bluuebunny/crossref_metadata_2025 huggingface dataset:
Response of a String to an Accelerating Mass
Authors: Rodeman R. , Longcope D. B. , Shampine L. F.
Published: November 2010

The response of a string to a mass particle undergoing a constant horizontal acceleration from rest has been calculated. The string deflection is expressed in terms of the transverse mass motion. A delay-differential equation is solved both numerically and asymptotically for the mass velocity. String profiles are presented at subsonic and supersonic speeds. Two oppositely traveling jumps in string displacement are found to appear as the mass is accelerated through the wave speed of the string.
The Contact Problem for a Rigid Cylinder Pressed Between Two Elastic Layers
Authors: Gladwell G. M. L.
Published: November 2010

The paper concerns the plane-strain problem of a rigid cylinder pressed between two identical elastic layers supported by rigid bases along which they may slide without friction. The essential difficulty of the problem is that there are three contact zones, one between the cylinder and the layers, and two, symmetrically placed, between the layers; the extent of these regions has first to be found. Alblas has given an iterative solution to the problem which reduces to a closed-form solution when the layers are half spaces. The purpose of the paper is to show that there is an elegant approximate solution of the half-space problem which is well suited to computation and which converges to the closed-form solution. The solution depends on some remarkable results obtained by extending the Chebyshev polynomials to the whole of the real line. The paper also provides a single-step approximate solution of the two-layer problem.
The Crack-Contact and the Free-End Problem for a Strip Under Residual Stress
Authors: Bakioglu M. , Erdogan F.
Published: November 2010

The plane problem for an infinite strip with two edge cracks under a given state of residual stress is considered. The residual stress is compressive near and at the surfaces and tensile in the interior of the strip. If the crack is deep enough to penetrate into the tensile zone, then the problem is one of crack-contact problem in which the depth of the contact area is an unknown which depends on the crack depth and the residual stress profile. The problem has applications to the static fatigue of glass plates and is solved for three typical residual stress profiles. In the limiting case of the crack crossing the entire plate thickness, the problem becomes a stress-free end problem for a semi-infinite strip under a given residual stress state away from the end. This is a typical stress diffusion problem in which decay behavior of the residual stress near and the nature of the normal displacement at the end of the semi-infinite strip are of special interest. For two typical residual stress states the solution is obtained and some numerical results are given.
Plane Stress Fields Induced by Moving Heat Sources in Butt-Welding
Authors: Karlsson L.
Published: November 2010

Mathematical models of the cooling of large butt-welded plates are investigated. One thermoelastic infinite plate and one thermoelastic semi-infinite plate are considered. On the infinite plate two concentrated heat sources of constant power move with constant velocity along a straight line toward each other. They meet and are then immediately removed from the plate. On the semi-infinite plate one concentrated heat source of constant power moves with constant velocity along a straight line perpendicularly toward the edge and is removed as it reaches the plate edge. The straight plate boundary is thermally adiabatic and mechanically free. A previous investigation showed that transverse tensile stresses arise behind the two heat sources on the infinite plate when they approach each other and behind the single heat source on the semi-infinite plate when it approaches the plate boundry. Here it is shown that after removal of the heat source(s) such tensile stresses remain much longer in the semi-infinite plate than in the infinite plate. The transverse tensile stresses may explain the tendency of hot cracking in the end portion of a butt-weld.
Circumferential Edge Crack in a Cylindrical Cavity
Authors: Keer L. M. , Luk V. K. , Freedman J. M.
Published: November 2010

The elastostatic problem of a circumferential edge crack in a cylindrical cavity is investigated. The problem is formulated by means of integral transforms and reduced to a singular integral equation. The numerical scheme of Erdogan, Gupta, and Cook is used to obtain the relevant physical quantities and the stress-intensity factors, and crack opening displacements are computed for several values of crack length.
The Effect of Principal Bending Curvature on the Lateral Buckling of Uniform Slender Beams
Authors: Peters D. A.
Published: November 2010

The general lateral buckling equation is developed for a uniform, slender, simply supported beam fixed in torsion and with a load applied at the shear center of the midspan cross section. In this general equation, the effect of principal bending curvature (i.e., beam deflection prior to buckling) is completely accounted for. Therefore, a distinction is made between beams fixed in torsion about the deformed or undeformed elastic axis, and distinct boundary conditions are derived for each case. The equations for each of the two support conditions are then specialized to include only the first-order effect of principal bending curvature and these equations are compared with similar equations for cantilever beams and beams in pure bending. Finally, simplified buckling load formulas are derived and compared with numerical solutions of the general equations for each of the lateral buckling configurations. The comparison shows that the approximate formulas provide good estimates for the buckling load and that the classical buckling load formulas that neglect principal bending curvature are not always conservative for infinitely slender beams.
Linear Stability of Flow in a Concentric Annulus
Authors: Agarwal A. K. , Garg V. K.
Published: November 2010

