bluuebunny/crossref_metadata_2025 huggingface dataset:
Green element method for 2D Helmholtz and convection diffusion problems with variable velocity coefficients
Authors: Onyejekwe Okey Oseloka
Published: June 2004

Computation of 2D Helmholtz and transient convection diffusion problems with linear reaction and variable velocity components are implemented with the Green element method (GEM). GEM's fundamental solution which is derived from the diffusion differential operator simplifies the numerical procedure considerably, and together with the Green's second identity, an element to element treatment of the inhomogeneous terms is guaranteed. The reported numerical experiments reveal that the method can be relied on to yield faithful results. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005
Mixed finite element methods for generalized Forchheimer flow in porous media
Authors: Park Eun‐Jae
Published: June 2004

Mixed finite element methods are analyzed for the approximation of the solution of the system of equations that describes the flow of a single‐phase fluid in a porous medium in ℝd, d ≤ 3, subject to Forchhheimer's law—a nonlinear form of Darcy's law. Existence and uniqueness of the approximation are proved, and optimal order error estimates in L∞(J; L2(Ω)) and in L∞(J; H(div; Ω)) are demonstrated for the pressure and momentum, respectively. Error estimates are also derived in L∞(J; L∞(Ω)) for the pressure. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005
Laser surface hardening using proper orthogonal decomposition for a threedimensional example
Authors: Hömberg Dietmar , Volkwein Stefan
Published: June 2004

Laser surface hardening of steel is formulated in terms of an optimal control problem with bilateral control constraints. The state equations are composed of a semilinear heat equation and an ordinary differential equation, which describes the evolution of the high temperature phase. In this work a three‐dimensional example is solved numerically by utilizing model reduction based on proper orthogonal decomposition (POD).
Balanced truncation model reduction for descriptor systems
Authors: Stykel Tatjana
Published: June 2004

We present a generalization of a balanced truncation model reduction method for descriptor systems. This method is closely related to the proper and improper controllability and observability Gramians and Hankel singular values that can be computed by solving projected generalized Lyapunov equations. We demonstrate the application of balanced truncation model reduction to the semidiscretized Stokes equation.
Feedback Control Of Industrial Robots By Means Of Stochastic Optimization Techniques
Authors: Aurnhammer Andreas , Marti Kurt
Published: June 2004

The standard engineering approach in control of industrial robots assumes all model parameters are known exactly and therefore can be modeled by their nominal values. Due to stochastic variations of the material, manufacturing errors, modeling errors and most important stochastic variations of the workspace environment (e.g. stochastic payload mass) this assumption does not hold. Hence, an approach that models these parameters by means of random variables was proposed, cf. [1]. Solving this substitute optimal control problem by means of direct optimal control discretization techniques allows the numerical computation of approximate optimal stochastic reference trajectories for the on‐line control process. These optimal reference trajectories are ‐ according to the chosen probability distribution ‐ valid for a variety of parameter configurations and are more stable toward parameter uncertainties. However, due to the stochastic parameters in the robots dynamic model, in the on‐line control process still deviations from the reference trajectories appear. Hence, a method for the construction of feedback controllers based on feedback linearization is presented.
Minimising the variance under convex constraints
Authors: Hirth Ulrich
Published: June 2004

I treat the problem of minimising the variance functional on a certain closed convex subset of L2(P) by means of the variational inequality, obtaining an explicit formula for the solution and analysing the dependence of the solution on the initial data.
On the motion of a shape memory cantilever subject to harmonic end displacement and proposal for a microdamper
Authors: Rizzoni Raffaella
Published: June 2004

In [8] a model for the description of the dynamics of martensitic materials has been proposed. The model is specifically intended for materials whose free energy grows steeply away from the energy wells. Essentially, it is the multi‐well analog of ordinary rigid body mechanics with three additional features: the stress is not treated as arbitrary (the average of its normal component on the interfaces enters the theory in a non trivial way), a certain component of the local balance of the linear momentum is used, and kinetic laws for interfacial motion are introduced based on ideas of Eshelby [6] and Abeyaratne and Knowles [1, 2].

In this contribution the model is specialized to a cantilever subject to harmonic end displacement and made of two different variants of martensite separated by a system of parallel interfaces. The equations governing the motion of the cantilever when the displacement at its free extremity is prescribed are obtained. This very preliminary study could serve as a basis for the design of a microdamper.
Impact of correlation structure on drainage in open rough walled fractures
Authors: Neuweiler Insa , Sorensen Ivan , Kinzelbach Wolfgang
Published: June 2004

The spatial correlation structure of heterogeneous parameters plays an important role in upscaling of many flow and transport processes in porous media and fractures. We analyze upscaling of a slow drainage process in a horizontal open rough walled fracture. The applicability of upscaled continuum models for this kind of flow process is discussed. We consider two different fracture aperture distributions with different spatial correlation properties. One is described by a slowly decaying, the other one by a Gaussian autocovariance. The flow process is modelled using an invasion percolation model, which takes the in plane curvature of the fluid cluster into account. Results are compared to laboratory experiments in artificial plexiglas fractures. Different averaging procedures are tested in order to assess the applicability of continuum models. Independently of the correlation structure of the fracture aperture field, spatial averages do not converge to a continuum formulation. Ensemble averages do converge, however, they only give probabilistic information and are not applicable to model drainage in a fracture.
Spline‐Based Elastic Image Registration
Authors: Rohr Karl
Published: June 2004

