bluuebunny/crossref_metadata_2025 huggingface dataset:
Behavior of Viscoelastic Media Under Small Sinusoidal Oscillations
Superposed on Finite Strain
Authors: Goldberg W. , Lianis G.
Published: October 2011

In this paper, we examine the response of an incompressible elastomer when it is subjected to small, steady-state oscillations superposed on a large steady deformation. The material is assumed to be isotropic in its undeformed state, and its viscoelastic behavior is characterized by means of two different approximate theories: (a) Lianis’ approximation of the theory of finite linear viscoelasticity, and (b) Bernstein, Kearsley, Zapas’ elastic fluid theory, Signorini approximation. Theoretical expressions are developed for the uniaxial stress in a body subjected to steady-state sinusoidal oscillations superposed on a state of steady, finite, uniaxial extension, using both theories. A complex modulus is defined, which reduces to the complex modulus of infinitesimal viscoelasticity when the finite strain is zero. Experiments were performed on three different polymers and the observed response is compared with that predicted by both theories.
On a Class of Two-Degree-of-Freedom Oscillations
Authors: Kane T. R. , Kahn M. E.
Published: October 2011

Following a description of the class of systems under consideration, resonance conditions are obtained by means of Floquet theory, and Hamilton-Jacobi theory is used to study the character of resonant oscillations.
A Mixed Problem for an Elastic Ring
Authors: Yau Wen-Foo
Published: October 2011

Along the two contours of a doubly connected region, mixed boundary values of slipless nature are prescribed. The problem is formulated on a complex z-plane in terms of a Hilbert functional equation involving a holomorphic function φ(z). Based on plane theory of elasticity, the solution is found in the form of a double series. An effective method of successive approximation is shown for the computation of the coefficients of the series. Numerical examples of the field of stress and deformation are illustrated with diagrams. By superposition, the solution presented can be used to solve another class of mixed problems in elasticity involving frictionless indentation.
Axisymmetric Stress Field Around Spheroidal Inclusions and Cavities in a Transversely Isotropic Material
Authors: Chen W. T.
Published: October 2011

A spheroidal inclusion is embedded in an elastic matrix composed of a different material. Both materials are transversely isotropic with the material property axes parallel to the geometric axis of the spheroid. At the interface, the two materials are bonded. The matrix is subjected to a uniform axisymmetric stress field at infinity. Explicit expressions for the stress and displacement fields in the inclusion and the matrix will be presented. The analysis is within the realm of classical linear elasticity.
A Generalized Analysis of Conically Bent Plates by Large-Deflection Theory
Authors: Pao Y. C.
Published: October 2011

This paper presents a general method of solution for the problem which concerns bending plates into cones. The plates considered are those whose thickness obeys the power-law. The large-deflection theory of von Ka´rma´n for plates is employed and the distortion of the cross-section of the bent plate is obtained in terms of generalized hypergeometric functions. Numerical examples are given and results are presented in graphic form. It is shown that by tapering the plate according to a negative power-law, the cross-sectional distortions can be reduced considerably. Also discussed is an analogy between the anticlastic deformation of a plate bent into a cone and the lateral deflection of a conical shell subjected to normal pressure.
Thermomechanical Coupling Behavior of Viscoelastic Rods Subjected to Cyclic Loading
Authors: Huang N. C. , Lee E. H.
Published: October 2011

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.
An “Optimal” Solution of Saint-Venant’s Flexure Problem for a Circular Cylinder
Authors: Bogy David B.
Published: October 2011

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.
Continuum Plasticity Theory in Relation to Solid Solution, Dispersion, and Precipitation Hardening
Authors: Wu T. T. , Drucker D. C.
Published: October 2011

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.
Imperfection Sensitivity of Externally Pressurized Spherical Shells
Authors: Hutchinson J. W.
Published: October 2011

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.
Large-Deformation Theory of Shells of Revolution
Authors: Flu¨gge W. , Chou S-C.
Published: October 2011

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.
Computational Approaches to the Min-Max Response of Dynamic Systems With Incompletely Prescribed Input Functions
Authors: Sevin Eugene , Pilkey Walter
Published: October 2011

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 mx¨ + g(x, x˙) = 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, x˙). 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, x˙). Results obtained by dynamic and linear programming for specified forms of g(x, x˙) are given as functions of load duration.
On the Effects of Source Proximity on the Dynamic Stresses Around a Cylindrical Cavity
Authors: Jakub M. T. , Mow C. C.
Published: October 2011

