0


RESEARCH PAPERS

J. Appl. Mech. 1960;27(1):1-4. doi:10.1115/1.3643901.

The governing equation of turbulent lubrication in three dimensions, equivalent to the Reynolds equation of laminar lubrication, is derived. The problem of a slider bearing with no side leakage is then analyzed. An exact solution is found in closed form. Bearing characteristics are also established. It is found that the Reynolds number is an important parameter in the problem of turbulent lubrication. Furthermore, it is shown that the laminar lubrication may be considered as the special case of the present study. A numerical example is also included.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):5-15. doi:10.1115/1.3643936.

Stationary solution on the effect of a wall on two-phase (solid particles in gas) turbulent motion shows that the intensity of motion of solid particles is affected by the presence of the wall and the distribution of turbulent intensity of the stream near the wall. The intensity of motion of solid particles can be significantly higher than the turbulence intensity of the mean stream. These modifications are consequences of Bernoulli force acting between the wall and the particle.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):16-24. doi:10.1115/1.3643893.

An approximate method, known as the heat-balance integral, is used to determine the melting rate of a finite slab which is initially at a uniform temperature below the melting point. The slab is acted upon by a constant heat input at one face and has its other face either insulated or kept at its initial temperature. The first three terms of series solutions in an intrinsically small parameter are obtained for the time histories of melting and the temperature distribution in the slab.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):25-33. doi:10.1115/1.3643930.

Tube sheets of U-tube and bayonet-tube exchangers differ from those of floating-head exchangers in that they receive no external support from the staying or column action of the tubes. The strengthening effect of tube-bending reaction is here investigated, evaluated quantitatively, and presented in the form of simple design factors. These factors are functions of a parameter ua , a measure of the relative “barreling” rigidity of the tube bundle as compared to the flexural rigidity of the tube sheet. With stiff tubes and flexible tube sheets (high ua ) the reinforcement due to tube bending is considerable and, in the central region of the tube sheet, the deflection and curvature are essentially independent of any tube-sheet property. At low ua the benefit gained is negligible.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):34-40. doi:10.1115/1.3643931.

Two sets of expressions are obtained for residual stresses and deformations resulting from bending processes in which initially flat sheets are permanently deformed to sheets having finite radii of curvature. One of these sets applies for sheets whose concave surfaces have radii of curvature under load which are greater than 0.84 times the sheet thickness, and is associated with a residual plastic zone in the interior of the sheet. The other set applies whenever the afore-mentioned radii of curvature are less than 0.84 times the sheet thickness, and is associated with residual plastic zones in the bar interior and near the concave boundary of the sheet.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):41-44. doi:10.1115/1.3643932.

Equations are developed for the radial and tangential stresses in a cylinder that has been shrunk on a rigid shaft. The analysis is made for a material having elastic properties and behaving according to a power-function speed-effect law.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):45-53. doi:10.1115/1.3643933.

Solutions are obtained for annular disks and tubes made of a linearly strain-hardened material, loaded by a uniform tensile load on the outer boundary. The strain-hardening is assumed to follow a kinematic hardening flow law. In addition, a second solution for tubes which accounts for finite deformation is determined. Some numerical comparisons are made with existing isotropic hardening solutions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):54-58. doi:10.1115/1.3643934.

The three partial differential equations derived by Dr. E. Reissner2, 3 have been reduced to a fourth-order partial differential equation resembling that of the classical plate theory and to a second-order differential equation for determining a stress function. The general solution for the two partial differential equations has been applied to a simply supported plate with a constant load p and to a plate with two opposite edges simply supported and the other two edges free. Numerical calculations have been made for the simply supported plate and the results compared with those of classical theory. The calculations for a wide range of parameters indicate that the deviation is small.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):59-64. doi:10.1115/1.3643935.

With the use of J2 deformation theory, the stress-concentration factor at a circular hole in an infinite sheet of strain-hardening material subjected to equal biaxial tension at infinity is found for a variety of representative materials. The analysis exploits a transformation which permits the calculation of the stress-concentration factor without determining the stress distribution in the sheet. Subsequent calculations reveal that, for a monotonically increasing applied stress, the stress history at all points in the sheet is nearly radial.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):65-73. doi:10.1115/1.3643937.