The stability of fully developed, parallel flow in a rigid, concentric annulus to infinitesimal disturbances is analyzed. It is found that the annular flow is spatially stable to axisymmetric disturbances upto a modified Reynolds number of 10,000.
On the Tensile and Compressive Strength of Solids Weakened (Strengthened) by an Inhomogeneity
Authors: Tirosh J.
Published: November 2010

By considering the stress interaction between an inhomogeneity embedded in an elastic brittle-like solid and the preexisting microcracks (“Griffith cracks”) inherent to the solid, several puzzling phenomena concerning the apparent anomalous “size effect” on the fracture strength of solids weakened (strengthened) by a cutout (reinforcement) are explained quantitatively. The various conditions under which a cylindrical inhomogeneity in an otherwise homogeneous body enhances the strength of the body or weakens it when the body is subjected to load normal to the cylindrical axis are revealed and discussed. In particular it is shown that uniaxial tensile and compressive critical loads required to fracture material with various hole sizes are predictable as confirmed by experiments with quasi-isotropic composite materials, rocks, and high strength alloys found in the open literature. The entries to these predictive functions are the two independent fracture properties of the material; tensile strength and toughness of the virgin material, or the typical size of the Griffith cracks. As a by-product, the extremely high compressive strength of a material (with respect to its tensile strength) with vanishingly small inhomogeneity emerges.
Stable Postbuckling Equilibria of Axially Compressed, Elastic Circular Cylindrical Shells: A Finite-Element Analysis and Comparison With Experiments
Authors: Maewal A. , Nachbar W.
Published: November 2010

Postbuckling behavior of clamped circular cylindrical shells of finite length under uniform axial compression is analyzed using a potential-energy-based, displacement finite-element method. Contour maps of equal radial deflection computed from this analysis for one-tier and two-tier postbuckled, stable equilibrium patterns show very good agreement with experimentally measured contour maps for a polyester shell with L/R = 0.7 and R/h = 405. Developed for these computations, and essential for them, are: (a) A 48 DOF shell element; (b) A method to calculate accurately for the perfect shell the nonlinear fundamental path and its bifurcation points. The lowest such bifurcation point does not correspond to the first observed postbuckle pattern, which is reproduced by calculating the continuous equilibrium path from the sixth bifurcation point. Patterns of successive postbuckling shapes that are formed under additional end-shortening are determined by using a special technique to calculate equilibrium paths extending continuously from still higher bifurcation points on the fundamental path.
An Exact Solution for the Superseismic Stage of Dynamic Contact Between a Punch and an Elastic Body
Authors: Thompson J. C. , Robinson A. R.
Published: November 2010

The superseismic stage of contact between a rigid punch and a linearly elastic medium is studied by the self-similar potential technique. It is shown that the instantaneous values of contact force, contact area, and the rate of penetration of the punch are given by simple algebraic expressions. The stress fields for the mathematical idealization of a velocity distribution “concentrated” in a manner analogous to the integrable singular stress field beneath a point load is given. Using these stresses as influence functions permits the stress field beneath any punch to be computed once the time and spatial variation of the velocity imposed within the contact region has been determined.
Three-Dimensional Elasticity Solution and Edge Effects in a Spherical Dome
Authors: Cheng Shun , Angsirikul T.
Published: November 2010

The subject of this analysis is a homogeneous, isotropic, and elastic spherical dome of uniform thickness subjected to prescribed edge stresses at the end surface. Starting from three-dimensional equations of theory of elasticity, solutions of Navier’s equations and the characteristic equation are obtained. Eigenvalues are computed for various values of the thickness and radius ratio and their special features are analyzed. Coefficients of the nonorthogonal eigenfunction expansions are then determined through the use of a least-squares technique. Many numerical results are obtained and illustrated by figures. These results show that the method presented herein yields very satisfactory solutions. These solutions are fundamental to the understanding of thin shell theories.
The Effect of Reflections on Nonlinear, Transient Pulse Propagation in Laminated Composites
Authors: Seymour B. R. , Mortell M. P.
Published: November 2010

The transient response of a laminated composite is treated. The effects of quadratic and cubic nonlinearity in the stress-strain law and reflections at interfaces are included.
Free-Vibration Analysis of Rectangular Plates With Clamped-Simply Supported Edge Conditions by the Method of Superposition
Authors: Gorman D. J.
Published: November 2010

In this paper attention is focused on the free-vibration analysis of rectangular plates with combinations of clamped and simply supported edge conditions. Plates with at least two opposite edges simply supported are not considered as they have been analyzed in a separate paper. It is well known that the family of problems considered here have presented researchers with a formidable challenge over the years. This is because they are not directly amenable to Le´vy-type solutions. It has been pointed out in the literature that most of the existing solutions are approximate in that they either do not satisfy exactly the governing differential equation or the boundary conditions, or both. In a new approach taken by the author the method of superposition is exploited for handling these dynamic problems. It is found that solutions of any degree of exactitude are easily obtained. The governing differential equation is completely satisfied and the boundary conditions are satisfied to any degree of exactitude by merely increasing the number of terms in the series. Convergence is shown to be remarkably rapid and tabulated results are provided for a large range of parameters. The immediate applicability of the method to problems involving elastic restraint or inertia forces along the plate edges has been discussed in an earlier publication.
Godunov-Conte Method for Solution of Eigenvalue Problems and Its Applications
Authors: Elishakoff I. , Charmats M.
Published: November 2010