Analysis of the interaction of a cylindrical wave impinging on a cylindrical cavity is presented. It is assumed that a line source is located an arbitrary distance from the cavity and that its strength varies harmonically in time. The resulting dynamic stress concentration factors at the cavity wall are determined by considering the wave-diffraction effects. Numerical results indicate that the dynamic stress concentration factors around the cavity are dependent upon (a) distance from the source to the cavity, (b) wave number, and (c) the Poisson ratio of the medium. At high wave number (high frequency), the response to an incident cylindrical wave becomes almost identical with the response to an incident plane wave. At low wave number, however, the response departs drastically from all previous investigations where the incident wave was assumed to be a plane wave. Stress concentration factors substantially higher than those determined in earlier studies were noted in the present analysis.
The Influence of the Curvature of Spherical Waves on Dynamic Stress Concentration
Authors: Moon F. C. , Pao Y-H.
Published: October 2011

From a study of scattering of spherical compressional waves by a spherical cavity in an elastic solid, the dynamic stresses on the surface of the cavity are computed and compared with those due to plane compressional waves. At low frequencies, stresses due to spherical waves, even with a very small curvature, are higher than the corresponding ones for plane waves. Only when the incident wavelength is shorter than the distance between the source and the cavity can a spherical wave be approximated by a plane wave.
Multiplication and Interpolation of Moire´ Fringe Orders by Purely Optical Techniques
Authors: Sciammarella C. A. , Lurowist N.
Published: October 2011

Two new, purely optical techniques are introduced to increase the sensitivity of the moire´ method. One of the techniques makes it possible to observe moire´ fringes of fractional orders. Observation of moire´ fringes of the p/5-order are reported, which means that, with the 300-lines-per-in. grid utilized in the examples presented in the paper, it is possible to observe the same pattern that could be observed with a 1500-lines-per-in. grid. The other technique makes it possible to read fractional orders by a compensation technique similar to Tardy’s compensation process utilized in photoelasticity.
Rolling and Sliding Contact Stress Parameters in Elastohydrodynamic Lubrication
Authors: Schoeppel R. A. , Evan-Iwanowski R. M.
Published: October 2011

The fatigue life at high operating speeds of machine components, such as bearings, gears, and cams, depends upon the shape and magnitude of the elastohydrodynamic pressure distribution. Studies show that two bodies in rolling contact at high speeds indicate a significant departure from the usual Hertzian pressure distribution present at low rolling speeds. The contact stress distribution for an elastohydrodynamic pressure distribution in an infinitely large plate is determined in this paper. The pressure peak on the outlet side of the contact area and the long pressure sweep on the inlet side of the contact area create a pressure distribution which is asymmetrical. The pressure peak has a significant effect on the normal and shear stresses. Superimposing contact stresses due to sliding indicates a considerable change in the stresses resulting from sliding direction.
On a Class of Models for the Yielding Behavior of Continuous and Composite Systems
Authors: Iwan W. D.
Published: October 2011

A class of one-dimensional models for the yielding behavior of materials and structures is presented. This class of models leads to stress-strain relations which exhibit a Bauschinger effect of the Massing type, and both the steady-state and nonsteady-state cyclic behavior are completely specified if the initial monotonic loading behavior is known. The concepts of the one-dimensional class of models are extended to three-dimensions and lead to a subsequent generalization of the customary concepts of the incremental theory of plasticity.
Effects of Anisotropy in Axisymmetric Cylindrical Shells
Authors: Gulati S. T. , Essenburg F.
Published: October 2011

The solution of the problem of the generally anisotropic axisymmetric circular cylindrical shell is obtained employing a recent shell theory given by Naghdi. The practical importance of the presence of the circumferential displacement components and the twisting couple arising due to the presence of anisotropy, as well as the significance of the inclusion of the coupled effects of transverse shear deformation and anisotropy, are illustrated by a specific example.
Energy Dissipation of Nonlinear Critically Damped Systems During Impact
Authors: Lakin G. , Sachs H. K.
Published: October 2011

The paper discusses the criteria of the most effective energy dissipation of either an object falling upon a viscoelastic foundation or a vehicle striking a barrier, such that the impacting mass does not separate (rebound) from the support structure, and the maximum deceleration of the striking mass is a minimum.
Stress Analysis of Cracked Rectangular Beams
Authors: Westmann R. A. , Yang W. H.
Published: October 2011

