bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Stepped Thrust Bearing—A Solution by Relaxation Methods
Authors: Kettleborough C. F. 
Published: June 2021

Abstract
Analytical investigation into the stepped thrust bearing was first carried out by Lord Rayleigh, whose solution neglected side leakage. More recently Archibald has presented a solution with side leakage not neglected but limited by the step being straight across the bearing surface perpendicular to the direction of motion. This paper gives an alternative solution, using relaxation methods, which is applicable to any shape of the step. Results show that the load capacity of the completely internal step is much greater than that for the simple tilting slider.
On the Strain Energy of Shells
Authors: Langhaar H. L. , Carver D. R. 
Published: June 2021

Abstract
In a previous paper, the strain energy of a shell was derived with the aid of the assumption that only the linear terms in the thickness co-ordinate z need be retained in the expressions for the strains. Recently, Bleich and DiMaggio derived a strain-energy expression for circular cylindrical shells without using power series in z. The present paper shows that power series in z may be eliminated, in general, and that the errors caused by linearizing approximations are frequently significant.
A Numerical Solution for the Nonlinear Deflection of Membranes
Authors: Shaw F. S. , Perrone N. 
Published: June 2021

Abstract
A numerical method of solution for the nonlinear deflection of thin flat membranes subjected to normal forces as well as forces in the plane of the membrane has been given by Hencky. The equations he solved were first derived by Föppl, and they also follow directly from the von Kármán nonlinear plate equations on formally making the plate stiffness zero. Föppl’s equations are two in number, one being of fourth order and the other second. The unknown quantities are a stress function and the normal displacement. Hencky’s method of solution does not seem capable of easy generalization. The same class of membrane problems is reconsidered here. By casting the problem entirely in terms of displacement components three simultaneous nonlinear second-order partial differential equations are obtained, and a technique is here devised by means of which these equations can be solved without difficulty using finite-difference approximations in conjunction with a relaxation-iteration procedure. Various simple preliminary examples are discussed, after which an example involving a rectangular region is considered in complete detail. The technique devised can be used for a region of any shape, including the case where the boundary is curved, and also for any arbitrary given load system.
Tables for Frequencies and Modes of Free Vibration of Infinitely Long Thin Cylindrical Shells
Authors: Baron M. L. , Bleich H. H. 
Published: June 2021

Abstract
Tables are presented for the quick determination of the frequencies and shapes of modes of infinitely long thin cylindrical shells. To make the problem tractable, the shells are first treated as membranes without bending stiffness, and the bending effects are introduced subsequently as corrections. The underlying theory is based on the energy expressions for cylindrical shells. The tables cover the following range: lengths of longitudinal half wave L from 1 to 10 radii a; number n of circumferential waves from 0 to 6. The results apply for Poisson’s ratio ν = 0.30.
The Plasticity of an Isotropic Aggregate of Anisotropic Face-Centered Cubic Crystals
Authors: Hershey A. V. 
Published: June 2021

Abstract
The plasticity of a polycrystalline aggregate is expressed in terms of the plasticity of the individual grains. It is assumed that the local deviation of stress from the average stress is proportional to the local deviation of strain from the average strain, and it is assumed that plastic flow begins when there is an average of three active slip systems per grain. The plastic states of a grain are mapped as a function of the orientation of the crystallographic axes. A coexistence of different states of strain with different rotations of the axes at the same state of stress can be correlated with the occurrence of deformation bands. A range of orientations is illustrated in which the axes tend to congregate quickly and then move more slowly toward a stable end orientation. The residual strain which would be observed by x-ray diffraction after the release of stress is calculated for three sets of diffracting planes. The applications of the theory have so far been limited to face-centered cubic polycrystals with intrinsic elastic isotropy.
A Simple Nomogram for the Ratios of Octahedral to Maximum Shearing Stresses and Its Physical Interpretation
Authors: Zizicas G. A. 
Published: June 2021

