Showing papers in "Acta Mechanica in 1970"
TL;DR: Gegenstand der vorliegenden Untersuchungen ist das Stromungsfeld in der Umgebung einer rotierenden Kugel as discussed by the authors.
Abstract: Gegenstand der vorliegenden Untersuchungen ist das Stromungsfeld in der Umgebung einer rotierenden Kugel. Diese sool in einer unendlich ausgedehnten, ruhenden viskosen Flussigkeit mit konstanter Winkelgeschwindigkeitω0 um einen Durchmesser rotieren.
97 citations
TL;DR: In der vorliegenden Arbeit wird eine Verallgemeinerung der Untersuchungen vonG. J. Taylor [1] uber die Stromungen zwischen zwei rotierenden Zylindern vorgenommen.
Abstract: In der vorliegenden Arbeit wird eine Verallgemeinerung der Untersuchungen vonG. J. Taylor [1] uber die Stromungen zwischen zwei rotierenden Zylindern vorgenommen. Wesentlich ist in dem von uns betrachteten Fall, das die die Instabilitat hervorrufende Zentrifugalkraft eine Funktion der Breitenkoordinate ist. Dadurch ist es moglich, das unterschiedliche Stromungszustande raumlich nebeneinander existieren konnen. Es wird uber eigene Messungen des Reibungsmomentes berichtet, die einenReynolds-Zahl-Bereich von funf Zehnerpotenzen erfassen. Im laminar-turbulenten Ubergangsgebiet gibt es eine ganze Anzahl von moglichen Stromungszustanden. Diese werden diskutiert und den Mesergebnissen des Reibungsmomentes zugeordnet.
84 citations
TL;DR: In this article, complete constitutive equations are given for the slow flow of a linear viscous fluid through an anisotropic linear elastic solid, and a uniqueness theorem is stated for this model.
Abstract: The discussions of constitutive equations and their use in related studies by a number of writers for interacting continua, which is based on the form of theory given byGreen andNaghdi [1], is shown to be satisfactory for many purposes even though the expressions given for the partial stresses are incomplete. Complete constitutive equations are given in this paper, and a uniqueness theorem is stated, for the slow flow of a linear viscous fluid through an anisotropic linear elastic solid.
51 citations
TL;DR: In this paper, an asymptotic solution for the contact problem of a rigid cylindrical stamp and a very thin elastic layer was found for contact problems of a stamp and an elastic layer.
Abstract: An asymptotic solution is found for the contact problem of a rigid cylindrical stamp and a very thin elastic layer In the solution terms of exponential decrease are neglected consistently Two cases are considered: a layer which is fixed to a rigid base and a layer which can slide without friction along the base Compressible and incompressible materials are treated
45 citations
TL;DR: In this article, the authors consider a layer of finite thickness loaded in plane strain by a stamp with a straight horizontal base, which is smooth and rigid, and the stamp is pressed vertically into the layer and is slightly rotated by an external moment load subsequently.
Abstract: We consider a layer of finite thickness loaded in plane strain by a stamp with a straight horizontal base, which is smooth and rigid. The stamp is pressed vertically into the layer and is slightly rotated by an external moment load subsequently. Two cases are considered successively: the lower side of the layer is attached to a rigid base and, secondly, the lower side is allowed to slide without friction along the base. The paper is divided into two parts. The first part deals with an asymptotic investigation of a thin layer and the second one refers to a thick one.
31 citations
TL;DR: In this paper, the analysis of instability of a gas-liquid interface when accelerated in a direction perpendicular to its plane has been found to be a singular perturbation problem, solved by the method of succesive approximations.
Abstract: The analysis of instability of a gas-liquid interface when accelerated in a direction perpendicular to its plane has been found to be a singular perturbation problem. The problem is solved by the method of succesive approximations. The results which are determined to the third order, differ qualitatively and quantitatively from those of the linear theory. Surfactension and curvature are included in the analysis. The growth factor of the interface is found to depend not only on the wave number but also on the amplitude of the initial disturbance. The results are in good agreement with the experiments.
