bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Contact Problems of Inflated Cylindrical Membranes With a Life Raft as an Example
Authors: Wu Chien-Heng
Published: November 2010

The class of contact problems involving inflated cylindrical membranes is studied. It is shown that the governing equations can be reduced to quadratures provided that the contact stress is normal to the membrane. As an example, the problem of a loaded life raft is analyzed in detail. It is found that the load on the life raft is a maximum when the life raft is just completely submerged in the water. Moreover, for loads less than the maximum load, there exist two equilibrium states, one floating and one submerged. The floating state, however, is the state of least energy.
Dynamic Response of Cylindrical Shells With Initial Stress and Subjected to General Three-Dimensional Surface Loads
Authors: Liao E. N. K. , Kessel P. G.
Published: November 2010

This paper presents general solutions for both Flu¨gge’s and Donnell’s equations governing the displacements of the midsurface of a thin circular cylindrical shell, simply supported at both ends, of finite length, under initial twoway stress and subjected to general time-dependent surface loads. Analytical solutions are presented to the specific problems of a stationary radial point force and a stationary point couple. A numerical comparison of Donnell’s and Flu¨gge’s theories is made for these specific problems for a wide variety of shell parameters including initial stress. It is found for the case of a dynamic point force or point couple that Donnell’s theory is satisfactory for thin and very short shells (h/a ≤ 0.01 and l/a ≤ 2).
Dynamic Stresses Around Elliptical Discontinuities
Authors: Schroll K. R. , Cheng S. L.
Published: November 2010

The influence of an elliptical discontinuity on the stress distribution in an otherwise uninterrupted and unbounded elastic medium subjected to the passage of both P- and SV-waves is examined. The elliptical scatterer is either empty or filled with a rigid and infinitely dense material. Ratios of the maximum stresses on the elliptical scatterer boundary to the maximum stress of the incident wave are computed to demonstrate the effect of dynamic stress concentrations. Results are presented which show the influence on the stresses of the ellipse eccentricity, the normalized wave number as well as the ratio of nondimensional source distance to wavelength.
The Flow of a Laminar, Incompressible Jet Along a Parabola
Authors: Plotkin A.
Published: November 2010

The flow of a laminar, incompressible jet along a parabola in the absence of an external stream is analyzed using the techniques of second-order boundary-layer theory. The first-order solution is the Glauert wall-jet solution. Second-order corrections in the jet due to the effects of curvature and displacement are obtained numerically after the external flow is corrected to account for the displacement effect. The shear stress at the wall is calculated and it appears that for values of the Reynolds number at which the governing equations are valid the jet does not separate from the parabola.
Thermal Instability in Differentially Heated Inclined Fluid Layers
Authors: Unny T. E.
Published: November 2010

In an inclined adversely heated fluid layer confined between two rigid boundaries in a slot of large aspect ratio it is found that the unicellular base flow in the conduction regime becomes unstable with the formation of stationary secondary rolls with their axes along the line of inclination (x-rolls) for large Prandtl number fluids and axes perpendicular to the line of inclination (y-rolls) for small Prandtl number fluids. However, for angles near the vertical, the curve of the critical Rayleigh number versus inclination for x-rolls rises above that for y-rolls even for large Prandtl number fluids so that in a vertical fluid layer only cross rolls (y-rolls) could develop. The stability equations, as well as the results, reduce to those available for the horizontal fluid layer for which x-rolls are as likely to occur as y-rolls. It is seen that even a small inclination to the horizontal is enough to assign a definite direction for these two-dimensional cells, this direction depending on the Prandtl number. It is hoped that this basic information will be of help in the determination of the magnitude of the secondary cells in the postinstability regime and the heat transfer characteristics of the thin fluid layer.
Prediction of the Flow and Heat Transfer in a Rectangular Wall Cavity With Turbulent Flow
Authors: Chin E. , Rafiinejad D. , Seban R. A.
Published: November 2010

