bluuebunny/crossref_metadata_2025 huggingface dataset:
A constitutive model for shape memory alloy fibres and its applicability to prestressed composites
Authors: Kohlhaas Benedikt , Klinkel Sven
Published: December 2011

This contribution is concerned with a constitutive model for shape memory fibres. The 1D‐constitutive model accounts for the pseudoplastic and shape memory effect (SME). The macroscopic answer of the material is determined by the evolution from a twinned martensitic lattice into a deformed and detwinned one. On the macroscopic scale these effects are responsible for the upper boundary of the hysteresis which is situated around the origin of the stress‐strain‐diagram. During the phase transition process inelastic strains arise. When the lattice is fully detwinned, a linear elastic branch at the end of the hysteresis is observed. The initial state of the material is recovered by unloading and heating the material subsequently. The constitutive model is derived from the Helmholtz' free energy and fulfils the 2nd law of thermodynamics. For the present model five internal state variables are employed. Two of them are used to describe the inelastic strain and a backstress. The others represent the martensitic volume fraction and are necessary to describe the SME. The latter variables are depending on the deformation state as well as on temperature. A change on temperature goes along with a reduction of the inelastic strain. The model is incorporated in a fibre matrix discretization to prestress the surrounding structure. The boundary value problem is solved for a truss element applying the finite element method. Examples will demonstrate the applicability in engineering structures. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Geometrically Nonlinear Continuum Thermomechanics with Surface Energies Coupled to Diffusion
Authors: McBride Andrew , Steinmann Paul , Javili Ali , Bargmann Swantje
Published: December 2011

Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad‐hoc manner. This work briefly describes a thermodynamically consistent, nonlinear, continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
FE2 Modelling of Hybrid Sandwich Composites
Authors: Chambon Cécile , Diebels Stefan
Published: December 2011

This paper presents a procedure to simulate the behaviour of a sandwich composite material. The classical solution to model this kind of structure is the plate theory. Nevertheless, because of the incapacity to take non‐linear material behaviour into account, this method cannot be used to model our problem. Indeed, the sandwich structure contains metallic layers, and their behaviour is elasto‐plastic. For these reasons, a numerical homogenisation will be presented. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Energy‐Minimization in Atomic‐to‐Continuum Scale‐Bridging Methods
Authors: Eidel Bernhard , Stukowski Alexander , Schröder Jörg
Published: December 2011

The focus of this contribution is on a novel, improved technique for energy minimization in atomic simulations and its adaption to a variationally consistent formulation of the quasicontinuum (QC) method. The optimization algorithm called FIRE for Fast Inertial Relaxation Engine can be understood as a modification of the Steepest Descent (SD) method, which improves SD by accelerating the system in the direction of the force, making the minimization more aggressive. The performance of FIRE is assessed in a representative example against well‐established optimization methods with respect to efficiency and stability. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multiscale Modeling of Nanocrystalline Materials: A Variational Approach
Authors: El Sayed Tamer , Gürses Ercan
Published: December 2011

This paper presents a variational multi‐scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc‐material is modeled as a two‐phase material consisting of a grain interior (GI) phase and a grain boundary (GB) phase. A rate‐independent isotropic porous plasticity model is employed to describe the GB phase, whereas a crystal‐plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the GI phase. Assuming the rule of mixtures, the overall behavior of a given grain is obtained via volume averaging. The scale transition from a single grain to a polycrystal is achieved by Taylor‐type homogenization. It is shown that the proposed model is able to capture the inverse Hall‐Petch effect. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Thermo‐Mechanical FE2 Simulation Scheme for Abaqus
Authors: Regener Benjamin , Krempaszky Christian , Werner Ewald , Stockinger Martin
Published: December 2011

A fully coupled multi‐physics (thermo‐mechanical) multi‐length scale (macro‐micro) finite element based simulation scheme for the commercial FE code Abaqus is introduced. The coupling of scales, initial boundary value problems on the macro‐ and micro‐scale as well as the micro‐scale testing procedure, which completes the consistent loop across the scales, are outlined. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Extraction of effective material parameters with application to sandwich structures
Authors: Sehlhorst Hans‐Georg , Düster Alexander , Diebels Stefan , Rank Ernst
Published: December 2011