For the geometric alignment of image data we propose spline‐based schemes utilizing anatomical point landmarks. We have developed three different types of elastic registration approaches which have different properties and thus differ w.r.t. their suitability for certain registration applications. All approaches are both computationally efficient and can be applied for multimodal images. Our approaches have been successfully applied for the registration of 2D and 3D tomographic images of the human brain.
On time‐dependent behaviour of controlled turbulent flow with separation and reattachment
Authors: Neumann J.
Published: June 2004

Results from numerical simulations of separating and reattaching turbulent boundary layer flow over a backwardfacing step are analysed with respect to the time‐dependent flow behaviour. Beside the well‐known roll‐up of the separated shear‐layer (“Kelvin‐Helmholtz instability”) and the ejection of subsequently formed large‐scale structures (denoted as “shedding”), another unsteady phenomenon which is commonly called “flapping” can be observed. Additionally, the effects of open‐loop passive and active flow control methods are investigated.
Testing the Exactness of Convex Relaxations for Robust LMI Problems
Authors: Scherer Carsten
Published: June 2004

We consider non‐convex robust linear matrix inequality problems and general families of convex relaxations based on multipliers that cover a whole variety of known concrete versions. In this framework we provide new tests for when these relaxations are exact that go beyond a recently suggested rank‐one principle, and we reveal applicability to an asymptotically exact relaxation sequence.
Homogenization of bone elasticity based on tissue‐independent (‘universal’) phase properties
Authors: Hellmich Christian , Ulm Franz‐Josef , Dormieux Luc
Published: June 2004

As candidates for tissue‐independent phase properties of cortical and trabecular bone we consider (i) hydroxyapatite, (ii) collagen, (iii) ultrastructural water and non‐collagenous proteins, and (iv) marrow (water) filling the Haversian canals and the intertrabecular space. From experiments reported in the literature, we assign stiffness properties to these phases (experimental set I).

On the basis of these phase definitions, we develop, within the framework of continuum micromechanics, a two step homogenization procedure: (i) At a length scale of 100 – 200 nm, hydroxyapatite (HA) crystals build up a crystal foam ('polycrystal'), and water and non‐collagenous organic matter fill the intercrystalline space (homogenization step I); (ii) At the ultrastructural scale of mineralized tissues, i.e. 5 to 10 microns, collagen assemblies composed of collagen molecules are embedded into the crystal foam, acting mechanically as cylindrical templates. At an enlarged material scale of 5 to 10 mm, the second homogenization step also accommodates the micropore space as cylindrical pore inclusions (Haversian and Volkmann canals, inter‐trabecular space), that are suitable for both trabecular and cortical bone. The input of this micromechanical model are tissue‐specific volume fractions of HA, collagen, and of the micropore space. The output are tissue‐specific ultrastructural and microstructural (=macroscopic=apparent) elasticity tensors.

A second independent experimental set (composition data and experimental stiffness values) is employed to validate the proposed model. We report a a good agreement between model predictions and experimentally determined macroscopic stiffness values. The validation suggests that hydroxyapatite, collagen, and water are tissue‐independent phases, which define, through their mechanical interaction, the elasticity of all bones, whether cortical or trabecular.
Towards a consistency proof for immiscible lattice BGK
Authors: Kehrwald Dirk
Published: June 2004

Emanating from the incompressible Navier‐Stokes equations, a widely used mathematical model of immiscible twophase flow is rigorously derived. Once the model is fixed, it is analysed to what extend the immiscible lattice BGK method approximates the solution of the model equations. Using equivalent moment analysis and some elementary tools from differential geometry we are able to show weak consistency if certain well founded but unproven presumptions hold.
Dynamics of Ship–Motion
Authors: Kreuzer Edwin , Pick Marc‐André
Published: June 2004

The ship capsizing problem is one of the major challenges in naval architecture. The IMO criterion regarding capsize stability is still the righting lever curve of static stability calculated for calm water. For the prediction of large–amplitude motions the dynamic loads have to be included. The capsizing of a ship in regular waves is resulting from a sequence of bifurcations in the ship's motion: The determination of bifurcations is possible using path‐following techniques of nonlinear dynamics. Existing tools are, however, without adaption not readily applicable for the determination of bifurcations. The main and until now unsolved problem is the necessity of including memory integrals to describe the ship hydrodynamics. First results with simple algorithms show two different scenarios leading to capsizing due to increasing wave amplitudes.
Forced vibrations of gearboxes with time dependent meshing stiffnesses
Authors: Hajžman M. , Zeman V. , Byrtus M.
Published: June 2004

The contribution presents the efficient method of the mathematical modelling of gearboxes with time dependent meshing stiffnesses. A gearbox is considered including a housing and an interior rotating shaft system with gears. Further the paper deals with an analysis of vibrations excited by the important sources of the internal excitation in gear meshing. The theory is applied to a simple test‐gearbox.
FRF simulation of structural joints with uncertain parameters
Authors: Hanss Michael , Oexl Stefan , Gaul Lothar
Published: June 2004