The method originally presented by Godunov and modified by Conte for solution of two-point boundary-value problems, is outlined here as applied to eigenvalue problems. The method (which avoids the loss of accuracy resulting from the numerical treatment, often associated with stability and vibration analysis of elastic bodies) consists of parallel integration of the set of k homogeneous equations under the Kronecker-delta initial conditions which are orthogonal (k being the number of “missing” conditions), after each step. Subject to Conte’s test, the set of solutions is reorthogonalized by the Gram-Schmidt procedure and integration continues. The procedure prevents flattening of the base solutions, which otherwise become numerically dependent. The method is applied to stability analysis of polar orthotropic plates, and as in the isotropic case (as shown by Yamaki), it is seen that assumption of symmetric buckling results in a stability overestimate for an annular plate.
The Sliding of a Rigid Indentor Over a Power Law Viscoelastic Layer
Authors: Nachman A. , Walton J. R.
Published: November 2010

The problem of the sliding of a rigid asperity over a power law viscoelastic layer is examined in the realistic limit of infinite (dimensionless) layer thickness. For a contact interval of unit length, asymptotic expansions for the normal traction over the interval together with several other physically relevant quantities (e.g., the friction coefficient) are developed in terms of an appropriate asymptotic sequence of powers of the (dimensionless) layer thickness.
A Ray Theory for Elastodynamic Stress-Intensity Factors
Authors: Achenbach J. D. , Gautesen A. K.
Published: November 2010

Elastodynamic stress-intensity factors generated by the interaction of wave motions with a crack are analyzed. It is shown that in an asymptotic approximation, which is valid for high frequencies, the stress-intensity factors at the edge of a crack are related to the fields of incident rays by a matrix of stress-intensity factor coefficients, which can be computed from canonical solutions. The canonical solutions are provided by the fields describing diffraction by a semi-infinite crack of plane body waves and plane surface waves, which are incident under an arbitrary angle with the edge of the crack. Several applications of the theory are presented. For cracks of finite length, the contributions due to the traveling back and forth of rays between the two crack tips is taken into account in a simple manner, to yield results which are in excellent agreement with numerical results obtained by other authors.
Influence of Rotatory Inertia on Steady-State Crack Propagation in a Finite Plate Subjected to Out-of-Plane Bending
Authors: Fossum A. F.
Published: November 2010

A dynamic stress-intensity factor and energy release rate are obtained for a running semi-infinite crack traversing a strip of elastic material subjected to out-of-plane bending. It is shown that the maximum ratio of crack tip velocity to shear wave velocity is identical to the maximum ratio of flexural wave velocity to shear wave velocity in the limit of vanishingly small wavelength. The dynamic stress-intensity factor is written as the product of a static stress-intensity factor multiplied by a function of Poisson’s ratio and crack tip velocity the function decreasing monotonically with increasing crock tip velocity. The energy release rate is shown to be independent of crack tip velocity for this type of problem.
Analysis of Sheet Metal Stamping by a Finite-Element Method
Authors: Wang N.-M. , Budiansky B.
Published: November 2010

On the basis of the nonlinear theory of membrane shells, a general finite-element procedure is developed for calculating the deformations in the stamping of sheet metal by arbitrarily shaped punches and dies. The sheet material is assumed to be elastic-plastic and satisfy a rate-insensitive, Mises-type flow rule taking into account finite deformation, work-hardening and normal anisotropy. Coulomb friction is assumed at the contacting surfaces between sheet and punch and between sheet and die. Numerical results obtained from application of the procedure to the hemispherical punch stretching of circular sheets are compared with existing axisymmetric solutions and experimental data.
Analytical Solutions of Viscous Flow in Constricted or Widened Tubes
Authors: Van Dooren R.
Published: November 2010

The steady laminar axisymmetric flow of a Newtonian viscous homogeneous incompressible fluid through constricted or widened circular tubes is studied. Assuming that the tube wall is slightly curved with the axial distance as described by an exponential function, an analytical method is presented based on the perturbation method in connection with a transformation that maps the curved tube domain into a rectangular region. The results for the velocity, the pressure, and the wall shear stress for various values of the Reynolds number and of the parameters specifying the exponentially curved wall, are represented and discussed in detail. The necessity of the assumption that the flow is two dimensional is justified.
Angled Elliptic Notch Problem in Compression and Tension
Authors: Wu H.-C. , Chang K.-J.
Published: November 2010

