bluuebunny/crossref_metadata_2025 huggingface dataset:
Biegung von endlichen Torusschalen unter Berücksichtigung der Schubdeformation
Authors: Hübner W.
Published: May 2007

Es werden Torusschalen mit Kreisquerschnitt unter Verwendung der linearen Theorie flexibler Schalen behandelt. Die Belastung erfolgt ausschließlich durch ein reines Biegemoment. Dabei erhält man die bekannte Abplattung und Spannungsverlagerung zur Mitte hin. Bei den hier behandelten endlichen Schalen sind diese Effekte für jeden Querschnitt verschieden, was von den Verhältnissen an den Enden abhängt. Dabei werden zwei technisch sinnvolle Grenzfälle, die ‘dünnen Flansche’ und die ‘starren Flansche’, betrachtet. Hier wird das Problem unter Berücksichtigung der Schubdeformation und der Torsionsmomente behandelt. Ihr Einfluß erweist sich besonders bei den ‘starren Flanschen’ und bei größeren Vorkrümmungen als bedeutend. Das System wird durch zwei partielle Differentialgleichungen je sechster Ordnung beschrieben und durch Fourier‐Reihenansätze in zwei Koordinatenrichtungen gelöst. Als wichtige Ergebnisse werden das Biegeverhalten und die Spannungsverteilungen dargestellt.
Monotone Data Smoothing by Quadratic Splines via Dualization
Authors: Schmidt J. W.
Published: May 2007

For monotone smoothing of univariate data sets an objective function is used which represents a trade‐off between curvature minimization and interpolation. The monotonicity condition is taken into the constraints. Using quadratic splines this smoothing problem is discretized by a quadratic program, and this in turn can be dualized in such a way that an unconstrained program results. In addition, a return‐formula holds true by means of which the optimal spline is directly computed from a solution of the dual problem. Thus, from a numerical point of view this approach is attractive. Here the dualization is performed via Fenchel's theory. For computing the needed Fenchel conjugates it is convenient to fix one of the variables.
An Enclosing Theorem and a Monotone Iterative Scheme for Elliptic Systems Having Nonmonotone Nonlinearities
Authors: Carl S.
Published: May 2007

This paper presents an existence and enclosure result for solutions of semilinear elliptic systems in case that the nonlinearities do not possess any monotonicity properties. Moreover, it is shown that even in this case one is able to establish a monotone iterative scheme for constructing the solution, provided that a certain matrix, which is related to the spectrum of an associated linear differential operator, is positive definite.
Determination of Seiche Periods Using the Rayleigh‐Schrödinger Technique
Authors: Lundberg P.
Published: May 2007

Calculating the periods of long standing waves in closed oblong basins is a classical problem within limnology and oceanography. Particular difficulties arise when the basin under consideration displays topographical variations, and in general it proves necessary to resort to approximative procedures for these cases. Traditionally the resulting eigenvalue problem has been resolved with collocation methods, but in the present study it is shown that a perturbation technique can be used instead.
On Deformation under Strain Path with a Corner
Authors: Gupta N. K. , Lauert H.‐A. , Zdebel U.
Published: May 2007

Ck15 steel tubular specimens were subjected to two straight line strain paths making an angle of 0° to 90° with each other and typical histories of stress and strain are presented. A comparison with the predictions of generalized theory developed by Lehmann [1] in the frame of continuum mechanics and thermodynamics has been made with a view to studying the influence of the main parameters encountered in the description of large non isothermal deformation.
Globale rheonichtlineare Schwingungen, Anwendung auf parametrische Stromgeneratoren
Authors: Dum R. , Schmidt G.
Published: May 2007

Untersucht werden parametererregte nichtlineare Schwingungen, bei denen die Parametererregung mit linearer und nichtlinearer Trägheit verbunden ist wie in Beispielen, die unter anderem von A. Weigand, K. Klotter und W. W. Bolotin untersucht wurden. Durch trigonometrische Iteration ergeben sich Resonanzkurven und Stabilitätsgrenzen. Anwendungen auf parametrische Stromgeneratoren werden dargestellt.
The Dynamics of a Ball Rolling on a Rotating Plane
Authors: Holden J. T. , King A. C.
Published: May 2007

In the absence of any viscous or rolling resistance, a ball set on a uniformly rotating horizontal plane does not leave the plane but moves in a circular orbit. The equations of motion, when both viscous drag and rolling resistance are present, were set up by Fufaev [1] and Abdelkader [2] obtained a complicated implicit solution of the equations. In this paper we show that solutions may be found explicitly. The solutions depend on two parameters which determine whether the ball spirals towards, or away from, the axis of rotation, onto a circular orbit, or onto a fixed point.
Response of a Viscous Liquid Column to Axial Excitation in Zero‐Gravity
Authors: Bauer H. F.
Published: May 2007

The response of a viscous liquid column to axial excitation has been determined analytically. For a simplified analytical treatment the no‐slip condition at the top and the bottom of the liquid column has been abandoned, while the normal condition could be satisfied. The free liquid surface elevation, the radial‐ and axial velocity distribution have been presented for various surface tension parameters σa/qv2, aspect ratios l/a and at various locations inside and along the liquid bridge as functions of the forcing frequency parameter Ωa2/v. It could be noticed that due to viscosity the resonance amplitudes are finite and that the lowest resonance is sharply tuned.
Biothrogonale Entwicklungen der Verteilungsdichte und ihre Anwendung zur Analyse stochastischer Systeme. Teil II: Beispiele
Authors: Ahlbehrendt N. , Sperling L.
Published: May 2007