In this contribution we present a first‐order numerical homogenization approach which allows for extracting effective linear elastic properties of heterogeneous materials. The approach is based on the window or self consistency method where a representative microscopic subdomain is embedded into a window of effective properties. Since these properties are not known in advance they have to be determined iteratively. For the discretization of the micro structures we use the Finite Cell Method, which is a fictitious domain method of higher‐order. It is very well suited for efficiently discretizing complicated geometries stemming, for example, from tomography (CT‐scans). In the numerical examples we will investigate a bending test of a sandwich plate which is composed of a polymeric core with thin faceplates made of Aluminum. Firstly, effective properties of the core are extracted and then applied to a macroscopic numerical model. The numerical results are validated by experiments. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Micromechanics model for tortuosity and homogenized diffusion properties of porous materials with distributed micro‐cracks
Authors: Timothy Jithender Jaswant , Meschke Günther
Published: December 2011

Continuum micromechanics [2,3] is used to model tortuosity within the context of ion transport to obtain the homogenized diffusivity of intact and micro‐cracked porous materials. A novel cascade homogenization technique to model ion diffusion in porous materials is proposed. A REVuc that represents the porous material is modelled as a spherical pore‐space inclusion in a recursively updated matrix with an initial diffusivity without any tortuosity. A REVc representing the micro‐cracked material is modelled with prolate ellipsoidal inclusions representing micro‐cracks embedded in a porous matrix [4]. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Microstructural driven computational modeling of polymers
Authors: Tkachuk Mykola , Linder Christian
Published: December 2011

The key focus of this work is the polymer microstructure which is the origin of the overall material response. In elastomers random three‐dimensional networks are formed by long macromolecules connected at the cross‐links by vulcanization or permanent entanglements. The mechanical response of these materials is mainly entropic and is related to the number of conformations that flexible polymer chains can attain. The available kinetic theories link the entropy of a single chain to such microscopic quantities as the end‐to‐end distance between the cross‐links or the constraining tube diameter among others. The central issue of micromechanically‐based material modeling is the relation between these quantities and the macroscopic deformation. In this work this connection is established by a network homogenization approach. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Computational Homogenization of Damage in the Hardened Cement Paste due to Alkali Silica Reaction
Authors: Wu Tao , Temizer İlker , Wriggers Peter
Published: December 2011

In this contribution, the model of the concrete deterioration due to the alkali silica reaction(ASR) at the microscale is set up. Based on a three‐dimensional micro computer‐tomography, a finite‐element mesh is constructed at the micrometer length scale and 3D coupled Chemo‐Themo‐Mechanics model in the hardened cement paste(HCP) and computational homogenization of damage are addressed in this contribution. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Large Eddy Simulations of Swirling Nozzle‐Jet Flow Undergoing Vortex Breakdown
Authors: Luginsland T. , Kleiser L.
Published: December 2011

We developed a numerical setup to simulate swirling jet flow undergoing vortex breakdown. Our simulation code CONCYL solves the compressible Navier‐Stokes equations in cylindrical coordinates using high‐order numerical schemes. A nozzle is included in the computational domain to account for more realistic inflow boundary conditions. Preliminary results of a Re = 5000 compressible swirling jet at Mach number M a = 0.6 with an azimuthal velocity as high as the maximum axial velocity (swirl number S = 1.0) capture the fundamental characteristics of this flow type: At a certain point in time the jet spreads and develops into a conical vortex breakdown. A stagnation point‐flow in the vicinity of the jet axis is clearly visible with the stagnation point located close to the nozzle exit. The stagnation point precesses in time around the jet axis, moving up‐ and downstream. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Analysis of mass transfer in thin liquid films on spinning disks using the integral method
Authors: Prieling Doris , Steiner Helfried
Published: December 2011

The present work applies the integral method to analyze the momentum and mass transfer in thin liquid films on spinning disks, with the aim to describe the complex process of wet chemical etching of rotating silicon wafers The obtained results capture very well the essential features of the etching activity on the disk, and are in good agreement with experimental results. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On higher order effects in marginally separated flows
Authors: Scheichl Stefan , Kluwick Alfred , Braun Stefan
Published: December 2011

If the angle of attack α of a slender airfoil reaches a critical value αs flow separation is known to occur at the upper s surface. Further increase of α initially leads to the formation of a short laminar separation bubble which has an extremely weak influence on the external flow field – a phenomenon known as marginal separation – but then rather rapidly causes a severe change of the flow behaviour, leading to leading edge stall. According to the asymptotic theory of marginal separation holding in the limit of large Reynolds numbers Re, the flow in the neighbourhood of the separation bubble is governed by an integro‐differential equation. This so‐called interaction equation contains a single controlling parameter which relates the angle of attack to the Reynolds number, with a value Γs corresponding to αs. Some recent results concerning higher order s s corrections to this theory and their effect on the stability of steady solutions will be presented. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Influence of Thermal Stratification on the Stability of Ekman‐Couette‐Flow
Authors: Withalm Martin , Hoffmann Norbert P.
Published: December 2011