The strain failure criterion previously proposed by the first author is applied to obtain solutions for the angled elliptic notch problem subject to compressive and tensile loads. The theory compares favorably with experiments in both cases. This indicates that the proposal of the crack plane being normal to the direction of the maximum tensile strain for brittle fracture is essentially correct.
A Thick-Walled Cylinder With an Axisymmetric Internal or Edge Crack
Authors: Erdol R. , Erdogan F.
Published: November 2010

The paper considers the elastostatic axisymmetric problem for a long thick-walled cylinder containing a ring-shaped internal or edge crack. Using the standard transform technique the problem is formulated in terms of an integral equation which has a simple Cauchy kernel for the internal crack and a generalized Cauchy kernel for the edge crack as the dominant part. As examples the uniform axial load and the steady-state thermal stress problems have been solved and the related stress-intensity factors have been calculated. Among other findings the results show that in the cylinder under uniform axial stress containing an internal crack the stress-intensity factor at the inner tip is always greater than that at the outer tip for equal net ligament thicknesses and in the cylinder with an edge crack which is under a state of thermal stress the stress-intensity factor is a decreasing function of the crack depth, tending to zero as the crack depth approaches the wall thickness.
On the Stress Field and Surface Deformation in a Half Space With a Cuboidal Zone in Which Initial Strains Are Uniform
Authors: Chiu Y. P.
Published: November 2010

A solution is given for the stress field and surface deformation in a half space in the presence of uniform inelastic strains in a subsurface cuboidal domain. The problem is solved by using the full space solution of two cuboids with specified initial strain and relieving the stress acting normal to their plane of symmetry. The solution for stresses and surface deformations are obtained in closed form. Numerical results are given for stresses and surface displacement as a function of the depth of the cuboidal element.
Dynamic Response of Circular Plates Resting on Viscoelastic Half Space
Authors: Lin Y. J.
Published: November 2010

Dynamic responses of circular thin plates resting on viscoelastic half space subject to harmonic vertical and rocking excitations are studied. The analysis is based on the assumption that the contact between the plate and the surface of the half space is frictionless. This dynamic mixed boundary-value problem leads to sets of dual integral equations which are reduced to Fredholm integral equations of the second kind and solved by numerical procedures. The numerical results show that the rocking impedance function is independent of the plate flexibility, but the vertical excitation is not.
Variable Viscosity Effect on the Laminar Water Boundary Layer on Heated Cones
Authors: Yao L.-S.
Published: November 2010

Heat transfer and shear stress may be significantly affected by buoyancy-forced and associated free-convection motions in many forced-convection flows. A crossflow is induced when a uniform, horizontal stream passes along a heated, axisymmetric slender body. The crossflow effects on heat transfer and shear stress grow as the fluid flows downstream, and eventually become one of the dominant mechanisms even for a moderate-speed forced-convection flow. Early study of the longitudinal cylinder flow showed that the crossflow may destabilize the boundary layer and degrade the heat transfer over the upper half of the body. On the other hand, heating can be used to stabilize the water boundary layer due to its temperature-dependent viscosity, since (dμ/dT) of water is negative. However, the influences of the pressure gradient on the destabilizing crossflow effect and on the stabilizing variable-viscosity effect have never been studied before. It is important to know the interaction of the buoyancy-force effect and the variable-viscosity effect under the non-zero pressure gradient conditions in stabilizing the boundary layer by heating. In this paper a similarity solution is presented for a three-dimensional boundary layer on a heated cone to stimulate the water flow past the forward part of an axisymmetric slender body. The numerical solutions of the ordinary differential equations reduced by the similarity transformation are presented in the region near the vertex of the cone. The results indicate that the crossflow grows as the fluid flows downstream for the cone of its half angle less than 66.25°. For a cone of its half angle larger than 66.25°, the magnitude of the crossflow is about the same order as that of the axial flow in the neighborhood of the cone vertex and is suppressed by the favorable pressure gradient as the fluid moves downstream. The effect of the temperature-dependent water viscosity has been shown to enhance the favorable pressure-gradient effects and to counterbalance the crossflow effects.
Influence of Elasto-Plastic Transition on the Inelastic Response of Beams and Plates
Authors: Raghavan K. S. , Rao S. S.
Published: November 2010

The paper deals with a study of the significance of elastoplastic transition state in the dynamic response of Euler beams and thin plates. The study is based on a comparative evaluation of the responses predicted by two independent approaches that use (i) stress-strain relation and basic plasticity theory and (ii) moment-curvature relation; assuming the shape factor to be unity. Responses are evaluated by way of finite-element idealization followed by numerical integration. It is found that the simplified model, based on moment-curvature relations, underestimates the response by a significant amount for longer durations of the applied load.
Impact Buckling of Thin Bar Via Monte Carlo Method
Authors: Elishakoff I.
Published: November 2010

Impact buckling of elastic bars with initial imperfections is studied. The latter are assumed to be a normally distributed random function of the space coordinate with given mean function and autocorrelation function. The initial imperfection and additional deflection function are expanded in terms of the vibration model of the corresponding perfect structure without an axial force. Fourier coefficients of the expansion for the initial imperfection function are simulated numerically, and the statistical behavior of the buckling time (time to first failure) is determined.
A New Cumulative Damage Model—Part 3
Authors: Bogdanoff J. L.
Published: November 2010

