techniques (lapping, sawing, grinding). While it has been long established that Si undergoes a series of stress driven phase transitions upon compression and subsequent pressure release, to the authors' knowledge, no material model is available that adequately captures this behavior. In particular, reverse transformation in unloading has received too little attention. A novel phenomenological, thermomechanical model based on experimental observations and MD predictions is presented in this work. It captures both the cd‐Si → β‐Si transition upon compression and the β‐Si → a‐Si transition upon rapid decompression, which are most relevant for indenter loading. To control inelasticity in unloading, the dissipation function was augmented by a kinematic constraint on the tensorial internal variable. In stress space, the transformation surfaces are hyperboloids of revolution aligned along the hydrostatic axis. The non‐linear model was numerically implemented in a finite element code using an iterative implicit algorithm and successfully applied to simple loading cases. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application of the Green Tensor to the Modeling of Solution‐Precipitation Creep
Authors: Günther Christina , Ilic Sandra , Hackl Klaus
Published: December 2011

Our aim is to present a mechanical model for solution‐precipitation creep, a diffusive deformation process occurring in polycrystalline and granular materials. Within the scope of the model, a Lagrangian consisting of the elastic power and dissipation is proposed. The former is kept in a standard form typical for linear material behavior while the latter is assumed as a surface integral depending on the velocity of the material transport and the velocity of the motion of the boundary. The minimization with respect to the total deformations leads to the equilibrium equation which is solved analytically, by using Green's function. The evolution equations are obtained as the result of the minimization with respect to the internal variables and are solved via finite element method. The contribution closes with a numerical example showing the deformation of a polycrystal consisting of hexagonal crystals. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Towards the simulation of grinding processes – a thermoplastic single grain approach
Authors: Holtermann Raphael , Menzel Andreas , Hortig Christian , Svendsen Bob
Published: December 2011

The current work aims at the modelling and simulation of metal grinding processes with focus on the thermal behaviour resulting from the interaction of tool and workpiece. Starting from a two‐dimensional model of a single grain, representative numerical experiments are carried out based on the variation of grain geometry and its spatial position relative to the workpiece to predict the resulting load‐displacement‐behaviour.

Here, a thermoelastic viscoplastic constitutive model is used to capture thermal softening of the material taken into account. Referring to previous research, an adaptive remeshing scheme, based on a combination of error estimation and refinement indication is used to overcome mesh dependence, allowing to resolve the complex deformation patterns and to predict a realistic thermomechanical state of the resulting workpiece surface. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Zur Modellierung von Aushärtevorgängen in Polymeren unter Verwendung von Stoffgesetzen der Viskoelastizität und Viskoplastizität
Authors: Landgraf Ralf , Ihlemann Jörn
Published: December 2011

Polymere finden ein breites Anwendungsgebiet sowohl im Ingenieurbereich als auch in weiteren Disziplinen, wie zum Beispiel der Medizintechnik. Neben einer Vielzahl von Anwendungen für kunststofftechnische Bauteile spielen Polymere ebenso als Füge‐, Füll‐ oder Dichtwerkstoffe eine große Rolle. Als Beispiele seien Klebeverbindungen oder der Einsatz von akrylischen Knochenzementen (PMMA) in der Medizin genannt. Ein phänomenologischer Ansatz zur Modellierung der Aushärtung solcher Werkstoffe geht zurück auf Lion und Höfer (2007). Auf Grundlage des bestehenden Ansatzes werden unterschiedliche mechanische Teilstoffgesetze zur Abbildung der mechanischen Eigenschaften untersucht und in das bestehende Konzept eingearbeitet. Hierbei kommen Stoffgesetze der Viskoelastizität und Viskoplastizität bei großen Deformationen zum Einsatz. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Micromechanical creep model for pure copper
Authors: Ozhoga‐Maslovskaja Oksana , Altenbach Holm , Naumenko Konstantin , Prygorniev Oleksandr , Vodka Oleksii
Published: December 2011