The Ekman‐Couette‐System consists of two infinitely extended plates which are sheared in opposite directions over a fluid and are additionally rotated about their normal axis. In the case of angular velocities which tend to zero, the system becomes the classical Couette‐System, whereas for high angular velocities the boundary layers of the upper and lower plate are separated and represent Ekman boundary layers. For both limit cases the influence of thermal stratification on the stability of the base flow has been a subject of research for some time, but not so for moderate angular velocities. This was the motivation for doing a linear stability analysis for that case, including both stable and unstable stratification for a Prandtl number equal to unity. The results show, that as expected, stable stratification is suppressing the emergence of stationary as well as Type I‐ and Type II‐shear‐instabilities, while unstable stratification is supporting them. For unstable stratification, the system can also become unstable to a convection instability with all its properties known from other systems, except for that their orientation angle is not coincidental but determined due to the influence of the shear and Coriolis forces. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nitsche‐XFEM for a transport problem in two‐phase incompressible flows
Authors: Lehrenfeld Christoph
Published: December 2011

We consider the transport of a dissolved species in a divergence‐free immiscible incompressible two‐phase flow modeled by a convection diffusion equation. The so‐called Henry interface condition leads to a jump condition for the concentration at the interface between the two phases. This discontinuity of the solution render the numerical solution on unfitted meshes difficult. Furthermore time discretization on moving interfaces and handling typically convection dominant situations makes the overall problem delicate. We propose a numerical method using extended finite elements and a Nitsche‐type technique combined with streamline diffusion stabilization. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Viscous linear instability of a sheared liquid‐gas interface ‐ Effect of a velocity deficit near the interface
Authors: Otto Thomas , Boeck Thomas , Rossi Maurice
Published: December 2011

The initial state of liquid atomization by a fast gas stream is considered by viscous linear spatial stability analysis for parallel two‐fluid flow. The unbounded basic velocity profile is characterized by different asymptotic velocities and a velocity deficit near the interface. We examine the influence of the velocity deficit on the spatial growth rates of two competing modes originating from the Kelvin‐Helmholtz and viscosity contrast mechanisms. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical study of liquid/liquid slug flow in a capillary microreactor
Authors: Dittmar Ina , Ehrhard Peter
Published: December 2011

The great advantage of microreactors is associated with an extremely large surface‐to‐volume ratio. Hence, microreactors permit promising operating conditions, such as almost‐perfect heat or mass transfer. This, of course, requires that the hydrodynamics is well understood. The hydrodynamics of a liquid/liquid slug flow in a micro‐capillary is characterized by a complex vortex structure in both the disperse and the continuous phase. The disperse phase, in our investigations, is not wetting the walls and, thus, a thin film of the continuous phase persist between the disperse phase and the wall. Due to this phenomenon, a relative movement between disperse and continuous phase is possible and, indeed, observed. Understanding of these complex phenomena allows for a control of the hydrodynamics, and thus, to tailor the heat and mass transport in a desired manner.

Apparently, several effects influence the hydrodynamics. The main dimensionless groups are a Reynolds number, a Capillary number, and the ratio of viscosities and densities of both phases. To study the physics of this complex two‐liquid system, a modified level‐set method in conjunction with an immersed‐boundary formulation is engaged. Presently, the simulations are time‐dependent and axially‐symmetric in nature. The mesh resolution represents a challenge, as the spatial resolution has to resolve the thin film between the disperse phase and the wall adequately. All simulations are implemented within the software OpenFOAM. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Instable Waves between Rough Elastic Bodies in Sliding Contact
Authors: Graf Matthias , Ostermeyer Georg‐Peter
Published: December 2011

Most sliding bodies are not perfectly flat, but show a rough surface topography or tribological layer. This paper analyses a sliding system consisting of two elastic bodies with continuous contact and steady sliding. Surface topographies are taken into account by an inertia film on one of the sliding surfaces. A linear model is developed that allows an analytical solution. As a typical tribological system, the contact between pad and disc in a brake system is discussed. It can be shown that unstable elastic waves travel through the contact between both bodies. This instability is opened only when a tribological layer on the brake pad is taken into account. This microscopic excitation can cause a loss of stability of the entire (brake) system. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Two‐dimensional ultrasound Doppler velocimeter for velocity field measurements of liquid metal flows
Authors: Franke Sven , Fischer Andreas , Büttner Lars , Czarske Jürgen , Räbiger Dirk , Eckert Sven
Published: December 2011