23 citations
TL;DR: In this article, the authors extend the method of asymptotic integration of the three dimensional elasticity equations to dynamic problems, which consists of the expansion of all field variables and introduced length scales in terms of a small plate parameter.
Abstract: Two dimensional theories for the vibrations of transversely isotropic elastic plates are derived without initially specifying the spatial dependence of the field variables on the thickness coordinate. This is accomplished by extending the method of asymptotic integration of the three dimensional elasticity equations to dynamic problems. The method consists of the expansion of all field variables and introduced length scales in terms of a small plate parameter. Substitution into the elastcity equations leads to field equations of various orders. The lowest order system of equations yields the simplest plate equations. Higher order systems introduce thickness effects.
22 citations
TL;DR: In this article, a homogeneous continuum model is presented to describe the dynamic behavior of a laminated medium, including the effects of temperature variations, on the basis of assumed two-term expansions of the displacements and the temperature increments across the thicknesses of the layers, the state of deformation and temperature distribution in the composite are described by six fields, i.e., gross displacements, local deformations, gross temperatures and local temperature variations.
Abstract: A homogeneous continuum model is presented to describe the dynamic behavior of a laminated medium, including the effects of temperature variations. On the basis of assumed two-term expansions of the displacements and the temperature increments across the thicknesses of the layers, the state of deformation and the temperature distribution in the composite are described by six fields, i. e., gross displacements, local deformations, gross temperatures and local temperature variations. Balance equations are derived for the stress resultants and the first moments of the stresses across the thicknesses of the layers, as well as for resultant heat fluxes and their moments. A set of constitutive equations is presented for a laminated medium composed of layers of two anisotropic thermoviscoelastic solids. The special cases of isotropic thermoviscoelastic layers, anisotropic thermoelastic layers, and isotropic thermoelastic layers are discussed briefly.
18 citations
TL;DR: In this article, a non-linear theory of periodic gravity waves in an incompressible inviscid liquid is presented and the problem which is found to be a singular perturbation problem is treated accordingly with considerable ease.
Abstract: A non-linear theory of periodic gravity waves in an incompressible inviscid liquid is presented. The problem which is found to be a singular perturbation problem is treated accordingly with considerable ease. Results for frequency, surface profile and potential function are calculated up to third order as series in powers of a parameter which is the ratio of the amplitude to wavelength. Unlike the linear theory, in this third-order theory, the frequency is found to depend on the amplitude also and decreases with increasing amplitude. The results agree with those obtained earlier by a complicated and labourious method and confirmed by experiments.
17 citations
TL;DR: In this article, the verallgemeinerte Elektrodynamik vonMie weist den Weg zu einer Lagrange-Dichte, die eine Funktion entweder der kinematischen or dynamischen Grosen ist.
Abstract: Die Kontinuumstheorie wandernder Versetzungen steht in mathematischer Analogie zu denMaxwellschen Gleichungen der Elektrodynamik Diese Analogie zeigt, das die derzeitige lineare Versetzungstheorie unvollstandig ist und durch konstitutive Gleichungen zwischen dynamischen und kinematischen Grosen erganzt werden mus Die verallgemeinerte Elektrodynamik vonMie weist den Weg zu einer Lagrange-Dichte, die eine Funktion entweder der kinematischen oder der dynamischen Grosen ist Wahrend die Spannungsfunktionen des Kontinuums im statischen Falle Reaktionskrafte sind, werden sie im Felde wandernder Versetzungen eingepragte Krafte, die uber konstitutive Gleichungen mit den Versetzungsdichten verbunden sind
16 citations
TL;DR: In this paper, a generalized theory of the thermoelasticity of an elastic half-space subjected to thermal and mechanical disturbances at its free surface is considered and an approximation of the general solution is obtained in closed form valid at temperatures near absolute zero, resulting in expresssions for temperature and strain response due to arbitrary inputs at the free boundary.
