bluuebunny/crossref_metadata_2025 huggingface dataset:
The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid
Authors: Shelley Joseph F. , Yu Yi-Yuan
Published: October 2011

Presented in this paper is a solution in series form for the stresses in an infinite elastic solid which contains two rigid spherical inclusions of the same size. The stress field at infinity is assumed to be either hydrostatic tension or uniaxial tension in the direction of the common axis of the inclusions. The solution is based upon the Papkovich-Boussinesq displacement-function approach and makes use of the spherical dipolar harmonics developed by Sternberg and Sadowsky. The problem is closely related to, but turns out to be much more involved than, the corresponding problem of two spherical cavities solved by these authors.
Two Secondary Effects in Bending of Slit Thin-Walled Tubes
Authors: Rimrott F. P. J.
Published: October 2011

During bending of a slit, thin-walled circular tube two secondary effects are observed to occur simultaneously. One, the so-called Brazier effect, occurs in thin-walled tubes generally when they are subjected to bending, and consists of an ovaling of the cross section. The second effect is a peculiarity of slit tubes only and manifests itself as an overlap of the free edges. The severity of both effects depends upon the location of the slit. The bending moment and the radial and tangential displacements have been determined as function of the curvature for four different slit locations with respect to the neutral axis. The value of the curvature at instability has also been derived. Subsequently an approximate equation has been obtained for the cantilever. The results of experiments on a cantilever are compared with the theoretical predictions.
Instability Strains in Plane Sheet Under Biaxial Stress
Authors: Hillier M. J.
Published: October 2011

The stress ratios, loads, and plastic strains at instability are calculated for a flat metal sheet subjected to the following loading paths: (a) Proportional stressing, (b) sequential loading, and (c) proportional loading.
Symmetric Deformations of Viscoelastic-Plastic Cylinders
Authors: Crochet M. J.
Published: October 2011

This paper, in the main, contains a general solution for a viscoelastic-plastic hollow circular cylinder under internal pressure and in the state of plane strain. The medium is assumed to be isotropic and homogeneous, and the constitutive equations used are a special case of those given in [1]. Solutions for both loading and unloading from a viscoelastic-plastic state are considered, and numerical results are obtained for the specific case of an incompressible cylinder under a step pressure. Also discussed briefly is the torsion of a viscoelastic-plastic cylinder, the solution of which is again illustrated by a numerical example.
The Contact Problem for Viscoelastic Bodies
Authors: Yang Wei Hsuin
Published: October 2011

The viscoelastic contact problem is extended to cover general linear materials and arbitrary quadratic surfaces of the bodies in contact. Use of integral operator constitutive relations permits solution by comparison with a known integral identity in potential theory, as used by Hertz in the original elastic solution. Examples are given for the case of indentation of a viscoelastic half-space by a rigid spherical indenter and the case of contact between two spheres with different material properties.
Hot-Wire Measurements in a Radial Turbulent Jet
Authors: Heskestad Gunnar
Published: October 2011

Results from hot-wire measurements in an approximate radial turbulent incompressible jet of air are reported. In the range of measurements, the jet did not attain a self-preserving form. The mean velocity profiles at various radial locations were quite similar, while the mean-square turbulent velocity profiles were similar only away from the jet center plane, and the lateral intermittency distributions were highly dissimilar. Data for the energy balance of the turbulent motion were obtained at a convenient downstream location.
Fully Developed Laminar Flow in a Stepped Rectangular Channel
Authors: Djojodihardjo R. H. , Thorpe J. F.
Published: October 2011

The problem considered is that of fully developed, laminar incompressible flow in a stepped rectangular channel. An analytical solution is obtained for the velocity profile by using the variational method. Velocity profiles are computed for a specific case by truncating the series expressions and evaluating the coefficients numerically (Rayleigh-Ritz method). These velocity profiles are compared to those obtained by solving a set of finite difference equations. The solution of the problem provides information for the velocity at a step discontinuity in width between parallel plates and permits an evaluation of one-dimensional methods of attacking the same problem.
Consequences of an Inequality in Nonequilibrium Thermodynamics
Authors: Meixner J.
Published: October 2011

The paper contains an outline of a new approach to the thermodynamics of irreversible processes. This approach is based on a fundamental inequality which is derived from the Second Law of Thermodynamics under the assumption that the material is, in a well-defined sense, thermodynamically stable. If one confines one’s attention to situations in which the intensive parameters deviate only little from their original equilibrium values, one can invoke the well-developed mathematical theory of linear passive systems, and one arrives at very general statements on continuous materials. An important feature of this approach consists in the fact that the value of the entropy in non-equilibrium states does not appear in the equations. Therefore, there is no need to specify it by special and questionable assumptions. It is also possible to cast the equations governing the irreversible processes in a form which introduces appropriate internal variables. This leads to a thermodynamic formalism with a well-defined entropy even in nonequilibrium states. The latter is also a thermodynamic potential in the proper variables and leads to a nonnegative entropy-production term. This formalism satisfies the principle of local state or, equivalently, is deterministic in the sense that a complete knowledge of the state at time t1 and of the interaction of the system with the surroundings for t ≥ t1 permits us to predict the future development of the system without the need to endow the material with a memory.
Impact of a Nonlinear Viscoplastic Rod on a Rigid Wall
Authors: Ting T. C. E.
Published: October 2011