We present a novel fluid flow measurement system based on the pulsed‐wave ultrasound Doppler velocimetry being able to determine two‐dimensional velocity fields. It applies for the measurement of unsteady liquid metal flows driven by electromagnetic forces concerning the research field of magnetohydrodynamics. The application of advanced processing techniques enable high data acquisition rates and concurrently a high spatial resolution facilitating to resolve transient liquid metal flow structures which could not been acquired so far. An experimental setup utilizing liquid metal in a cubic vessel exposed to a stationary rotating magnetic field was used to validate the reliability of the measurement system. The swirling fluid motion in its horizontal section could be resolved into a velocity field grid of 24 × 24 vectors while achieving frame rates of about 30 fps. Results from a further study driving liquid metal in a cylindrical vessel by a pulsed rotating magnetic field are presented. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Control of two‐dimensional turbulent wall jet on a coanda surface
Authors: Florin Frunzulica , Alexandru Dumitrache , Octavian Preotu , Horia Dumitrescu
Published: December 2011

The Coanda effect that is the tendency of a fluid jet to stay attached to an adjacent curved surface that is very well shaped has been employed to improve the performance of various devices. The main objective of this paper is to investigate ways of keeping the flow attached to a larger length of a Coanda surface. There are considered two possibilities: one passive, which uses a slot that connects the low pressure and high pressure points on the Coanda surface and an active one, based on the principle of synthetic jet, created through an orifice located near the point of detachment of the jet. Reynolds averaged Navier‐Stokes simulations (RANS) with shear stress transport k‐ω (SST model) of Menter have been used to compute the two‐dimensional turbulent wall jet. The numerical results are presented for the two methods considered. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical Study of Creeping Liquid Metal Flow in the Presence of a Permanent Magnet
Authors: Pulugundla Gautam , Karcher Christian
Published: December 2011

In this paper, we present the numerical study of interaction of a liquid metal flow with a small permanent magnet. Such an analysis is of fundamental interest for applications involving Lorentz Force Velocimetry (LFV). As a canonical problem, we consider the flow of liquid metal in the creeping flow regime (Re=0.01) through a square duct with electrically insulating walls. For this setup, we perform magnetohydrodynamic (MHD) simulations by coupling the commercial finite volume solver FLUENT and finite element solver COMSOL Multiphysics. Parametric analyses are performed at different relative positions of the permanent magnet with respect to the duct and with different magnetisation directions. The analyses provide good reference results for qualitative understanding of MHD flows exposed to non‐uniform magnetic fields. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Laminar magnetohydrodynamic duct flow in the presence of a magnetic dipole
Authors: Tympel Saskia , Krasnov Dmitry , Boeck Thomas , Schumacher Jörg
Published: December 2011

We study magnetohydrodynamic flow of a liquid metal in a straight duct. The magnetic field is produced by an exterior magnetic dipole. This basic configuration is of fundamental interest for Lorentz force velocimetry (LFV), where the Lorentz force opposing the relative motion of conducting medium and magnetic field is measured to determine the flow velocity. The Lorentz force acts in equal strength but opposite direction on the flow as well as on the dipole. We are interested in the dependence of the velocity on the flow rate and on strength of the magnetic field as well as on geometric parameters such as distance and position of the dipole relative to the duct. To this end, we perform numerical simulations with an accurate finite‐difference method in the limit of small magnetic Reynolds number, whereby the induced magnetic field is assumed to be small compared with the external applied field. The hydrodynamic Reynolds number is also assumed to be small so that the flow remains laminar. The simulations allow us to quantify the magnetic obstacle effect as a potential complication for local flow measurement with LFV. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Euler‐Bernoulli Beam with Boundary Control: Stability and FEM
Authors: Miletic Maja , Arnold Anton
Published: December 2011

We consider a model for the time evolution of a piezoelectric cantilever with tip mass. With appropriately shaped actuator and sensor electrodes, boundary control is applied and a passivity based feedback controller is designed to include damping into the system. Assuming that the cantilever can be modeled by the Euler‐Bernoulli beam equation, we obtain a coupled PDE‐ODE system. First we discuss its dissipativity, and its asymptotic but non‐exponential stability. Next we derive a FEM using piecewise cubic Hermitian shape functions that is still dissipative. This is illustrated on a numerical simulation. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stability of stationary states of a quantum energy transport model for semiconductors
Authors: Röhrig Elisa , Pinnau René
Published: December 2011

Due to the ongoing miniaturization of devices quantum effects are no longer negligible in semiconductor modeling. Also temperature effects play a role for example when identifying hot spots in devices. QET models, which can be derived via moment method from the Wigner‐BKG model, include both physical features. We analyze the stability of stationary states. Suitable numerical methods and computational results are presented. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Variational formulations in continuum mechanics
Authors: Scholle Markus
Published: December 2011

Variational formulations of the governing equations are of great interest in continuum mechanics: on the one hand a deeper theoretical insight in the respective system is possible, on the other hand variational formulations give rise for the development of semi‐analytical and numerical methods like Ritz' direct method, especially FEM.