For the simulation of systems with uncertain parameters, the application of fuzzy arithmetic proves to be a practical approach. The uncertainties in the model parameters can be taken into account by defining them as fuzzy numbers, and the uncertain system can then be simulated by applying fuzzy arithmetic based on the so‐called transformation method. As an example, a normally‐loaded joint which connects two rods in axial direction is discussed in the paper. A worst‐case scenario for the frequency response function (FRF) of the coupled rods with uncertainties in the joint can be obtained, and additionally, one can get information about how much each of the uncertain model parameters contributes to the overall uncertainty of the model output at different frequencies of excitation.
Dynamic analysis of sandwich beams with interlayer slip
Authors: Heuer Rudolf
Published: June 2004

Force induced dynamic bending of sandwich beams composed of three symmetrically arranged layers are studied. Moderately thick elastic layers made of dissimilar transversal isotropic materials are considered. If rigid bond between the layers cannot be achieved, due to relative deformation of the connectors an interlayer slip occurs, that can significantly affect both strength and deformation of the layered structure. Analyzing two special cases of interlaminar connections, i.e., “perfect bond” and “elastic interlayer slip”, a complete analogy between the corresponding initialboundary value problems is derived. Hence, the dynamic response of the beam with elastic interlayer slip can be determined directly from the solution of the perfectly bonded sandwich beam with moderately thick faces.
The piecewise full decoupling method for dynamic problems
Authors: Kranjčević Nenad , Stegić Milenko , Vranković Nikola
Published: June 2004

The piecewise full decoupling method is a new developed numerical procedure of explicit integration based on piecing together local linear solutions. The method is applied for solving piecewise linear dynamic systems under periodic excitations. Close agreement is found between obtained results and published findings of a harmonic balance method and a finite element method in time domain.
Design of Friction Dampers for Mistuned Bladed Disks
Authors: Panning L. , Sextro W. , Popp K.
Published: June 2004

Friction damping devices such as underplatform dampers are widely used in turbomachinery applications to reduce blade vibration amplitudes. In this paper, a model is presented briefly to calculate the forced response of mistuned bladed systems with friction dampers. Some results will give an insight in the vibrational behavior of frictionally damped bladed disks and how the damping gain is affected by the damper properties.
Avoidance of Stick‐Slip Motion by Vibration Control
Authors: Popp K. , Rudolph M.
Published: June 2004

This paper deals with the excitation mechanisms of friction induced vibrations and recently found methods to avoid these vibrations. It is remarkable, that mechanisms of excitation and avoidance are closely related and, infact, the presented idea and realization of vibration control is derived from theoretical investigation of excitation mechanism. The basic mechanism will be explained and two methods of vibration control will be demonstrated theoretically and by experiment. The concept of fluctuating normal forces is the basic idea behind the two methods of vibration control. In the first case the fluctuating normal forces are generated by an additional oscillator connected to the basic stick‐slip oscillator. In the second case, fluctuating normal forces are generated directly by a magnetic actuator.
Orbital Stability of Skyhooks
Authors: Steindl Alois
Published: June 2004

The sky‐hook, that is a string forming a connection from the surface of the Earth to a satellite in geostationary orbit, which may be used as track for an Earth to space elevator, is an old dream of mankind, originating about 100 years ago in Russia. Besides the question of feasibility from a technological point of view also the question concerning the stability of such a configuration has not yet been completely solved. Under the assumption that a proper material (e.g. “Bucky Tubes” with very high tensile strength and small density) is available, making the connection possible from the technological point of view, we address the question of stability of the radial relative equilibrium of a very long tapered string on a circular geosynchronous orbit around the Earth.
Eigenpath analyses of friction induced vibrations depending on the friction coefficient
Authors: Wagner N. , Gaul L.
Published: June 2004

The tracking of eigenvalues and eigenvectors for parameterized matrices is of major importance in stability problems. A continuation method for approximating complex eigenpaths of parameter‐dependent matrices is proposed. The presence of a multiple eigenvalue (especially when it is defective) is inherently connected with an ill‐conditioned Jacobian and calls for a special treatment of the approach. Therefore, an invariant subspace is used to circumvent the difficulties of passing possible branch points. The procedure is illustrated by means of an example coming from structural dynamics.
Possibilities of Optimal and Adaptive Control Laws Design in Piezoelectric Smart Structures
Authors: Nestorović‐Trajkov Tamara , Köppe Heinz , Gabbert Ulrich
Published: June 2004