Barenblatt and Ishlinskii [5] considered the impact of a viscoplastic rod on a rigid wall in which the relation between stress and strain rate is linear. In this paper, their analysis is generalized to a power-law relation between stress and strain rate so that their results may be reduced as a special case. Some strikingly different behaviors are observed between linear viscoplastic materials and nonlinear viscoplastic materials. Comparisons are also made between the viscoplastic solution obtained here with the rate-independent, rigid-plastic solution by Lee and Tapper [2]. It is shown that the curves which represent the residual strains versus the axial length along the rod are concave upward for all viscoplastic rods. For the rate-independent, rigid-plastic rods, on the other hand, they are concave downward.
On Some Problems in Spherically Isotropic Elastic Materials
Authors: Chen W. T.
Published: October 2011

In this paper, we study the elasticity problem of a spherically isotropic elastic medium bounded by two concentric spherical surfaces. General solutions in terms of infinite series are presented. Specifically, we consider some axisymmetric problems such as: concentrated force in an infinite medium, stress concentration due to a spherical cavity, and a steadily rotating shell. In all these cases, the infinite series terminate, and closed-form solutions are possible. Steady-state thermal stress problems are also considered.
Harmonic Rocking of a Rigid Rectangular Body on a Semi-Infinite Elastic Medium
Authors: Awojobi A. O.
Published: October 2011

Dual integral equations representing the mixed boundary-value problem of the rocking of an infinitely long, rigid rectangular body on the free surface of a semi-infinite elastic medium are here solved. Dynamic stress distributions under the rigid body and resonance curves for motion of the body are derived from the solution of these equations. A graphical representation of the theoretical results provides a novel method for estimating Poisson’s ratio of soil from a knowledge of the rocking frequency of a building. Suitable published results of tests on actual buildings have been used to indicate the application of this method.
Nonlinear Flexural Vibrations of Thin Circular Rings
Authors: Evensen D. A.
Published: October 2011

The nonlinear flexural vibrations of thin circular rings are analyzed by assuming two vibration modes and then applying Galerkin’s procedure on the equations of motion. The results show that vibrations involving either a single bending mode or two coupled bending modes can occur. Theory and experiment both indicate a nonlinearity of the softening type and the existence of these coupled-mode vibrations. Test results for the steady-state response are in good agreement with the calculated values, and the deflection modes used in the analysis agree with the experimental mode shapes. The analytical and experimental results exhibit several features that are characteristic of nonliner vibrations of axisymmetric systems in general and of circular cylindrial shells in particular.
The Effect of Lateral Hydrostatic Pressure on the Instability of Elastic Solids, Particularly Beams and Plates
Authors: Kerr Arnold D. , Tang Sam
Published: October 2011

The instability of a rectangular solid in plane strain subjected axially to a constant pressure p and laterally to a constant hydrostatic pressure q is investigated; a modification of the problem is treated in reference [1] in which the lateral load q was assumed to be constant directional. It was found that, unlike the constant directional q, the hydrostatic pressure q stabilizes the solid, but with increasing q/p, the destabilizing effect due to the caused deformations predominates. It is also shown that a number of investigators, who concluded that beams will not buckle when q = p, based their conclusions on formulations which are not valid in this range and that their conclusions are not correct.
On the Validity of the Plastic Theory of Structures for Collapse Under Highly Localized Loading
Authors: Anderson C. A. , Shield R. T.
Published: October 2011

This paper investigates the significance of structural theory solutions for structures composed of perfectly plastic materials when the loading is of a highly localized nature. Limit analysis is applied to illustrative problems in order to compare the actual collapse loads with those provided by the structural theory. For strip loading problems it is found that, as the width of the loaded region decreases, the transition from failure predicted by structural theory to failure due to local plastic flow is very abrupt, and the structural theory is accurate even for strip widths which are small compared to the thickness of the structural element. For a circular plate under a central disk of pressure, however, the results obtained indicate that plate theory does not apply when the diameter of the disk is less than the plate thickness.
Slow Steady Flow of a Viscous Liquid in an Annulus With Uniform Arbitrary Injection and Suction Velocities Along the Walls
Authors: Das S. P.
Published: October 2011

The problem considered here is the slow steady flow of a viscous liquid through the annulus between two coaxial porous circular cylinders which ejects liquid over one wall and sucks in at the other wall, the velocities of injection and suction being uniform but arbitrary. The effects of wall porosity on velocity and pressure distributions are calculated following the method of superposition.
Dynamic Stresses Around a Fluid-Filled Cavity
Authors: Mow C. C. , Workman J. W.
Published: October 2011