Parts 1 and 2 presented a stochastic model of the cumulative damage process that for the first time makes it possible to take a comprehensive view of the entire process. Some of the properties of the model were discussed and some fatigue and wear data were considered. It also was shown that data on time to failure is not sufficient to characterize the process and that prediction of life under changed conditions is of necessity subject to error which cannot be removed based only on life time data. The purpose of this part is to demonstrate that since it is now possible to take a comprehensive view of the entire process accuracy in life prediction under changed conditions can be improved by the acquisition of additional data of a specific type. This data provides increasing knowledge of member (sample) function behavior that is essential for improvement in predictive accuracy.
Concerning a Creep Surface Derived From a Multiple Integral Representation for 304 Stainless Steel Under Combined Tension and Torsion
Authors: Mark R. , Findley W. N.
Published: November 2010

It is shown that a creep surface, defined in terms of a prescribed creep rate, can be determined from the multiple integral formulation representing the creep data. The creep surface for 304 stainless steel was found to be in good agreement with a Mises ellipse. Observed creep rate vectors for this alloy were found to be normal to a Mises ellipse. These results were obtained from creep tests performed on 304 stainless steel under combined tension and torsion at 593°C (1100°F). Creep strains observed for at least 100 hr were adequately represented by a power function of time, the exponent of which was independent of stress. A third-order multiple integral representation together with a limiting stress below which creep does not occur was employed to describe satisfactorily the constant stress creep data.
Annular Dome Subjected to Uniform Load Over an Eccentric Circular Area
Authors: Ainso H.
Published: November 2010

A general method is presented for solving shallow shell problems with finite boundaries and with an arbitrarily placed load that is uniformly distributed over a circular area of radius r0. A known solution for the distributed load on an unbounded shell is used to describe the load effects, and this particular solution is combined with Reissner’s general solution of the shallow shell equations in such a manner that all the boundary conditions are satisfied. Numerical results have been obtained for a shallow shell, clamped at the outer boundary and having a circular polar aperture free of tractions and support.
Roots of Lambda Matrices
Authors: Thurston G. A.
Published: November 2010

A numerical method is outlined for computing roots of determinants of lambda matrices. Convergence of the method is quadratic as long as the derivative of the determinant does not vanish at the root. When the derivative is zero, the method may still converge in special cases. Three examples of mechanics problems giving rise to lambda matrices are included.
Accurate Nonlinear Equations and a Perturbation Solution for the Free Vibrations of a Circular Elastic Ring
Authors: Simmonds J. G.
Published: November 2010

A set of geometrically nonlinear equations is derived for the plane motion of an elastically homogeneous circular ring. For vibrations that are primarily flexural, extensional strain, transverse shearing strain, and rotary inertia terms are shown to be negligible and the equations are reduced to two-coupled cubic equations for the axial force and rotation at a cross section. For free vibrations whose linear part is a single term harmonic in space and time, a perturbation solution shows that the frequency always initially decreases with amplitude (softening nonlinearity). The frequency amplitude relation agrees exactly with recent, independent work by Maewal and Nachbar, but differs substantially for low wave numbers from earlier work of others who used shallow shell-type approximations.
The Nonlinear Behavior of Elastic Slender Straight Beams Undergoing Small Strains and Moderate Rotations
Authors: Rosen A. , Friedmann P.
Published: November 2010

The nonlinear behavior of slender and initially straight beams is investigated. A set of equilibrium equations for a beam undergoing moderate rotations and small strains is derived. The derivation includes several assumptions which are clearly stated and explained. These equations are used to investigate the deformations of a cantilevered beam which is loaded by a concentrated transverse load at the free end. The numerical results are in very good agreement with the experimental results.
An Introduction to the Variable Inertia Flywheel (VIF)
Authors: Ullman D. , Velkoff H.
Published: November 2010

A flywheel with variable moment of inertia, combining the functions of energy storage and power control is introduced. Potential designs are presented and the basic physical governing equations developed. Examples of the flywheel system powering a constant angular rate, frictional load, and an accelerating automobile are presented. Limitations of and potential for future development which become evident in the examples are discussed.
Dynamics of Flexible Cylinders in Axisymmetrically Confined Axial Flow
Authors: Pai¨doussis M. P. , Pettigrew M. J.
Published: November 2010

This paper describes experiments in which flexible cylinders placed centrally within a narrow cylindrical flow channel were subjected to axial flow. The dynamical behavior of such cylinders, either cantilevered or supported at both ends, is described, both in liquid and in simulated two-phase flows; the effect of several parameters, such as the annular confinement, was investigated. It was observed that, with increasing flow, the cylinder is subject sequentially to instabilities of increasing mode number, confinement severely destabilizing the system. The experimental observations are compared to a theoretical model for the dynamics of such systems. In the case of liquid flow, agreement is qualitatively good and quantitatively fair—keeping in mind the experimental difficulties. In the case of two-phase flows, theory and experiment do not agree.
Membrane Mode Solutions for Impulsively Loaded Circular Plates
Authors: Symonds P. S. , Wierzbicki T.
Published: November 2010