Possibilities of the controller design for piezoelectric smart structures are considered in the paper. The modelbased approach, which relies on the finite element modal analysis of structures, is used. As an alternative, system identification is suggested in cases when the real plant or its prototype is available for studying. Dynamics of piezoelectric active materials used as actuators and sensors is taken into account in the modelling procedure. The aim of control is vibration suppression in the sense of magnitudes reduction as well as the isolation of undesirable frequencies from the response spectra. For known plant models and available a priori information on the type of excitation or disturbances, optimal LQ tracking control systems perform good behavior. Owing to the approximation of the real structure's behavior by the finite element model and by modal reduction, the full infinite‐dimensional dynamics of an elastic structure cannot be completely captured. Introduced inaccuracies could be compensated for if they are viewed as the source of the model parameters variation and therefore by employing adaptive control laws. The adaptive control design is considered from this point of view. The application possibilities are illustrated by examples of piezoelectrically controlled structures.
Computer Algebra Algorithms for Control Related Tests of Implicit Dynamic Systems
Authors: Schlacher Kurt , Zehetleitner Kurt
Published: June 2004

This contribution is focused on control related tests for implicit dynamic systems, like accessibility, observability or input to output, input to state linearizability. Since the performance of these tests needs tedious symbolic calculations, computer algebra systems are the ideal tool to cope with this problem. Accessibility and observability are exemplarily used to present a new approach based on Lie groups. It is shown that non accessible or non observable systems admit Lie‐groups acting on their solutions such that distinguished parts remain unchanged. This fact allows us to apply this technique, as well as its realization by computer algebra algorithm, to several fundamental problems in control.
Stability of Linear Parameter Varying and Linear Switching Systems
Authors: Wirth Fabian
Published: June 2004

We consider stability of families of linear time‐varying systems, that are determined by a set of time‐varying parameters which adhere to certain rules. The conditions are general enough to encompass on the one hand stability questions for systems that are frequently called linear parameter varying systems in the literature and on the other hand also linear switching systems, in which parameter variations are allowed to have discontinuities. Combinations of these two sets of assumptions are also possible within the framework studied here. Under the assumption of irreducibility of the sets of system matrices, we show how to construct parameter dependent Lyapunov functions for the systems under consideration that exactly characterize the exponential growth rate. It is clear that such Lyapunov functions do not exist in general. But every system of our class can be reduced to a finite number of subsystems for which irreducibility holds.
Non‐linear Model Based Control for a Hydraulically Actuated Mobile Harbour Crane
Authors: Aschemann Harald , Hild Ingo , Hofer Eberhard P.
Published: June 2004

Active damping of oscillations performed by the rope suspended payload becomes a more and more important feature for mobile harbour cranes characterised by their non‐linear kinematic structure. This contribution presents a nonlinear control scheme for a hydraulically actuated mobile harbour crane, which is based on a multibody model of the mechanical configuration. The decentralised control structure consists of a combined feedforward and feedback control law for each crane axis and includes a compensation for the most dominant coupling between the axes due to centrifugal acceleration. By this, crane operation can be simplified and handling performance can be increased in particular for less experienced crane operators and, moreover, automatised container handling becomes an attractive feature for operating mobile harbour cranes. The efficiency of the proposed control scheme is emphasized by selected simulation results.
Dynamic Simulation of Colliding Trains for Buffer Stop Dimensioning
Authors: Grabner Gerald , Kecskeméthy Andrés
Published: June 2004

This paper describes an application of multibody dynamics to the determination of global physical behavior patterns that mimic traditional empirical laws. The main idea is to sift out such patterns from virtual experiments carried out with a simulation package. The concrete investigation in this setting is the dynamics of trains colliding onto buffer stops. Using a rigid‐body model with nonlinear couplers featuring hysteresis, it is shown that, for typical train constellations, the highest load at the buffer stops is almost independent of the number of coaches, and that the value and the location of the maximum force within the train does not increase from a particular train length on. These results are compared with traditional formulas for dimensioning of buffer stops used in rail‐vehicle industry.
Repair of Laminates by External Patches — Analysis and Optimisation
Authors: Engels Heiko , Becker Wilfried
Published: June 2004

The present contribution considers the patch repair of a damaged laminate where the damaged laminate material has been removed by cutting or drilling a hole. The respective analytical assessment of such a repair configuration can be performed by the complex potential method. In order to determine the optimal repair design the present work also addresses the well‐approved techniques of mathematical structural optimisation.
Modeling of a Constrained Porous Material with an Inclusion
Authors: Giovine Pasquale
Published: June 2004

A recently developed theory allows to describe a porous solid with very large lacunae partially, or totally, filled by a uid inclusion like an atypical immiscible mixture which consists of a solid with an ellipsoidal microstructure and of a classical fluid. Here we investigate the condition of saturation when the fluid inclusion is incompressible.
A New Micromechanically Based Approach for the Elastic Response of Rubber–like Materials at Large Strains
Authors: Göktepe Serdar , Miehe Christian
Published: June 2004

The approach models the elasticity of a rubber–like materials based on micro–structure that can be symbolized by a micro–sphere. The proposed model incorporates both non–a.ne deformation of unconstrained chains and superimposed constraint e.ects of tube–like topological formations in a consistent manner. Framework of the constitutive modeling and numerical examples illustrating the excellent predictive capacity of the model are presented.
An Application of the Binary Model to Dynamic Finite Element Analysis
Authors: Haasemann Georg
Published: June 2004

A new custom .nite element (FE) code based on the Binary Model is developed. The program is capable for investigation of the dynamic material properties of textile reinforced composites such as during impact. Therefore, the established formulation of the Binary Model for boundary value problems in Ref. [1,2,3] is enhanced to initial value problems. Regarding the investigation of the impact behavior, the program provides an apt .exibility in determination of boundary conditions. The calculations of di.erent models show the precision and reasonableness of the results from this FE program.