The dynamic stresses at the boundary of a cavity filled with an inviscid compressible fluid during the passage of a plane dilatational wave train are determined in this paper. The steady-state response or admittance function is obtained for the plane-strain case. It is found that, at critical wave numbers, the intensity of the boundary stresses is significantly higher than that predicted under static loading. It is shown that these high intensities are due to resonance in the fluid and that the resonance conditions can be predicted once the properties of the medium and the fluid are known.
Elastic Response of Thin Spherical Shells to Axisymmetric Blast Loading
Authors: Baker W. E. , Hu W. C. L. , Jackson T. R.
Published: October 2011

Both an infinite-series solution and a finite-difference solution have been obtained to the problem of elastic response of a complete, thin, spherical shell to axisymmetric transient pressure loading. The two solutions are compared to each other for two specific examples and are also compared with previously published experimental data for one of the examples. The authors conclude that either solution is usable for engineering predictions of dynamics shell response. They also recommend conduct of more carefully controlled experiments for comparison with theory.
On the Transient Motion of a Rigid Spherical Inclusion in an Elastic Medium and Its Inverse Problem
Authors: Mow C. C.
Published: October 2011

This paper gives additional results in the transient response of a rigid spherical inclusion in an elastic medium due to a periodic disturbances. The locations of the poles in the admittance functions are examined for a wide range of density ratios and Poisson’s ratio of the medium. In addition, results are obtained on the inverse problem. It was shown that the incident pulse can be easily derived from the motion of the inclusion. In particular, when the densities of the inclusion and the medium are the same, the incident pulse is a function of the linear sum of motion, first and second derivatives of the motion of the inclusion.
Moire´ Patterns of Partial Derivatives of Displacement Components
Authors: Parks V. J. , Durelli A. J.
Published: October 2011

The knowledge of the partial derivatives of displacement components is essential in strain analysis. Two methods of determining these partial derivatives using moire´ effects are presented in this paper. One consists of superposing two shifted copies of the same deformed grating of lines. The other consists of superposing two shifted copies of moire´ patterns of displacement components. Explanations of the phenomena, based on the parametric properties of superposed families of lines, are given. Applications to the determination of the nonlinear deformation and strain tensor are included.
Some Remarks on Spherical Shells
Authors: DeSilva C. N. , Cohen H.
Published: October 2011

The present paper treats the deformation of a spherical shell within the framework of a linear bending theory which includes the effect of transverse-shear deformation. A two-term asymptotic solution of the governing equations is obtained which embraces all terms of an order retained in the formulation of the theory. The solution is valid within a physically important domain of the shell and reduces to the previously known one-term asymptotic solution of the classical bending theory. The problem of variable thickness is also discussed. The behavior of the thickness function may be such as to require in the solution a correction term which may contribute significantly to the deformation. This solution is applied to a treatment of the deformation of a rotating, completely closed spherical shell stiffened by an annular disk located normal to the axis of the spin.
Dynamic Axisymmetric Buckling of Shallow Conical Shells Subjected to Impulsive Loads
Authors: Fulton R. E.
Published: October 2011

A theoretical investigation is made of the axisymmetric snap-through buckling of a shallow conical shell subjected to an idealized impulse applied uniformly over the surface of the shell. The shell is assumed to behave as a single-degree-of-freedom system, and a study is made of the strain energy at maximum displacement: i.e., zero velocity. Under certain conditions this equilibrium position becomes unstable and the shell can snap through (or buckle). Nonlinear strain displacement equations are used and solutions are obtained for clamped and simply supported boundaries at the edge of the shell. Results for the cone are compared with similar results for a shallow spherical cap having the same rise as the cone. This comparison indicates that the spherical shell can resist a larger impulse than the conical shell before buckling.
Stress Waves Generated by Heat Addition in an Elastic Solid
Authors: Zaker T. A.
Published: October 2011

The problem of stress-wave generation in a linear thermoelastic solid by internal heat addition is investigated on the basis of a one-dimensional model of material response. A method of integration of the governing equations is given for the case of power deposition with arbitrary time and space variation. Closed-form results are presented for the half-space and the finite slab for power deposition which is a step function in time and exponential with distance from one surface, assuming negligible heat conduction. The influence of thermal diffusion on the stress field is estimated in terms of a dimensionless parameter representing the ratio of characteristic times of stress-wave propagation and thermal diffusion.
Gravity Flow of Frictional-Cohesive Solids—Convergence to Radial Stress Fields
Authors: Jenike A. W.
Published: October 2011

Evidence is presented to the effect that general stress fields in the steady, gravity flow of frictional-cohesive solids in converging channels in plane strain and in axial symmetry approach geometrically similar radial stress fields in the region of the vertex. Radial stress fields were discussed in an earlier paper [1].
Method for Determining the Instantaneous Center of Acceleration for a Given Link
Authors: Schiller R. W.
Published: October 2011

A method using the inflection circle is presented which extends the use of the Joukowski theorem and permits the determination of the instantaneous center of acceleration of a link without a complete acceleration analysis of the given mechanism.
Deterioration in Strength of Brittle-State Porous Bodies
Authors: Huang P. C.
Published: October 2011