Large deflections of a clamped circular plate subjected to axially symmetric impulsive loading are obtained by means of the mode approximation technique. The mode shapes and accelerations are determined by equations assuming simple membrane action. The predicted deflections and response times are compared with quantities measured in recently published experiments on plates of steel, titanium, and lead. In view of the extreme simplicity of the approximate method, the good agreement at large deflections, observed in the case of the two structural metals, is of practical interest.
A Closed Crack Tip Terminating at an Interface
Authors: Comninou Maria , Dundurs J.
Published: November 2010

Considering a crack that lies in one solid, but has a tip that touches an interface with a second solid, Bogy found that the assumption of a traction-free crack tip leads to oscillating singularities for certain combinations of materials. Such oscillating singularities lead to overlapping of the crack faces, and the purpose of this article is to eliminate the oscillating singularities by allowing the crack tip to be closed. Using an asymptotic analysis and incorporating the effect of friction, the nature of the singularity at the closed crack tip is established and the various consequences explored.
A Continuum Theory for Materials With Directional Porosity
Authors: Curran J. H. , Carroll M. M.
Published: November 2010

A theory is developed for porous materials with directionally dependent lineal porosity. The assumed form of the directional dependence leads to an idealization of the porous material as a continuum with ordinary and dipolar displacements. The field equations for a linearized isothermal elasticity theory are derived for isotropic materials with nondirectional lineal porosity in the reference state.
Elastic-Plastic Tension-Torsion in a Circular Bar of Rate-Sensitive Material
Authors: Meguid S. A. , Campbell J. D.
Published: November 2010

A theoretical and numerical investigation is made of the behavior of a circular bar of elastic-viscoplastic material subjected to either proportional or nonproportional straining in tension and torsion. The tensile properties of the material are assumed to be adequately represented by the empirical formula of Bodner and Symonds, which is based on experimental results for mild steel. The analysis employs Perzyna’s generalization of von Mises’ yield criterion, and the associated plastic flow rule. Elastic compressibility is taken into account. The stresses, strains, and loading paths are determined for four prescribed straining paths; the results were obtained by solving numerically, using Crout’s method with partial pivoting, a system of six simultaneous quasi-linear partial differential equations of hyperbolic type. Closed-form analytical solutions are also obtained for the stresses, load, and torque corresponding to fully plastic conditions; interaction curves are plotted relating load and torque under these conditions, for quasi-static straining and for a range of finite effective strain rates.
Plane Strain Compression of Rigid-Perfectly Plastic Strip Between Parallel Dies With Slipping Friction
Authors: Das N. S. , Banerjee J. , Collins I. F.
Published: November 2010

This paper presents the results of computer calculations of a class of slipline solutions for compression between parallel dies with slipping friction at the die-metal interface such that the frictional shear traction is a constant proportion of the yield stress. The slipline fields considered here have previously only been suggested qualitatively. The fields are of “indirect type”, requiring the solution of linear integral equations. They have been analyzed and computed here using the recently developed matrix operator procedure. The numerical results obtained are compared with those obtained from approximate upper bound and other “technological” theories.
Postbuckling Analysis of Continuous, Elastic Systems Under Multiple Loads—Part 2: Applications
Authors: Plaut R. H.
Published: November 2010

In Part 1, a theoretical stability analysis of continuous, elastic systems subjected to multiple independent loads was developed. Postbuckling behavior and imperfection-sensitivity were investigated. Three examples are presented here to illustrate the procedures and results of that study. The first example consists of a cantilever subjected to a pair of concentrated axial loads, one applied at the tip and the other at midspan. In the second example, involving nonconservative loading, an axial load and a follower load are applied at the tip of a cantilever. Finally, a shallow arch under three concentrated vertical loads is considered, in order to demonstrate a case with prebuckling deformations.
Overstability of a Viscoelastic Fluid Layer Oscillating in a Vertical Periodic Motion and Heated From Below
Authors: Onyegegbu S. O.
Published: November 2010

This Note examines the effect of vertical periodic motion on the stability characteristics of a viscoelastic fluid layer in a classical Benard geometry. Numerical solutions show that a resonant type behavior which enhances stability occurs at oscillation frequencies near the convective natural frequency of the viscoelastic fluid, while the effect of the periodic motion vanishes as the oscillation frequency gets very large.
Gravity Flow of Granular Materials in Conical Hoppers
Authors: Nguyen T. V. , Brennen C. , Sabersky R. H.
Published: November 2010