Abstract: The one-dimensional problem of an elastic half-space subjected to thermal and mechanical disturbances at its free surface is considered, using a generalized theory of the thermoelasticity which takes into account a finite velocity of propagation of thermal disturbances. An approximation of the general solution is obtained in closed form valid at temperatures near absolute zero, resulting in expresssions for temperature and strain response due to arbitrary inputs at the free boundary. These general expressions are applied to the particular problem of a step-strain input at the boundary and the results compared with previous work. The problem of a half-sine temperature pulse input is also treated.
TL;DR: In this paper, angegeben wird eine Losungsmethode, die fur jede Art von Querschnitt Verwendung finden kann.
Abstract: Alle bisher bekannten exakten wie auch Naherungsmethoden zur Losung des Torsionsproblems hangen von der Gestalt des betreffenden Querschnittes ab. Von den vorhandenen speziellen Losungen besitzt nur ein kleiner Teil praktische Bedeutung. Im folgenden wird eine Losungsmethode angegeben, die fur jede Art von Querschnitt Verwendung finden kann. Das Torsionsproblem wird mit Hilfe desCauchyschen Integralsatzes auf eine inhomogeneFredholmsche Integralgleichung fur die Wolbfunktion am Querschnittsrand zuruckgefuhrt und mittels desNystrom-Verfahrens gelost. Wenn die Wolbfunktion entlang der Querschnittsberandung bekannt ist, konnen Torsionsspannungen und Torsionstragheitsmomente auf einfache Weise bestimmt werden. Die Methode wird auf einige in der technischen Praxis vorkommende Beispiele angewendet. Ihr groster Vorteil liegt in der Moglichkeit, Querschnitte mit einspringenden Ecken zu behandeln.
TL;DR: In this paper, the steady motion of a given amount of gas or liquid, in an infinite liquid under the action of buoyancy forces is examined, where surface tension is assumed to be very large in order to maintain the spherical shape of the drop.
Abstract: The steady motion of a given amount of gas or liquid, in an infinite liquid under the action of buoyancy forces is examined. Surface tension is assumed to be very large in order to maintain the spherical shape of the drop. Velocity and velocity gradients are determined exactly in the limiting case of largeReynolds numbers. The earlier theory ofHarper andMoore is modified to take into account the diffusion of vorticity in the front stagnation region. Although the two theories differ significantly, experimental evidence is not detailed enough to distinguish between the results of both theories.
TL;DR: In this paper, the bestimmung von Stromfunktion and Geschwindigkeitsfeld eines Wirbels in sehr allgemeinen Scherstromungen aus den linearisierten Eulerschen Gleichungen wird mittels Fourier-Transformation auf die Losung eines Randwertproblems einer gewohnlichen Differentialgleichung zuruckgefuhrt.
Abstract: Die Bestimmung von Stromfunktion und Geschwindigkeitsfeld eines Wirbels in sehr allgemeinen Scherstromungen aus den linearisiertenEulerschen Gleichungen wird mittels Fourier-Transformation auf die Losung eines Randwertproblems einer gewohnlichen Differentialgleichung zuruckgefuhrt. Aus dem asymptotischen Verhalten dieser Losungen fur kleine bzw. grose Werte des Parameters wird auf das Verhalten der Geschwindigkeit im Unendlichen bzw. in der Nahe des Wirbels geschlossen und die Gultigkeit des Satzes vonKutta-Joukowski bewiesen. Mit dem Geschwindigkeitsfeld kennt man auch den Kern der Integralgleichung, aus der sich analog zurPrandtl-Glauertschen Theorie die Wirbelbelegung eines unendlich dunnen Profils bestimmen last.
TL;DR: In this article, the consequences of the entropy production inequality for a mixture of two incompressible isotropic non-linear elastic solids are investigated and some isothermal elastostatic problems involving large deformations of such a mixture are shown to be maintainable by surface tractions alone.
