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RESEARCH PAPERS

J. Appl. Mech. 1963;30(3):321-328. doi:10.1115/1.3636556.

This paper is concerned with a theory of viscoelastic/plastic solids which reduces to that of the classical (linear) viscoelasticity as one limiting case and to the (inviscid) theory of elastic/plastic solids in another. Whereas the viscoelastic strain rates are assumed to be derivable from the appropriate creep integral laws of classical viscoelasticity, the plastic strain rates in stress space are dependent not only on the path history but also the time history of stress. After postulating the existence of a regular loading surface in the viscoelastic-plastic state and deducing the appropriate criterion for loading, a major portion of the paper is devoted to establishing (a) the convexity of the loading surface, (b) the direction of the plastic strain-rate vector in stress space, and (c) the structure of the constitutive equations for the plastic strain rates. The loading surface of the present theory (in contrast to that of the inviscid theory of plasticity), being dependent on certain measures representing time history of stress, is allowed to change its shape continually; this has implications in the interpretation of experimental results dealing with the determination of the initial and subsequent yield surfaces where corners are observed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):329-334. doi:10.1115/1.3636557.

This paper presents a comparison of the theoretically and experimentally determined frequencies and zero displacement lines for the normal mode vibrations of shallow spherical shells. Results are given for the clamped-edge and the momentless-edge boundary conditions. Calculations of frequencies and loci of zero displacement components for various shell sizes were made on an IBM 650 computer for the rotationally symmetric vibrations only, as the theory is not available for the case of asymmetric vibrations. Experiments were performed to determine the vibration characteristics both for the symmetric and the asymmetric vibrations. Several model shells constructed of steel were used for the purpose.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):335-341. doi:10.1115/1.3636558.

A method is developed to find the stresses and strains in an incompressible viscoelastic hollow cylinder with moving inner radius contained by an elastic case and subject to internal pressure under the assumption of a state of plane strain. Stresses and strains are computed for a material with deviatoric stress-strain relations characteristic of a standard solid. The numerical computation is carried out with the aid of an IBM digital computer 1620 and is intended to illustrate the effects of the thickness of the cylinder, of the rate of increase of the internal pressure, and of the strength of the reinforcement provided by the elastic shell.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):342-346. doi:10.1115/1.3636559.

Singularities for uniformly moving and static concentrated forces on shallow circular cylindrical shells are obtained in terms of the integrals of the products of cylindrical and circular functions. Some relations between the solutions of Helmholtz’s equation and the solutions of bi-Helmholtz’s equation are also given.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):347-354. doi:10.1115/1.3636560.

The axially symmetric pressure signal produced by the longitudinal impact of a semi-infinite elastic cylindrical shell upon a rigid obstacle is determined by using membrane theory. Using this simplified theory, it is possible to obtain not only the leading term of an asymptotic expansion for large values of time, but also additional terms.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):355-362. doi:10.1115/1.3636561.

Free vibrations and forced vibrations of an infinitely extending plate resting on an elastic foundation and carrying a mass are solved. Then the amplitudes of the free vibrations produced by an impulse applied to the mass on the plate are determined, and it is found that two kinds of vibration are produced in the plate: One is a free vibration and the other is a special vibration, which consists of an infinite number of free vibrations and resembles a damped oscillation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):363-366. doi:10.1115/1.3636562.

Based on the general theory of thin plates and shells previously developed by the first author, which holds also for oblique coordinate system, the problem of buckling of simply supported parallelogram plates is treated. Numerical values of the critical stresses of buckling under compression and shear are calculated, respectively, for plates having angles between 45 and 135 deg, and for side ratios 1 and 2.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):367-372. doi:10.1115/1.3636563.

A dynamical system having multiple degrees of freedom and under parametric excitation is governed by a system of ordinary differential equations with periodic coefficients. In this paper a first-approximation analysis is carried out and criteria for instability are derived explicitly.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):373-378. doi:10.1115/1.3636564.

The stresses and deflections of thin rectangular beams of arbitrary variable depth, in pure bending, according to the theory of plane stress, are considered. They are obtained in the form of series; the first term of each series is identical with the strength-of-materials solution and the others represent the necessary correction to that theory. This form of the solution is chosen because of its convenience in the study of the relationship between the Bernoulli-Euler and the exact solution. The former is found to be quite accurate for thin beams and, when certain conditions are satisfied by the ordinates (and their spanwise derivatives) of the upper and lower edges of the beam. The Bernoulli-Euler theory is ambiguous in prescribing the position of the axis of a beam of variable cross section; admissible choices for the axis are presented.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):379-383. doi:10.1115/1.3636565.