A theory is presented to predict the deterioration in strength for a structure composed of a brittle-state porous material which has been subjected to a damaging tension field. Based on the theory, a degradation factor can be formulated as a means of evaluating the residual strength numerically. A proposed material function for a brittle-state porous medium was evaluated experimentally and was found to be satisfactory for an alumina material. The modulus of elasticity at room temperature of the same material has been found to increase with the density ratio in semi-logarithmic form.
Review on Space-Time Correlations in Turbulent Fluids
Authors: Favre A. J.
Published: October 2011

Turbulent flows, even when stationary on the average, are time-dependent. The study of such flows must take into account their statistical properties, not only spatial but temporal as well. A review is given of the main results of space-time measurements pertaining to: (a) In incompressible flows, double and triple velocity correlations, double correlations of wall pressure and of wall pressure and velocity of the main flow; (b) in compressible flows, double correlations of pressure at the wall and outside supersonic boundary layers, and autocorrelations of velocity in a supersonic wake. The space-time correlations give evidence to the heredity and (a) the convection velocities of the vorticity and entropy modes, as compared to the mean material convection velocity, and (b) the propagation of the acoustical mode.
Elastic Wave Propagation in Rods of Arbitrary Cross Section
Authors: Rosenfeld R. L. , Miklowitz Julius
Published: October 2011

A study is made of the problem of transient elastic wave propagation when a load is applied to one end of an infinitely long rod of arbitrary cross section. Fourier and Laplace transforms aid in developing a general solution in the form of a sum over all modes of harmonic wave propagation and integrals over all wavelengths. An expansion at long wavelength reveals two types of modes of propagation which are called longitudinal and radial shear modes. For a suddenly applied pressure, the long-distance, long-time response is found to be an integral of the Airy integral.
Large Deformation of a Rigid, Ideally Plastic Cantilever Beam
Authors: Ting Thomas C. T.
Published: October 2011

A new formulation is presented for the deformation of a rigid, ideally plastic cantilever beam with an attached tip mass under impact loading at its tip. The effects due to arbitrarily large displacements are rigorously taken into account. The results are compared with Parkes’ solution2 in which the geometry changes are neglected. Comparisons with experiments3, 4 show that neglect of the geometry changes is responsible for part of the discrepancies between Parkes’ theory and the experiments.
Wave Propagation in a Thin Cylindrical Shell
Authors: Spillers William R.
Published: October 2011

A solution is presented for a semi-infinite cylindrical (Timoshenko type) shell subjected to dynamic loading at one end using the method characteristics. Explicit results are obtained for the propagation of discontinuities. These results are combined with a simple numerical procedure to obtain the solution in all regions. Numerical examples are given for an elastic and a viscoelastic material and comparisons are made to previous results concerning wave propagation in shells.
Traveling Force on a Timoshenko Beam
Authors: Florence A. L.
Published: October 2011

Wave solutions are obtained by the Laplace-transform method for a semi-infinite beam subjected to a concentrated load moving at a velocity which may be supersonic, intersonic, or subsonic with respect to the bending and shear-wave velocities of the beam. Curves are drawn showing the velocity distribution behind a load moving supersonically.
A Study of the Nonlinearly Related Modal Solutions of Coupled Nonlinear Systems by Superposition Techniques
Authors: Atkinson C. P. , Taskett Beverly
Published: October 2011

The coupled nonlinear oscillating systems studied do not possess linear normal modes. The nonlinearly related modes of m1x¨1+∑k=1nakx1k+∑k=1nAk(x1−x2)k=0m2x¨2+∑k=1nbkx2k−∑k=1nAk(x1−x2)k=0(1)withk=1,3,5,...... are expressed as superpositions of the linear normal modes of each of the homogeneous systems of the form m1x¨1+akx1k+Ak(x1−x2)k=0m2x¨2+bkx2k−Ak(x1−x2)k=0(2) whose force fields are superimposed to yield the force field of equations (1).
On the Almost Sure Stability of Linear Dynamic Systems With Stochastic Coefficients
Authors: Caughey T. K. , Gray A. H.
Published: October 2011

In this paper a Lyapunov type of approach is used to obtain sufficient conditions guaranteeing the almost sure stability of linear dynamic systems with stochastic coefficients. The results are generalized to include a certain class of nonlinear system and also to guarantee the almost sure boundedness of the forced oscillations of linear dynamic systems with stochastic coefficients.
Further Results on Parametric Excitation of a Dynamic System
Authors: Hsu C. S.
Published: October 2011

A dynamic system having multiple degrees of freedom and being under parametric excitation has been studied in an earlier paper [2]. However, the analysis given there necessitates certain restrictions on the distribution of the natural frequencies of the system. In this paper those restrictions are removed. The analysis presented here shows how to obtain a constant matrix whose eigenvalues determine the stability or instability of a system of ordinary differential equations with periodic coefficients at a given excitation frequency. The constant matrix is expressed entirely in terms of the given system parameters and the excitation frequency.
Newton’s Method Applied to Problems in Nonlinear Mechanics
Authors: Thurston G. A.
Published: October 2011

