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RESEARCH PAPERS

J. Appl. Mech. 1967;34(1):1-7. doi:10.1115/1.3607624.

Discussion of similarity laws for jet noise as suggested by experiments. Construction of a model line emitter. Near-field pressure covariances and spectra. Phase coherence of the near-pressure-field, nonlinear couplings in the process of generation of turbulence.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):8-10. doi:10.1115/1.3607674.

The problem of Stokes’ flow for a sphere in arbitrary external flow pattern is solved using a particular scalar Green’s function. By this method, the uniqueness of solution is clearly shown, and arbitrary flows (linear shear flow, Poiseuille flow, and so on) are seen to be as straightforward as simple uniform flow.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):11-15. doi:10.1115/1.3607611.

The paper gives an analysis of the temporal growth of vorticity when water contained in a large vertical cylindrical tank flows out through a small hole in the base of the tank. The results indicate both an exponential growth of vorticity from the rotation of the frame of reference and an exponential growth of the residual vorticity in the water. Two main cases are considered; (a) the case when the initial swirl component does not vary in the vertical direction, (b) the case when the swirl component decreases downwards. The latter case simulates the effect of a tank bottom boundary layer or other vertical shear layer on the vorticity growth. While the analysis relates to a simplified model of the physical situation and also entails approximations, it nevertheless indicates that when a downwardly decreasing gradient of swirl velocity exists, a reversal from an initial clockwise residual swirl to a final counterclockwise rotation (in the Northern Hemisphere) may be anticipated. This is in accord with cited experimental results.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):16-22. doi:10.1115/1.3607619.

The velocity profiles for an infinite, cylindrical bearing are obtained by means of a small-eccentricity perturbation calculation. The modified Reynolds number appears as a parameter, and velocity profiles are presented for modified Reynolds numbers of 10−3 , 10−2 , 10−1 , 1, 10, and 102 . The most significant difference in the velocity profiles for the various Reynolds numbers is the appearance of components which are 90 deg out of phase with the film thickness at the larger values of the modified Reynolds number. The consequences of these components are discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):23-28. doi:10.1115/1.3607644.

This paper presents a procedure to analyze the free and forced liquid sloshing motions in an axisymmetric tank of arbitrary shape at low-gravity environments. The free-vibration problem is solved by extending the analysis of Satterlee and Reynolds for a circular cylindrical tank with a flat bottom. The forced-motion problem is solved by first expanding the velocity potential, the interface wave height, and the forcing functions in terms of the normal mode shapes obtained in the free-vibration analysis. The solutions hold for any arbitrary horizontal translational motion of the tank.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):29-36. doi:10.1115/1.3607664.

The flow of incompressible, viscous, electrically conducting fluids in circular pipes in the presence of an applied transverse magnetic field is analyzed theoretically and experimentally. The relations among the Hartmann number, the Poiseuille number, skin friction coefficient, the Reynolds number, sensitivity, and wall conductivity are discussed. The experimental results using carbon pipe, stainless-steel pipe, and glass pipe are in good agreement with theoretical calculations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):37-42. doi:10.1115/1.3607665.

Using the strain-mapping method for the Tresca yield condition, the yield surface is derived for a cylindrical shell with a wall reinforced by longitudinal ribs on one side. Results are given for the case where the axial load is zero. As a sample problem utilizing this surface and as an appropriate method for solving nonlinear equations, the solution of a cantilever shell under constant pressure is obtained.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):43-48. doi:10.1115/1.3607666.

Exact invariant stress and deformation functions for doubly curved (nondevelopable) shells are derived. The invariant stress function reduces the six shell equilibrium equations into a single equation in the stress function and moment resultants. The deformation function reduces the three surface strain-displacement relations into a single compatibility equation in the strains and deformation function, in terms of which the changes of curvature are also expressed. Application of these functions in the formulation of an approximate bending theory for shells is presented.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):49-55. doi:10.1115/1.3607667.