Die neun Beispiele unterschiedlicher eindimensionaler, nichtlinearer stochastischer Systeme des vorliegenden Teils II belegen die im Teil I, Abschnitt 4, allgemein gegebenen Empfehlungen und Einschätzungen, insbesondere bezüglich der Anwendbarkeit der gegenüber den bisher bekannten Spezialreihen QME(pG) und QME(po/ϕ) erheblich verallgemeinerten QME(po/F) auf eine breitere Klasse von stochastischen Systemen, sowie die Konstruktivität des in Teil I, Abschnitt 3, angegebenen Auswahlkriteriums für po(z) zum Aufbau einer QME(po/F) mit polynomialem Funktionensystem Fk(z/po) im eindimensionalen Fall. Die Beispiele sind auf die näherungsweise Berechnung der ersten beiden stationären Momente beschränkt.
A Direct BEM for Magnetic Fields
Authors: Schmidt G. , Strese H.
Published: May 2007

In the paper we consider a direct Boundary Element Method for the field calculation of magnetic heads, based on the solution of two Fredholm integral equations of second resp. first kind. We study the solvability and the convergence of the given approximation method.
Shifting Tendency Functions of a System with Friction Affected Constraints and Equilibrium Zones
Authors: Klepp H. , Meyers A.
Published: May 2007

The result of mathematical investigations of a balanced system with friction affected constraints are presented. In order to predict the system behaviour under perturbations inside the equilibrium zone, difference functions and shifting tendency functions are defined. With the help of deflections till the end of motion, respectively inital accelerations, these functions are established. The effect of friction and perturbation parameter variation on the shifting tendency functions is analysed, and the specific influence of the friction affected constraints is pointed out.
Effects of Mixed Convection and Viscous Dissipation on Heat Transfer about a Porous Rotating Sphere
Authors: Hatzikonstantinou P.
Published: May 2007

The effect of viscous dissipation on forced and mixed convection, when the flow is caused by a uniformly accelerated free stream velocity about a rotating sphere, is studied numerically. Results are presented for gases with Prandtl number 0.71 and for various values of the rotational velocity and the buoyancy (A) and viscous dissipation (E) parameters, when the surface of the sphere has a constant temperature. The surface of the sphere is considered to be impermeable or porous subjected to suction or injection. The heat transfer rate Nu and the wall shear stress are also calculated. The increase of the viscous dissipation yields to the decrease of Nu. As E increases the heat transfer rate becomes independent of buoyancy for E > 0, while it depends strongly on the buoyancy when E < 0. The number Nu increases with suction while decreases with injection.
On the Non‐Abelian Motor Calculus
Authors: Stumpf H. , Badur J.
Published: May 2007

A nonlinear (non‐abelian) extension of the motor analysis is considered. The semi‐direct product T(3) δ SO(3) is introduced and the associated Lie algebra is given. Nonlinear generalisation of the grad‐, rot‐ and div‐operators are presented. An energetic product for variables conjugate with respect to the energy is defined.
On the Connection Between Mechanical Force Equilibrium and Nonlinear Programming
Authors: Rapcsák T. , Szenthe J.
Published: May 2007

Analytical mechanics is a branch of classical mechanics whose basic problem is the characterization of the motion and of the equilibrium positions of the systems of material points. Physicists and mathematicians have been dealing for a long time with this problem and though almost all books on mechanics may contain a part discussing this subject, the standard mathematical treatment of this problem seems to be not yet complete. This paper will attempt at the systematization of mathematical problems relevant to the force equilibrium of mechanical systems with a finite degree of freedom, the determination of possible velocities in case of general constraints and the comparison of the principle of virtual work and the Courtivron principle. The main aim of the paper is to demonstrate that mathematical programming can advantageously be applied to mechanics.
Enclosure Methods as Applied to Linear Periodic ODEs and Matrices
Authors: Adams Prof. Dr.‐Ing. E. , Cordes D. , Keppler H.
Published: May 2007

Concerning linear ODEs with periodic coefficients, enclosure methods are presented for the verification of (i) asymptotic stability of the homogeneous ODEs and (ii) the existence of periodic solutions of the nonhomogeneous ODEs. In the case of forcing stochastic “interval point processes”, (iii) the set of (classical) solutions and marginal distribution functions concerning this set are enclosed. A sufficient matrix test with respect to (i) is directly applicable for the verification of |λi| < 1 or Re (λi) < 0 for the eigenvalues λi or λi of related matrices. Numerical examples show the power of the presented enclosure methods, among others in applications concerning gear drive vibrations.
A Model for Non‐Symmetric Flow of Suspensions through Cylindrical Channels
Authors: Perkkiö J.
Published: May 2007

The velocity profile, shear rate, and shear stress in two‐ or three‐dimensional “layered” flow of a suspension were calculated analytically or numerically. The densities of the suspended particles and the suspension fluid were assumed to be different. The viscosity of the suspension was assumed to increase either exponentially or linearly from the top to the bottom of the channel. The maximum velocity was shifted towards the top of the channel, and the vertical skewing of the velocity profiles increased, as the viscosity of the lower layers increased. The shear rate was markedly decreased near the bottom of the channel, and increased near the top of the channel. The shear rate profile became highly nonlinear when the viscosity increased. The shear stress distribution was approximately piecewisely linear. The minimum of shear stress was shifted upwards similarly as the minimum of shear rate when the viscosity increased.
Practical Fourier Analysis — Error Bounds and Complexity
Authors: Brass H.
Published: May 2007