The work done for this paper is partially sponsored by the German Research Community (DFG) in the context of the priority program (SPP) no. 1123.
Geometrically nonlinear homogenization analysis of hyperelastic solid foams
Authors: Hohe J. , Becker W.
Published: June 2004

The present study is concerned with the macroscopic material response of solid foams and other highly microheterogeneous solids in the finite strain regime. For the homogenization of the microstructure, a strain energy based procedure is proposed. This procedure is subsequently employed for the analysis of the macroscopic behavior of two‐dimensional model foams. Distinct effects of a deformation induced cell wall re‐alignment are observed which cannot adequately be included in pure small strain analyses.
On the interrelation of the basic laws of continuum mechanics
Authors: Kienzler Reinhold , Herrmann George
Published: June 2004

It has been shown by the present authors in a recent paper [1] that if some conservation and balance laws of continuum mechanics are represented in a 4 × 4 form, balance of linear physical momentum (i. e., stress) and balance of mass become closely linked. This seemingly novel result was reached in a completely ad‐hoc fashion by treating time on the same level as the spatial coordinates, and not as parameter, as it is usually done.

In order to place the above ad‐hoc result on a firmer foundation and since it is in the theory of relativity that space and time are considered on the same footing, an attempt is made to derive several tensors of continuum mechanics in a systematic manner as 4 × 4 invariant objects.
Analytical solution of a plate bending problem using symbolic algebra
Authors: Kovács Ádám
Published: June 2004

The estimation of critical voltage in a capacitive micro‐switch leads to a thin plate bending problem. This paper deals with the correct mathematical formulation taking into account deflection‐dependent electrostatic force. The relative simple geometry allows the reduction of the structure to a beam problem. With the use of Ritz‐method and the variational symbolic program Mathematica analytical closed form solutions have been obtained. Polynomial and trigonometric trial functions have been used to determine the deflection of the plate. It has been proved, that the critical collapse voltage is much overestimated, if constant electrostatic forces are assumed.
Boundary Value Problems of the Theory of Thermoelasticity with Microtemperatures
Authors: Svanadze Merab
Published: June 2004

The boundary value problems of the steady oscillations of the linear theory of thermoelasticity with microtemperatures are investigated. The uniqueness and existence theorems of solution of the boundary value problems by means of the boundary integral method (potential method) are proved. The Sommerfeld‐Kupradze type radiation conditions are established. The existence of eigenfrequencies of the interior homogeneous boundary value problems of steady oscillations is studied.
Kontaktprobleme elastischer Walzen in nichtsymmetrischer Kontaktsituation
Authors: Walter H. , Braun M.
Published: June 2004

Untersucht werden die ebenen Spannungen und Verschiebungen zylindrischer Walzen in nichtsymmetrischen Kontaktsituationen. Für eine Walze mit starrem Kern und eine elastische Vollwalze werden das Verschiebungs‐ und Spannungsfeld sowie die Randlasten als Fourier‐Reihen im Polarwinkel entwickelt. Unter der Voraussetzung linearer Elastizität sind die Ansätze für nichtsymmetrische Lastsituationen mit komplexen Koeffizientenfunktionen darstellbar. Der Anpreßvorgang erfolgt quasistatisch, muß aber wegen der Ausbildung von Haft‐ und Gleitbereichen inkrementell betrachtet werden.
On modelling of dynamic problems for elastic periodic plates
Authors: Wozniak Czeslaw , Wierzbicki Ewaryst
Published: June 2004

The subject of analysis are thin elastic plates with a periodic structure along the midplane. The aim of this contribution is to formulate a new effective 2D‐model of the plate, i.e. a 2D‐model represented by equations with constant coefficients. It is assumed that the period lengths are of an order of the mean plate thickness.
Mathematical models for elastodynamics of biperiodic layered composites
Authors: Wozniak Margaret , Wozniak Czeslaw
Published: June 2004

By a biperiodic composite we mean a composite solid which has a plane periodic structure and the properties of which are constant in the direction normal to this plane. The aim of the contribution is to formulate a certain new mathematical model describing the macroscopic (overall) behaviour of biperiodic composites and to apply this model to dynamics of laminates with a periodically waved laminae.
Numerical Modelling of Contact Problems with Application to Porous Media
Authors: Yang F. , Ehlers W. , Markert B. , Ammann M.
Published: June 2004

Contact problems are highly non‐linear because of the non‐penetration inequality in the contact interface. To solve such problems, different constraint methods are used to transform the inequality into an equality problem [4]. Concerning the contact of two isotropic fluid‐saturated porous solids which consist of an immiscible mixture of a solid skeleton and a fluid pore content [3], the non‐penetration constraint can be applied to the mixture approach by accounting additionally for the pore‐fluid interchange between the contacting porous solids. Except for the contact between the solid skeletons of two solids, it is important to determine the interaction forces exerted by the pore‐fluid on the pore‐fluid and the porous skeleton. In this contribution, it is assumed that at the permeable contact boundaries, the fluid effective pressure and the fluid mass flux across the surface are continuous [1].
3D rheological model of transversal isotropic elastoplastic body
Authors: Naumov Victor , Palmov Vladimir , Schrefler Bernard
Published: June 2004