A general method for analysis of the behavior of a flexible frictionless shaft of any arbitrary configuration running inside of a guide tube with negligible clearance and transmitting torque is presented. The method is applied to two configurations: (a) Segment of a plane circular arc. (b) Segment of a helical arc. The first configuration was discussed partially in a Russian publication where the solution for the angular displacement of an unloaded shaft was derived from first principles. The theory also is applied to the analysis of a switching device composed of a Wire-In-Tube with corrections to the solution given there.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):384-390. doi:10.1115/1.3636566.

Analytical equations of the types required to define ballistic perforation dynamics are developed. These equations concern both blunt and sharp-nosed fragments, perforating plates normally and at oblique impact angles. Residual velocities are defined in terms of magnitude and direction. Analytical models and confirming experimental data, which are presented here, specifically concern the ballistic velocity-impact range to about 25 percent of the velocity of longitudinal sonic waves in the impacting materials.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):391-395. doi:10.1115/1.3636567.

The load-deformation curve is obtained for a thin tube crushed between two parallel, rigid plates. It is found that the influence of geometry changes after initial yield results in increased load-carrying capacity. In addition, the effects on the yield condition due to direct stress and shear are quantitatively discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):396-400. doi:10.1115/1.3636568.

A thick-walled circular cylinder acted on by pressure, axial end load, and twisting moment is analyzed under the assumption that end effects are negligible. The locus of all load points (interaction surface) for which unaccelerated flow of a perfectly plastic material can occur is found parametrically. Certain special cases are considered and the results compared with those of shell theory.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):401-409. doi:10.1115/1.3636569.

Solutions are obtained for the large plastic deformations of a cylindrical membrane with rigid end closures subjected to an internal pressure loading. A plastic linearly hardening material obeying Tresca’s yield criterion and the associated flow rule is considered. It is found that, in general, a shell passes through three stages of deformation, finally assuming a spherical shape. The instability pressure (maximum pressure) may be reached in any of the stages depending on the length/diameter ratio of the shell and the hardening modulus of the material. Although numerical integration is required to obtain solutions for shells in the first stages of deformation, the solution in the final stage is given in closed form.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):410-414. doi:10.1115/1.3636570.

A procedure for treating plane-elasticity problems in simply connected regions, consisting of use of numerical mapping methods in order to apply the Muskhelishvili complex variable method, is demonstrated. This approach now makes the whole complex variable method susceptible to automatic solution on a digital computer. An example is considered for which the exact solution was known; a comparison to the finite-difference solution for this example is also made.

Topics: Elasticity , Computers
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):415-418. doi:10.1115/1.3636571.

A classical substitution procedure for solving Poisson’s equation ∇2 φ = −K is extended by application of certain coordinate transformations suggested by the functional form of K. The method is applied to the determination of fluid-velocity fields in two curvilinear geometries.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):419-425. doi:10.1115/1.3636572.

Continuing a series of studies on the fracture analysis of elastic bodies, the present paper provides a complex variable method for evaluating the strength of stress singularities at crack tips encountered in the flexure and torsion of cylindrical bars. As a result of the complex flexure functions being sectionally holomorphic for crack problems, the singular character of the shearing stresses is found to be of the type r−1/2 , where r is radial distance from the crack point. Crack-tip stress-intensity-factor solutions are given for problems involving both imbedded and surface cracks in bars. The results suggest the possibility of extending the Griffith-Irwin theory of static fracture to flexural and torsional problems.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):426-429. doi:10.1115/1.3636573.

It is demonstrated that the form of the energy-dissipation equation which describes thermoelectric and thermomagnetic generators is greatly dependent on the choice of dependent variables in the coupled equations used to describe the devices. If “natural” coordinates are chosen, the energy dissipation will always contain two terms—the Fourier conduction term and Joulean heating term. If “unnatural” coordinates are chosen, the energy-dissipation equation will contain three terms. A brief solid-state consideration demonstrates how a bound on the figure-of-merit temperature product can arise in terms of fundamental physical parameters.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):430-434. doi:10.1115/1.3636574.

Five methods of calculating aerodynamic stagnation-point heat transfer at velocities of 25,000 to 40,000 fps are considered. Three of these methods are simple extrapolations of techniques previously developed for calculations below 25,000 fps. The other two are methods especially developed for velocities above 25,000 fps. The five methods are: The method of Fay and Riddell [1]; the method of Scala [2]; the reference enthalpy method [3]; the method of Adams [4]; and the method of Cohen [5]. Methods [4] and [5] are the methods developed for the higher velocities. The results are presented in graphical form. It is found that the extrapolation of the reference enthalpy method and the correlation formula of Fay and Riddell yield results so close to those of Cohen that, in view of the uncertainties involved in the latter method, using the former two methods over the range of values considered in the present paper yields results at least as satisfactory as those of Cohen for equilibrium flow. Furthermore it is found that extrapolation of the formula of Fay and Riddell for frozen flow yields results sufficiently close to those obtained by the method of Adams that, in view of the uncertainties of the latter method, the advantage of its use over the former in the range of values under consideration is questionable.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):435-442. doi:10.1115/1.3636575.