Despite these benefits, there are many problems in continuum mechanics for which a variational principle is not available. The reason for this is that in contrast to conservative Newtonian mechanics, where the Lagrangian is given as difference between kinetic and potential energy, no generally valid construction rule for the Lagrangian has been established in the past.

In this paper a construction rule is developed, on the Galilei‐invariance of the system, leading to a general scheme for Lagrangians the individual analytical form of which is determined by an inverse treatment of Noether's theorem. This procedure is demonstrated for an elastically deforming body. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Short‐Term Prediction of the Sea State Dynamics
Authors: Chabchoub Amin , Hoffmann Norbert P.
Published: December 2011

Forecasting of the sea level plays a key role to control on‐ and offshore facilities. First, we start with a determinstic time series method based on the state space embedding to determine the vector field of the nonlinear dynamical system and deduce the solution of its corresponding high‐order differential equation. Second, We assume that the sea state is a stochastic process governed by a deterministic part and by noise so that this dynamical system can be modelled by the Langevin equation. We extract the nonlinear dynamical system considering fluctuations directly from a measured time series by estimating the drift vector and the diffusion matrix of the Fokker‐Planck equation. In order to determine the prediction accuracy, the numerical solutions of the deterministic model and the Langevin equation are compared to the data values at future time. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Set‐valued processes induced by parameterised stochastic differential equations with an application to Tuned Mass Dampers
Authors: Schmelzer Bernhard , Oberguggenberger Michael , Adam Christoph
Published: December 2011

In this paper ordinary stochastic differential equations whose coefficients depend on uncertain parameters are considered. An approach is presented how to combine both types of uncertainty (stochastic excitation and parameter uncertainty) leading to set‐valued stochastic processes. The latter serve as a robust representation of solutions of the underlying stochastic differential equations. The mathematical concept is applied to a problem from earthquake engineering, where it is shown how the efficiency of Tuned Mass Dampers can be realistically assessed in the presence of uncertainty. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Isogeometric structural shape optimization using a fictitious energy regularization
Authors: Friederich Jan , Scherer Michael , Steinmann Paul
Published: December 2011

In isogeometric analysis, NURBS basis functions are used as shape functions in an isoparametric finite‐element‐type discretization. Among other advantageous features, this approach is able to provide exact and smooth representations of a broad class of computational domains with curved boundaries. Therefore, this discretization method seems to be especially convenient for computational shape optimization, where a smooth and CAD‐like parametrization of the optimal geometry is desired. Choosing boundary control point coordinates of an isogeometric discretization as design variables, an additional design model can be avoided. However, for a higher number of design variables, typical drawbacks like oscillating boundaries as known from early node‐based shape optimization methods appear. To overcome this problem, we propose to use a fictitious energy regularization: the strain energy of a fictitious deformation, which maps the initial to the optimized domain, is employed as a regularizing term in the optimization problem. Moreover, this deformation is used for efficiently moving the dependent nodes within the domain in each step of the optimization process. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Shape optimisation analysing the inner structure of sensitivity matrices
Authors: Gerzen Nikolai , Barthold Franz‐Joseph
Published: December 2011

This contribution deals with sensitivity analysis in nodal based shape optimisation. Sensitivity analysis is one of the most important parts of a structural optimisation algorithm. The efficiency of the algorithm mainly depends on the obtained sensitivity information. The pseudo load and sensitivity matrices which appear in sensitivity analysis are commonly used to derive and to calculate the gradients and the Hessian matrices of objective functions and of constraints. The aim of this contribution is to show that these matrices contain additional useful information which is not used in structural optimisation until now. We demonstrate the opportunities and capabilities of the new information which are obtained by singular value decomposition (SVD) of the pseudo load and sensitivity matrices and by eigenvalue decomposition of the Hessian matrix. Furthermore, we avoid jagged boundaries in shape optimisation by applying a density filtering technique well‐known in topology optimisation. Numerical examples illustrate the advocated theoretical concept. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Re‐visiting structural optimization of the Ziegler pendulum: singularities and exact optimal solutions
Authors: Kirillov Oleg
Published: December 2011