Die praktische Berechnung der Fourier‐Koeffizienten geschieht gewöhnlich mit Hilfe der Formel Es gibt andere Formeln Q, die die gleiche Information (nämlich die Funktionswerte f(vh), v = 0, 1, …, n ‐ 1) benutzen, aber einen kleineren (Maximal‐) Fehler in der Klasse 𝔑s der periodischen Funktionen mit beschränkter s‐ter Ableitung garantieren. Insofern verschwendet das übliche Vorgehen Information. Ziel dieser Arbeit ist eine Abschätzung dieses Verlustes. Zu diesem Zweck wird untersucht, welche Genauigkeit überhaupt erreichbar ist, und es werden ziemlich scharfe Schranken für den Fehler von QSt (als Funktion von (s, p, n)) hergeleitet.
Saint‐Vénant Solutions for Beam Buckling Problems
Authors: Theocaris P. S. , Lazopoulos C.
Published: May 2007

Das Knickproblem für einen einfach unterstützten Balken unter axialer Belastung wird diskutiert unter der Annahme der semiinversen Saint‐Venant‐Lösungen anstelle der Bernoullischen Balkenkonvention. Das Motiv für die vorliegende Studie waren die experimentellen Daten, die durch die empfindliche experimentelle Methode der Kaustiken erhalten wurden.
Compatibility Conditions at Corners between Walls and Inflow Boundaries for Fluids of Maxwell Type
Authors: Renardy M
Published: May 2007

Wir zeigen einen Existenz‐ und Eindeutigkeitssatz für stationäre Strömungen von Flüssigkeiten mit differentiellen konstitutiven Gleichungen vom Maxwellschen Typ. Die hier untersuchten Strömungen sind kleine Störungen einer ebenen Poiseuilleströmung, und es wird angenommen, daß die Scherrate in der ungestörten Poiseuilleströmung hinreichend klein ist. Das Problem ist gestellt in einem rechteckigen Gebiet, wobei die Flüssigkeit durch eine Seite hinein‐ und durch die gegenüberliegende Seite hinausfließt. Das Interesse konzentriert sich in erster Linie auf Kompatibilitätsbedingungen, welche die Daten des Problems erfüllen müssen, um Singuläritäten an den Ecken zwischen der Seite, durch die die Flüssigkeit hineinströmt, und den Wänden zu vermeiden.
Some Thermodynamic Aspects of Finite Amplitude Unloading Waves in Hyperelastic Strings
Authors: Haddow J. B. , Wegner J. L.
Published: May 2007

Einige thermodynamische Aspekte von Entlastungswellen endlicher Amplitude in hyperelastischen Saiten, die einfachem Zug unterworfen sind, werden untersucht. Von den Saiten wird angenommen, daß sie inkompressibel sind mit ihren isothermen Spannungs‐Drehnungs‐Relationen, die durch die Money‐Rivlin‐Verformungsenergiefunktion bestimmt werden. Der Zweck der Untersuchung ist die Erforschung des Einflusses des Entropiesprungs über Stöße und die Berechtigung für die Verwendung einer isothermen Spannungs‐Dehnungs‐Relation. Resultate für Saiten, die strenge Entropieelastizität zeigen, werden verglichen mit jenen für die Saiten, die piezotrope Elastizität zeigen. Für strenge Entropieelastizität kann die innere Energie als Funktions der Temperatur allein dargestellt werden, und für piezotrope Elastizität sind die mechanischen und thermischen Effekte ungekoppelt.
Analysis angepaßter Quadraturmethoden für Integralgleichungen zweiter Art: Konvergenzeigenschaften
Authors: Micke André
Published: May 2007

Diese Arbeit beschäftigt sich mit einer Klasse von Approximationsmethoden für Integralgleichungen zweiter Art mit Operatoren , wobei das Intervall [a, b] endlich, die Funktion y stetig ist und der Kern k möglicherweise Unstetigkeiten oder eine schwache Singularität besitzt. Die betrachteten Näherungsoperatoren haben Stützstellen, die den Eigenschaften des Kernes — beispielsweise eine Unstetigkeitstrajektorie — angepaßt sind. Eine allgemeine Konvergenztheorie für Approximationsverfahren dieser Art wird vorgestellt. Die Approximationseigenschaften der Operatoren KM werden zurückgeführt auf die der zugrundegelegten Quadratur.
Turbulente Strömungen in konzentrischen Ringspalten (Asymmetrische Profile)
Authors: Szablewski Witold
Published: May 2007

Die Verschmelzung der zwei voneinander verschiedenen Turbulenzstrukturen — Schubspannung τ1(∥τ1∥≠∥τ0∥) an der inneren Wand r1, Schubspannung τ0 an der äußeren Wand r2 des Zylinders — erfolgt mittels eines linearen Ansatzes in dū/d(r — r1) für die turbulenten Schubspannung in der axialen, nicht mehr dem Einfluß der Wand unterliegenden Schicht der Strömung. Übereinstimmung mit Messungen.
A Boundary Layer Phenomenon for Linear Systems with a Rank Deficient Matrix
Authors: Bohl E
Published: May 2007

This paper considers linear systems with a singular matrix and provides a regularization to compute all solutions. If the system is a perturbation of a rank deficient matrix, a boundary layer phenomenon is possible. Systems of the kind considered occur in enzyme kinetics. A particular example and numerical results are given.
Branch Inclusion in Generic Hopf Bifurcation: General Approach
Authors: Schneider K. R. , Heinz G.
Published: May 2007

By using averaging transformations we determine approximations of higher order for the family of bifurcating periodic solutions in the generic case of Hopf bifurcation. These approximations permit the application of the Newton‐Kantorovič Theorem to derive inclusions of the amplitude and period.
Enhanced Accuracy and Applicability of Analytico‐Numerical Solutions to Ordinary Differential Problems
Authors: Reali M , Dassie G
Published: May 2007