Abstract
A nomogram constructed exclusively by means of straight lines is presented, giving the ratio of the octahedral to the maximum shearing stresses for all possible stress distributions in terms of the nondimensional ratios of the two principal stresses to the one of maximum absolute value. The physical interpretation of the nomogram is discussed. It is shown that states of stress with constant ratio of octahedral to maximum shearing stress are represented by straight lines. To such lines are found to correspond fixed values of the deviatoric parameter μ = 2 S 2 - S 1 - S 3 S 1 - S 3 in agreement with a recent observation by Novozhilov. The values of μ are given directly by the nomogram.
Polyaxial Stress-Strain Relations of a Strain-Hardening Metal
Authors: Batdorf S. B. , Budiansky Bernard 
Published: June 2021

Abstract
The authors assess a plastic stress-strain law of anisotropic strain-hardening type which they previously developed on the basis of explicit consideration of the polycrystalline nature of metals and the mechanism of plastic deformation. The assumptions made are reviewed, together with the successes and limitations of the theory. The authors indicate the lines along which they feel that improvement of the theory is to be sought.
Rigid-Plastic Analysis of Symmetrically Loaded Cylindrical Shells
Authors: Hodge P. G. 
Published: June 2021

Abstract
A general method is presented for finding the stress and incipient velocity distribution in a symmetrically loaded cylindrical shell at collapse. The results are based upon a linearized yield surface, and a method is given for obtaining this linearized surface directly. The techniques are illustrated with reference to open and closed cylindrical shells under uniform external pressure. In each case the shell is specified completely by a single parameter c defined as the ratio of the half-length of the shell to the geometric mean of the radius and half-thickness; c = L / a ! . It is found that for moderately large values of c, the limiting load is greater for the closed shell, while for small c the reverse is true.
Steady-State Vibrations of Beam on Elastic Foundation for Moving Load
Authors: Kenney J. T. 
Published: June 2021

Abstract
This paper presents an analytic solution and resonance diagrams for a constant-velocity moving load on a beam on an elastic foundation including the effect of viscous damping. The limiting cases of no damping and critical damping are investigated. The possible velocities for the propagation of free bending waves are found and their relation to the critical velocity of the beam is studied.
Prediction and Evaluation of Sensitivity to Transient Accelerations
Authors: Kornhauser M. 
Published: June 2021

Abstract
The determination, presentation, and interpretation of inertia-sensitivity data are discussed with application to inertia devices and to shock-resistant structures. Theoretical analysis of the single-degree-of-freedom system for response to acceleration-time pulses, amplification factors, and inertia sensitivity are used as a basis for discussion of actual devices. Effects of deviations from the ideal mass-spring system are considered. Practical use of sensitivity data is discussed with regard to the reliability of laboratory methods, the accuracy of field measurements, and variability of service conditions. Criteria are suggested for design of inertia mechanisms and design of structures for resistance to shock.
Mechanism of Fretting Corrosion
Authors: Uhlig Herbert H. 
Published: June 2021