This paper is concerned with the solution of mixed boundary-value problems arising from the longitudinal shear and Saint-Venant torsion and flexure of cracked prismatic beams. The members considered have a rectangular cross section with planar edge cracks extending the length of the beam. The problem is reduced to a pair of dual-series equations, the solution of which is obtained by a method due to Sneddon and Srivastav [1]. Numerical results are presented for a variety of quantities of physical interest.
Numerical Solution for Two-Dimensional Elastic Wave Propagation in Finite Bars
Authors: Bertholf L. D.
Published: October 2011

Numerical solutions of the exact equations for axisymmetric wave propagation are obtained with continuous and discontinuous loadings at the impact end of an elastic bar. The solution for a step change in stress agrees with experimental data near the end of the bar and exhibits a region that agrees with the one-dimensional strain approximation. The solution for an applied harmonic displacement closely approaches the Pochhammer-Chree solution at distances removed from the point of application. Reflections from free and rigid-lubricated ends are studied. The solutions after reflection are compared with the elementary one-dimensional stress approximation.
Large Amplitude Asymmetric Waves in a Spinning Membrane
Authors: Advani S. H.
Published: October 2011

Linear transverse vibrations and wave motions of a spinning membrane have been studied by Lamb and Southwell [1]. This Note gives an exact solution for nonlinear, flexural, asymmetric waves for a special case of a membrane spinning with two nodal diameters and no nodal circles.
Decay of Turbulent Axisymmetrical Free Flows With Rotation
Authors: Chervinsky A. , Lorenz D.
Published: October 2011

Previous studies on turbulent swirling jets are extended to cover general axisymmetrical turbulent free flows with rotation, with particular considerations of free jets and wakes. The equations governing the flow are integrated subject to the pertaining boundary conditions making use of the usual boundary-layer approximations. The axial and tangential components of velocity are assumed to retain similar forms of radial distributions and a set of two ordinary first-order differential equations is derived, the solution of which describes the axial decay of the maximal axial and tangential velocities. Integration of the differential equations in the particular case of uniform external velocity subject to conditions at the orifice results in a set of two second-order algebraic equations which are readily solved. The theoretical solutions derived for a free jet are compared with available experimental results.
On the Unified General Solutions of Linear Wave Motions of Thermoelastodynamics and Hydrodynamics With Practical Examples
Authors: Wong P. K.
Published: October 2011

In analogy to the development of the potential equations of motion of linear elastodynamics, the governing potential equations for linear wave motions of hydrodynamics and thermoelastodynamics are systematically exploited. As a result of these developments, problems of linear wave motions of homogeneous, isotropic, thermally conducting multi-layered elastic solids and viscous fluids can be systematically solved for the media whose boundaries are described by rectangular, circular, parabolic, and elliptic cylindrical coordinates, as well as by spherical and conical coordinates. Five practical examples are analytically solved to illustrate how the use of the potential equations of motion leads to more systematic solution procedures; these examples can be used for the modeling studies of aero and hydrospace vehicles, geological wave problems, and macroscopic biomechanics.
Hydrostatic Creep of Solid Plastics
Authors: Findley W. N. , Reed R. M. , Stern P.
Published: October 2011

Experiments were performed on several plastics under constant hydrostatic pressures up to 50,000 psi. Measurement of linear strain indicates that the volume decreases with time at constant pressure in accordance with a power function of time. The exponent of time was about the same as observed for tension or torsion creep of the same material. Recovery upon abrupt release of pressure was nearly instantaneous, except for the thermal effect resulting from decompression. Partial release of pressure resulted in a time-dependent recovery. The instantaneous recovery was explained in terms of the opening up of the polymer structure on release of pressure.
Moving Load on a Plate Resting on an Elastic Half Space
Authors: Achenbach J. D. , Keshava S. P. , Herrmann G.
Published: October 2011

An elastic plate supported by a semi-infinite elastic continuum is subjected to a moving line load. Both welded and smooth contact between plate and foundation are considered. Dynamic solutions for the bending moments in the plate are presented that are time-invariant relative to a coordinate system moving with the load. Resonance effects at certain critical velocities are discussed. The response of the system depends significantly on the relative stiffness of plate and half space and on the type of contact. For the relatively stiff plate certain resonances occur for smooth contact but not for welded contact. For subcritical load velocities the bending moments are calculated and compared with corresponding bending moments for a plate on a Winkler foundation. The Winkler foundation is adequate for smooth contact and small load velocities.
Analysis of the Propagation of Plane Elastic-Plastic Waves at Finite Strain
Authors: Lee E. H. , Wierzbicki T.
Published: October 2011