Structural optimization of non‐conservative systems with respect to stability criteria is a research area with important applications in fluid‐structure interactions, friction‐induced instabilities, and civil engineering. In contrast to optimization of conservative systems where rigorously proven optimal solutions in buckling problems have been found, for non‐conservative optimization problems only numerically optimized designs were reported. The proof of optimality in the non‐conservative optimization problems is a mathematical challenge related to multiple eigenvalues, singularities on the stability domain, and non‐convexity of the merit functional. We present a study of the optimal mass distribution in a classical Ziegler's pendulum where local and global extrema can be found explicitly. In particular, for the undamped case, the two maxima of the critical flutter load correspond to a vanishing mass either in a joint or at the free end of the pendulum; in the minimum, the ratio of the masses is equal to the ratio of the stiffness coefficients. The role of the singularities on the stability boundary in the optimization is highlighted and extension to the damped case as well as to the case of higher degrees of freedom is discussed. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multiobjective optimization with expensive objectives applied to a thermodynamic material design problem
Authors: Pieper Martin
Published: December 2011

In many technical optimization problems, simulations of physical processes determine the objective function. Usually the runtime for these simulations is larger than a few minutes. Therefore a coupling with favorable optimization algorithms is not practicable. A promising solution is to work with different, simplified physical models, with reduced simulation time. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A structural optimization approach for passanger car tires with consideration of uncertainties
Authors: Serafinska Aleksandra , Graf Wolfgang , Kaliske Michael
Published: December 2011

In order to support the design process of passenger car tires, a multi‐objective optimization approach based on Finite Element Analysis (FEA) can be utilized. Providing a reliable and high quality design requires the consideration of data uncertainty within the optimization process. This uncertainty is caused predominantly by instable production conditions of tire components as well as incomplete information concerning e.g. loading. In order to capture the state of information which is indeed available in such engineering applications, an uncertainty model, which enables modelling fragmentary or dubious information as well as mathematical formulation of expert specifications and evaluations has to be applied. The presented requirements are fulfilled by the uncertainty model fuzziness. Therefore, an approach of multi‐objective optimization with consideration of fuzzy quantities was developed. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Grid transfer operators for multigrid methods
Authors: Donatelli Marco
Published: December 2011

Local Fourier analysis (LFA) is a classical tool for proving convergence theorems for multigrid methods (MGMs). Analogously, the symbols of the involved matrices are studied to prove convergence results for MGMs for Toeplitz matrices. We show that in the case of elliptic partial differential equations (PDEs) with constant coefficients, the two different approaches lead to an equivalent optimality condition. We argue that the analysis for Toeplitz matrices is an algebraic generalization of the LFA which allows to deal not only with differential problems but also, e.g., with integral problems. A class of grid transfer operators related to the B‐spline's refinement equation is discussed as well. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On optimal step‐length gradient eigensolvers
Authors: Neymeyr Klaus
Published: December 2011

Gradient iterations for the minimization of the Rayleigh quotient are robust and (with a proper preconditioning) fast iterations to compute approximations of the smallest eigenvalue of a self‐adjoint elliptic partial differential operator. Up to now sharp convergence estimates were only known for the basic fixed‐step size preconditioned gradient iteration (also called preconditioned inverse iteration). Recently sharp convergence estimates have been proved for optimal step size (preconditioned) gradient iterations. These new estimates are compared with previous results. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical simulation of (nearly) incompressible material, using adaptive mixed finite element method
Authors: Balg Martina , Meyer Arnd
Published: December 2011

In this paper we present a way to numerically simulate large deformations of incompressible material and the corresponding hydrostatic pressure by using a mixed, adaptive finite element method (FEM). Starting from the system of differential equations we will derive the weak nonlinear formulation, which can be solved with a Newton's method. In every iteration step this will lead to a saddle point problem. By using Taylor Hood finite elements we will obtain a discrete, indefinite problem, which can be handled with the Bramble Pasciak conjugate gradient method. Finally we give a numerical example. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
hp‐TDG/IPDG for Parabolic Obstacle Problems
Authors: Banz Lothar , Stephan Ernst P.
Published: December 2011

We present a mixed hp‐FE time DG method combined with an interior penalty DG method for parabolic obstacle problems. The discrete Lagragian multiplier set is spanned by basis functions which are biorthogonal to the basis functions of the primal variable. This allows us to write the discrete mixed problem as a problem of finding the root of a strongly semi‐smooth function. In turn, this problem is solved by a locally Q‐quadratic converging semi‐smooth Newton method. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Convergence of adaptive FEM for elliptic obstacle problems
Authors: Feischl Michael , Page Marcus , Praetorius Dirk
Published: December 2011