This report concerns the potential of analytico‐numerical techniques based on Taylor series developments for solving classes of ordinary differential problems presenting remarkable numerical difficulties. Such techniques which are rather flexible and easily programmable may lead to very accurate solutions as is demonstrated with two problems which are worked out in detail. The first problem models a strongly non‐linear event, an underwater explosion leading to spherical bubble oscillations characterized by ultrarapid variations of the bubble/water interface velocity. The second problem, a steady‐state convective‐diffusion calculation, is also solved in a very accurate way even for very large Peclet numbers when solutions obtained form specific discretization techniques are much less accurate.
Untersuchungen zur werkstoffmechanischen Stabilität metallischer Faserverbundwerkstoffe mit geschädigter Struktur bei zyklischer thermomechanischer Belastung
Authors: Dressler R , Ismar H , Ripplinger W
Published: May 2007

Das Verhalten eines faserverstärkten Bauteils mit metallischer Matrix wird unter zyklischer thermomechanischer Belastung simuliert. Die metallische Matrix des Verbundwerkstoffes wird durch ein weiterentwickeltes Zweiflächenverfestigungsmodell auf der Grundlage des Übergangsfließpotentials beschrieben, um die typischen nicht‐linearen Effekte zyklischer Plastizität und deren Temperaturabhängigkeit zu berücksichtigen. Es wird eine spröde, intermetallische Schicht zwischen Faser und Matrix angenommen, die sich linear‐elastisch verhält. Ohne ein neues FE‐Netz erzeugen zu müssen, können wir numerisch das Fortschreiten eines anfänglich existierenden Risses innerhalb der Zwischenschicht verfolgen. Auf der Grundlage dieses Werkstoffmodells untersuchen wir die werkstoffmechanische Stabilität an dem ausgewählten Beispiel eines faserverstärkten Rohers.
Optimal Control in Nonlinear Evolution Equations with Constraints
Authors: Kampowsky W.
Published: May 2007

This paper continues the investigations of the author [5] – [12] concerning optimal control of nonlinear evolution equations with monotone operators. Necessary optimality conditions are derived where additional constraints in a general from for the state and the control are allowed. As applications a Dirichlet boundary control problem and a time‐optimal problem are considered.
On the Stability in Obstacle Problems with Applications to the Beam and Plate
Authors: Miersemann E. , Mittelmann H. D.
Published: May 2007

New stability results are proved for solutions to variational inequalities with an eigenvalue parameter. These describe obstacle problems and rather general nonconstant obstacle functions are considered. Sufficient conditions are given for the solution bifurcating at the critical load to define a minimum of the associated energy functional. One of the results is that the stability behavior depends discontinuously on the obstacle. Applications to the beam and plate are given both in analytical and numerical form.
On the Method of Asymptotic Expansions for Plates
Authors: Molnárka Gy.
Published: May 2007

The method of asymptotic expansion is an efficient method for simplifying complicated mathematical problems. But if the small parameter is a geometric one the physical interpretation of the result is more difficult. Here we present a new asymptotic expansion connected with the equation describing the deformation of linear plates. The steps of this method can be physically interpreted analoguosly as in the earlier methods however the resulting equation is different.
Modellierung von Verdrängungsvorgängen in Laborversuchen
Authors: Aavatsmark I.
Published: May 2007

Ein Modell für eindimensionale Zweiphasenströmung in porösen Feststoffen wird aufgestellt. Unterschiedliche Randbedingungen für die Verdrängungsversuche des Flutens, der kapillaren Aufsaugung und der Schweredränage sind nötig. Die sich ergebenden Anfangsrandwertaufgaben besitzen starke Nichtlinearitäten und Singularitäten. Die einzelnen Glieder der Differentialgleichung und der Randbedingungen werden erörtert. Bei der Diskretisierung werden die mathematischen Eigenschaften der Differentialgleichung herangezogen. Somit wird das diskrete Verfahren unter Berücksichtigung der Erhaltung, der Flußkonsistenz und der Monotonie aufgestellt. Wegen der Monotonie sind in der Nähe der stationären Lösung sehr große Zeitschritte erlaubt. Abschließend werden Beispiele numerischer Simulationen der genannten Verdrängungsvorgänge gegeben.
Dynamic Buckling Estimates for Discrete Systems under Step Loading
Authors: Kounadis A. N. , Mallis J. , Raftoyiannis J.
Published: May 2007

This paper deals with nonlinear dynamic buckling analysis of imperfection sensitive or more generally limit point discrete systems under suddenly applied loads of infinite duration. Static and dynamic stability conditions and respective buckling estimates for such systems without or with damping are properly established. It was shown that the static stability criterion associated with zero total potential energy and negative definite second variation leads always to exact dynamic buckling loads for one‐degree‐of‐freedom systems if damping is ignored, and to lower bound buckling estimates if this effect is included. It was also found that such a static criterion leads always to lower bound dynamic buckling estimates for multi‐degree‐of‐freedom systems with or without damping. Moreover, it was established that dynamic buckling associated with an unbounded (damped or undamped) motion occurs for that magnitude of the load for which the velocity of the phase point corresponding to any one of the generalized coordinates of the system vanishes for the first time.
An L1‐Stable Scheme for Linear Turning Point Problems
Authors: Vulanović R.
Published: May 2007

A finite‐difference scheme for linear turning point problems is proposed. Its stability in the discrete L1 norm and the second order accuracy are investigated.
Response of a Viscous Liquid Column to Pitching‐ and Roll‐Excitation in Zero‐Gravity Environment
Authors: Bauer H. F.
Published: May 2007

The response of a viscous liquid column to pitching‐ and roll excitation has been determined. For a simplified analytical treatment the no‐slip condition at the top and the bottom of the liquid column has been abandoned in the pitching case. The responce of the free liquid surface displacement and the velocity distribution has been determined as a function of the reduced frequency Ωa2/v for various surface tension parameters σa/ϱv2. Due to viscosity the resonance amplitudes are finite and disappear for higher modes and shorter liquid bridges. The velocity distribution, effective moment of inertia and effective damping was obtained for the liquid in roll excitation.
Behaviour of a System Under Harmonic Excitation Inside an Equilibrium Zone
Authors: Klepp H. J.
Published: May 2007