The propagation of plane elastic-plastic waves of one-dimensional strain is analyzed. Such waves are generated by the detonation of explosives in contact with the surfaces of plates and by impact of plates and are commonly utilized for measuring material characteristics under high pressures. Only one nonzero displacement component occurs—that normal to the plate surface. The resulting dilatation leads to dominant thermomechanical coupling effects, and these, and influences of finite strain, are included in the analysis. Because plasticity plays a secondary role, a simple rate-independent theory is adequate. Since heat conduction can be neglected because of the high speed of wave propagation, the dynamic equations and the constitutive relations are effectively uncoupled, and the problem reduces to one in the classical Karman-Taylor-Rakhmatulin theory of plastic waves. Appropriate stress-strain relations for inclusion in that theory are developed here for an aluminum alloy. The analysis for shock propagation is also given.
Stress Intensity Factors for Penny-Shaped Cracks: Part 1—Infinite Solid
Authors: Smith F. W. , Kobayashi A. S. , Emery A. F.
Published: October 2011

An expression is developed for the stress intensity factor of a penny-shaped crack in an infinite elastic solid subjected to nonaxisymmetric normal loading. The stress intensity factor can then be determined for penny-shaped cracks in infinite or finite solids subjected to symmetric loading about the plane containing the crack. The singular state associated with the embedded crack with finite, nonaxisymmetric normal loading is that of plane strain. Results are also presented for two problems: A penny-shaped crack subjected to two symmetrically located concentrated forces and a penny-shaped crack in a large beam subjected to pure bending.
Stability Criteria for Second-Order Dynamical Systems With Time Lag
Authors: Bhatt S. J. , Hsu C. S.
Published: October 2011

Stability of second-order dynamical systems with time lag is investigated by using Pontrjagin’s theorems on the zeros of exponential polynomials. The time-lag term may involve the displacement, the velocity, or the acceleration. Systems with negative damping coefficient and/or negative spring constants are also considered. It is shown that a delayed feedback signal of proper strength and proper delay is capable of stabilizing such dynamical systems with negative damping and/or negative spring constants. It is also found that some earlier results given in [2] for the restricted case where the damping coefficient is positive and the spring constant is non-negative are defective. The stability criteria obtained here are expressed in terms of inequalities which impose upper and lower bounds for the system parameters.
Stability Charts for Second-Order Dynamical Systems With Time Lag
Authors: Hsu C. S. , Bhatt S. J.
Published: October 2011

Stability criteria for second-order dynamical systems with time lag are presented here in a simple chart form. The results cover negative as well as positive values of the parameters. These stability charts for second-order difference-differential equations are likely to serve the same purpose as the Strutt-Ince chart does for the Mathieu equation.
An Approximate Procedure for the Solution of a Class of Transient-Wave Diffraction Problems
Authors: Peralta L. A. , Carrier G. F. , Mow C. C.
Published: October 2011

The description of even the gross features of the response to an incident stress pulse of an infinite elastic solid with a hole or obstruction requires very extensive calculations [1]. On the other hand, the response of such elastic systems to a harmonic incident wave is much less intricate. It is well known that the response to any given incident pulse can be constructed from the solution of the harmonic wave problem. Furthermore, it is clear that the computational difficulty associated with this synthesis can be reduced enormously when a suitable, algebraically simple approximation to the harmonic response can be found. In this paper, a useful rule for choosing the appropriate approximation to the harmonic wave response is presented. This method is shown to give results in agreement with known solutions. The procedure is also applied to problems where only solutions to the harmonic wave case are available. The most important potential use of the technique lies in the possibility that, for some classes of structures, one may be able to identify the parameters of the approximate harmonic response with simple macroscopic properties of the system. Such an identification would not only save much labor but would also identify design criteria for the optimization of the system.
First-Passage Time in a Random Vibrational System
Authors: Gray A. H.
Published: October 2011

The first-passage problem in a random vibrational system is solved by means of approximations which convert the problem to a first-order one-dimensional Markov process. Laplace transforms are used to evaluate the mean square time to failure.
A Note on the Determination of an Upper Bound on Displacement Rates for Steady Creep Problems
Authors: Martin J. B.
Published: October 2011

A method is described whereby the displacement rate at any point on the surface of a body undergoing steady creep may be bounded from above. The method is restricted to n-power stress-strain rate relations, and is of most significance in the nonlinear case.
An Experimental Study of the Stability of an Externally Pressurized, Gas-Lubricated Thrust Bearing
Authors: Licht L. , Elrod H. G.
Published: October 2011