Abstract
A review of the facts suggests that the mechanism of fretting corrosion includes a chemical factor and a mechanical factor, with observed damage, in general, resulting from both. An asperity rubbing on a metal surface is considered to produce a track of clean metal which immediately oxidizes, or upon which gas rapidly adsorbs. The next asperity wipes off the oxide or initiates reaction of metal with adsorbed gas to form oxide. This is the so-called chemical factor of fretting. In addition, asperities dig below the surface to cause a certain amount of wear by welding or shearing action in which metal particles are dislodged. This is the mechanical factor of fretting. Metallic debris produced by fretting is thought not to oxidize spontaneously, as proposed by the molecular-attrition theory, but instead converts partially to iron oxide by secondary fretting action of particles rubbing against themselves or adjacent surfaces. This accounts for the fact that Fe2O3 is found by x ray to be the major corrosion product and metallic iron is present, if at all, in only very small amount. The quantitative expression for fretting corrosion derived on the basis of the foregoing model for relatively large values of load, frequency, and slip is W ( total ) = ( k 0 L 1 ⁄ 2 - k 1 L ) C f + k 2 l L C where W is the specimen weight loss, L is the load, C is the number of cycles, f is the frequency, l the slip, and k0, k1, and k2 are constants. The first two terms are the chemical factor of fretting corrosion and the third term is the mechanical factor. Accordingly, the equation predicts that fretting-corrosion weight loss is a hyperbolic function of frequency, is parabolic with load and linear with number of cycles or magnitude of slip. Furthermore, the terms concerned with a frequency effect disappear when the chemical factor is suppressed, as is observed when fretting tests are conducted in nitrogen. These conclusions are confirmed by the reported data. In addition, the calculated reaction-rate constant for oxidation of a freshly formed iron surface obtained from fretting data is reasonable and falls between two independently observed values. In our experiments, the chemical or corrosion factor falls within 6 to 78 per cent of the total observed fretting damage, depending on conditions of test. Remedial measures are outlined in light of the data and the proposed mechanism.
Small Rotationally Symmetric Deformations of Shallow Helicoidal Shells
Authors: Reissner Eric 
Published: June 2021

Abstract
Known solutions for transverse bending and plane stress of flat circular ring plates are generalized so as to apply to shallow helicoidal shells. The pitch of the middle surface of the shell is responsible for a coupling of what would be separate problems of plane stress and transverse bending for flat plates. Explicit results are obtained for an important sample problem. A general property of helicoidal cantilever shells is stated. Criteria are obtained indicating, in terms of the parameters of the shell (a) the range of applicability of the results obtained, and (b) the range in which the shell behaves like a flat plate.
On Turbulent Jet Mixing of Two Gases at Constant Temperature
Authors: Pai S. I. 
Published: June 2021

Abstract
The fundamental equations of both two-dimensional and axially symmetrical turbulent jet mixing of two gases at constant temperature are derived and discussed. A general method of solution of these equations is given. The most important factors in these equations are the turbulent exchange coefficient for velocity distribution and that for density distribution. In general, these coefficients are not equal. If we assume that these coefficients are the same, an analytic solution for the mixing of two uniform streams is found which is an extension of Görtler’s solution for the case of homogeneous fluids. The first-order effect of the difference in densities of the two gases in the mixture on the velocity distribution is small. For two-dimensional and axially symmetrical jet from small opening, if the turbulent exchange coefficients are assumed to be the same, the velocity distribution for the case of homogeneous fluid is the first-order approximation of the velocity distribution in the jet of the mixing of two gases and the density distribution is the same as the velocity distribution. Finally, the effect of the difference in the two turbulent exchange coefficients is discussed. It is found that the ratio of turbulent-exchange coefficient for density distribution to that for velocity distribution is larger than 1, and may be as high as 2, and the ratio increases as the difference in density of the two gases increases. The larger this ratio is, the wider the spread of the density distribution than that of velocity distribution will be.
The Stress Problem of Vibrating Compressor Blades
Authors: Schnittger Jan R. 
Published: June 2021

Abstract
In order to demonstrate the general nature of the actual vibrations of compressor and turbine blades, the author undertakes a simplified analysis in which a single stiff blade, with one translational and one pitching mode, is studied. It is shown that all problems of stress in vibrating compressor blades whether they arise from forced or self-sustained vibrations may be related to the magnitude of finite mechanical or aerodynamic disturbances.
Acceleration in Mechanisms
Authors: Hinkle R. T. , Ip C. , Frame J. S. 
Published: June 2021

Abstract
An equation is derived for finding the instantaneous radii of curvature for the paths of relative motion described by the coincidental points of contact of direct-contact mechanisms, and a graphical method for solving the equation for these radii is developed. A proof of the validity of the equivalent linkage for direct-contact mechanisms is presented.
Problems of Plane Elasticity for Reinforced Boundaries
Authors: Radok J. R. M. 
Published: June 2021