Many problems in mechanics are formulated as nonlinear boundary-value problems. A practical method of solving such problems is to extend Newton’s method for calculating roots of algebraic equations. Three problems are treated in this paper to illustrate the use of this method and compare it with other methods.
On the Stresses in a Semi-Infinite Strip Subjected to a Concentrated Load
Authors: Ling Chih-Bing
Published: October 2011

This Note presents an exact solution for the stresses in a semi-infinite strip subjected to a symmetrically placed concentrated load. The solution is constructed by method of images. The resulting system of equations, which consists partly of integral equations and partly of algebraic equations, is solved by method of successive approximations. Convergence of the method is proved.
Stresses in a Thick Plate With Axially Symmetric Loading
Authors: Lardner T. J.
Published: October 2011

The problem of the thick elastic plate with a symmetric circular pressure loading is considered. The normal stress distribution on the midplane and for two positions off the midplane is obtained by a numerical integration of the solutions. A comparison of the stress distribution on the midplane is made with previous results.
Buckling of Axially Compressed Circular Cylindrical Shells at Stresses Smaller Than the Classical Critical Value
Authors: Hoff N. J. , Rehfield L. W.
Published: October 2011

Closed-form solutions are given of the linear Donnell equations defining the buckling of thin-walled circular cylindrical shells subjected to uniform axial compression. In addition to the classical simple support conditions requiring the vanishing of the radial displacement, the axial bending-moment resultant, the axial additional normal-stress resultant, and the circumferential displacement, three other, equally justifiable, simple support conditions are defined and studied in the case of the semi-infinite shell. Two of them yield buckling stresses amounting to about one half the classical critical stress.
Random Vibrations of Plates With Large Amplitudes
Authors: Herbert R. E.
Published: October 2011

The theory of the Markoff process and the associated Fokker-Planck equation is used to investigate the large vibrations of beams and plates with arbitrary boundary conditions subjected to while-noise excitation. An expression for the joint probability-density function of the first N-coefficients of series expansions of the middle surface displacements is obtained. Detailed calculations presented for simply supported beams and plates show that the probability-density function of the modal amplitudes is non-Gaussian and statistically dependent. Numerical computations for the plate indicate a significant reduction of the mean-squared displacement for values of the parameters well inside the range of practical considerations. Furthermore, for the square plate, the percent reduction is greatest.
Creep Rupture of Rotating Disks and Thin Shells of Revolution
Authors: Shoemaker E. M.
Published: October 2011

A theoretical analysis is made of the time to rupture for steady-state creep of: (a) A rotating thin circular disk of arbitrary profile, and (b) a rotating thin hollow shell of revolution. The results for the disk are given in terms of an integral; the special case of constant temperature distribution is considered explicitly. Results are tabulated and plotted for a disk initially of constant thickness for various parameter values. The rupture time for shells is given in closed form.
Transient Response of a Rigid Spherical Inclusion in an Elastic Medium
Authors: Mow C. C.
Published: October 2011

The transient response of a rigid spherical inclusion of arbitrary density embedded in an elastic medium owing to an incident pulse is examined in this paper. The Fourier-integral method is used, and an exact solution of the response is obtained. It is found that the acceleration and velocity of the inclusion are substantially different from those of the medium. A slight difference in the time history of the displacement between the inclusion and the medium is also noted.
Transmission of Force Between Two Semi-Infinite Solids
Authors: Dundurs J. , Hete´nyi M.
Published: October 2011

Elasticity solutions for a concentrated force near a smooth interface between two semi-infinite solids are given in terms of the Papkovich-Neuber displacement functions. The traction transmitted by the interface is found to possess several interesting properties. Furthermore, the traction for a smooth interface is compared with that for a perfect bond between the two semi-infinite solids. The limiting case of the force approaching the interface is discussed, and it is found that a parallel force in combination with a smooth interface is void of physical meaning.
Transient Cooling of a Spherical Mass of High-Temperature Gas by Thermal Radiation
Authors: Viskanta R. , Lall P. S.
Published: October 2011

This paper considers the transient cooling of a spherical mass of high-temperature gas which is surrounded by the cold atmosphere. The ionization and dissociation phenomena are neglected, and it is assumed that energy transfer by convection is negligible in comparison to radiation. The radiation transfer problem has been formulated exactly. For the case of a gray gas, approximate solutions are obtained for the temperature inside the sphere as functions of time and space coordinate by the method of moments. The local radiation flux is then evaluated for two different initial temperature distributions and several value of the optical radius.
A Study of Linearized Approximations to the Boundary-Layer Equations
Authors: Schetz Joseph A. , Jannone Joseph
Published: October 2011