A Unit Cell made of copper is simulated and investigated under creep conditions within the framework of micromechanics. Geometrical 3D model of the copper microstructure is represented as a Unit Cell with grains of random crystallographical orientation and geometry. Such simulation enables algorithm of Voronoi tessellation. The stress‐strain behavior of grains in the general case is anisotropic due to the ordered crystalline structure. The anisotropic model for a material with a cubic symmetry is implemented in Abaqus and used to assign behavior of grain interior in elastic and creep regions. Material parameters for elastic model are taken from elastic tests of single crystal copper [1]. Power law material parameters for creep model are taken from creep test performed for single crystal copper [2]. The model parameter ξ is validated numerically. Creep results are presented for the case of proportional loading during the primary and secondary creep. Statistical analysis of creep curves received for 55 different realizations of Unit Cell geometry is carried out. As a result confident interval and mathematical expectation of creep data are calculated. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A constitutive model for a high alloyed cast CrMnNi TRIP‐steel
Authors: Prüger Stefan , Kuna Meinhard
Published: December 2011

The macroscopic material model, proposed by Papatriantafillou [1], is adopted to describe the rate dependent flow behaviour and the temperature and stress state dependent γ‐α′ phase transformation of a newly developed cast TRIP‐steel. Simple test of the implemented model revealed that the evolution of the martensite volume fraction is not predicted correctly in case of inelastic deformation and subsequent unloading. Therefore, we present an improved model for the γ‐α′ phase transformation and show that these predictions are due to the choice of the corresponding thermodynamical driving force. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Comparison of different distortional hardening models suitable for the analysis of magnesium
Authors: Shi Baodong , Mosler Joern
Published: December 2011

HCP metals such as magnesium are characterized by a strong interplay between dislocation slip and deformation‐induced twinning. These micromechanical processes result in a complex macroscopic behavior. More precisely, in addition to classical isotropic and kinematic hardening, the shape of the macroscopic yield function changes during deformation as well. This effect which is frequently referred to as distortional hardening is particularly pronounced in case of non‐radial loading paths typical for most forming processes. Consequently, a physically sound distortional hardening is of utmost importance for several technically relevant applications. In the present contribution, three different of such enhanced hardening models are critically analyzed. Focus is on the modeling of magnesium. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the simulation of nonlinear hardening in metallic materials using the concept of representative directions
Authors: Shutov Alexey , Freund Michael , Ihlemann Jörn
Published: December 2011

We generalize a uniaxial model of finite strain viscoplasticity using the concept of representative directions. As a result, a new phenomenological material model is obtained, which can describe the mechanical behavior under arbitrary loading conditions. The original uniaxial model takes the nonlinear isotropic and kinematic hardening into account, but it does not cover the distortional hardening. We show that the isotropic and kinematic hardening is completely retained during the process of generalization. Moreover, the distortional hardening effects are naturally induced by the concept. The resulting material model is validated by a comparison with real experimental data. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Boundary value problems of steady vibrations in the theory of thermoelasticity with microtemperatures
Authors: Svanadze Merab
Published: December 2011

In this paper the linear theory of steady vibrations of thermoelasticity with microtemperatures for isotropic solids with microstructure is considered. The uniqueness and existence theorems of solutions of the internal and external second boundary value problems (BVPs) by means of the boundary integral method (potential method) and the theory of singular integral equations are proved. The existence of eigenfrequencies of the internal homogeneous BVP of steady vibrations is studied. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stability of the mixed time partitioning methods in relation to the size of time step
Authors: Gawronska Elzbieta , Sczygiol Norbert
Published: December 2011