The subject of this experimental investigation is the phenomenon of self-excited vibrations occurring in externally pressurized, gas-lubricated bearings. The experimental program pursued here is guided by predictions based on prior analysis. An apparatus is designed and instrumented to provide for the variation of governing parameters and for the accurate determination of their critical values. Stability bounds are obtained for a circular thrust bearing and the experimental results are compared and contrasted with previously reported, theoretical stability limits.
Deformation of Open Spherical Shells Under Arbitrarily Located Concentrated Loads
Authors: Wilkinson J. P. , Kalnins A.
Published: October 2011

An exact solution is derived for the Green’s function of an open rotationally symmetric spherical shell subjected to any consistent boundary conditions. The fundamental singularity of the Green’s function is expanded in series according to the addition theorems of Legendre functions, and the solution for a spherical shell subjected to an arbitrarily situated, harmonically oscillating, normal, concentrated load is obtained explicitly in terms of associated Legendre functions. The corresponding static Green’s function is obtained simply by setting the driving frequency equal to zero. Numerical results for the displacements and stress resultants of an example are presented in detail.
Slip Strains and Stresses in Polycrystalline Aggregates Under Cyclic Load
Authors: Tung T. K. , Lin T. H.
Published: October 2011

In an aggregate under moderate loads, plastic deformation is considered to occur in favorably oriented crystals on single active slip systems. The residual stresses, due to the slip strains, are expressed in terms of the slip strains by an equivalent problem in elasticity. The resolved shear stresses, owing to the combined effects of the slip strains and the external load, are in turn related to the slip strains by material property. The slip-strain distribution can thus be determined, and the stress distribution follows. Analytical solutions are obtained for a cyclic load of constant amplitude, under certain simplifying assumptions. They agree closely with rigorous, numerical incremental calculations for a specific case. For materials that strain-harden against reverse slip in each infinitesimal region, decreasing hysteresis loops occur with cyclic loading, and the present results corroborate the essential features of an earlier analysis by Orowan.
An Extension of the Hu-Washizu Variational Principle in Linear Elasticity for Dynamic Problems
Authors: Barr A. D. S.
Published: October 2011

The Hu-Washizu variational principle in linear elasticity in which displacement, strain, and stress can be independently varied is extended, for application to dynamic problems, to include independent variation of the velocities associated with the displacements. Such independent variation is of value in the construction of approximate theories for beams and plates.
Some First-Passage Problems in Random Vibration
Authors: Crandall S. H. , Chandiramani K. L. , Cook R. G.
Published: October 2011

First-passage problems for a lightly damped linear oscillator excited by white noise are described for two types of initial conditions and three different types of barrier configurations. The qualitative behavior of the probability distribution of the time to first passage is discussed. Two numerical procedures utilizing high-speed digital computers are outlined, and quantitative results for first-passage probability densities are displayed. The asymptotic behavior of this density for long mean times to failure is discussed, and a table of experimentally determined mean times to failure is included.
Three-Dimensional Stress Distribution Around an Elliptical Crack Under Arbitrary Loadings
Authors: Kassir M. K. , Sih G. C.
Published: October 2011

As a companion problem to that of a flat elliptical crack subject to a uniform tension perpendicular to the crack plane, this paper deals with the case of arbitrary shear loads. Upon superposition, solutions to problems of an infinite solid containing an elliptical crack subjected to loads of a general nature may be obtained. It is shown that the three-dimensional stresses near the crack border can be expressed explicitly in terms of a convenient set of coordinates r and θ defined in a plane normal to the edge of the crack. In such a plane, the local stresses in a solid are found to have the same angular distribution and inverse square-root stress singularity as those in a two-dimensional body under the action of in-plane stretching and out-of-plane shear. This result will, in general, hold for any plane of discontinuity bounded by a smooth curve. Such information provides a clear interpretation of current fracture-mechanics theories to three dimensions. In particular, stress-intensity factors kj(j = 1, 2, 3), used in the Griffith-Irwin theory of fracture, are evaluated from the stress equations for determining the fracture strength of elastic solids with cracks or flaws.
Transport Processes in Magnetosolidmechanics
Authors: El-Saden M. R. , Arnas O. A.
Published: October 2011