The initial postbuckling behavior of a shallow section of a spherical shell subject to external pressure is studied within the context of Koiter’s general theory of postbuckling behavior. Imperfections in the shell geometry are shown to have the same severe effect on the buckling strengths of spherical shells as has been demonstrated for axially compressed cylindrical shells. Large reductions in the buckling pressure result from small deviations, relative to the shell thickness, of the shell middle surface from the perfect configuration.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):56-58. doi:10.1115/1.3607668.

In this paper, nonlinear membrane equations are derived for a shell of revolution under the assumption that not only are the displacements and rotations large, but that, also, large strains are admitted. The equations, therefore, are aimed at shells which are not only very thin, but which are also made of a material which permits large elastic strains. The special difficulties resulting from this extension of the theory are discussed. As an example for the application of the equations, a circular toroid subjected to internal pressure is studied. Numerical results are given for a level of loading which lies clearly outside the domain of a large-deflection, small-strain theory.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):59-64. doi:10.1115/1.3607669.

A multisegment method is developed for the solution of two-point boundary-value problems governed by a system of first-order ordinary nonlinear differential equations. By means of this method, rotationally symmetric shells of arbitrary shape under axisymmetric loads can be analyzed with any available nonlinear bending theory of shells. The basic equations required by the method are given for one particular theory of shells, and numerical examples of a shallow spherical cap and a complete torus subjected to external pressure are presented in detail. The main advantage of this method over the finite-difference approach is that the solution is obtained everywhere with uniform accuracy, and the iteration process with respect to the mesh size, which is required with the finite-difference method, is eliminated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):65-72. doi:10.1115/1.3607670.

Approximate solutions are obtained, by Newton’s method, for shells subjected to uniform and/or point loads in the prebuckled or postbuckled configurations. Comparison of results with numerical solutions shows maximum deviations of 5 percent for clamped shells subjected to uniform loads in the prebuckled configuration. Similar comparisons for other cases show larger deviations. A characteristic load is developed which compares favorably with numerical buckling loads.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):73-80. doi:10.1115/1.3607671.

This paper treats the axisymmetric vibration of thin elastic shells. Estimates of natural frequencies and modes are obtained for a general class of domes by applying the approximations obtained in a previous paper by one of the authors. Numerical results are obtained for ellipsoidal shells, and one new theoretical result is found.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):81-86. doi:10.1115/1.3607672.

This paper presents an analysis into the dynamic response of a long cylindrical sandwich shell under a moving axially symmetric ring load. The shell is assumed to be orthotropic and subjected to an initial axial stress. The uniform velocity of the load is prescribed and only the steady-state response is considered. Numerical results indicate the effects of various relevant parameters. The behavior of orthotropic sandwich cylinders under initial stress is compared with that of homogeneous isotropic cylindrical shells free of initial stress, and differences are pointed out.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):87-90. doi:10.1115/1.3607673.

Linear, nonlinear, and dynamic programming formulations are developed for the solution of the min-max response of a single-degree-of-freedom dynamic system with incompletely prescribed input functions. The problem is: Given an oscillator whose equation of motion is mẍ + g(x, ẋ) = f(t), subject to stated initial conditions, and acted upon by a forcing function, f(t), which is nonnegative, and of specified finite duration and total impulse, find the particular forces which produce the least possible maximum displacement of the oscillator, and find this bounding value. Previously, Sevin developed an analytical technique for the solution which is inherently dependent upon a linear undamped form for the restoring force g(x, ẋ). In the current work, an alternate statement of the problem is presented which lends itself to tractable computational formulations involving less stringent restrictions on g(x, ẋ). Results obtained by dynamic and linear programming for specified forms of g(x, ẋ) are given as functions of load duration.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):91-99. doi:10.1115/1.3607675.