In this paper we focus on stability of a mixed time partitioning methods in relation to time step size which is using in numerical modelling of two‐component alloys solidification. We present the numerical integration methods to solve solidification problems in a fast and accurate way. Our approach exploits the fact that physical processes inside a mould are of different nature than those in a solidifying cast. As a result different time steps can be used to run computations within both sub‐domains. Because processes that are modeled in the cast sub‐domain are more dynamic they require very fine‐grained time step. On the other hand a heat transfer within the mould sub‐domain is less intense, and thus coarse‐grained step is sufficient to guarantee desired precision of computations. We propose using a fixed time step in the cast and its integer multiple in other parts of mould. We use one‐step explicit and implicit time integration Θ schemes. These time integration schemes are applied to equations obtained after spatial discretization. The implicit scheme is unconditionally stable, but stability of the explicit scheme depends on the size of time step. Critical time step size can be determined on the basis of eigenvalues of the amplification matrix that depend on the material properties, size and type of the finite element. In this work we present the manner of determining the critical time step and its affect on the course of numerical simulation of solidification. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Direct numerical simulation of particles in a fluid interacting with a wall
Authors: Lechner Christiane , Kuhlmann Hendrik C.
Published: December 2011

We develop a code to be applied in the context of the cleaning of wafer surfaces by hydrodynamic forces. Our goal is to study the detachment of (submicron) particles, exposed to a shear flow, from a wall by means of direct numerical simulation. The particles are treated as rigid bodies fully interacting with the fluid.

To simulate moving particles in the fluid we implement an immersed boundary method with direct forcing into OpenFOAM. The particle‐wall interaction is treated with a soft contact model. As first simple examples we study the elastic normal impact of a cylinder onto a wall as well as the onset of sliding of a cylinder pressed to a horizontal wall by gravity under a time‐depended drag force. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Finite element solution of the Kohn‐Sham equations
Authors: Schauer Volker , Linder Christian
Published: December 2011

Many properties of condensed matter as for example electric conductivity, magnetism as well as the mechanical response upon external excitations are determined by the electronic structure of the material. Its evaluation represents a coupled, quantum mechanical many body problem, consisting of the positively charged atomic cores and the negatively charged, fermionic electrons. By the Hohenberg‐Kohn theorem a method was established to calculate the ground state electron density through a density functional. Then the Kohn‐Sham equations resemble a nonlinear, single electron problem with an effective potential, accounting for the Coulomb interactions between the particles as well as for quantum mechanical effects. They can be solved within a self consistent field procedure. In this work a real space formulation for the calculation of the electronic structure in the context of density functional theory is shown. In a first step a finite element based solution algorithm for the Kohn‐Sham equations is developed, based upon which the electron density is obtained in a non‐periodic setting. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the Reconstruction and Computation of Dual‐Phase Steel Microstructures Based on 3D EBSD Data
Authors: Brands Dominik , Schröder Jörg , Balzani Daniel , Dmitrieva Olga , Raabe Dierk
Published: December 2011

In this contribution we reconstruct the three dimensional microstructure of a dual‐phase steel based on the tomographic experimental data provided by the 3D electron backscatter diffraction (3D EBSD) method. The cross sections of the resulting microstructure are compared to the 2D reconstruction, which are obtained directly from the 3D EBSD data. We also perform FE‐simulations based on these geometries and observe comparable results in 2D and 3D. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Hybrid Micro‐Macro‐Modeling of Evolving Anisotropies and Length Scales in Finite Plasticity of Polycrystals
Authors: Frankenreiter Ilona , Rosato Daniele , Miehe Christian
Published: December 2011