A theoretical and experimental investigation has been made of the two-dimensional, aerodynamic characteristics of flexible airfoils or sails with no thickness. Thin-airfoil theory has been used to calculate the shapes of the camber lines as a function of angle of attack and excess length of material over the chord length. It is found that for specific eigenvalues of a nondimensional chordwise tension parameter, specific shapes arise for which there is no stagnation point. Some eigenmodes also correspond to boundaries between stable and unstable airfoil shapes. Lift, center of pressure, shapes, and pressure distributions are determined for the entire practical range of angle of attack. An experimental investigation of the lift, drag, and moment of quasi-two-dimensional flexible airfoils has been made, and the measurements have been compared with theory. Certain of the aerodynamic characteristics are in good accord with theory, but certain others are not, principally because of fabric porosity and boundary-layer separation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):443-447. doi:10.1115/1.3636576.

A combined theoretical and experimental investigation is made of the instability of a liquid film around a long, horizontal, circular cylindrical body in still air. In the theoretical investigation, a modified Taylor-type analysis is applied to a simplified physical model. Due to the curvilinear nature of the liquid-air interface, the surface tension as well as the radius of the cylinder are found to play important roles in the establishment of a criterion of instability of the problem. A critical wave length along the length of the cylinder is also found for which the instability will be amplified most rapidly. Such a critical wave length, then, naturally suggests the critical interval distance at which droplets formed as a direct consequence of the instability will break away from the liquid film. In the experimental investigation, measurements were made of a visually observable critical distance of the liquid film around each of several cylinders of different sizes. For two liquids of considerably different surface tension, the results in all cases agree closely with the suggestions made by the theoretical critical wave length.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):448-452. doi:10.1115/1.3636577.

Foam is a compressible medium which can have a density corresponding to that of a liquid and a compressibility corresponding to that of a gas. As a result, compressibility effects such as choked flow can be obtained at relatively low velocities. It is not possible to make “Mach number tables” for foam—as it is for gas—since the properties depend on stagnation foam density as well as Mach number. The equations for the flow of foam are nondimensionalized and presented in a form such that universal curves can be produced. This simplification facilitates the manipulation of the equations; for example, the test for a sonic throat follows easily from the formulation, and an approximation is found that applies near the throat. The procedure for calculating the characteristics of one-dimensional duct flow is outlined, and the charts necessary to carry out the graphical computation are shown in this paper.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):453-460. doi:10.1115/1.3636578.

In a previous paper the authors proposed constitutive equations for the analytical description of gelling incompressible materials. This set of equations is used to predict the steady-state Couette-type flow between concentric cylinders under relative rotation. The solution for the thixotropic material is given in terms of five material parameters accounting for the phenomena of “breakdown” and “recovery” in rigidity. Analysis shows that dependence of the solution on the loading history occurs if a certain inequality is satisfied by the five material parameters.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1963;30(3):461-463. doi:10.1115/1.3636579.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):463-464. doi:10.1115/1.3636580.

It is shown that a damper applied to the spherical bearing at the ends of a rotating shaft to damp pitch and yaw motions of the journal bearing can markedly reduce the deflection caused by unbalance near critical speeds. Equations are given for optimizing the damping and for computing the damping moment which must be carried by the journal bearing. It is shown that with optimum damping of a centrally loaded uniform shaft, the load carried by the journal bearing in the critical-speed range is no more than 67 percent greater than it would have been for a rigid shaft. The corresponding moment carried by the journal bearing is less than the amount which would develop at the mid-length of the shaft in the absence of elastic deflections.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):464-466. doi:10.1115/1.3636581.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):466-467. doi:10.1115/1.3636582.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):467-468. doi:10.1115/1.3636583.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):468-471. doi:10.1115/1.3636584.
Abstract
Topics: Torque , Deformation
Commentary by Dr. Valentin Fuster

DISCUSSIONS

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

BOOK REVIEWS

J. Appl. Mech. 1963;30(3):478-479. doi:10.1115/1.3636601.
FREE TO VIEW
Abstract
Topics: Creep , Metals
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):479. doi:10.1115/1.3636602.
FREE TO VIEW
Abstract
Topics: Functions
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):479. doi:10.1115/1.3636603.
FREE TO VIEW
Abstract
Topics: Thin shells
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):479. doi:10.1115/1.3636604.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1963;30(3):479-480. doi:10.1115/1.3636605.
FREE TO VIEW
Abstract
Topics: Stress , Gears
Commentary by Dr. Valentin Fuster

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