A multi‐body‐system in form of a deformable parallelogram with friction affected constraints is considered. The system possesses an equilibrium zone. Under the action of a harmonic excitation the system migrates inside the zone. By numerical simulation it is found that the directions and speeds of migration are indicated by the shifting tendency functions established for the equilibrium zone.
Eine FEM‐Methode für ein quasistationäres elektrisches Feld
Authors: Lucht W , Radke Th.
Published: May 2007

Auf der Basis der quasistationären Maxwellschen Gleichungen wird für einen elektrisch betriebenen Reaktor das elektrische Feld E ermittelt. Es wird für einen praktisch realistischen Fall eine auf einem beschränkten Gebiet abgeschlossene Randwertaufgabe für E formuliert, für die eine Finite‐Elemente‐Approximation angegeben wird.
On Certain Problems of Heat Conduction in Periodic Composites
Authors: Matysiak S. J.
Published: May 2007

The paper deals with the problems of transient heat conduction in periodic rigid composites. The unit cell of the body is assumed to be composed of four different materials (see Fig. 1). The homogenized model of the composite is presented as well as two examples are discussed.
Block Runge‐Kutta Methods on Parallel Computers
Authors: van der Houwen P. J. , Sommeijer B. P.
Published: May 2007

In this paper block methods for solving ODEs on parallel computers are constructed. Most block methods found in the literature produce approximations to the exact solution at equidistant points. Here, we allow that the approximations correspond to nonequidistant points like the intermediate approximations computed in Runge‐Kutta methods. This approach enables us to improve the order of accuracy. We concentrate on explicit methods such that they are suitable for use on parallel computers.
On the Iterative Solution of van Roosbroeck's Equations
Authors: Gajewski H. , Gärtner K.
Published: May 2007

In 1950 VAN ROOSBROECK has derived a system of nonlinear partial differential equations which is used now generally as the base for numericla modelling carrier transport in semiconductors. In this paper we deal with the iterative solution of the linearized van Roosbroeck system. This problem arises from the numerical realization of Newton's method as well as the small‐signal analysis of devices.
Optimal Design of an Elastic or Elasto‐plastic Beam with Unilateral Elastic Foundation and Rigid Supports
Authors: Hlaváček I. , Lovišek J.
Published: May 2007

A class of optimal design problems is considered, where the state problem is governed by a variational inequality. The latter includes a nonlinear monotone operator, the coefficients of which are chosen as the design (control) variables. Moreover, the set of admissible functions depends on the control, as well. Existence of an optimal design is proven on an abstract level. Some applications are presented to the optimization of a beam on a unilateral elastic foundation. Finite element approximations are proposed and a convergence result is proven.
Irreduzible Invarianten eines Tensors vierter Stufe
Authors: Betten J. , Helisch W.
Published: May 2007

Nach Hilberts Theorem besitzt jeder Tensor eine Integritätsbasis, d. h. eine begrenzte Anzahl von Invarianten, derart, daß jede beliebige Invariante sich als ganze rationale Funktion der Elemente dieser Integritätsbasis darstellen läßt. Anders als beim Tensor zweiter Stufe ist eine solche Integritätsbasis für einen Tensor vierter Stufe bisher unbekannt. Als Vorstufe zu deren Bestimmung werden im folgenden Aufsatz Systeme von irreduziblen Invarianten eines Tensors vierter Stufe im zwei‐ und dreidimensionalen Euklidschen Raum aufgestellt.
Ebene Wirbelfelder bei kompressiblem Hauptstrom
Authors: Albring W.
Published: May 2007

Ursprünglich waren Wirbelfelder als Integrale der Kontinuitätsgleichung und der Navier‐Stokes‐Gleichung für Strömungen mit konstant bleibender Dichte eingeführt worden. Die Strömungsakustiker hatten diese Wirbelfelder zum Berechnen von Schallquellen benutzt und gefragt, wie sie modifiziert werden müß für eine Gasströmung mit veränderlicher Dichte, in der die Hauptgeschwindigkeit nicht klein gegenüber der Schallgeschwindigkeit ist. Es zeigt sich, daß die bekannten Wirbelfelder unverändert auch in Gasströmungen benutzt werden dürfen, solange die Wirbelgeschwindigkeit klein gegenüber der Hauptgeschwindigkeit und der Schallgeschwindigkeit bleibt.
On the Three‐Dimensional Cerruti Problem for an Elastic Nonlocal Half‐Space
Authors: Nowinki J. L.
Published: May 2007

The classical Cerruti problem of a half‐infinite elastic space acted upon by a tangential surface load is examined in its nonlocal context taking the constitutive equations in the Kroener‐Eringen form. After a brief discussion of the values of the nonlocal moduli, a summary of the nonlocal Kelvin problem serving as a basis for the solution of the Cerruti problem is given. By appeal to Westegaard's twinned gradient procedure (determining the effects of a change of poisson's ratio) mapped into a Fourier exponential transform space, a transition from the Kelvin to the Cerruti problem via the Boussinesq problem is achieved. An example illustrating in some detail the calculation of stress is added.
Solvability of a Stationary Problem on the Plane Motion of Two Viscous Incompressible Liquids with Non‐Compact Free Boundaries
Authors: Socolowsky J.
Published: May 2007

A free boundary value problem for the motion of two heavy viscous, incompressible, capillary liquids, for instance in coating processes, is investigated. The flow domain and the two free interfaces are non‐compact and various corners occur. The existence and uniqueness of a generalized solution is proved in weighted Hölder‐spaces.
A Dual Perturbation Series Analysis of Homoclinic Bifurcation for Autonomous Systems
Authors: Smith P. , Yorke J. M. E.
Published: May 2007