The general subject of linearized approximations to the boundary-layer equations is considered in terms of the behavior, both qualitative and quantitative, of the resulting approximate solutions. In this regard, two nonsimilar flow problems are treated by various methods which are based upon the linearized concept. The results are analyzed and compared both with each other and “exact” numerical solutions where available. Linearization in the von Mises plane is considered in some generality and typical results are compared with those obtained by the more conventional physical plane linearization technique. In particular, it is shown that the use of the total pressure rather than the velocity as the dependent variable has important advantages even for constant pressure flow problems when subjected to a linearized treatment in the von Mises plane. Finally, specific recommendations are made as to the approach best applied to a given type of physical problem.
Dynamic Plastic Buckling of a Thin Cylindrical Shell Containing an Elastic Core
Authors: Lindberg H. E.
Published: October 2011

Stiffening by means of an elastic core is demonstrated to increase significantly the resistance of a cylindrical shell to buckling from an external impulsive pressure. Both theory and experiments show that the elastic core constrains the shell to absorb more energy by membrane plastic flow. Inclusion in the theory of a continuously changing tangent modulus of the shell material leads to a critical core modulus which depends on the hoop strain and explains the increased wave numbers observed in the experiments with stiff cores.
On the Nature of Moving Cracks
Authors: Cotterell B.
Published: October 2011

It is shown that the dynamic elastic-wave equations can be integrated quite simply in the neighborhood of the tip of a moving crack. A simple approximation to the exact solution is given. From examination of the dynamic stress field, arguments are presented to explain the increase in fracture toughness and fracture surface roughness with crack velocity. It is also postulated that fracture paths, asymmetrical to the applied loading, can be stable if their velocity of crack propagation is great enough.
Nonlinear Transverse Vibrations of a Spinning Disk
Authors: Nowinski Jerzy L.
Published: October 2011

Using the von Karman field equations, large amplitude vibrations of a spinning disk are analysed. For definiteness, the disk is assumed to be free, and its deflection is represented by a two-term polynomial. A vibration mode associated with two nodal diameters is studied in more detail. A familiar phenomenon of a decreasing period of vibration with an increasing amplitude is corroborated. The results specialized to the linear case show a close agreement with the classical results of Lamb and Southwell. The dependence of the membrane stresses on the amplitude of vibration and the velocity of spin is discussed.
Electrokinetic Energy Conversion
Authors: Osterle J. F.
Published: October 2011

Energy conversion by the mechanism of electrokinetics is investigated. A device capable of converting either electrical power into pumping power or pumping power into electrical power in the steady state is studied. The basic equations coupling voltage, pressure, current and flow rate are established and simplified in the light of existing experimental evidence. Operating characteristics for both the fluid pumping and the electrical generation mode are determined and illustrated by example problems. The results indicate that with water as the working fluid, conversion efficiencies of only 0.392 percent are possible.
Channel-Flow of Conducting Fluids Under an Applied Transverse Magnetic Field
Authors: Germeles Apostolos E.
Published: October 2011

The most general steady state solution is derived for the laminar flow of an incompressible, viscous and electrically conducting fluid in a one-dimensional channel under an applied transverse magnetic field. The channel can act as an electromagnetic flowmeter or pump. The effect of the conductivity of the walls is included. The solution has two unknown constants and, by choosing them properly, it can be made to fit the solution of all two-dimensional channels whose geometry approaches in the limit that of the one-dimensional channel. This is done in detail for the two-dimensional channels with rectangular and annular cross-section.
Longitudinal Impact on Viscoplastic Rods—Linear Stress-Strain Rate Law
Authors: Ting T. C. T. , Symonds P. S.
Published: October 2011

Hohenemser and Prager [1] proposed a constitutive law for a solid of Bingham type We use a form of this law to study some cases of longitudinal impact on a bar causing large plastic strains. The results are intended to be of use in the design of impact tests on structural metals and in the interpretation of data from them, as well as helpful in guiding similar studies on materials with more complex plastic strain rate behavior.
The Inverse Problem in Transient Heat Conduction
Authors: Sparrow E. M. , Haji-Sheikh A. , Lundgren T. S.
Published: October 2011

A general theory is devised for determining the temperature and heat flux at the surface of a solid when the temperature at an interior location is a prescribed function of time. The theory is able to accommodate an initial temperature distribution which varies arbitrarily with position throughout the solid. Detailed analytical treatment is extended to the sphere, the plane slab, and the long cylinder; and it is additionally shown that the semi-infinite solid is a particular case of the general formulation. The accuracy of the method is demonstrated by a numerical example. In addition, a numerical calculation procedure is devised which appears to provide smooth, nonoscillatory results.
Dependence of Stress Upon Temperature Gradient for an Ideally Elastic Solid Isotropic and Homogeneous in the Reference State
Authors: Marris A. W. , Villanueva J.
Published: October 2011

This paper postulates that the stress tensor of a Cauchy-elastic material depends upon the first temperature-gradient vector in addition to the deformation gradient and local temperature. Consequences of this postulate are examined for the particular cases of a body constrained to no deformation and to simple isochoric shear.
Wave Propagation in a Viscoelastic Material With Temperature-Dependent Properties and Thermomechanical Coupling
Authors: Petrof Robert C. , Gratch Serge
Published: October 2011