A 3D theory of microplasticity for an anisotropic elastoplastic body is presented. This theory is proposed for the phenomenological description and analysis of deformation of a superconducting cable under the transversal cyclic loading. Obtained constitutive equations reflect the possibility to describe hysteresis loops during cyclic loading of the material. They reflect the fact that these hysteresis loops don't depend on the strain rate. Developed theory deals with phenomenological anisotropy of elastoplasticity which is a characteristic property of the superconducting cable. This cable consists of a large number of strands oriented in general along the cable axis.
Interparticle contact forces in fine cohesive powders. Theory and experiments
Authors: Quintanilla M. A. S. , Castellanos A. , Valverde J. M.
Published: June 2004

The flow of fine powders is strongly influenced by interparticle contact forces. Depending on the interparticle load force the contact behavior can be elastic, fully plastic or elasto‐plastic. We propose a model for the elasto‐plastic loading regime that yields a nonlinear dependence of the interparticle adhesion force on the interparticle load force. Interparticle forces are also obtained experimentally. Theoretical results are in reasonable agreement with experimental data.
Transverse Force at the Yield Hinge during End Controlled Plane Bending and the Influence of its Neglect on the Shape Error
Authors: Reigl Martin , Lippmann Horst
Published: June 2004

End controlled plane bending is an air bending process for tubes, profile bars and sheet metal, where the work‐piece is clamped at its ends only and where its prescribed final shape is reached by the controlled motions of the chuckings. The corresponding deformation is generated by moving a yield hinge or a yield zone from one end of the work‐piece to the other [1]. In this way many kinds of prescribed final shapes can be obtained like, among others circular, plane spiral, or elliptic arcs, which was proved by experiments [2]. The transversal force disappears in the moving yield hinge in the case of bending a circular arc. In many other cases, the transversal force is small compared with the normal force and can therefore be neglected. This simplifies the control software and reduces restrictions on the material law. However if the prescribed final shape has a strong curvature gradient, this simplification can lead to a remarkable shape error and will then not be allowable. The shape error depends also on the bending force, which is a free parameter in the bending process. On the example of bending a brass bar with L‐shaped cross section into a quarter elliptic arc, the shape error is quantified in dependence of the bending force.
Ein mikro‐polares Modell für Fasersuspensionsströmungen und dessen erste numerische Abschätzung
Authors: Altenbach Holm , Dyogtyev Oleksandr , Naumenko Konstantin , Zhilin Pavel
Published: June 2004

Für die Festigkeit eines Bauteils aus kurzfaserverstärktem Polymer ist die Orientierung der Fasern entscheidend. Zur Vorhersage der Ausrichtung von Fasern benötigt man ein Modell für die der Strömung der Suspension. Nachfolgend wird ein mikropolares Modell für das Fließen von Suspensionen mit Fasern und dessen erste numerische Abschätzung diskutiert.
On the modelling of nonlinear electro‐mechanical coupled ferroelectrica
Authors: Romanowski H. , Schröder J.
Published: June 2004

In this contribution we discuss a simple phenomenological model for an assumed transversely isotropic ferroelectric crystal. We focus on the theoretical formulation and numerical treatment of the coupled electro‐mechanical behaviour. The main goal of this investigation is to capture the main characteristics of nonlinear ferroelectrica, such as the polarization‐electric‐field and the quadratic strain‐electric‐field (butterfly) hysteresis loops. The history dependency is modelled via two internal variables, the irreversible polarization and its conjugated irreversible electric‐field.
A Macroscopic Erosion Model
Authors: Steeb H. , Diebels Stefan
Published: June 2004

We present a continuum‐mechanically based model to describe erosion/deposition, growth/atrophy and remodeling phenomena. The considered model is based on the thermodynamically consistent Theory of Porous Media. The mixture is assumed to consist of a solid constituent, a fluid constituent and an abrasive constituent containing the fluidized particles. The abrasive process is described by a phase transition modeled in terms of mass exchange between the solid and the abrasive constituents. The balance equations of the present model are formulated in a general setting within the material space. Assuming several a‐priori restrictions for some specific applications and evaluating the balance of entropy specializes the constitutive equations for the considered model.
Zur Anwendung elasto‐plastischer Schädigungsmodelle im Stahl‐/Stahlbeton‐Verbundbau
Authors: Schröder K.‐U. , Nasdala L. , Rothert H.
Published: June 2004