The stresses in the plastic range around a normally loaded circular hole in an infinite sheet are found numerically on the basis of both J2 deformation and incremental theories. The results of deformation theory are quantitatively assessed in the light of a criterion, recently developed by Budiansky, for the acceptability of deformation theories. The criterion is completely satisfied. Moreover, the results obtained by using these two different theories of plasticity do not differ greatly despite the fact that the stress paths are far from being radial.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):74-78. doi:10.1115/1.3643938.

The dynamic behavior of a simple mechanical model composed of two Timoshenko beams connected by springs is studied. The accuracy of a quasi-static solution and of Saint Venant’s principle is studied for various rates of load application.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):79-86. doi:10.1115/1.3643939.

After a rather complete exploratory program described in previous papers, the photothermoelastic method was applied to the experimental evaluation of thermal-stress theories. The new technique was correlated with several theories which analyzed the transient thermal stresses in idealized wing structures of high-speed aircraft. Various theories were investigated which represented the same idealized wing models and differed from each other only in the simplifying assumptions regarding the temperature distributions in skin and webs. The theories were evaluated by duplicating the boundary and initial conditions on plastic models and then by correlating the theories with the observed fringe orders in nondimensional form. A significant general conclusion was reached after correlating the available theories and experimental results. Owing to simplifying assumptions concerning the thermal behavior in the flanges, thermal stresses predicted by the available theories are all higher than the experimental observation. In some cases the discrepancy is as great as 30 per cent.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):87-92. doi:10.1115/1.3643940.

A problem of finding the stresses in an infinite circular cylinder having an infinite row of spherical cavities of the same size under axial tension is studied theoretically. Maximum stresses in the cylinder are calculated by a perturbation method, in each case the radius of the cavity and the distance between the centers of the neighboring cavities being varied. From consideration of the results obtained, some conclusions are made regarding the effects of the surface and the cavities on the stresses.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):93-103. doi:10.1115/1.3643941.

This investigation is concerned with the transient temperature and thermal-stress distribution generated in a semi-infinite slab if a finite segment of its edge is subjected to a sudden uniform change in temperature. The slab is supposed to be free from external loads and its faces are assumed to be insulated. Exact solutions in series form are obtained both for the heat-conduction problem and for the associated thermoelastic problem. The latter is treated quasi-statically within the classical two-dimensional theory of elasticity. The thermal stresses appropriate to the generalized plane-stress solution vanish identically in the limit as time tends to infinity. The space and time dependence of these stresses is examined in some detail with a view toward tracing the evolution of this well-known, steady-state degeneracy. Finally, the results corresponding to an instantaneous heating or cooling of a portion of the boundary are used to study the effect upon the stresses of gradual changes in the surface temperature.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):104-106. doi:10.1115/1.3643882.

The stress-strain relations of Flügge and Byrne for thin elastic shells are inverted to express strain quantities, and therewith the strain energy, in terms of stress resultants and couples. In this form, and upon omission of terms which are small of order h2 /R2 , the stress-strain relations and the strain-energy expression are shown to be simply related to corresponding results of Trefftz. The strain-energy formula of Trefftz is generalized to arbitrary orthogonal middle surface co-ordinates.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):107-110. doi:10.1115/1.3643883.

The impact problem for a rigid-plastic beam is formulated by using an interaction curve relating shearing force and bending moment for fully plastic action, and allowing for shear and rotary inertia effects. Using a simplified interaction diagram, the problem of point-impact loading is solved for a special case. The analysis shows that the shear effects are of considerable importance when the parameter μ0 = 2Q0 l/M0 is less than 20 where Q0 and M0 are plastic-carrying capacities of the cross section for pure shear and bending, respectively, and 21 is the length of the beam.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):111-119. doi:10.1115/1.3643884.