The paper focuses on an efficient multiscale approach to the description of evolving anisotropies in polycrystals. The predictive description of complex overall effects needs multiscale methods, taking into account basic ingredients of the material microstructure by model‐inherent scale‐bridging techniques. Straightforward homogenization‐based multiscale methods, such as FEM2 type two‐scale bridgings, are too time consuming for the solution of real engineering problems. A computationally manageable approach is provided by hybrid micro‐macro‐modeling techniques, which combine a purely macroscopic modeling with selected microstructural bridging techniques. Of particular importance are crystal reorientation mechanisms, which cause texture‐based anisotropies at the macroscale. The coupling is realized by homogenization‐based definitions of macroscopic structural tensors, which account for the evolving orientation texture. A crucial aspect is the combination of this hybrid texture modeling with further anisotropy effects, caused by dislocation‐structures. They are mainly responsible for hardening effects related to changes of the strain path. Furthermore, a particular account is taken on size effects and length scales by embedding the hybrid modeling technique into an extended theory of gradient‐plasticity. This results in a computationally efficient hybrid two‐scale model for polycrystalline plasticity, whose capability is demonstrated by means of representative benchmarks. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Effective elastic properties of 3D polypropylene microstructures of an injection moulded plate via different homogenization schemes
Authors: Laschet Gottfried , Baranowski Thomas , Kashko Tanya , Arping Tim
Published: December 2011

The mechanical properties of a polypropylene (PP) part depend on its morphology and degree of crystallinity. To evaluate its effective elastic behaviour two upscaling schemes are developed and compared. In the 1st method the spherulites are assumed to be isotropic and vary linearly with the spherulite diameter. In the 2nd one, the homogenization is performed successively on two scales. At the nanoscale, the bilamina of amorphous and crystalline phases is homogenized. Then, at the microscale, a 3D radial distribution of effective bilamina is homogenized. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonlinear stability characteristics of the pressure‐gradient driven flow between walls in a rotating system under the influence of the Coriolis force
Authors: Khan Muhammad Ijaz , Vasanta Ram Venkatesa
Published: December 2011

The paper addresses the question of the disturbance propagation when the plane channel flow on a rotating system is under the influence of the Coriolis force. The problem is approached through the method of Stewartson and Stuart (1971) to handle bifurcation characteristics. It starts from solving the linear (eigenvalue) problem and extends the same to handle growing distubances in the vicinity of the neutral surface. Solution for the problem addressed over the range of flow parameters characterised by the dominant physical mechanism affecting transition, viz. the Tollmien‐Schlichting mechanism or the Coriolis force mechanism, will be presented.. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A mixed least‐squares formulation of the Navier‐Stokes equations for incompressible Newtonian fluid flow
Authors: Schwarz Alexander , Schröder Jörg
Published: December 2011

The goal of this contribution is the numerical simulation of Newtonian fluid flow. In order to solve the governing incompressible Navier‐Stokes equations, a mixed finite element based on a least‐squares formulation is presented. We derive a div‐grad first‐order system resulting in a three‐field approach with stresses, velocities, and pressure as unknowns, see e.g. Cai et al. [1], which is the basis for the associated minimization problem. Finally, a numerical example is presented to show the applicability and performance of the considered formulation. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Inflow Treatment for the Simulation of Subsonic Jets with Turbulent Nozzle Boundary Layers
Authors: Bühler S. , Kleiser L.
Published: December 2011

The state of the boundary layer at the nozzle exit of a circular nozzle‐jet configuration has an important influence on the development of the shear layer and the emitted sound. Of special interest is the acoustic near‐field obtained when the nozzle exit boundary layer is fully turbulent. The turbulent inflow generation and the inflow boundary treatment are important issues to be addressed. We use the Synthetic Eddy Method (SEM) to generate a turbulent inflow which reproduces mean flow and Reynolds stress profiles of specified reference data. The spatially and temporally varying synthetic fluctuations are imposed in the simulation by a forcing term added to the governing equations which is active in a small region downstream of the inflow boundary. This forcing in combination with characteristic boundary conditions allows for passing of upstream‐propagating acoustic waves and avoids an uncontrolled drift of mean‐flow quantities. We employ this inflow boundary treatment for a subsonic nozzle‐jet flow simulation at a Reynolds number of ∼ 9500 and Mach number of 0.9. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Thermocapillary flow on a gas‐liquid surface under normal and reduced gravity
Authors: Heiland Hans Georg , Schade Klaus‐Peter , Wozniak Günter
Published: December 2011