Abstract
Based on N. I. Muskhelishvili’s approach to problems of plane elasticity, a general method has been deduced for the solution of problems of reinforced cutouts in infinitely thin sheets. As an illustration, the circular reinforced hole has been treated in detail and the results have been related to those obtained experimentally and theoretically by other authors. The solution for other shapes of cutouts will be greatly simplified, since full use may be made of the theory of conformal transformations.
Stress Distributions in Nonsymmetric Rotating Rays
Authors: Hodge P. G. 
Published: June 2021

Abstract
The centrifugal forces acting upon a rotating ray will produce longitudinal stresses along the ray. If the ray is not symmetric, these stresses will result not only in a longitudinal force, but also in a bending moment. A technique for finding the stress distribution in this case is developed and illustrated by means of simple examples. The limiting elastic speed and the maximum speed before large-scale plastic deformation commences are computed. An indication is given of how similar methods may be used to analyze a rotating disk with no plane of symmetry perpendicular to the axis.
Studies on Scabbing of Solids Under Explosive Attack
Authors: Broberg K. B. 
Published: June 2021

Abstract
The purpose of this paper is to analyze the mechanism of the scabbing phenomenon that occurs when an intense shock wave in a solid is reflected against a free surface. Only plane shock waves with normal incidence to the free surface are discussed. The shock wave is assumed to be initiated by the detonation of an explosive (especially TNT with a loading density of 1.5 g/cm3). The calculations are based upon values given by H. Jones and A. R. Miller (for the detonation pressure), D. J. McAdam (for the strength of the material at combined stresses), P. W. Bridgman (for the quantitative behavior of the material at very high pressures) and, finally, upon results from the author’s own experiments regarding the impulse and the pressure-time curve at detonation in contact with a metal surface. It is shown that fracture sometimes is likely to occur in several parallel layers of the material. Experiments have been performed which support the theoretical analysis. The research was carried out at the Royal Swedish Fortification and Works Administrative Service, Stockholm.
An Approximate Nonuniform Bending Theory and Its Application to the Swept-Plate Problem
Authors: Plass H. J. 
Published: June 2021

Abstract
Differential equations and boundary conditions are derived, by means of the calculus of variations, for cylindrical bars in nonuniform bending. The resulting equations are used, together with similar nonuniform torsion equations, to obtain deflections and stresses in swept cantilever plates of uniform rectangular cross section. Comparisons are made with experimental results for plates with four different sweep angles. The theory predicts deflections quite close to those found experimentally. Stresses computed from the equations, however, are not in as close agreement. It is also noticed that the theory is less accurate for large sweep angles than for small ones.
Thermal Stresses in Rectangular Strips—II
Authors: Born J. S. , Horvay G. 
Published: June 2021

Abstract
Stresses and deformations in rectangular strips due to various longitudinal temperature distributions are presented in formulas, tables, and graphs. The results are important for slabs, plate assemblies, rectangular ducts, tube-sheet ligaments; they apply, in a more qualitative fashion, also to cylindrical bodies.
A Study of the Speed of Sound in Porous Granular Media
Authors: Brandt H. 
Published: June 2021

Abstract
A theory is developed to explain the influence of pressure, porosity, and liquid saturation on the speed of sound through a porous granular medium. An aggregate of randomly stacked spherical particles of four different sizes is used as a model for the porous medium. The volume-pressure relationship of the aggregate is determined by means of the Hertz theory for the deformation of elastic and isotropic spheres in contact. This relationship is extended to embrace the case of liquid saturation of the aggregate. The bulk modulus is derived from the volume-pressure relationship and the speed of sound is determined from the bulk modulus. It is shown how the theory can be extended to apply to the speed of sound through an aggregate comprised of nonspherical granules and finally, in an approximate form, through a consolidated granular medium. As an example of the application of the latter the speed of sound through sandstone under various conditions of pressure and saturation is predicted, and agreement is noted between the predicted results and those derived experimentally.
Buckling of Laminated Columns
Authors: Clark L. G. 
Published: June 2021