An approximate solution to the flow of a cohesionless granular material in a conical hopper is presented. The material is modeled as a perfectly plastic continuum which satisfies the Mohr-Coulomb yield condition. Analytical expressions of the mass flow rate and the wall stress are derived and compared to some experimental data and other analyses.
Dynamics of a Wobbling Symmetric Disk
Authors: Dudek J. A.
Published: November 2010

The motion of the metering element of the common “nutating” or wobbling disk water meter is described and expressions are derived for the case where there are no externally applied torques. This motion is defined by a single equation of motion and two holonomic constraints.
An Experimental Investigation of Several Low-Area-Ratio Water Jet Pumps
Authors: Sanger N. L.
Published: November 2010

Several low-area-ratio jet pumps were evaluated experimentally in water. Principal geometrical variables investigated were area ratio, throat length, and nozzle spacing. Diffuser geometry was also varied, but to a lesser degree. Experimental values of efficiency and head ratio were compared to a one-dimensional theoretical prediction method previously found to be applicable to moderate and high-area-ratio pumps. Two related cavitation prediction parameters were developed and compared to experimental data.
On the Control and Stability of One Class of Biped Locomotion Systems
Authors: Vukobratovic´ M. , Juricˇic´ D. , Frank A. A.
Published: November 2010

The control and stability properties of a “simplified dynamic system” representing a particular biped gait are discussed. The simplified dynamic system consists of an algorithmically controlled lower limb system and a movable point mass. The concepts of repeatability and cyclicity are introduced by means of this model. These concepts provide the basis for control considerations in this class of systems. They lead to conditions which guarantee the maintenance of a gait. Stability of such nonlinear systems cannot be considered by classical techniques. To study stability, the concept of disturbance to nonlinear dynamic systems is introduced. This concept leads to a measure of stability by a quantity termed an “index of capability.” A method of computation for this index for this class of machines is shown.
Response of Elastic Bodies to a Uniformly Accelerating Point Force
Authors: Raske T. F. , Joung Ki Sub
Published: November 2010

An analysis based upon linear theory is presented for determining the dynamic response of a simply supported beam, rectangular plate and shallow cylindrical shell to a point force of variable magnitude uniformly accelerating across the surface of these elastic bodies. It is shown that resonant conditions are not associated with problems of this type. Typical deflection profiles are included for a constant magnitude point force accelerating across a beam.
Free Molecule Flow Through a Vacuum Seal
Authors: Yu H. S. , Sparrow E. M.
Published: November 2010

An analysis is made of the rate of the mass flow through a vacuum seal separating two rarefied gas environments. The determination of the mass throughflow characteristics involves the formulation and solution of a coupled system of six integral equations. The formulation is performed using the methods of kinetic theory. Numerical solutions are carried out for a wide range of values of the seal geometrical parameter. Mass flow results evaluated from these solutions are presented graphically. In addition, representative distributions of the mass fluxes at the participating surfaces are given.
Discussion: “Flow Past a Right Circular Cylinder in a Rotating Frame” (Boyer, D. L., 1970, ASME J. Basic Eng., 92, pp. 430–435)
Authors: Jacobs S. J.
Published: November 2010

An analysis of low Rossby number and low Ekman number flow between parallel plates shows that the interior flow is irrotational and two-dimensional for all Rossby numbers and Ekman numbers in the range R0≪1, E≪1. The extra condition R0≪E1/2 is not needed for this proof.
Sound Generation in Subsonic Turbomachinery
Authors: Morfey C. L.
Published: November 2010

Sources of noise in axial-flow machines are studied theoretically with the aid of a simplified two-dimensional model. The analysis leads to estimates of the discrete-frequency sound output from interacting blade rows, and provides a basis for subsequent study of broad-band sources.
The Breakup of Superheated Liquid Jets
Authors: Lienhard John H. , Day James B.
Published: November 2010

Observed average breakup lengths are presented for free orifice jets of superheated water and liquid nitrogen, and subcooled water. Dimensionless, semiempirical expressions are developed for both flashing, and aerodynamic and/or capillary, breakup, and verified with data. The distribution function for breakup length is predicted for the superheated case with the help of Boltzmann statistics.
Cavitation Erosion Studies With Venturi and Rotating Disk in Water
Authors: Syamala Rao B. C. , Lakshmana Rao N. S. , Seetharamiah K.
Published: November 2010

A study of the cavitation erosion behind blunt bodies with varying hydrodynamic factors of flow, such as, the test time, length of cavity, velocity, and pressure; the geometrical parameters of the system, namely, the size and shape of the cavitating body, its aspect-ratio, and its surface roughness; and the mechanical properties of the materials, namely, the density, yield strength, tensile strength, engineering strain energy, hardness, ultimate resilience, percent elongation, percent reduction in area and elastic modulus are reported. The study of the volume eroded along with the hydrodynamic factors of the flow and the geometrical parameters of the system in general indicated that a critical zone of cavitation conditions exists in which the erosion caused is very severe. This critical zone is described by a range of values of V/l (α Strouhal frequency, f for detachment of cavities). Among the correlations studied for the inverse of rate of volume eroded as a function of individual and twin mechanical properties, the product of ultimate resilience and Brinell hardness showed the best correlation.
Calculations of the Flow of Natural Gas Through Critical Flow Nozzles
Authors: Johnson R. C.
Published: November 2010

