On the nullification of stress-concentration factors by stress equalization

During a recent design study involving a critically stressed “tongue-and-groove” type compression joint of dissimilar materials, a novel technique was conceived for nullifying the effects of an otherwise high local stress-concentration factor. In principle, the nominal stresses in the tongue-and-groove portions of the joint are forced to be uniform. For idealizedfit conditions, the stress concentration in the fillet under this stress-equalized condition is theorized to approach unity (1.00). In the present paper, experimental verification is provided.     

A variational principle for a class of layered media

A variational principle is stated which describes the isothermal flow of a class of ideal incompressible materials, of which the ideal non-Newtonian liquid and the rigid-plastic von Mises solid are special cases. The principle is extended to multi-layered media separated by a prescribed interface. An inverse method is outlined for the determination of the common surface between two materials for flows parallel to a given plane.     

Zur Rheologie der Torfbearbeitung

Zusammenfassung Zur rheologischen Charakterisierung nordwestdeutschen Hochmoortorfes genügt allein die Fließgrenze. Sie ist abhängig von der Torfart und bei mechanischer Vorbehandlung von der Gesamtzahl der Rührerumdrehungen. Die Erniedrigung der Fließgrenze durch Bearbeitung wird mit Hilfe eines einfachen Strukturmodells gedeutet.Der Vergleich zweier Bearbeitungsmaschinen bei jeweils gleichen Fließgrenzen des Torfes ergibt, daß das Momentenverhältnis nur von der Rührerbauart, nicht von der Torfart abhängt. Damit ist die Bestimmung der Fließgrenze durch Rührertypen möglich, bei denen die Meßsehwierigkeiten des Rotationsviskosimeters nicht auftreten. Weiter folgt daraus, daß das Verhältnis der spezifischen Arbeiten zweier Rührer, die gleichen Torf bis zur gleichen Fließgrenze bearbeiten, ebenfalls von der Torfart unabhängig ist. Die Abhängigkeit von der Rührerbauart ist relativ gering.Die kraftwirtschaftliche Bewertung verschiedener Rührerkonstruktionen läßt sieh infolge der geringen Unterschiede der spezifischen Arbeiten und der großen Versuchsstreuung nur durch sehr viele Einzelmessungen sichern.     

An actuator-disc model for the prediction of abrupt stall in an axial compressor rotor

The representation of loss in a cascade by the appearance of blockage has been extended to deal with blade rows by the use of a source distribution to represent this blockage, and in the case of the actuator disc approximation, the presence of sources is confined to an axi-symmetric dìstribution over the actuator disc. It is found that if a typical dependence of loss (and consequently diffusion ratio) upon incidence for each section of an axial compressor rotor is represented in this manner, the influence of blockage on the axial velocity distribution may be found using the potential equation combined with the usual actuator disc approximation. Study of the behaviour of the controlling ordinary differential equation for the axial velocity ahead of the disc reveals that as the flow is reduced, the equation contains a singularity within the range of radius and a meaningful solution does not exist. This result is interpreted as the limit to continuous operation and reasonable agreement between this predicted limit and the appearance of abrupt stall (experimentally) is found.     

Das Digitale Beukenmodell mit nichtkonstanten Koeffizienten — eine Matrixmethode zur Lösung nichtlinearer Ausgleichsvorgänge

Zusammenfassung Mit Hilfe des Digitalen Beukenmodells mit nichtkonstanten Koeffizienten lassen sich ein- und mehrdimensionale Ausgleichsvorgänge berechnen. Besonders einfach ist das Verfahren, wenn nur die Wärmeleitfähigkeit von der Temperatur oder der Diffusionskoeffizient von der Konzentration abhängig ist. Der Hauptvorteil des Digitalen Beukenmodells liegt in der einfachen Handhabung. Für viele praktische Fälle kann die Rechenzeit gegenüber dem herkömmlichen reinen Differenzenverfahren entscheidend verkürzt werden. Das Digitale Beukenmodell mit nichtkonstanten Koeffizienten ist die genaueste Rechenmethode für nichtlineare Ausgleichsvorgänge.