The aim of the present work is the study of the thermocapillary flow phenomenon at 1‐g, μ‐g conditions and the transition between 1‐g and μ‐g. The experimental results were observed with a novel high speed imaging system using a combination of a monochrome high speed CCD camera and a liquid crystal tunable filter. The flow velocity and the temperature patterns could be measured simultaneously from the seeded thermochromic liquid crystals, which change colour depending on their temperature. We investigated the thermocapillary flow with an experimental setup, where a bubble is positioned in a liquid matrix under a heated wall. The µ‐g experiments were conducted in the drop tower of the ZARM‐Institute of the University of Bremen. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Efficiency of a DC magnetic field used for braking the flow within a continuous casting mould
Authors: Miao Xincheng , Timmel Klaus , Eckert Sven , Lucas Dirk , Gerbth Gunter
Published: December 2011

The continuous casting technology provides about 90 percent of the world steel production. The application of DC magnetic fields in form of so‐called electromagnetic brakes is considered for an effective flow control with substantial capabilities to improve the product quality or to enhance the productivity of the process. The main effect of the DC magnetic field is supposed to result in a uniform reduction of the maximum velocities in the discharging jet from the submerged entry nozzle and to damp violent turbulent fluctuations. However, the electromagnetic braking of such highly turbulent and complex flows is complicated phenomenon and has not been understood fully until now. We present numerical and experimental investigations focusing on the fluid flow in the continuous casting mould under the influence of a transverse magnetic field. Numerical calculations were performed using the software package CFX with an implemented RANS‐SST turbulence model. the non‐isotropic nature of the MHD turbulence was taken into account by specific modifications of the turbulence model. Corresponding experimental investigations were carried out at the mock‐up LIMMCAST at HZDR. The comparison between our numerical calculations and the experimental results display a very well agreement. An important outcome of this study is the feature that the magnetic field does not provide a continuous reduction of the velocity fluctuations at the nozzle port. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Phase resolved measurements of the statistical flow behavior of a backward‐facing step flow controlled by a sinusoidal Lorentz‐force
Authors: Neumann Mathias , Büttner Lars , Weier Tom , Czarske Jürgen
Published: December 2011

In order to gain deeper inside into the behavior of a Lorentz‐force controlled flow behind a backward‐facing step, measurements with a laser Doppler velocity profile sensor were undertaken. By varying the frequency of the sinusoidal Lorentz‐force the influence on the turbulence statistics was studied. Moreover, phase resolved measurement data is presented. The results confirm the characteristic frequency determined on basis of the momentum thickness beforehand. The aim of this study is to understand the influence of the different incitation signals and to reduce the reattachment length. The statistical results show a dependency of the turbulence degree on the excitation frequency as well as a deformation of the flow profile behind the step. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Divergence of a thin elongated plate in supersonic gas flow
Authors: Boris Loginov , Tatyana Badokina , Youri Rousak
Published: December 2011

Buckled forms of a thin elastic flexible elongated plate lying on elastic base in supersonic gas flow are computed by bifurcation theory methods. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Selection of minimizers for one‐dimensional Ginzburg‐Landau functional with 3‐well potential by singular lower‐order term
Authors: Raguž Andrija
Published: December 2011

We consider a variant of the Ginzburg‐Landau type functional in one dimension with 3‐well potential, penalized by lower‐order term which has singularity in one of the zeros of the potential function. Based on the approach developed in the paper G. Alberti, S. Muller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54, 761‐825 (2001), we obtain Gamma‐convergence and provide description of the minimizers as small parameter epsilon tends to zero. We show that introduction of singular lower‐order term results in appropriate selection of the minimizers. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Explicit solution of the boundary value problem of the theory of thermoelasticity with microtemperatures for elastic circle
Authors: Tsagareli Ivane , Svanadze Maia M.
Published: December 2011