The mass flow rate of methane and 19 natural gas mixtures through critical flow nozzles has been calculated. The calculation assumes the flow to be one-dimensional and isentropic. The pressure range is 0 to 1000 psi and the temperature range is from 450 to 700 deg Rankine. From a study of the results, a simple empirical method for making this mass flow rate calculation is proposed. This method would apply to natural gas mixtures whose composition is known and whose components have no more than four carbon atoms.
Relaxation of Compression Springs at High Temperatures
Authors: Siegel M. J. , Athans D. P.
Published: November 2010

An analysis is developed to determine the relaxation of cylindrical compression springs at temperatures where creep is predominantly steady state and the effect of transient creep and anelastic strain is small. Springs which operate under these conditions must be designed for limited life. Equations are derived which predict the relaxation of springs directly from tensile creep data for various materials. Using creep data for 18-8 stainless steel and Inconel-X, families of design curves are presented which give the time-temperature initial-stress relationships for various stress-relaxation ratios. These curves are useful in selecting an initial design stress for a specific operating temperature.
Off-Design Performance Characteristics of Supercavitating Hydrofoils in Cascade
Authors: Oba R.
Published: November 2010

The performance characteristics of supercavitating flapped foils in cascade, (such as the lift coefficient, the drag-lift ratio, and the limiting inlet flow speed) are calculated, for various cascade arrangements and flap angles, as well as flap-chord ratios, e. The extreme case when e = 1.0 corresponds simply to adjusting the cascade angle, such as in the Kaplan-turbine runner. It is found that the poor supercavitating cascade performance characteristics at conditions other than the designed condition, that is, the off-design performance characteristics, are noticeably improved with the use of flapped foils. The characteristics of cascaded foils without flaps, especially where there are no adjustments in cascade angle, make their use impractical in the off-design condition.
An Investigation of the Effect of Cavitation Bubbles on the Momentum Loss in Transient Pipe Flow
Authors: Weyler M. E. , Streeter V. L. , Larsen P. S.
Published: November 2010

Based on experimental observations of pressure changes during hydraulic transients in pipe flow with column separation, a physical model was hypothesized and correlated with the data to provide a semiempirical “bubble shear stress” which can be used to predict the increased momentum loss observed under column separation conditions. The “bubble shear stress” arises from the nonadiabatic expansion and collapse of gas bubbles present throughout the low pressure column separation flow, and is found to be proportional to the strength of passing pressure waves, and a weak function of the amount of gas trapped on the pipe walls.
Theoretical Investigation of the Switching Mechanism in a Bistable Wall Attachment Fluid Amplifier
Authors: Epstein M.
Published: November 2010

A theory based on turbulent jet entrainment properties is presented for the prediction of unsteady end wall switching behavior in a bistable wall attachment fluid amplifier. Good agreement is obtained between theoretically predicted switching times and experimental results. The analysis also indicates the experimentally observed dwell phenomena and computed dwell times compare well with reported experimental values.
Use of Fracture Mechanics in Reactor Vessel Surveillance
Authors: Mager T. R. , Yanichko S. E.
Published: November 2010

This paper presents the basis for utilizing fracture mechanics technology based upon data obtained from small Charpy V-notch specimens incorporated in reactor vessel surveillance programs. Included is a brief background on linear elastic fracture mechanics and a discussion of reactor surveillance programs in general. Data obtained from published literature are organized and an empirical approach is proposed to utilize the fracture mechanics technique in surveillance programs. A typical problem is included to demonstrate that the approach discussed can be successfully applied to nuclear pressure vessel safety analysis.
Frequency Response of Fluid Lines With Nonlinear Boundary Conditions
Authors: Strunk R. D.
Published: November 2010

The harmonic distortion generated when a fluid line is terminated by a nonlinear orifice characteristic is analyzed by using a perturbation method of solution. The perturbation method is shown to be representative of the true phenomenon and to give very good quantitative as well as qualitative information by comparing the results to a numerical solution of the nonlinear equations. The results presented describe the distortion phenomenon as a function of several dimensionless ratios.
Flow in Rotating Straight Pipes of Circular Cross Section
Authors: Ito¯ H. , Nanbu K.
Published: November 2010

The friction factor for fully developed flow in smooth wall straight pipes of circular cross section rotating at a constant angular velocity about an axis perpendicular to its own has been measured in the Reynolds number range from 20 to 60,000. Empirical equations for friction factors for small values of RΩ/R were presented for both laminar and turbulent flow. In the case of laminar flow, an approximate analysis based on the assumption that the flow consists of a frictionless central core surrounded by a boundary layer was presented. The results were in good qualitative agreement with experimental results in regard to the friction factor, velocity distribution in the plane of symmetry and pressure distribution along the circumferential wall of the pipe.