We treat the convergence of adaptive lowest‐order FEM for some elliptic obstacle problem with affine obstacle. For error estimation, we use a residual error estimator which is an extended version of the estimator from [2] and additionally controls the data oscillations. The main result states that an appropriately weighted sum of energy error, edge residuals, and data oscillations satisfies a contraction property that leads to convergence. In addition, we discuss the generalization to the case of inhomogeneous Dirichlet data and non‐affine obstacles χ ∈ H2(Ω) for which similar results are obtained. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Identification of Starshape Constant Conductivity Inclusion from Boundary Measurement
Authors: Garnadi Agah D.
Published: December 2011

The problem of determining the interface separating a starshape support of constant conductivity inclusion from boundary measurement data of a solution of the corresponding PDEs is considered. An equivalent statement as a nonlinear integral equation is obtained. The problem is implemented using Fourier method. Numerical experiment based on simplified iteratively regularized Gauss‐Newton method (sIRGNM) is presented. MSC classes: 31A25, 35R30, 65N21. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A coupled FEM/DG approach for the simulation of cavitating micro foams
Authors: Kopecz Stefan , Meister Andreas , Wünsch Olaf
Published: December 2011

We consider difficulties which arise during our simulations of cavitating micro foams. The compatibility of velocity and transport, satisfaction of a maximum principle and generalization of an incompressible Navier‐Stokes solver. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Fully conservative, skew‐symmetric finite difference schemes for compressible flows on distorted grids
Authors: Reiss Julius , Sesterhenn Jörn
Published: December 2011

We present a fully conservative finite difference scheme for the compressible Navier‐Stokes equations. Due to its skew‐symmetry in the momentum equation it is possible to have no physical or artificial damping. Therefore it is especially suited for simulations of configurations where perfect conservation is needed along with low damping. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Lie splitting on polygonal domains
Authors: Ostermann Alexander , Schratz Katharina , Spielberger Georg
Published: December 2011

In this short note, we discuss the convergence properties of splitting methods for the time integration of parabolic evolution equations. Through numerical experiments we show that the Lie splitting method suffers from an order reduction on non‐convex polygonal domains. An in‐depth study of the local error allows us to explain this behavior and to understand the improved convergence properties of a related scheme, the Douglas‐Rachford method. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An optimization of a Mindlin‐Timoshenko beam with a dynamic contact on the boundary
Authors: Bock Igor
Published: December 2011

We deal with the optimal control problem governed by a hyperbolic variational inequality describing the perpendicular vibrations of a Mindlin‐Timoshenko beam clamped on the left end with a rigid obstacle at the right end. A variable thickness of a beam plays the role of a control parameter. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Variational design sensitivity analysis of dual problems with applications to error analysis
Authors: Materna Daniel , Barthold Franz‐Joseph
Published: December 2011

Dual or adjoint solutions play an important role in many fields which deal with local quantities of interest. This contribution is concerned with a novel approach for the sensitivity of the dual solution itself, i.e. we investigate the change in the dual solution at a deformed configuration of the material body due to changes in the design of the body. We consider a general variational framework and present the application of the proposed approach to the prediction of changes in the quantity of interest as well as error analysis for the truncation error of classical first‐order sensitivity relations. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On ℋ︁2‐model reduction of linear parameter‐varying systems
Authors: Benner Peter , Breiten Tobias
Published: December 2011

In this paper, we will discuss an advantageous relation between a special class of linear parameter‐varying systems and bilinear control systems. This will automatically lead to parameter‐preserving model reduction techniques. Furthermore, we review a recently introduced interpolation‐based ℋ2‐framework for bilinear control systems. By means of a numerical example, the efficiency of the new method will be underlined. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Controllability properties and prediction‐free control of linear systems with incommensurate delays
Authors: Gehring Nicole , Rudolph Joachim , Woittennek Frank
Published: December 2011

For linear delay systems with incommensurate (lumped) delays necessary and sufficient conditions for the freeness of the system over the ring of entire functions in ${\rm I\!\!\!C}(s)[e^{-\tau_1 s},\ldots,e^{-\tau_r s}]$ are given. In contrast to the commensurate case the ring does not have the Bézout property. Therefore, additional criteria are needed involving also special properties of pure delay systems. Based on these results a prediction‐free flatness‐based control is designed for a system of two vibrating strings with a point mass and single boundary input. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Trajectory Planning for a Non‐Flat Mechanical System Using Time‐Reversal Symmetry
Authors: Knoll Carsten , Röbenack Klaus
Published: December 2011