Abstract: The consequences of the entropy production inequality are investigated for a mixture of two incompressible isotropic non-linear elastic solids. Some isothermal elastostatic problems involving large deformations of such a mixture are shown to be maintainable by surface tractions alone and are solved for a general form of theHelmholtz free energy function.
TL;DR: Dasd'Alembertsche Prinzip wird durch Glieder, bei denen die Zeit unabhangig von den Raumkoordinaten mitvariiert wird, wobei als Faktoren der Variation der Zeit Verbrennungswarme and Warmestrom auftreten.
Abstract: Dasd'Alembertsche Prinzip wird durch Glieder, bei denen die Zeit unabhangig von den Raumkoordinaten mitvariiert wird, erweitert, wobei als Faktoren der Variation der Zeit Verbrennungswarme und Warmestrom auftreten. Aus einerLagrangeschen Zentralgleichung gewinnt man das Prinzip vonHamilton und dieLagrangeschen Bewegungsgleichungen. Diese werden fur den Fall eines nichtholonomen Zeitvektors diskutiert, wobei sich Zusatzglieder ergeben, die als eineLorentz-Kraft interpretiert werden konnen.
TL;DR: A thermodynamic foundation for isothermal plasticity is laid on the basis of the hypotheses that during plastic deformation the infinitesimal increment Δγ of irreversible entropy depends on the current state of stress and the stress increment.
Abstract: A thermodynamic foundation for isothermal plasticity is laid on the basis of the hypotheses that (a) during plastic deformation the infinitesimal increment Δγ of irreversible entropy depends on the current state of stress and the stress increment and (b) that Δγ>0 for plastic deformation, whereas Δγ=0 for elastic deformation. The existence of a yield locus is established as a consequence. Constitutive eaqutions for small and large deformations are then derived. The small deformation constitutive equations coincide with the classical forms that rest on the grounds of mechanical stability.
TL;DR: In this article, the authors consider a class of boundary value problems arising from quasi-static deformation of physically nonlinear viscoelastic solids and present a scheme for characterization of mechanical response in a manner compatible with an algorithm for numerical solution of nonlinear boundary value problem.
Abstract: This paper considers a class of boundary value problems arising from quasi-static deformation of physically nonlinear viscoelastic solids. A scheme for characterization of mechanical response in a manner compatible with an algorithm for numerical solution of nonlinear boundary value problems is discussed. An illustrative example of an axially deformed statically indeterminate nonlinear viscoelastic rod is included.
TL;DR: In this article, the authors investigated the noncyclic squeeze films in full and half journal bearings in the presence of an axial magnetic field and found that the squeezing in a short circuit case is slower than that in an open circuit case.
Abstract: Hydromagnetic noncyclic squeeze films in full and half journal bearings in the presence of an axial magnetic field have been investigated theoretically. Both for full and half journal bearing, it is found that the squeezing in a short circuit case is slower than that in an open circuit case. In both the cases the time of approach is increased by the application of magnetic field.
TL;DR: In this paper, the Umschlag einer laminaren Rohrstromung wird untersucht, and the Mesergebnisse zeigen, das die meisten Grosen einer intermittierenden Stromung von der Einlaufstromung abhangen.
Abstract: Der Umschlag einer laminaren Rohrstromung wird untersucht. Die Mesergebnisse zeigen, das die meisten Grosen einer intermittierenden Stromung von der Einlaufstromung abhangen. Zwei Grosen sind jedoch vom Einlauf unabhangig: der Wachstumsfaktor, der das Ausbreiten einer turbulenten Zone in die umgehende laminare Stromung beschreibt, und die mittlere Lange der turbulenten Zonen bzw. die Langenverteilung. Das bedeutet, das somit der Wachstumsfaktor wie auch die Langenverteilung gut fur eine quantitative Beschreibung der Intermittenz einer Rohrstromung geeignet sind. Die Tatsache, das der Wachstumsfaktor in einem gewissen Reynoldszahlenbereich gleich Null ist, gibt der Intermittenz die Bedeutung einer stabilen Stromungsform. Die gemessenen Verteilungen lassen sich gut durch log-Normalverteilungen darstellen; das erlaubt Ruckschlusse auf die Entstehung der turbulenten Zonen.