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The digital Beuken-Model with non-constant coefficients — a matrix method for the solution of non-linear diffusion processes

By the help of the digital Beuken-Model with nonconstant coefficients it is possible to compute one- or multidimensional diffusion processes. Especially simple is that method, if only the thermal conductivity depends on the temperature or if the diffusion coefficient depends on the concentration. The main advantage of the digital Beuken-Model is its simple handling. In many practical cases the computing time can be shortened decisively to the traditional difference methods. The digital Beuken-Model with non-constant coefficients is the most exact computing-method for the solution of nonlinear diffusion processes.

     

Response of circular clamped plates to square-wave stress pulses

An account is given of an experimental investigation of the reeponse of clamped circular mild-steel plates of various thicknesses subjected to rectangular stress pulses over a small circular region. The stress pulses were transmitted to the plates through a 1/2-in.-diam shock bar and the strain-time responses of the plates were measured. The stress-wave interactions between the bar and the plates were measured for a number of thicknesses and the effect of the applied stress on the extent of the plastic deformation was determined. It was found that the elastic response was accurately predicted by the theory of Sneddon and the plastic response behaved according to a simple modification of this theory. The interaction between the stress pulse and plates of various thickness was theoretically predicted and found to be in excellent agreement with experimental measurements. The final plate deflections were theoretically predicted using a rigid viscoplastic theory and was in substantial agreement with the data. From this theory, the data were analyzed to determine the visco-plastic constant or relaxation time of the material. It is proposed that this testing arrangement is a suitable and convenient method for determining dynamic yield properties under biaxial-loading conditions.     

The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion

The problem of an anisotropic ellipsoidal inclusion which undergoes a stress-free transformation strain (in the sense of J.D. Eshelby) is considered, and the following theorem is proved: If an ellipsoidal region in an infinite anisotropic linear elastic medium undergoes, in the absence of its surroundings, a stress-free transformation strain which is a polynomial of degree M in the position coordinates x_t, then the final stress and strain state in the transformed inclusion, when constrained by its surroundings, is also a polynomial of degree M in x_t.     

Strain-optic law for a certain class of birefringent composites

A strain-optic law for a certain class of birefringent fiber-reinforced composite materials is developed. The strain-optic law requires both mechanical and optical characterization of the material. Previous investigations have hypothesized the existence of three independent optical properties for the anisotropic birefringent material. The strain-optic relation developed in this study, however, requires only a single strain-optic coefficient, coupled with four independent mechanical material properties, for prediction of the optical response of a birefringent anisotropic material. Experimental results are presented which show good agreement with the developed strain-optic relation. Finally, the isoclinic parameter is investigated and preliminary evidence is presented which indicates a correspondence between principal-strain direction and optical isoclinic angle.     

The buckling load of an elastically supported cantilevered column with continuously varying cross section and distributed axial load

Summary The solution for the buckling load of an elastic supported cantilevered column with continuously varying cross section and distributed axial load is developed. Boundary conditions are formulated for fixed and elastic support. The critical loads are tabled for an usual variation in cross section and axial load distribution as function of the ratio between respectively rigidities and axial forces at fixed and free end, the variation of the rigidity and axial forces given by their degrees of the polynomial variation and rotation stiffness of the elastic support.

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Übersicht Es wird die Knicklast für eine elastisch gelagerte, freitragende Säule mit stetig veränderlichem Querschnitt und stetig verteilter Axiallast berechnet. Die Randbedingungen sind für feste sowie für elastische Lagerung formuliert worden. Für einen übliczen Bereich von Querschnitten und Axiallasten werden die kritischen Lasten in Tabellen angegeben. Dabei wurde das Verhältnis zwischen der Steifigkeit und den Axiallasten am festen und freien Ende variiert.

     

A unified theory of thermoviscoplasticity of crystalline solids

A unified theory of thermoviscoplasticity of crystalline solids is presented. In particular it is shown that a thermodynamics for ‘viscoplastic’ materials can be accommodated within the framework of modern mechanics of materials with memory. The basic physical concepts are derived from the consideration of dislocation behaviour of crystalline solids. Relationships of the present approach to several of the existing theories of plasticity are examined.