Consideration is given to the problem of a solid conducting heat and electrical currents in the presence of externally applied magnetic fields. Interactions due to the thermoelectric, thermomagnetic, and galvanomagnetic effects are taken into consideration. The general three-dimensional governing equations are established. The generalized Ohm’s law and Fourier’s law of heat conduction as formulated by the methods of nonequilibrium (irreversible) thermodynamics are employed. The governing equations are used for the analysis of a one-dimensional steady-state case, assuming constant thermophysical properties. The variations of temperature, electric field, magnetic field, and electric and thermal current densities are presented analytically and graphically. The second law of thermodynamics imposes certain limitations on the validity of the results. These limitations are discussed in detail.
Strain-Rate Effects in the Propagation of Torsional Plastic Waves
Authors: Baker W. E. , Yew C. H.
Published: October 2011

A new method was developed for determining the dynamic stress-strain relationships of materials subjected to high rate of torsional loading. In addition, an investigation of propagation of torsional plastic waves in a long tube was conducted. Commercially pure copper was used throughout both investigations. In the material property studies, shear strains up to 20 percent and shear strain rates to 2100/sec were obtained. The results indicated that copper exhibits significantly lower strain-rate effects than those previously obtained by the longitudinal loading method. In the studies of plastic wave propagation, shear strain-time records at several cross sections along the tube were compared with computed results obtained from the strain-rate-independent and strain-rate-dependent theories. It is concluded that the computed results based on the strain-rate-dependent theory give better agreement with the experiments.
A Correspondence Principle for Free Vibrations of a Viscoelastic Solid
Authors: Fisher G. M. C. , Leitman M. J.
Published: October 2011

A correspondence principle for free vibrations in the classical linearized theory of viscoelasticity is established. It is shown that, for motions which are either irrotational or solenoidal, there is always an associated elastic problem with the following properties: (a) Every mode shape for the viscoelastic problem is also a mode shape for the elastic problem; and (b) the viscoelastic frequencies can, in principle, be calculated from a knowledge of the elastic spectrum and the relevant relaxation function. It is further shown that, in general, for motions which are neither irrotational nor solenoidal, this correspondence exists only for the restricted class of viscoelastic materials for which the behavior depends essentially upon one relaxation function. The paper concludes with the observation that the correspondence also exists for those approximate theories in which there appears only one relaxation function.
The Strength of Thin-Walled Cylinders Subjected to Dynamic Internal Pressures
Authors: Costantino C. J.
Published: October 2011

The equation of motion governing the response of long (infinite) cylinders to dynamic internal pressures is derived. Since large displacements and wall-thinning effects are taken into account, elastic behavior of the material is neglected. The material is assumed to be rigid-plastic, with strain-hardening being taken into account through the Ludwik power strain-hardening law. Numerical results are presented for a range of hardening constants from 0.01 to 1.0, covering the range applicable to most materials of interest. The form of the dynamic pressure considered is an initially peaked, linearly decaying pressure pulse. Charts are presented giving the pressure and duration required to produce a given final radius of the cylinder.
A Displacement Bound Principle for Inelastic Continua Subjected to Certain Classes of Dynamic Loading
Authors: Martin J. B.
Published: October 2011

The paper presents an inequality relating statically admissible stress fields and kinematically admissible displacement fields for continua composed of inelastic materials which obey a postulated criterion of stability. The inequality is used to compute displacement bounds for inelastic continua subjected to certain classes of dynamic loading.
Steady-State Biaxial Creep
Authors: Stowell E. Z. , Gregory R. K.
Published: October 2011

Tensile and torsional stresses were applied simultaneously to each of a series of identical thin-walled aluminum-alloy tubes at an elevated temperature (400 F). Different combinations of stresses were chosen so that the combined stress intensity was kept substantially constant. Simultaneous measurements were made of the resulting tensile and torsional creep strains; the tests were not stopped at any specific time but were continued until the creep had definitely entered the final stage. This procedure permitted accurate estimates to be made of the steady-state creep rates which are independent of the time. It was found that (a) the splitting of the strain-rate intensity into its individual components was accurately predictable from the splitting of the known stress intensity into its components; and (b) the absolute magnitude of the individual steady-state creep rates was predictable from a knowledge of the applied stresses and the relation between tensile stress only and tensile steady creep rate, to an accuracy of about 20 percent. An analysis of the creep rates between the time of load application and the time of achievement of the steady state, necessarily somewhat crude, disclosed a strong probability that the relations which govern the splitting of the strain-rate intensity into its individual components persist even in the transient region. A theoretical Appendix gives the details for the computation of stresses under the conditions of the experiment.
Impact Buckling of a Thin Bar
Authors: Lindberg H. E.
Published: October 2011