Experiments are reported involving elastic-plastic pulses due to explosive loading at one end of long, annealed, commercially pure, aluminum rods at room temperature and at elevated temperatures up to 750 deg F. The stress waves were detected by a condenser microphone at the far end of the rod and, in some cases, by strain gages at a cross section distant from the impact end. The essential features of the recorded velocity-time profiles and strain-time profiles are found to be in agreement with the predictions of rate independent elastic-plastic theory which takes a Bauschinger effect into account. At room temperature, the reference dynamic stress-strain curve does not differ appreciably from the quasi-static stress-strain curve whereas at elevated temperatures there appears to be a marked difference between the dynamic and quasi-static stress-strain curves. The experiments also serve to determine the dynamic proportional limit which is found to be fairly insensitive to temperature. Since the maximum plastic strains are small at cross sections remote from the impact end, the measurements, and consequently the conclusions, are limited to small strains beyond the proportional limit.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):100-103. doi:10.1115/1.3607607.

The exact solution to the problem of diffraction of plane harmonic polarized shear waves by a half-plane crack extending under antiplane strain is constructed. The solution is employed to study the nature of the stress field associated with an extending crack in an elastic medium excited by stress waves.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):104-110. doi:10.1115/1.3607608.

The equations of motion of a linear elastic solid have been used to study the propagation of transient compressional disturbances in anisotropic plates, generated by several types of surface and edge loadings. A particular orientation of the axes of material symmetry was chosen, and several classes of anisotropic media have been considered. From the exact solutions obtained, a far-field analysis based on a low-frequency, large-wavelength approximation is given; and numerical results are presented for copper, ice, zinc, beechwood, and several isotropic media for comparison purposes.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):111-118. doi:10.1115/1.3607609.

A “method of images” series solution is obtained which converges rapidly for a simply supported, long beam with a high-velocity, moving concentrated load. Each term of the series is a Fourier integral solution for an appropriate semi-infinite beam problem. The integrals are evaluated in closed form for the beam without a foundation and have a simple asymptotic evaluation for the beam with an elastic foundation. In particular, the asymptotic results provide a solution for the “critical” load velocity, for which a “steady-state” solution does not exist, and for the limiting case of infinite load velocity, for which the beam is given an initial uniform lateral velocity.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):119-126. doi:10.1115/1.3607610.

Scattering of plane harmonic compressional and shear waves (P and SV-waves) by a semi-infinite rigid-smooth strip or ribbon which is a plane barrier with its top and bottom surfaces being confined normally, but free in lateral directions, is treated. Under the condition that displacements must be regular, exact solutions for the combined incident and scattered-wave fields are obtained in terms of Weber’s parabolic cylinder functions. Principal stresses are calculated on both sides of the strip and the stresses are shown to be singular of the order (kr)−1/2 , where k is the incident wave number and r the radial distance from the tip.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):127-132. doi:10.1115/1.3607612.

The problem of longitudinal oscillation of a viscoelastic rod of finite length including the effect of thermomechanical coupling has been studied. The material is assumed to be thermorheologically simple. The almost steady oscillation superposed on a slowly varying temperature distribution permits representation as a boundary-value problem which is solved numerically by iterative procedures. Calculations are made for different stress levels and frequencies. It is found that the temperature increases considerably after a length of time of vibration although the stress level is low. A steady state of temperature can be reached if the temperature at one end of the rod is fixed and a radiation boundary condition is prescribed at the other end.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):133-136. doi:10.1115/1.3607613.

When a uniform heat flow in an infinite orthotropic solid is disturbed by the presence of a long circular insulated cavity, local intensification of the temperature gradient occurs in the neighborhood of the cavity. This report describes a study of the stress field induced by the temperature distribution. The linear plane (plane stress or plane strain) thermoelastic problem is solved by using the complex variable technique. The analysis may also be used for other steady-state thermal stress problems in an orthotropic medium.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):137-145. doi:10.1115/1.3607614.

Several boundary-value problems for semi-infinite bars made of a coupled thermoelastic material are solved by means of new functions. These arise in the solutions as “corrections” to classical tabulated functions such as the error function. However, they are not always small compared to their uncoupled equivalents. It turns out that the numerical differences in the solutions of a specific problem are usually small. But interesting phenomena are still found. The stresses produced in the coupled material are larger than those in the uncoupled one. The temperature generated on the face during impact of identical specimens is less than one might expect on simple intuitive grounds. Its time history is also quite interesting. Stress, strain, and thermal precursors exist but they do not propagate at a unique speed, while discontinuities propagate at the isothermal bar velocity. It is found that there is not much difference between the surface temperatures generated in a constant-velocity problem and one in which a constant acceleration is imposed. The temperature gradients are, however, different in these two problems.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):146-152. doi:10.1115/1.3607615.