Abstract
A theory is developed to determine the buckling of laminated columns composed of two or more laminations and riveted or fixed together at certain points along the column. The laminations can be of different size and material but must be long in comparison to the cross-sectional dimensions. The final result is presented in a form suitable for easy application. It is shown that for two laminations joined at an infinite number of points the problem reduces to that of a simple column. Two pinned-end columns were tested and the results are in satisfactory agreement with the theory.
Theoretical Determination of Rigidity Properties of Orthogonally Stiffened Plates
Authors: Huffington N. J. 
Published: June 2021

Abstract
The analysis of bending and buckling of orthogonally stiffened plates may be simplified by conceptually replacing the plate-stiffener combination by an “equivalent” homogeneous orthotropic plate of constant thickness. This procedure requires the determination of the four elastic rigidity constants which occur in the theory of thin orthotropic plates. Methods are presented whereby these quantities may be determined analytically in terms of the elastic constants and geometrical configuration of the component parts of the structure.
Combined Stress Tests in Plasticity
Authors: Phillips Aris , Kaechele Lloyd 
Published: June 2021

Abstract
A substantial number of combined stress tests on thin-walled tubes of aluminum 2S-O are reported. In most of the tests the tubes have been subjected to combined tension and torsion with variable stress ratios. In the last six tests each tube has first been subjected to uniaxial tension until sufficiently deep in the plastic region and then this state of uniaxial stress has been rotated while the magnitude of the principal stresses remained constant.
The purpose of the tests was to get information as to the validity of the incremental theories of plasticity. The results of these tests favor the incremental theories.
Displacements in an Elastic-Plastic Cylindrical Shell
Authors: Hodge P. G. 
Published: June 2021

Abstract
A reinforced cylindrical shell which is loaded with a uniform excess external radial pressure can support a load considerably greater than the elastic limit. While several recent investigations have been concerned with finding the collapse load of the shell, no attention has been paid to the corresponding deformations. Although rigid-plastic theory is sufficient to determine the collapse load, the more complex elastic-plastic theory must be used in investigating the displacements. In the present paper the elastic-plastic problem is stated for an ideal sandwich shell, and the stresses and deformations are computed for a particular example. Since the computations are found to be quite laborious, an approximate technique, applicable to all shells, is developed. The paper closes with some comments on the relation between the theoretical results and the behavior to be expected in real shells.
Bending and Torsion of Circular Cylinder Cantilever Beams of Cylindrically Aeolotropic Material
Authors: Ericksen W. S. 
Published: June 2021

Abstract
This paper deals with the problem of determining the components of stress and displacement associated with the flexure and torsion of a cantilever beam in the form of a hollow circular cylinder of cylindrically aeolotropic material. A solution satisfying the conditions of the theory of elasticity is obtained by the semi-inverse method of Saint Venant.
High-Frequency Extensional Vibrations of Plates
Authors: Kane T. R. , Mindlin R. D. 
Published: June 2021

Abstract
The equations of generalized plane stress are applicable to the extensional vibrations of plates only for the low modes of motion of thin plates. In this paper equations are derived which are applicable to both low and high modes of thin plates and to low modes of thick plates. As an example, the equations are solved for the case of axially symmetric vibrations of a circular disk and comparisons are made with the theory of generalized plane stress and with experiments.
Theoretical Considerations of Combined Thermal and Mass Transfer From a Vertical Flat Plate
Authors: Somers E. V. 
Published: June 2021

Abstract
In free-convective processes involving both thermal and mass transfer, since the driving force for the fluid motion has its source solely in the density difference from ambient, it is necessary to consider the thermal and mass-transfer processes simultaneously in solving any given problem. The present problem involves evaporation and condensation phenomena associated with free-convective thermal and mass transfer from a wetted isothermal vertical flat plate to a gas at an ambient temperature and mass concentration different from that on the plate. This problem presents itself in the practical case of vaporization cooling of equipment without forced circulation of the ambient gas.