We consider the perturbation of a Hamiltonian second‐order differential equation which has at least one homoclinic path. The perturbations take the form of damping (either linear or nonlinear) and self‐excitation as can occur typically in the equation for the van der Pol‐Duffing oscillator. The perturbation is a two‐stage process which involves first finding the perturbed homoclinic path, and then using this as the first approximation for neighbouring paths. By a process of matching solutions, leading term approximations for the periods and amplitudes of limit‐cycles which bifurcate internally and externally from the homoclinic path can be found. The symbolic computation system REDUCE has been used to facilitate integration of terms in the series.
On Density and Approximation Properties of Special Solutions of the Helmohltz Equation
Authors: Still G.
Published: May 2007

We consider eigenvalue problems for the Laplace operator on a region G. Especially if G is simply‐shaped, defect‐minimization methods with trial functions φ satisfying the Helmholtz equation Δφ + λφ = 0 may be suitable for the numerical solution of the problem. Such functions φ are given for example by the classical method of separation of variables. This paper is concerned with density and approximation properties of these special solutions of the Helmholtz equation with respect to the supremum‐norm.
On Convergence of Semidiscrete Ritz‐Galerkin Schemes Applied to the Boundary Control of Parabolic Equations with Non‐Linear Boundary Condition
Authors: Tröltzsch F.
Published: May 2007

The paper is concerned with Ritz‐Galerkin approximations of parabolic control problems, where the control is acting in a non‐linear boundary condition. At first the convergence of the Ritz‐Galerkin method for parabolic initial‐boundary value problems with non‐linear boundary condition containing “rough” boundary data is proved by semigroup techniques. Then this result is applied to show convergence of optimal values for approximated control problems.
On some Ramifications of the Center of Shear Problem
Authors: Reissner E.
Published: May 2007

This note generalizes an earlier analysis of the shear center and twist center problem within the framework of a suitably formulated mixed boundary value problem of three‐dimensional linear elasticity, by the consideration of more general boundary conditions than in [1], by a significant complementation of upper and lower bound formulas in [2], and by a method for the determination of the coordinates of these centers as functions of the applied loads for physically nonlinear elastic materials.
An Extension of Hamilton's Principle for Dissipative Continua
Authors: Albert H.‐F.
Published: May 2007

Hamilton's principle is derived for a continuum in the substantial (Lagrangian) description. There dissipative processes as well as initial and boundary conditions are incorporated. The Euler‐Lagrange equations of this principle are equivalent to the balances of mass, momentum, entropy, as well as these of certain extensive quantities not further specified, and constitutive relations for the dissipative fluxes as known from extended irreversible thermodynamics.
A New Approach to the Problem of Scattering of Water Waves by Vertical Barriers
Authors: Chakrabarti A. , Vijayabharathi L.
Published: May 2007

Using a modified Green's function technique the two well‐known basic problems of scattering of surface water waves by vertical barriers are reduced to the problem of solving a pair of uncoupled integral equations involving the “jump” and “sum” of the limiting values of the velocity potential on the two sides of the barriers in each case. These integral equations are then solved, in closed form, by the aid of an integral transform technique involving a general trigonometric kernel as applicable to the problems associated with a radiation condition.
Verallgemeinerte Diagonaldominanz bei nichtlinearen Funktionen. I
Authors: Frommer A.
Published: May 2007

Streng oder irreduzibel diagonal dominante Matrizen und M‐Matrizen sind alle in der Klasse der verallgemeinert diagonal dominanten Matrizen enthalten. Mit dem Begriff der verallgemeinert diagonal dominanten Funktion stellen wir hier ein analoges Konzept für nichtlineare Funktionen vor. Spezialfälle sind u. a. die für Anwendungen besonders wichtigen streng diagonal dominanten nichtlinearen Funktionen und M‐Funktionen. Schwerpunkt dieser Arbeit bildet die Untersuchung charakteristischer Eigenschaften verallgemeinert diagonal dominanter Funktionen sowie deren Zusammenhänge mit anderen Funktionenklassen. In einer zweiten Arbeit werden wir dann zeigen, wie mit dem Konzept der nichtlinearen verallgemeinerten Diagonaldominanz diverse alte und mehrere neue Konvergenzresultate für nichtlineare (insbesondere asynchrone) Iterationsverfahren auf einheitliche Weise hergeleitet werden können.
An Approximation Scheme for the Three‐dimensional Scattered Wave and Its Propagating Far‐field Pattern in a Finite Depth Ocean
Authors: Gilbert R. P. , Xu Y. , Thejll P.
Published: May 2007

This paper is the first step in solving the submersible identification problem. An efficient numerical scheme is presented for computing the far field generated by scattering acoustic waves from an arbitrary shape in a wave guide. The inverse problem of determining the object from the far fields is discussed.
General Contact Problem for a Circular Annulus
Authors: Fabrikant V. I.
Published: May 2007

A general formulation is given for the first time to the title problem. The method is based on the new results in potential theory obtained by the author earlier. The problem is reduced to a two‐dimensional integral equation with an elementary kernel. Several specific examples are considered.
On the Dual Reciprocal Variational Approach to the Signorini‐Fichera Problem. Convex and Nonconvex Generalization
Authors: Panagiotopoulos P. D. , Haslinger J.
Published: May 2007