A numerical method is developed for the analysis of one-dimensional wave propagation in viscoelastic media with temperature-dependent properties when thermomechanical coupling is significant. The method is applied to a specific case of longitudinal wave propagation in a finite rod with essentially sinusoidal stress variation at the two ends. The results show that, contrary to the usual assumption, such a system does not have the same response as a single-degree-of-freedom elastic system with viscous damping, as long as a realistic stress-strain relation is used.
On the Stability of Elastic Systems Subjected to Nonconservative Forces
Authors: Herrmann G. , Bungay R. W.
Published: October 2011

Free motions of a linear elastic, nondissipative, two-degree-of-freedom system, subjected to a static nonconservative loading, are analyzed with the aim of studying the connection between the two instability mechanisms (termed divergence and flutter by analogy to aeroelastic phenomena) known to be possible for such systems. An independent parameter is introduced to reflect the ratio of the conservative and nonconservative components of the loading. Depending on the value of this parameter, instability is found to occur for compressive loadings by divergence (static buckling), flutter, or by both (at different loads) with multiple stable and unstable ranges of the load. In the latter case either type of instability may be the first to occur with increasing load. For a range of the parameter, divergence (only) is found to occur for tensile loads. Regardless of the non-conservativeness of the system, the critical loads for divergence can always be determined by the (static) Euler method. The critical loads for flutter (occurring only in nonconservative systems) can be determined, of course, by the kinetic method alone.
Unsymmetrical Buckling of Thin Shallow Spherical Shells
Authors: Huang Nai-Chien
Published: October 2011

The axisymmetrical snapping of clamped shallow spherical shells has been studied by many authors. There is found to be a discrepancy between the experimental observation of the buckling pressure and their theoretical prediction. In this paper, a study is made of the buckling pressure based on the initiation of unsymmetrical deflection. An eigenvalue problem is formulated and the buckling pressures for shells of a large range of geometrical parameters are obtained numerically. The present work reduces the gap between experiment and theory.
Axisymmetric Free Vibrations of Conical Shells
Authors: Garnet Hyman , Kempner Joseph
Published: October 2011

The lowest axisymmetric modes of vibration of truncated conical shells are studied by means of a Rayleigh-Ritz procedure. Transverse shear deformation and rotatory inertia effects are accounted for, and the results are compared with those predicted by the classical thin-shell theory. Additionally, the results are compared when either of these theories is formulated in two ways: First, in the manner of Love’s first approximation in the classical thin-shell theory, and then by including the influence of the change of the element of arc length through the thickness. It was found that the Love and the more complex formulation yielded results which differed negligibly in either theory. The results predicted by the shear deformation-rotatory inertia theory differed significantly from those predicted by the classical thin-shell theory within a range of parameters which characterize short thick cones. These differences resulted principally from the influence of the transverse shear deformation. It was also found that within this short-cone range an increase in the shell thickness parameter was accompanied by an increase in the natural frequency. Moreover, the increase in frequency with increasing thickness parameter became less severe as the length-to-mean radius ratio was increased. For the longer cones, the frequency was virtually independent of the thickness.
The Plastic Deformation of Built-in Beams Due to Distributed Dynamic Loading
Authors: Conroy M. F.
Published: October 2011

This paper is concerned with the initial phase of behavior of a long built-in beam when subject to a dynamic transverse load which is uniformly distributed over a central segment. The beam is assumed to be made of a rigid, ideally plastic material and the yield condition is assumed to depend only upon the bending moment. The effects of transverse shearing deformation, rotary inertia and strain rate are neglected. In the analysis, the beam is taken to be of infinite length. Four possible types of initial phase of motion are found. The conditions under which the results of this analysis are applicable to finite built-in beams are defined and the behavior of finite beams when these conditions are not satisfied is briefly discussed.
Theory of the Vibrating String as an Angular Motion Sensor
Authors: Quick William H.
Published: October 2011

The important deviations from ideal “gyroscopic” behavior of the plane of a vibrating string, driven by longitudinal end motion, are obtained theoretically. The amplitude of lateral string oscillation is obtained, and perturbation methods are applied to determine conditions under which these oscillations begin and/or continue. Elastic asymmetry is shown to cause the string elements to move out of the nominal plane of vibration into thin elliptical orbits, balanced in a “field” which deviates from linearity because of tension variation. A general expression for orbital precession in a nearly-linear central field is derived and applied to string orbits to obtain the differential equation of motion of the nominal string plane. Finally, motion of the string plane caused by asymmetrical damping is derived.
Wave Heights and Damping Coefficients for Half-Submerged Ellipsoids in Low-Frequency Sway and Yaw
Authors: Lurye J. , Pinkus O.
Published: October 2011