In this paper we solve explicitly, by means of absolutely and uniformly convergent series, the 2D boundary value problem (BVP) of statics of the linear theory of thermoelasticity with microtemperatures for an elastic circle. The uniqueness theorem of the internal BVP is proved. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A time optimal control problem for the collision‐free robot motion planning
Authors: Landry Chantal , Gerdts Matthias , Henrion René , Hömberg Dietmar
Published: December 2011

A time optimal control problem for the computation of the fastest collision‐free trajectory of a robot surrounded by obstacles is presented. The dynamics of the robot is governed by ordinary differential equations. To build the collision avoidance criterion, the robot and the obstacles are represented as finite unions of convex polyhedra. Each polyhedron is described by a system of linear inequalities. This description combined with linear programming arguments allows us to include the collision avoidance as linear state constraints in the optimal control problem. The resulting system is then solved by a sequential quadratic programming method. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Differentiable evaluation of objective functions in sampling design with variance‐covariance matrices
Authors: Mommer Mario S. , Sommer Andreas , Schlöder Johannes P. , Bock H. Georg
Published: December 2011

In this short note we consider the differentiable evaluation of the objective function of the sampling design optimization problem based on the inverse of the Fisher information matrix, and where the integer design variables have been converted into real variables using a relaxation technique. To ensure differentiability and cover the full range of the variables, and thus improve the convergence behavior of derivative‐based optimization algorithms, we propose applying a Cholesky decomposition on the Fisher information matrix, but using a special higher precision floating point arithmetic to ensure stability. While each evalu‐ation of the functional becomes slower, the algorithm is much simpler, amenable to be used with automatic differentiation directly, and can be shown to be very stable. For many practical situations, this is a valuable trade‐off. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Symmetric Exchange of Variables and Stepwise Regression Methods
Authors: Niessner Herbert
Published: December 2011

A step in Gauss‐Jordan elimination may be seen as exchanging a dependent variable for an independent one. If at the same time one of them changes sign a symmetric system matrix remains symmetric with the pivot reversing sign [2]. This variant can efficiently be exploited inverting symmetric positive definite matrices but also for obtaining a most complete set of relevant statistical quantities in stepwise regression via normal equations proposed by Efroymson 1960 and improved by Breaux 1968. We compare this method with numerically more stable ones applying orthogonal transformations, in particular that of Eldéen 1972 using Householder transformations and that of Gragg‐LeVeque‐Trangenstein 1979 using modified Gram‐Schmidt. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Convergent geometric integrator for the Landau‐Lifshitz‐Gilbert equation in micromagnetics
Authors: Goldenits Petra , Praetorius Dirk , Suess Dieter
Published: December 2011

We consider a lowest‐order finite element scheme for the Landau‐Lifshitz‐Gilbert equation (LLG) which describes the dynamics of micromagnetism. In contrast to previous works, we examine LLG with a total magnetic field which is induced by several physical phenomena described in terms of exchange energy, anisotropy energy, magnetostatic energy, and Zeeman energy. In our numerical scheme, the highest‐order term which stems from the exchange energy, is treated implicitly, whereas the remaining energy contributions are computed explicitly. Therefore, only one sparse linear system has to be solved per time‐step. The proposed scheme is unconditionally convergent to a global weak solution of LLG. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Total Variation Diminishing Implicit Runge‐Kutta Methods for Dissipative Advection‐Diffusion Problems in Astrophysics
Authors: Happenhofer Natalie , Koch Othmar , Kupka Friedrich , Zaussinger Florian
Published: December 2011