Experiments are presented which demonstrate the statistical nature of the buckling of thin strips under very high axial compression. Probability distributions of wavelengths determined theoretically from assumed “white-noise” perturbations in initial shape are compared favorably with the experimental distributions. In other experiments, a new optical-lever method of recording lateral motions is used to observe bending waves and buckling in an impacted strip. From these and experiments on large-strain buckling of rubber strips it is concluded that effects of axial-wave propagation do not significantly influence the wavelengths at which the buckles form.
Axisymmetrical Creep Buckling of Clamped Shallow Spherical Shells
Authors: Huang Nai Chien
Published: October 2011

For a viscoelastic clamped shallow spherical shell, the vertical deflection due to uniformly distributed external pressure is a function of time. When time reaches a critical value, the shell may snap through suddenly. This critical time depends on the magnitude of the applied pressure as well as the shell geometry. The governing equations for large deformations of viscoelastic shells can be derived by applying the correspondence principle to the equivalent equations in the elastic case. The critical times for various shells under different pressures are evaluated numerically. If the deflection volume of the shell is a constant throughout the deformation process, the external pressure decreases due to relaxation of stresses in the viscoelastic shell. This decreasing external pressure is also calculated in this paper.
Symmetric Loading of Orthotropic Shells of Revolution
Authors: Steele C. R. , Hartung R. F.
Published: October 2011

In this paper, the problem of determining the stresses and deformations in a thin, homogeneous, orthotropic shell of revolution under the action of axisymmetric loads is reduced to the solution of a single inhomogeneous second-order linear differential equation with a complex dependent variable. Asymptotic solutions are obtained which are uniformly valid in both the steep and shallow regions of the dome-shaped shell. The complementary, or “edge-effect,” solutions are expressed in terms of Thomson’s functions of a noninteger order. The order depends both on the shape of the meridian curve at the apex of the shell and on the ratio of the elastic moduli. The particular solution is found in terms of an appropriate linear combination of the Lommel’s function and Thomson’s functions. This particular solution is equivalent to the well-known “membrane” solution in the steep portion of the shell but in the shallow portion gives significant bending stresses. The particular and complementary solutions are used to investigate the behavior of orthotropic pressure vessels with rigid rings clamped to the edges.
Asymmetric Mixed Boundary-Value Problems of the Elastic Half-Space
Authors: Westmann R. A.
Published: October 2011

Solutions are presented, within the scope of classical elastostatics, for a class of asymmetric mixed boundary-value problems of the elastic half-space. The boundary conditions considered are prescribed interior and exterior to a circle and are mixed with respect to shears and tangential displacements. Using an established integral-solution form, the problem is reduced to two pairs of simultaneous dual integral equations for which the solution is known. Two illustrative examples, motivated by problems in fracture mechanics, are presented; the resulting stress and displacement fields are given in closed form.
On the Buckling of Rings Subject to Impulsive Pressures
Authors: Stuiver W.
Published: October 2011

It is shown in this paper that previous, independent analyses of the phenomena of dynamic elastic instability and dynamic plastic-flow buckling of circular cylindrical shells can be combined in a single approach leading to results consistent with those that follow from these analyses. The response of the shell in both cases is governed by the interaction between the fundamental radial, purely extensional mode of deformation and inextensional flexural modes always present in the response. An analytical procedure is given for the determination of dominant modes in the elastic and plastic phases of the response, and the results of this procedure are verified by comparison with numerical and experimental data.
Natural Frequencies and Mode Shapes for Axisymmetric Vibration of Deep Spherical Shells
Authors: Ross E. W.
Published: October 2011

This paper contains the results of an approximate analysis of the axially symmetric vibrations of deep spherical elastic shells. The approximation is based on the asymptotic formulas for Legendre functions of large degree. The results are relatively simple approximate formulas for the natural frequencies and mode shapes under a variety of boundary conditions at the shell edge. The results agree very well with values obtained by Kalnins, using numerical methods.
Transient Response of a Periodically Supported Cylindrical Shell Immersed in a Fluid Medium
Authors: Herman Harry , Klosner J. M.
Published: October 2011

The dynamic response of a periodically simply supported, infinitely long, circular cylindrical shell to a pressure suddenly applied through the surrounding acoustic medium is investigated. The incident particle velocity is zero, and the pressure is assumed to have a harmonic spatial variation parallel to the shell axis. The exact solution is obtained by use of a Fourier integral transform, and the resulting inversion integral is evaluated by numerical and asymptotic integration. Two solutions to the same problem are obtained by using a plane and cylindrical wave approximation for the radiated field. The range of their applicability is investigated. For a steel shell in water ccs2=0.08815 it is found that, when the supports are placed three shell diameters apart, the use of the cylindrical wave approximation results in a 5-percent underestimation of the maximum deflection, while when the supports are placed one sixth of a shell diameter apart, the approximations are invalid.
Myklestad’s Method for Predicting Whirl Velocity as a Function of Rotational Velocity for Flexible Multimass Rotor Systems
Authors: Finkelstein A. R.
Published: October 2011