TL;DR: In this article, the results of three spezielle Formanderungen (reine Volumsanderung, reine Schubverzerrung and reine Gestaltanderung ohne Schub-verzergung) are investigated.
Abstract: Die bei isothermen, homogenen Zustandsanderungen zweier elastischer Korper—des linear-elastischen Korpers und desMooney-Rivlin-Besseling-Korpers—zu-oder abfliesenden Warmemengen werden berechnet, wobei fur den letzteren drei spezielle Formanderungen—reine Volumsanderung, reine Schubverzerrung und Gestaltanderung ohne Schubverzerrung—betrachtet werden. Die Ergebnisse sind graphisch dargestellt.
TL;DR: In this article, the authors considered the distribution of thermal stress in an infinite wedge-shaped solid having a crack on the bisector plane of the wedge angle and used the Mellin transform to solve the equations of elastic equilibrium.
Abstract: Of concern here is the distribution of thermal stress in an infinite wedge-shaped solid having a crack on the bisector plane of the wedge angle.Mellin transform is used to solve the equations of elastic equilibrium. The mixed boundary conditions lead to dual integral equations, which are reducible toFredholm integral equations of the second kind. A comparison of the crack energy when thermal stress is present with the same for an isothermal distribution shows considerable increase which may be attributed to non-uniformity of temperature.
TL;DR: Fur drei isentrope Deformationen (reine Volumsanderung, Schubverformung, and Gestaltsanderung) einesMooney-Rivlin-Besseling-Korpers berechnet.
Abstract: Fur drei isentrope Deformationen —reine Volumsanderung, Schubverformung und Gestaltsanderung ohne Schubverzerrung—werden die Temperaturanderungen einesMooney-Rivlin-Besseling-Korpers berechnet. Die Ergebnisse sind graphisch dargestellt.
TL;DR: In this article, the authors applied linear couple stress theory to investigate the stress distribution in a half plane due to a moving line load on the surface, and found that the couple stress effect depends on the speed of the moving load, the couple-stress parameter, and the Poisson's ratio.
Abstract: Linear couple stress theory has been applied to investigate the stress distribution in a half plane due to a moving line load on the surface. It is assumed that the load is moving slower than both the longitudinal and transverse wave speeds of the elastic media (subsonic case). It is found that the couple stress effect depends on the speed of the moving load, the couple-stress parameter, and thePoisson's ratio.
TL;DR: In this article, the theoretical value of the rupture time of a superplastic bar under a constant load is derived using the Hoff's criterion, and the constitutive equation of isothermal super-plasticity is taken from the result of recent research in metallurgy.
Abstract: UsingHoff's criterion, the theoretical value of rupture time of a superplastic bar under a constant load is obtained. The constitutive equation of isothermal superplasticity is taken from the result of recent research in metallurgy. A specific example is given.
TL;DR: In this article, the authors deal with an experimental determination of the stress distribution in a cylindrical shell with two diametrically opposite reinforced circular holes of different diameters, subjected to internal pressure.
Abstract: This paper deals with an experimental determination of the stress distribution in a cylindrical shell with two diametrically opposite reinforced circular holes of different diameters. The shell is subjected to internal pressure. Both brittle coating and three-dimensional photoelasticity were used in the analysis. The results obtained are compared with those corresponding to a non-reinforced hole in a cylindrical shell with and without ribs.
TL;DR: In this paper, a continuum theory of mixtures is used to develop a constitutive equation for fiber reinforced viscoelastic materials, which is used for fiber reinforcement in this paper.
Abstract: A continuum theory of mixtures is used to develop a constitutive equation for fiber reinforced viscoelastic materials.