The aim of the present paper is the study of a new variational formulation for the Signorini‐Fichera problem. It is the dual reciprocal variational formulation which gives rise to an inequality constrained minimum problem only with respect to the unknown unilateral displacements. In the present paper the dual reciprocal variational problem is formulated for general unilateral boundary conditions derived from convex or nonconvex superpotentials. We obtain boundary variational or hemivariational inequalities and we study both for the coercive and the most important semicoercive case the existence and uniqueness (if any) of the solution. To this end a new form of Korn's inequality at the boundary is applied.
Symbolverarbeitung in der Mechanik — Zwei Beispiele
Authors: Kreuzer E. J.
Published: May 2007

Die Symbolverarbeitung hat in der Mechanik bereits eine Reihe von Anwendungen gefunden; die Möglichkeiten des sympbolorientierten Rechnens mit Hilfe von Digitalrechnern sind aber heute noch längst nicht ausgeschöpft. In dieser Arbeit werden nach einigen grundlegenden Bemerkungen zu Symbolmanipulationsprogrammen zwei Beispiele aus der Mechanik herausgegriffen, bei denen die Symbolverarbeitung besonders vorteilhaft eingesetzt werden konnte: das Aufstellen von Bewegungsgleichungen und die Analyse nichtlinearer dynamischer Systeme.
Coupling of Elastic and Failure Properties of Initially Anisotropic Solids by Means of the Elliptic Paraboloid Failure Surface (EPFS) Criterion
Authors: Theocaris P. S. , Philippidis T. P.
Published: May 2007

The anisotropic failure criterion of the elliptic paraboloid failure surface is generally stated and appropriately formulated according to two postulates concerning safe loading paths. First the criterion is established for the generic anisotropic solid by assuming that it does not fail under hydrostatic compression and in the sequel a new hypothesis is conjectured according to which safe loading is the stress tensor whose associated strain tensor, in the context of Hookean elasticity, is spherical.
Ein Vergleich von Methoden zur Berechnung von thermisch bedingten mechanischen Spannungen unter Berücksichtigung der Erstarrung der Schmelze und der Bildung von Eigenspannungen
Authors: Hitzschke R.‐P. , Neundorf W.
Published: May 2007

Mit Bezug auf die thermische Erstarrung mit Phasenübergang flüssig/fest als eine technologische Variante der Glasverfestigung wird analysiert, wie Eigenverzerrungen beim Phasenübergang die Grundlage für Eigenspannungsquellen und somit von Eigenspannungen selber sind. Zwei vereinfachte Modelle und ihre numerische Behandlung werden vorgestellt.
Annular Liquid Jets: Formulation and Steady State Analysis
Authors: Ramos J. I.
Published: May 2007

The equations governing the fluid dynamics of long annular liquid, jets and long annular liquid membranes are derived by means of an integral formulation which is valid for Newtonian and non‐Newtonian Fluids. Analytical solutions for long, inviscid, steady state, annular liquid membranes are obtained in Eulerian coordinates as a function of the Froude and Weber numbers, nozzle exit angle, and pressure difference across the annular membrane. It is shown that the convergence length of the annular membrane increases as the Froude and Weber numbers, nozzle exit angle and pressure difference across the annular membrane are increased. The range of parameters for which the analytical solutions are valid is determined as a function of the Froude and Weber numbers for the case of zero nozzle exit angle and zero pressure difference. Analytical and numerical solutions for long, inviscid, steady state, annular liquid jets are also obtained and show that the convergence length decreases us the jet thickness‐to‐radius ratio at the nozzle exit is increased and increases at the Froude and Weber numbers, nozzle exit angle and pressure difference across the annular liquid jet are increased.
Verallgemeinerte Diagonaldominanz bei nichtlinearen Funktionen II: Anwendung auf asynchrone Iterationsverfahren und Beispiele
Authors: Frommer A.
Published: May 2007

Der zentrale Satz dieser zweiten Arbeit zur nichtlinearen verallgemeinerten Diagonaldominanz gibt ein relativ weitreichendes Resultat über die Konvergenz asynchroner Iterationsverfahren zur Nullstellenbestimmung verallgemeinert diagonal dominanter Funktionen. Durch Spezialisierung in zwei Richtungen (Betrachtung spezieller Funktionenklassen und/oder spezieller Iterations‐verfahren) erhalten wir daraus eine Reihe bekannter und viele neue Konvergenzresultate für nichtlineare Iterationsverfahren. Darüber hinaus enthält die vorliegende Arbeit einige Beispiele für in Anwendungen auftretende verallgemeinert diagonal dominante Funktionen.
Semianalytic Solution of Boundary Value Problems by Using Approximated Operators
Authors: Gartland E. C. , Grossmann C.
Published: May 2007

Adapted discretization methods can be obtained by a piecewise simplification of the differential operator and by exactly solving of the generated auxiliary problems. In the present paper we introduce a simple convergence analysis which rests on perturbed operators. Using special constructions of the perturbations the convergence of methods being based on piecewise truncated Taylor's expansions can be established. These methods are closely related to compact difference schemes.
A Sommerfeld‐Type Diffraction Problem with Second‐Order Boundary Conditions
Authors: Meister E. , Santos P. A. , Teixeira F. S.
Published: May 2007

An operator‐theoretic approach is used to study the problem of diffraction of time‐harmonic electromagnetic waves by a metalbacked dielectric half‐plane. The correspondent boundary value problem for the two dimensional Helmholtz equation is considered in a Sobolev space setting and is reduced to equivalent boundary integral equations of Wiener‐Hopf type in L+2(ℝ). An explicit analytical solution is obtained for the particular case of having the sam dielectric layer on both banks of the half‐plane.
ARMAX Modelling in Structural Dynamics – Approximations of the Differential Equations of Motion
Authors: Natke H. G. , Zamirowski M.
Published: May 2007