A simple numerical procedure is developed for determining the whirl velocity as a function of the rotational velocity for flexible multimass rotor systems that are difficult to handle by completely analytical procedures. The numerical procedure follows the Myklestad method, and introduces an effective mass moment of inertia for each disk to account for various ratios of whirl to shaft speed. The flexibility of supports is included.
Viscoelastic Behavior of Heterogeneous Media
Authors: Hashin Zvi
Published: October 2011

The macroscopic viscoelastic behavior of linear viscoelastic heterogeneous media is defined in terms of effective relaxation moduli and creep compliances. It is shown that these effective relaxation and creep functions are related to effective elastic moduli of elastic heterogeneous media by the correspondence principle of the theory of linear viscoelasticity. This analogy is applied to the determination of macroscopic behavior of some special kinds of viscoelastic heterogeneous media, in dilatation and shear.
The Application of the Principle of Stationary Potential Energy to Some Problems in Finite Elasticity
Authors: Levinson Mark
Published: October 2011

Two applications of the principle of stationary potential energy to the finite straining of a neo-Hookean (rubberlike) material are given in this paper. The major purpose of the work presented is to illustrate the suitability of energy methods for the solution of problems in finite strain theory since the literature of the subject does not contain mention of such solutions. One problem not amenable to the usual inverse methods of finite elasticity is studied approximately. The other problem, involving a stability question of an unusual sort, is handled with ease by means of the energy principle.
Upper Bounds and Saint-Venant’s Principle for Incompressible Potential-Flow Fields
Authors: Drake R. L. , Chou P. C.
Published: October 2011

An upper-bound approach to Saint-Venant’s principle is presented for incompressible potential-flow fields. Upper bounds for the velocity and its potential are found for the flow in a rectangular channel and in an axially symmetric cylindrical channel. It is found that any deviation in velocity distribution at the entrance of the channel which does not change the net flow attenuates to a negligible quantity beyond a section which is at a distance of two channel widths from the entrance.
Longitudinal Impact of a Semi-Infinite, Cylindrical, Viscoelastic Shell
Authors: Testa R. B. , Bleich H. H.
Published: October 2011

The response of a semi-infinite, cylindrical, viscoelastic shell to longitudinal impact is studied using the Laplace transform. The evaluation by asymptotic methods for large values of time also gives error estimates defining the range of applicability. It is found that, at sufficiently large distances from the point of impact, the oscillatory character of the response of an elastic shell to longitudinal impact is suppressed by viscous effects, resulting in nearly identical solutions for a viscoelastic shell and for an infinitely thin viscoelastic rod of the same material. In addition, it is shown that the solutions for shell and rod, with limitations, are also nearly identical for smaller values of time, where nonasymptotic solutions for the rod apply.
The Complementary Energy Theorem in Finite Elasticity
Authors: Levinson Mark
Published: October 2011

Other investigators have extended the complementary energy theorem (Castigliano’s theorem) to cover the finite deformation of elastic systems with a finite number of degrees of freedom (structures) and they then have indicated that the extension of the theorem to cover the finite deformation of an elastic continuum involved certain unstated difficulties. The present paper shows that when the strain tensor and Trefftz stress tensor, the usual choice of conjugate deformation and stress tensors, are chosen to characterize the finite deformation of an elastic continuum, one cannot establish a strict complementary energy theorem. It is then shown that a strict complementary energy theorem for the finite deformation of an elastic continuum can be established if what Fritz John calls the Lagrange strain and Lagrange stress tensors are used as the conjugate deformation and stress tensors characterizing the deformation.
Relaxation of Internal Forces in a Wound Reel of Magnetic Tape
Authors: Tramposch H.
Published: October 2011

Equations were developed to predict the relaxation of the internal stresses of a wound reel of magnetic tape, assuming a homogeneous and isotropic material which, under shear, exhibits instantaneous elasticity, delayed elasticity, and creep; and under hydrostatic stressing, shows elastic behavior. Numerical examples obtained with the aid of a high-speed digital computer indicated that the internal stresses introduced during the winding operation continue to relax. Given sufficient time in storage, the wound reel will approach stress-free conditions, thus exposing the tape to mechanical damage during transportation and reuse.