In determining the safety of foundations the assumption is usually made that the pressure distribution on the ground, in general unknown, is closely approximated by a constant one. Mathematically, the problem is thereby reduced to finding the components of stress and displacement in a half-space due to a uniform pressure on a portion of its plane boundary. The present paper contains an investigation of this problem for the case of loading over an area bounded by an ellipse. Two of the results are: (a) On the normal to the loading area through its center, the two principal stresses in planes parallel to the undeformed surface, compressive on and near the surface, become tensile within a depth smaller than the length of the corresponding principal axis of the loading area; (b) the normal deflection of the surface is greater at the extremity of the minor axis of the loading area than at the extremity of the major axis, the difference between the two values increasing with the ellipticity of the bounding curve.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):120-124. doi:10.1115/1.3643885.

Earth deflections beneath a prescribed boundary displacement were obtained theoretically and experimentally. The problem was stated in terms of a two-dimensional model and an attempt was made to design a corresponding experiment. Relative deflections between the surface of the earth and points of increasing depths within the earth were measured. The maximum depth was 42 ft 7 in, below the earth’s surface. Theoretical and experimental results were compared.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):125-131. doi:10.1115/1.3643886.

This study is concerned with the influence of axial inertia upon the elastic bending motion of initially slightly curved columns acted on by time-dependent axial forces. The equations of motion include both axial inertia and nonlinear strain terms. Numerical solutions were obtained for a similar problem previously studied by Hoff [1] but in which axial-inertia effects were neglected; i.e., the problem of a simply supported column initially bent in the shape of a half sine wave and loaded by displacing one end axially at a constant rate. The range of solutions pertains to conventional structural compression members (slenderness ratios less than 150), and to minimum rates of loading compatible with elastic response of common engineering materials. This study suggests that axial-inertia effects are of secondary importance in so far as the gross elastic response of conventional structural columns is concerned.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):132-138. doi:10.1115/1.3643887.

In order to compare the magnitude of bending stresses and shear stresses in beams under the action of impulsive forces, the values of these stresses are determined from the known differential equations for the Timoshenko beam. It is found that in the early stages, soon after the initiation of the motion, the shear stresses are of much larger magnitude than the bending stresses. This result indicates that for sufficiently large initial velocities first yielding will be in shear, a matter of consequence in plastic analysis.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):139-144. doi:10.1115/1.3643888.

In this paper, the theory is developed for the elastic-plastic response of a thin spherical shell to spherically symmetric internal transient pressure loading. Analytic solutions are obtained to the linear, small-deflection equations of motion for shell materials which exhibit various degrees of strain-hardening. Numerical solutions obtained by digital computer are also presented for the equations for large deflections obtained by accounting for shell thinning and increase in radius during deformation. The theory is compared with experiment, and is shown to be in good agreement.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):145-151. doi:10.1115/1.3643889.

A system of approximate, one-dimensional equations is derived for axially symmetric motions of an elastic rod of circular cross section. The equations take into account the coupling between longitudinal, axial shear, and radial modes. The spectrum of frequencies for real, imaginary, and complex wave numbers in an infinite rod is explored in detail and compared with the analogous solution of the three-dimensional equations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):152-158. doi:10.1115/1.3643890.

An exact solution of the equations of elasticity is found for a family of modes of vibration, or waves, in an infinite bar of rectangular cross section for certain ratios of width to depth. The solution is composed of coupled dilatational and equivoluminal waves and the four faces of the bar are free of traction.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):159-164. doi:10.1115/1.3643891.

Large amplitude oscillations of a simple pendulum whose support moves with a prescribed vertical oscillation are studied by an approximate method. Subharmonics of order 1/2, 1/4, 1/6, and 1/8 are discussed and the theoretical results are compared with experiments. The stability of the theoretical steady states is investigated by the method of Andronow and Will.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):165-171. doi:10.1115/1.3643892.

The present paper points out that Kromm’s [1] plane-stress solution, for compressional waves in an infinite elastic plate subjected to radial pressure in a circular hole at its center, has application to still another problem of interest. This is the problem of a stretched elastic plate in which a circular hole is suddenly punched. The plane-stress solution for the tensile circumferential stresses, generated by the unloading mechanism in punching, is given here. This solution is derived independently of Kromm’s work in which a rather special Laplace-transform technique was used. The derivation given here also makes use of the Laplace transform but in a more direct manner, employing the inversion integral and a contour integration. It is also shown that the present inversion technique offers important simplifying features over that used by Selberg [3] in the closely related plane-strain problem. The numerical results presented are of interest in fragmentation studies. It is shown that the dynamic circumferential stress field in the vicinity of the punched hole is quite severe; which would be important to the creation and propagation of radial cracks.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):172-176. doi:10.1115/1.3643894.