ARMAX models are popular in system identification. Spatial discretization of structural models leads to ordinary differential equations. The approximation of the differential quotients leads to ARX and ARMAX models of various orders. This approximation problem is discussed in the context of model order. Statistical studies due to a covariance equivalence of proposed models are investigated. Secondly, the inverse problem of identifying the physical parameters of the structural model from the ARMAX parameters within the approximation domain is also invesitgated.
Bewegungsgleichungen für Getriebesysteme
Authors: Brandl H. , Pfeiffer F.
Published: May 2007

Getriebesysteme sind baumstrukturierte Mehrkörpersysteme mit linear Kinematik aber nichtlinearen Kraftkopplungen, die durch Spiel, Kupplungen und Lager entstehen können. Es wird eine allgemeine Theorie für derartige Systeme hergeleitet, die für beliebige Konfigurationen gilt und die an praktischen Beispielen erprobt ist.
On Boundary Layer and Interior Equations for Higher‐Order Theories of Plates
Authors: Nosier A. , Reddy J. N.
Published: May 2007

Several shear‐deformation plate theories of symmetric laminated plates with transversely isotropic layers are reviewed and the governing equations of these theories are then recast into two equations: one for the interior of the domain and the other for the edge‐zone or the boundary layer. For the first time it si shown that the governing equations of the third‐order shear‐deformation theory of Reddy result in a sixth‐order interior equation and a second‐order edge‐zone equations. It is also demonstrated that in bending and stability problems, and under certain conditions in dynamic problems, the contribution of the edge‐zone equation is identically zero for a simply‐supported plate. The pure‐shear frequencies of a plate according to different theories are determined and compared.
On the Method of Characteristics in Rate‐Type Viscoelasticity with Non‐Monotone Equilibrium Curve
Authors: Mihâilescu‐Suliciu M. , Suliciu I.
Published: May 2007

The standard method of characteristics is applied to a hyperbolic system of partial differential equations describing the motion of a viscoelastic body. The equilibrium curve can be of the van der Waals type such that the system may describe phase transition phenomena. For isolated body problems, sufficient conditions are given on the time integration steps of the first and second numerical approximations such that the total energy of the numerical solution be a nonincreasing function of the number of time integration steps. This property is required since the total energy of the exact solution is a nonincreasing function of time as required by the second law of thermodynamics. Numerical examples of nonisolated body problems when the violations of the above conditions lead to numerical instabilities are presented elsewhere (see Introduction).
Steady Plane Orthogonal MHD Flows
Authors: Chandna O. P. , Nguyen P. V.
Published: May 2007

Complex variable technique is used to study steady plane orthogonal magnetohydrodynamic flows of a viscous incompressible fluid of infinite electrical conductivity. The equations of motion are recast in variables z = x + iy and z̄ = x − iy. Four exact integrals for four different flow geometries and Hamel's problem are considered to illustrate the developed theory.
Über die Anwendung der Randelementmethoden auf Probleme der Wellendiffraktion
Authors: Triantafyllidis Th.
Published: May 2007

Bei der Anwendung der Randelement‐ oder Randintegralmethode auf Gebiete, bei denen sog. „Schattenzonen”︁ entstehen, wird die Kausalität der Lösung verletzt. Da es hierüber bereits Veröffentlichungen mit gegensätzlichen Positionen gibt, wird in dieser Arbeit das Problem auf analytischem Weg behandelt. Für den Fall einer einfallenden SH‐ (shear horizontal) Welle auf eine zylindrische Inhomogenität im Vollraum wird sowohl die Randintegralmethode analytisch angewendet als auch die analytische Lösung des Problems angegeben. Beim Vergleich der beiden Lösungen stellt man fest, daß sie nicht identisch sind. Die Gründe für die Unstimmigkeiten zwischen den beiden Lösungen werden in dieser Arbeit diskutiert, und es wird die Möglichkeit einer korrekten Anwendung der Randelementmethode für solche Gebiete aufgezeigt.
The Poisson Processes of Actions and their Combinations
Authors: Murzewski J. W.
Published: May 2007

Four parameters characterize a random action process: the point‐in‐time mean value and its standard deviation, the rate of occurences and their mean duration. A cumulative distribution function of extreme values in a reference time is derived for a filtered Poisson process. A combination of two independent processes of actions is also analyzed and the overlapping effect is taken into account. The final formulae differ from those of Der Kiureghian and Wen. Characteristic and design values are determined in terms of the parameters of the action processes.
On the Nonlinear Stability of the Magnetic Bénard Problem with Rotation
Authors: Mulone G. , Rionero S.
Published: May 2007

The nonlinear stability of the magnetic Bénard problem with rotation is studied through the Lyapunov direct method. It is shown that, in the stress‐free case and for vanishing stress at the boundaries, the nonlinear critical Rayleigh number has the same behaviour as in the linear case. In particular, for a stationary convection, it shows an initial decrease with the Chandrasekhar number Q2 and for large Q2 it goes to infinity as Q.
On the Nonlinear Theory of Nonsimple Thermoelastic Materials with Voids
Authors: Ciarletta M. , Scalia A.
Published: May 2007

A nonlinear theory of nonsimple thermoelastic materials with voids is established. The continuous dependence upon initial state and supply terms of smooth thermodynamic processes is studied.
Creeping Flow Past a Porous Spherical Shell
Authors: Qin Yu. , Kaloni P. N.
Published: May 2007

An exact solution for the creeping flow past a porous spherical shell has been obtained using the Stokes & Brinkman equations. Expressions for the velocities and pressure fields both inside and outside of porous spherical shell are obtained and the force acting on the shell is also determined. It is found that the drag on a porous spherical shell is smaller as compared to the shell with solid core. Several limiting cases of the solution are also discussed. In particular it is shown that the solution obtained using Darcy's law can be derived easily with the appropriate choice of boundary conditions.