The authors consider the problem of an ellipsoid performing simple-harmonic swaying or yawing oscillations of small amplitude in the free surface of an ideal incompressible fluid, with gravity. The problem is examined in the limit of low frequency. The first nonzero term in the radiation pattern, which is a dipole term, and the damping coefficient, are found for sway. In the case of yaw the first nonzero term in the radiation pattern is a quadrupole term, and involves a higher power of frequency. Hence, the damping coefficient for yaw is of smaller order than the damping coefficient for sway, at low frequency. The strip-theory prediction of the sway damping coefficient is compared with the exact value and is shown to be too large by a factor of order K.
The Stability of a Circular Rod Laterally Constrained to Be in Contact With an Inclined Circular Cylinder
Authors: Paslay P. R. , Bogy D. B.
Published: October 2011

The stability of a rod loaded by an axial force and moment and gravity forces is considered by energy methods. The displacements are restricted in such a way that the rod must remain in contact with a rigid circular cylinder. The configuration is found to be stable for all loads unless the additional restriction is made that the cross-sectional elements of the rod do not rotate as they move around in contact with the cylinder. For these restricted displacements it is found that axial moment is not important in determining the stability of the configuration.
Impact on an Elastically Connected Double-Beam System
Authors: Seelig J. M. , Hoppmann W. H.
Published: October 2011

The paper presents the development and solution of the differential equations of motion of an elastically connected double-beam system subjected to an impulsive load. In addition to the theory there is presented a description of impact experiments on double beams. Theoretically and experimentally determined strains as functions of time are compared in the form of curves. The agreement is remarkably good for the type of load used.
Stress Distributions in Soft Metals Due to Static and Dynamic Loading by a Steel Sphere
Authors: Yew Ching-Hsie , Goldsmith Werner
Published: October 2011

The quasi-static and dynamic indentation of a hard steel sphere into a massive lead block, considered to represent a rigid perfectly-plastic half-space, has been investigated experimentally. The technique of visioplasticity was employed to calculate the stress pattern from which an empirical relation delineating the variation of hydrostatic pressure with depth of indentation was constructed. This expression was utilized in conjunction with a model of the surface-deformation process to describe the growth of the crater analytically. The force-indentation relation obtained in this manner agrees with that determined by direct observation to within 6 percent, while the predicted permanent crater depth was found to be 10.8 percent lower than that measured under dynamic conditions. The results of the present investigation have also been compared with solutions based upon the Haar-Karman criterion of yielding and upon the hypothesis of a constant flow pressure.
On a Variational Theorem in Elasticity and Its Application to Shell Theory
Authors: Naghdi P. M.
Published: October 2011

After stating a variational theorem which is a further generalization of known variational theorems and which has as its Euler equations all of the field equations and the boundary conditions of classical linear three-dimensional elasticity, the remainder of the paper deals with its application to shell theory. A new characterization of the basic system of field equations and the boundary conditions of the linear theory of elastic shells is derived which includes the effect of transverse shear deformation and involves only symmetric resultants and symmetric shell-strain measures. These results are of special significance in relation to those of a number of recent investigations in shell theory under the Kirchhoff-Love hypothesis in which the boundary-value problem of shell theory is recast in terms of symmetric (but not necessarily the same) variables.
Finite Burmester Theory in Plane Kinematics
Authors: Primrose E. J. F. , Freudenstein F. , Sandor G. N.
Published: October 2011

A unified treatment is presented of certain portions of Burmester theory by including finite as well as infinitesimal displacements. Theorems of R. Mueller concerning collinearity, order of contact, symmetry, and location of the Burmester points associated with infinitesimal, coplanar displacements of a plane, are extended to the more general case of arbitrary, coplanar displacements. Additional extensions relate to a recent study of infinitesimal displacements by G. R. Veldkamp [27] and, in some instances, are not related to earlier studies. The results of the present investigation are summarized in Table 2.
Note on the Deflection of a Viscoelastic Rectangular Plate Due to an Impulsive Load
Authors: Sarkar S. K.
Published: October 2011

In this Note the deflection of a linear viscoelastic plate due to a concentrated impulsive load, applied at a point on the plate, has been discussed. The material considered is of the Voigt type and the plate is a rectangular one.
Minimum-Weight Design for Pressure Vessels Reinforced With Inextensible Fibers
Authors: Pipkin A. C. , Rivlin R. S.
Published: October 2011

Axially symmetric membranes composed of inextensible fibers are considered. When the shape of the membrane and the tensile strength of the fibers are given, the minimum weight of fiber which can support a given internal pressure is proportional to the volume enclosed by the membrane. Minimum weight designs are isotensoid, i.e., every fiber is under the same tension. Every isotensoid design is a minimum weight design. Particular attention is devoted to geodesic isotensoid designs, in which fibers are required to lie along geodesics on the membrane. The equation relating the shape of the membrane to the distribution of fibers on it is obtained. When the shape is given, this equation is an integral equation for the fiber distribution, which is solved by using the Laplace transform. Illustrative examples involving cones, spheres, ellipsoids, and cylinders are solved.