The paper is concerned with the plane motion of a rigid-strain-hardening membrane attached to two parallel fixed supports. The membrane is subjected to a uniformly distributed transverse impulse and the subsequent motion of the membrane is to be determined with the particular emphasis on the variation of thickness in the final deflected shape. It is first shown that two essentially different initial modes of deformation exist depending on the average rate of hardening. For both modes, the analysis can be based on two types of waves of discontinuity until the moment when the compressive membrane forces occur in the middle region of the membrane. The presence of compressive forces will generally preclude the existence of a unique solution for further motion. The bending rigidity will probably have to be included into the analysis in order to obtain a unique solution. However, for the technically important rates of hardening and velocities, the kinetic energy of the membrane at the moment of occurrence of compressive forces is small compared with the initial energy, so that significant information could be obtained from the present analysis about the variation of thickness and hardening throughout the membrane.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):177-181. doi:10.1115/1.3643896.

Equations of motion of a hinged ramp supporting a sliding mass, which moves at constant velocity, are derived; these are shown to have no closed solution when the ramp is spring supported or when the cylinder force is proportional to the square of the velocity. For small velocities of the sliding mass the Coriolis term may be neglected and a good approximation to the solution of the equations is obtained by means of the Madelung transformation. The solutions by special methods are compared to the solutions obtained by standard numerical methods.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):182-186. doi:10.1115/1.3643897.

A method is developed for analytically locating the Burmester points for the motion of the coupler plane of a four-bar mechanism through five infinitesimally separated positions. The results of an example are compared with the results obtained by the graphical method of Müller for locating the Burmester points. The two methods are found to give essentially identical results.

Topics: Mechanisms , Motion
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):187-195. doi:10.1115/1.3643898.

Steady-state vibrations of a class of nonlinear discrete systems with an arbitrary number of degrees of freedom are studied. The co-ordinates of the system are first transformed to the principal co-ordinates corresponding to the linear part of the system. A perturbation scheme is used to obtain the solutions. Some special effects of the ratios of the linear natural frequencies on the qualitative nature of the solutions are demonstrated. Solutions are obtained for some specific problems and the results are checked against those obtained from an analog-type computer.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):196-200. doi:10.1115/1.3643900.

The degree of freedom or overconstraint of plane kinematic chains is determined by means of an analysis of independent loops. It is shown how the independent loops of a system may be identified and how they may be used to recognize certain special cases which do not fit into the framework of so-called “general formulas.” The independent loops may also be used to systematically formulate the governing kinematic equations of a system. It is shown that the equations so formulated are in general sufficient to solve for all unknown velocities and accelerations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):201-206. doi:10.1115/1.3643902.

Freudenstein’s approximate synthesis of planar four-bar linkages is generalized to spatial linkages, and the conditions under which this generalization is applicable are expressed. Three cases of synthesis of spatial linkages to generate functions of one variable between nonparallel axes are considered in detail: (a) The spherical four-bar linkage; (b) a variation of the four-bar linkage in which two turning pairs are replaced by ball-and-socket joints, a linkage which may be designed to generate arbitrary functions with up to seven accuracy points; and (c) a second variation of the four-bar linkage where three turning pairs are replaced by cylinder pairs, a linkage capable of being designed to generate a variable-pitch helical motion with three accuracy points.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1960;27(1):207-208. doi:10.1115/1.3643903.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):208. doi:10.1115/1.3643904.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):210-211. doi:10.1115/1.3643906.
Abstract
Topics: Buckling
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):211-212. doi:10.1115/1.3643907.
Abstract
Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Appl. Mech. 1960;27(1):221. doi:10.1115/1.3643926.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):221. doi:10.1115/1.3643927.
FREE TO VIEW
Abstract
Topics: Plasticity
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):221-222. doi:10.1115/1.3643928.
FREE TO VIEW
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(1):222. doi:10.1115/1.3643929.
FREE TO VIEW
Abstract
Topics: Heat , Mass transfer
Commentary by Dr. Valentin Fuster

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In