Durch die steigenden Anforderungen hinsichtlich Wirtschaftlichkeit und Komplexität an moderne Bauten rückt die Berücksichtigung nichtlinearer Werkstoffeigenschaften im Rahmen der Berechnung und Lebensdaueranalyse immer weiter in den Blickpunkt der Anwendung. Ein Bereich, in dem das nichtlineare Tragverhalten wesentliche Auswirkungen auf Bemessung und Konstruktion der Bauteile hat, ist der Stahl‐/Stahlbeton‐Verbundbau. In diesem Artikel wird ein elasto‐plastisches Schädigungsmodell für den Beton vorgestellt. Die Anwendung dieses Modells erfolgt im Rahmen der Simulation des Tragverhaltens eines Kopfbolzendübels eines Verbundträgers. Dieser Kopfbolzendübel ist auf den Stahlträger aufgeschweißt und dient der Schubübertragung zwischen Stahlträger und Stahlbetonplatte.
State of stress around a crack close to the boundary in a Rayleigh wave zone
Authors: Wille Ralf
Published: June 2004

The problem for an elastic half‐plane with a crack close to the boundary, located in a zone of Rayleigh surface waves, is generalized for a half‐plane with a crack obliquely oriented to the boundary. Fourier integral transformations are used to reduce the problem to the solution of a system of two coupled singular integral equations. The stress intensity factors are determined and related to the frequency of the external loads.
Analysis of coupled finite element and atomistic models
Authors: Abdi Tadesse , Sunyk Rudolf , Menzel Andreas , Steinmann Paul
Published: June 2004

This paper presents the coupling of finite element and atomistic models for the analysis of crystalline solids. The combined finite element and atomistic method has found a wide range of applications, e.g. in the study of crack propagation [1] and defects [2].
A 3‐D Model for Finite Viscoelsatic Swelling of Charged Tissues and Gels
Authors: Acartürk Ayhan , Ehlers Wolfgang , Abbas Ibrahim , Markert Bernd
Published: June 2004

Materials like soft biological tissues undergo large viscoelastic deformations during the swelling process. Following this, it is the goal of this contribution to merge the advances of finite viscoelasticity laws and the state of the art in electrochemical swelling theories within a well‐founded multiphasic concept. The numerical treatment is carried out fully 3‐d in the framework of the FEM.
Finite elements in shell analysis: A comparison of 3D‐p‐ and higher order shell elements
Authors: Nachname Christian , Hommel Jan‐Hendrik , Meschke Günther
Published: June 2004

The considerable progress in computational power has increased the attractivity of 3D‐p‐finite‐elements as a versatile tool in structural analysis. Due to its flexibility, the lack of various locking phenomena inherent to low order shell elements and the possibility of an a posteriori error assessment, 3D‐p‐finite‐elements have become an attractive alternative to the h‐method even for analyses of thin‐walled structures. In this paper a comparison of 3D‐p‐ and higher order shell elements concerning aspects of accuracy and efficiency is presented.
Mehrgitterberechnungen von nichtlinearen Hohlstrukturen
Authors: Bitzenbauer J. , Schweizerhof K.
Published: June 2004

Die Finite Elemente Untersuchung von aus Hohlzellen aufgebauten Körpern mit nichtlinearem Materialverhalten führt bei durchgängiger Diskretisierung der Mikrostrukturen üblicherweise auf sehr grosse Gleichungssysteme. Als eine effiziente Lösungsmethode empfehlen sich Mehrgittermethoden. Damit ist im Gegensatz zur rein homogenen makroskopischen Betrachtung die Berücksichtigung lokaler Effekte (z.B. in Grenzschichten) möglich. Anders als bei der Homogenisierung können mit Hilfe des vorgestellten Konzeptes auch komplett aperiodische Strukturen betrachtet werden. Während im klassischen Multigridverfahren die minimale Anzahl der zur Geometriebeschreibung notwendigen Finiten Elemente von der Geometrie selbst abhängig ist, besteht ein gröbstmögliches Gitter bei der Composite Finite Elemente Methode (CFE, [1,2,3]) aus einem Element. Als Anwendungsbeispiel dient ein Hohlkörper mit aperiodischem nichtlinearen Verhalten.
Finite element simulation of rubber‐like material behaviour under consideration of its microscopic structure
Authors: Böl M. , Reese S.
Published: June 2004

The structure of rubber‐like materials is characterized through chain‐like macromolecules which are linked together at certain points. This special design leads to a completely random three‐dimensional network. There exist several ways to specify rubber‐like material behaviour. Many scientists use the tool of statistical mechanics to transfer the information from the micro level to the macro level. In this context, one should mention e.g. the work of Treolar & Riding [1979] (full network theory) or the eight‐chain model suggested by Arruda & Boyce [1]. In the present contribution, the step from the micro level to the macro level is done by means of the finite element method. For this purpose, we derive a unit cell consisting of one three‐dimensional tetrahedral finite element and six truss elements lying on every edge of the tetrahedron. The truss elements represent the material behaviour of a certain group of polymer chains, whereas the tetrahedral elements ensure incompressibility. So, using a finite element model with a sufficiently high number of unit cells, we are able to model the well‐known macro‐mechanical material behaviour of rubber‐like polymers.
A Poroelastic Mindlin‐Plate
Authors: Busse Anke , Schanz Martin , Antes Heinz
Published: June 2004