Some mechanical systems have a special discrete symmetry property associated with the inversion of the direction of the time flow. This "time‐reversal symmetry" allows one to construct solutions of the equations of motion from other known solutions. In the present contribution we examine to which systems this property can be applied. Furthermore, we demonstrate how it can be used to determine an open loop control for equilibrium point transition by solving a stabilization problem in the negative time direction. As a non‐flat mechanical example the popular pole‐cart system is considered. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Advanced Control Design for Wind Turbines
Authors: Liu Yan , Susilo Martinus , Söffker Dirk
Published: December 2011

In this contribution, the concept of a general design platform for control system of wind turbines is proposed. Different models of wind turbine systems are summarized, a novel control strategy for wind turbine control is proposed as a general platform for control system design. Simulation results are presented demonstrating the success of the proposed control method based on one of the chosen models for the design platform. A benchmark model (NREL) is chosen for the platform in order to adjust the control system design. Finally, the design process of control system based on the general platform is given and explained. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Online powermanagement optimization of a fuel cell‐based hybrid electric powertrain
Authors: Marx Matthias , Söffker Dirk
Published: December 2011

In this paper an online optimization approach of the powermanagement of a fuel cell‐based hybrid electric powertrain system is desribed. Therefore two online optimization algorithms of the powermanagement control parameters are introduced and compared experimentally. The first one deals with parameters rating the performance of the system with respect to efficiency, availability, and lifetime. Using a pre‐defined load profile the optimal parameters can be determined for a given powermanagement. The second approach is based on the statistical properties of a predicted and online‐updated measured load profile defining the actual load profile characteristics. Depending on this load profile and with the knowledge of the design parameters of the system appropriate adaptive powermanagement parameters are determined. It becomes clear that the performance of the system with respect to the mentioned system properties can be improved by these approaches. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Model Predictive Control for Heating Ventilating and Air Conditioning Systems
Authors: Rehrl Jakob , Horn Martin
Published: December 2011

In heating ventilating and air conditioning (hvac) systems, model predictive control (mpc) is rarely used up to now. However, the following properties of hvac systems make mpc a well suited control methodology: the plant is a multiple input, multiple output system and its inputs are constrained – both in their value and in their rate of change. Moreover, several disturbances acting on the plant like varying outdoor air temperature or outdoor humidity can be measured. Furthermore, time constants are relatively large which makes it easy to perform the required optimization of the mpc strategy in time. This contribution presents the application of mpc to a real world hvac system. The considered hvac system consists of standard industrial components. The core components of the system are water‐to‐air heat exchangers, both for heating and for cooling purposes as well as a steam humidifier. Hence, air temperature and air humidity can be varied with the help of the investigated hvac system. The derivation of the plant model based on thermodynamic relations is presented as well as the application of the mpc strategy to the real world system. The plant contains some nonlinear elements which have to be dealt with when applying the mpc strategy. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Feedforward Design and Optimality Aspects for the Control of Mechatronic Systems
Authors: Stadlmayr Richard , Gahleitner Reinhard
Published: December 2011

This paper considers the tracking controller design for a mechatronic handling system. The presented approach is based on Port‐Hamiltonian systems and it achieves good tracking as well as good disturbance rejection based on a polynomial approach. A PBC controller stabilizes the trajectory and the feedforward part has to fulfill the given limitations and the time optimality. This approach avoids the solution of a boundary value problem and a real‐time integration of the internal dynamics. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Missing Point Estimation for steady aerodynamic applications
Authors: Vendl Alexander , Faßbender Heike
Published: December 2011

Model reduction in aerodynamic applications usually makes use of Proper Orthogonal Decomposition (POD). In this work a POD‐based method, called Missing Point Estimation (MPE), will be applied to steady state flows with variation of the flow parameter angle of attack. The basic idea of MPE is to select a subset of the computational grid points (control volumes) and limit the governing equations to these. Subsequently, the remaining equations are projected onto the POD subspace. This approach has the advantage that the nonlinear right hand side of the governing equations has to be evaluated only for some selected points (control volumes) which makes the MPE faster than classical Galerkin projection. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A flatness based view on state controllability of simple hyperbolic distributed parameter systems. A string with interior point mass.
Authors: Woittennek Frank
Published: December 2011

A flatness based approach to the analysis of state controllability of systems described by one or more boundary coupled 1D hyperbolic second order equations is analyzed on the basis of a nontrivial example. Introducing a state which corresponds to the parametrization of the solution trajectories by a so called flat output and establishing the state transformation to the original state space the controllability problem reduces to a simple interpolation problem. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)