Analytical methods are developed for treating steady-state axisymmetric thermoelastic problems defined in bispherical coordinates. Possible geometrical configurations include the infinite space with two spherical cavities of arbitrary radii and separation distance, the half-space with a spherical cavity, and the thick-walled shell having eccentric spherical boundaries. Thermal conditions must be prescribed at the surface of the body such that the temperature distribution is uniquely determined. The surfaces of the body are traction free. Numerical results for a half-space containing a spherical cavity heated to constant temperature with zero temperature on the plane and at infinity are presented in graphical form for representative geometrical variations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):153-159. doi:10.1115/1.3607616.

The Hertzian theory of elastic contact between spheres is extended by considering one of the spheres to be rough, so that contact occurs, as in practice, at a number of discrete microcontacts. It is found that the Hertzian results are valid at sufficiently high loads, but at lower loads the effective pressure distribution is much lower and extends much further than for smooth surfaces. The relevance to the physical-contact theory of friction and electric contact is considered.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):160-164. doi:10.1115/1.3607617.

In this paper, constitutive relations are derived for a linear Cosserat continuum possessing hemitropic symmetry. In such a continuum, the microstructure has a screwlike property, or handedness, and can support initial couple stresses of twist. These initial stresses serve as a model for cohesion. The introduction of free boundaries in such a medium brings about an unbalancing of the internal “cohesive” forces which results in a highly localized skin effect. This skin effect is represented by an outward, or inward, motion of a boundary layer, which is accompanied by microtwisting. A qualitative comparison is obtained with a specific solution based upon the linear elastic dislocation theory.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):165-174. doi:10.1115/1.3607618.

An asymptotic expansion procedure proposed by E. Reissner is applied to the simple Donnell equations for circular cylindrical shells, and a simple explicit solution is obtained for the interaction problem of an infinite cylinder reinforced by a central ring subjected to a nonuniform radial load. It is shown that the sign of the dominant stresses depends entirely upon whether the shell is reinforced by inside or outside rings. In addition, even when only the lower harmonic contributions are retained, good agreement with an exact solution for the case of concentrated loads is achieved.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):175-183. doi:10.1115/1.3607620.

In a recent paper, Sternberg and Knowles characterized implicitly the solution of a relaxed Saint-Venant flexure problem that is associated with the absolute minimum of the total strain energy among all solutions of this relaxed problem that correspond to a fixed resultant load and to the normal tractions on the ends of the cylinder inherent in Saint-Venant’s solution. In the present investigation, this optimal flexure solution is determined explicitly for a circular cylinder by means of the Papkovich-Neuber stress functions. The results obtained, which are in infinite-series form, are evaluated numerically and compared with the analogous results of Saint-Venant. The solution deduced here also supplies a quantitative illustration of Saint-Venant’s principle.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):184-186. doi:10.1115/1.3607621.

The method of optimal plastic design used by Marçal and Prager [1] is reviewed and generalized to arbitrary one and two-dimensional plastic structures, and the uniqueness of optimal designs is discussed.

Topics: Design
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):187-194. doi:10.1115/1.3607622.

The flexural-vibration characteristics of a symmetric, doubly infinite composite plate consisting of two outer layers of a linear viscoelastic material bonded to an elastic core have been examined, the viscous effects in the coating being represented by a complex shear modulus. Calculations of the dispersive and damping effects have been obtained for the lowest three modes by an extension of the exact Rayleigh-Lamb equations. Loss factors of the lowest modes have also been evaluated by two readily computed approximate methods; the results have been compared with those from the exact solution. The material constants were chosen to be representative of a high-polymer coating and an aluminum core. The modal behavior of the systems and coupling effects are discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):195-199. doi:10.1115/1.3607623.