We investigate the properties of dissipative full discretizations for the equations of motion associated with models of flow and radiative transport inside stars. We derive dissipative space discretizations and demonstrate that together with specially adapted total‐variation‐diminishing (TVD) or strongly stable Runge‐Kutta time discretizations with adaptive step‐size control this yields reliable and efficient integrators for the underlying high‐dimensional nonlinear evolution equations. For the most general problem class, fully implicit SDIRK methods are demonstrated to be competitive when compared to popular explicit Runge‐Kutta schemes as the additional effort for the solution of the associated nonlinear equations is compensated by the larger step‐sizes admissible for strong stability and dissipativity. For the parameter regime associated with semiconvection we can use partitioned IMEX Runge‐Kutta schemes, where the solution of the implicit part can be reduced to the solution of an elliptic problem. This yields a significant gain in performance as compared to either fully implicit or explicit time integrators. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of Multiphase Flows with Strong Shocks and Density Variations
Authors: Nowakowski Andrzej F. , Jolgam Shaban A. , Ballil Ahmed R. , Nicolleau Franck C.G.A.
Published: December 2011

The system of extended Euler type hyperbolic equations is considered to describe a two‐phase compressible flow. A numerical scheme for computing multi‐component flows is then examined. The numerical approach is based on the mathematical model that considers interfaces between fluids as numerically diffused zones. The hyperbolic problem is tackled using a high resolution HLLC scheme on a fixed Eulerian mesh. The global set of conservative equations (mass, momentum and energy) for each phase is closed with a general two parameters equation of state for each constituent. The performance of various variants of a diffuse interface method is carefully verified against a comprehensive suite of numerical benchmark test cases in one and two space dimensions. The studied benchmark cases are divided into two categories: idealized tests for which exact solutions can be generated and tests for which the equivalent numerical results could be obtained using different approaches. The ability to simulate the Richtmyer‐Meshkov instabilities, which are generated when a shock wave impacts an interface between two different fluids, is considered as a major challenge for the present numerical techniques. The study presents the effect of density ratio of constituent fluids on the resolution of an interface and the ability to simulate Richtmyer‐Meshkov instabilities by various variants of diffuse interface methods. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On Analytical Results for the Optimal Control of the quasi‐stationary Radiative Heat Transfer System
Authors: End Thomas
Published: December 2011

We state an optimal control problem of the coupled quasi‐stationary radiative heat equations consisting of the radiative transfer equation and the instationary heat transfer equation that model radiative‐conductive heat transfer. We give an existence and uniqueness result for the state equations and the adjoint equations of the quasi‐stationary radiative heat transfer system. For the optimal control problem the existence of a minimizer is proven. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Homogenization approach for optimal design of perforated layer in acoustic wave propagation
Authors: Rohan Eduard , Lukeš Vladimír
Published: December 2011

Homogenization provides a reduced model of the acoustic wave propagation through a periodically perforated layer immersed in an inviscid fluid. The shape of the perforation influences some parameters of the non‐local transmission condition. We developed and implemented numerically the sensitivity analysis for an optimal design of the perforation. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Pointwise numerical index determination of unstructured DAEs
Authors: Lamour René
Published: December 2011

The index of a DAE is a measure of the expected difficulties arising when solving it. The tractability index concept determines the index without knowing any solution. It is based on a matrix sequence with matrices of the same dimension as the DAE under consideration. For the numerical realization of the matrix sequence it is advantageous to use so‐called widely orthogonal projectors and to compute derivatives by means of algorithmic differentiation (AD) because of the higher accuracy. The presented method of numerical index determination may become a basic component on the way to a robust index monitor. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Characteristics of LTI descriptor systems
Authors: Müller Peter C.
Published: December 2011

Linear time‐invariant (LTI) descriptor systems Eẋ = Ax + Bu with regular matrix pencils λ(E − A) may be separated by an equivalence transformation into a “slow” and a “fast” subsystem. The consistent solution of the fast subsystem can be presented by the input u and its time‐derivatives. If these time‐derivatives appear explicitly, then the system behaviour is called improper, otherwise it is proper or even strictly proper. This contribution deals with the determination of the related characteristics based on the matrices E, A, B without applying the equivalence transformation: Index k, orders n1, n2 of the subsystems (n1 + n2 = n), (strictly) proper and improper transfer behaviour, degree of improperness of each individual input. These characteristics are calculated by rank conditions of suitable matrices composed of E, A, B. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)