The numerical treatment of noise insulation of solid walls has been an object of scientific research for many years. The main noise source is the bending vibration of the walls usually modeled as plates. Generally, walls consist of porous material, for instance concrete or bricks. Therefore, a poroelastic plate theory is necessary. A theory of dynamic poroelasticity was developed by Biot using the solid displacements and the pore pressure as unknowns. After formulating the poroelastic theory for thick plates, Mindlin's theory, a variational principle for this poroelastic thick plate model is developed. This is the basis of a Finite Element formulation.
An anisotropic finite 3D beam element for the analysis of piezoelectric structures
Authors: Butz A. , Klinkel S.
Published: June 2004

A finite element formulation for a 3D beam is presented to model rod like piezoelectric structures. Piezoelectricity is described by a mixed field theory that couples mechanical and electrical quantities. In this work the coupling between the mechanical stress and the electric displacement is considered. Therefore a 3D beam element formulation with nine degrees of freedom per node is introduced. Due to the poling process, the piezoelectric materials have anisotropic material properties which are taken into account in the presented beam formulation. Further more we suggest a special approximation for the electric potential through the cross‐section of the beam. An excentric beam formulation is used to model the layerwise design that is often found on piezoelectic structures.
Alternative Definitions of Micro–to–Macro Transitions in Particle Aggregates of Granular Materials
Authors: Dettmar Joachim , Miehe Christian
Published: June 2004

An alternative approach to the modelling of the overall macroscopic response of granular materials is presented based on micro–macro transitions. A homogenized macro–continuum is considered with locally attached granular microstructures. The new developments include a consistent transfer of micro–macro transitions from continuous to particle microstructures with a new overall macro–stress definition. Secondly, a new class of boundary conditions for displacements/ rotations on prescribed boundary–frame particles is presented that yields upper and lower bounds with regard to the aggregate stiffness. Thirdly, a unified implementation of the displacement/ rotation boundary constraints by a penalty method is developed that proves to be a convenient computational tool in explicit codes.
A DAE‐approach applied to elastic‐plastic material behavior using FEM
Authors: Ecker Steffen , Baaser Herbert , Gross Dietmar
Published: June 2004

Simulating elastic‐plastic material behavior with the finite element method (FEM), two different types of equations appear. The spatial discretization of the considered domain leads to a system of nonlinear equations for the unknown displacements, whereas the time‐evolution of the internal variables describing the inelastic state is governed by first order differential equations. Altogether a system of differential‐algebraic equations (DAE) has to be solved. In the following, the DAE‐concept is used to describe rate‐independent, associated plasticity, but it can also be applied to visco‐plastic material behavior. The advantage of using a BDF2‐method for time integration of the internal variables is emphasized and the differences between the classical 'elastic predictor – plastic corrector' approach and our method are pointed out. A comparison between both methods in terms of computational efficiency will also be presented. The numerical implementation is done in DAEdalon [2], a free available FEM‐Package.
Development of a Contact Element for Finite Deformations using the MortarMethod
Authors: Fischer Kathrin A. , Wriggers Peter
Published: June 2004

The Mortar method is based on domain decomposition techniques that allow powerful solutions of PDE's for nonmatching meshes. The variational formulation of the contact contributions is expressed with Lagrange multipliers which are discretized with special interpolation functions. A segmental contact description is used to dicretize nonmatching meshes. Applying this method to contact problems in engineering, attention has to be paid to finite deformations and curved bounded regions. With regard to later applications of higher order interpolation functions, a simple 2‐dimensional formulation with linear interpolation functions for the multipliers and the displacements is presented for frictional contact problems.
A Micro‐ Thermomechanical coupled Finite‐Element Model for the Simulation of Particulate Cellular Solids at Finite Strains
Authors: Freßmann Dirk , Wriggers Peter
Published: June 2004

A numerical model for the simulation of the complex material behaviour of particulate cellular solids on the mesolevel of single foam pellets is presented. During the deformation process, extremely large local deformations can occur, that are resolved using a displacement‐based arbitrary Lagrangian‐Eulerian approach. A special treatment of the thermomechanical problem is able to account for the highly non‐linear thermomechanical material behaviour of the foam material.
Numerical solution of flow through a cascade and over a profile with dynamicaland aeroelastic effects
Authors: Honzátko R. , Horáček J. , Kozel K.
Published: June 2004

The work deals with a numerical solution of 2D inviscid incompressible flow through a cascade and over a profile in a channel. The finite volume method in a form of cell‐centered scheme at triangular and qudrilateral mesh is used. The composite scheme applied to a numerical solution consists of more dissipative part (Lax‐Friedrichs scheme) and less dissipative part (Lax‐Wendroff scheme). Governing system of equations is the system of Euler equations. Two possibilities are considered.
Description for smooth contact conditions based on the internal geometry of contact surfaces
Authors: Konyukhov Alexander , Schweizerhof Karl
Published: June 2004

A kinematical approach, based on the consideration of the contact conditions in the local coordinate system, is proposed for the contact description and for consistent linearization. This leads to a simple structure of the tangent matrix, which is subdivided into main, rotational and curvature parts. Various alternatives neglecting parts of the contact tangent matrix are considered. Representative examples show the effectiveness of the proposed approach for contact problems with arbitrary large deformation.