Small volume fractions of very small particles in a pure metal eliminate easy glide in a single crystal and produce very high yield strength in a polycrystal. The validity of a partial explanation provided by the application of ordinary continuum mechanics on the microscale is explored here. Size effect associated with inhomogeneity of the metal matrix is seen to play a major role because a small volume fraction of rigid spheroidal particles in any homogeneous elastic-plastic matrix can contribute little to engineering yield strength and to subsequent work-hardening. However, particle strength in itself cannot provide the yield strength and flow level of a structural metal. The increased resistance to additional slip must be due mainly to the expanding network of intersecting slip triggered by many particles of very small size. This and the elastic distortion in the immediate vicinity of solute atoms and extremely small particles represent significant large local changes in geometry. Consequently, such predictions of the general theorems of conventional plasticity as the lack of influence of initial stress on flow level need not be valid.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):200-206. doi:10.1115/1.3607625.

Tests were conducted to determine the effects of irradiation and plastic deformation on the yield surfaces of polycrystalline copper. It was found that the principal effect of plastic deformation on unirradiated copper was to translate the yield surface without appreciably changing its size or shape. Irradiation, on the other hand, produced a very large change in the overall size of the initial yield surface; in other words, it produced an effect phenomenologically similar to extensive isotropic strain-hardening. In addition, the shape of the initial yield surface after irradiation was dependent on the plastic strain offset chosen to define yield. This effect was not observed for the unirradiated metal. Extensive plastic deformation after irradiation caused the yield surface to translate and grow smaller without significantly changing shape.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1967;34(1):207-209. doi:10.1115/1.3607626.
Abstract
Topics: Motion , Cylinders
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):209-210. doi:10.1115/1.3607627.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):210-212. doi:10.1115/1.3607628.
Abstract
Topics: Fourier series
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):212-214. doi:10.1115/1.3607629.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):216-217. doi:10.1115/1.3607631.
Abstract
Topics: Creep , Displacement
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):219. doi:10.1115/1.3607633.
Abstract
Topics: Equations , Shells
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):220-221. doi:10.1115/1.3607634.
Abstract
Topics: Torsion , Rods
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):223-226. doi:10.1115/1.3607636.

Approximate solutions to the conservative free-oscillation problem were obtained recently [1–4] through the use of ultraspherical polynomials. The present paper extends the technique to forced oscillations governed by

ẍ + g(ẋ) + f(x) = F0 sin pt + F1
Very accurate results are obtained either by setting the ultraspherical polynomial index λ = 0 or, better yet, by restricting the choice of λ such that the solution to the forced problem is a perturbation from the nonlinear free oscillation solution. Examples are given.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):226-227. doi:10.1115/1.3607637.
Abstract
Topics: Elastic waves
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):227-230. doi:10.1115/1.3607638.
Abstract
Topics: Deformation , Shells
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):230-232. doi:10.1115/1.3607639.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):234-236. doi:10.1115/1.3607641.
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):237-238. doi:10.1115/1.3607642.

An attempt is made to develop a law of the wall for a thick axisymmetric turbulent boundary layer in which the sublayer thickness is comparable to the radius of transverse curvature. Examination of the equations of motion in the viscous sublayer suggests a law similar to that in two-dimensional flow. Available experimental information is consistent with this law, but the structure of turbulence in such thick axisymmetric boundary layers would seem to need further study.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):239-240. doi:10.1115/1.3607643.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):240-243. doi:10.1115/1.3607645.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):243-245. doi:10.1115/1.3607646.
Abstract
Topics: Stress
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Appl. Mech. 1967;34(1):254. doi:10.1115/1.3607660.
FREE TO VIEW
Abstract
Topics: Stress
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):254. doi:10.1115/1.3607661.
FREE TO VIEW
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):254. doi:10.1115/1.3607662.
FREE TO VIEW
Abstract
Topics: Plasticity
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1967;34(1):254. doi:10.1115/1.3607663.
FREE TO VIEW
Abstract
Topics: Heat , Mass transfer
Commentary by Dr. Valentin Fuster

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