The steady, two-dimensional, constant properly flow and temperature distribution are calculated for turbulent flow in a square cavity over which there is a bounded flow with an initially uniform velocity. This is done by solutions of the finite-difference equations, stabilized for iteration by taking the first derivatives in the “upstream” direction. When such a solution incorporates corrections for the large truncation error produced by taking the derivatives in this way, results are obtained which compare favorably to many aspects of the available experimental data at a Reynolds number of 1.5 × 105. Velocity and temperature distribution are well predicted within the cavity and the shear layer, and wall temperatures are in excellent agreement with experiment over a considerable fraction of the wall area.
Radial Stress Release Phenomena in Plate Impact Experiments: Compression-Release
Authors: Stevens A. L. , Jones O. E.
Published: November 2010

A common objective in designing a postmortem type of plate-impact experiment is to be able to attribute the observable residual effects (such as residual strain, hardness, or dislocation density) primarily to the conditions which existed while the material was in a state of uniaxial strain. In the past it has generally been assumed that effects due to radial stress release phenomena, which are always present in such an experiment, are of secondary importance. In order to test the validity of this assumption, a two-dimensional Lagrangian finite-difference computer program is used to model physical experiments representative of common practice. Target plate dimensions, the target and flyer plate material, and the impact velocity are systematically varied for circular target plates with, and without, guard rings. The results show that in many cases the effects of radial release phenomena are too large to ignore. Conclusions are presented which serve as guidelines for designing experiments to minimize radial release effects.
Nonlinear Analysis of Two-Dimensional Problems in Concrete Creep
Authors: Rashid Y. R.
Published: November 2010

This paper deals with the analysis of plane and axisymmetric problems with concrete-like material behavior where nonuniform transient temperature fields and time-dependent cracking are considered. The material is treated as an aging viscoelastic isotopic substance characterized in its uncracked state by the constant Poisson’s ratio and the uniaxial creep function which is shown to obey an extended form of the time-temperature shift. A cracking criterion is postulated whose ingredients are a failure surface expressed in terms of principal strains and an interactive curve which takes stresses and strains into account. The stress-strain relations are formulated for discontinuous material behavior permitting crack formation in three orthogonal directions with arbitrary crack histories. The numerical analysis is obtained within the framework of the finite-element method and a step-by-step integration procedure. The method is applied to a concrete model and comparisons between analysis and experiment are given.
Finite Inflation of a Bonded Toroid
Authors: Hsu K. H.
Published: November 2010

A general approach to the numerical solutions for axially symmetric membrane problem is presented. The formulation of the problem leads to a system of first-order nonlinear differential equations. These equations are formulated such that the numerical integration can be carried out for any form of strain-energy function. Solutions to these equations are feasible for various boundary conditions. In this paper, these equations are applied to the problem of a bonded toroid under inflation. A bonded toroid, which is in the shape of a tubeless tire, has its two circular edges rigidly bonded to a rim. The Runge-Kutta method is employed to solve the system of differential equations, in which Mooney’s form of strain-energy function is adopted.
Transient Thermal Waves in the General Theory of Heat Conduction With Finite Wave Speeds
Authors: Norwood F. R.
Published: November 2010

The linear version of the general theory of heat conduction is employed to study the problem of a half space subjected to step time inputs of temperature. The solution is obtained by the use of the Laplace transform on time and the sine transform on space. Exact solutions, wave-front, and long-time approximations are obtained. The long-time solutions satisfy the classical heat equation. It is shown that stable solutions may be obtained under more relaxed conditions than those prescribed by the general theory.
On Free Vibrations at Temperature-Dependent Material Properties and Transient Temperature Fields
Authors: Olsson U.
Published: November 2010

The influence of the temperature-dependence of the material properties on the free vibrations of transiently heated structures is investigated. Analytical solutions are given for linear, exponential, and harmonic temperature variations when the material damping parameter, Poisson’s ratio, and Young’s modulus depend on the temperature.
Transient Stress Concentration by a Spherical Cavity in an Elastic Medium
Authors: Huang H. , Wang Y. F.
Published: November 2010

The problem of transient scattering of a plane step dilatational wave by a spherical cavity in an elastic medium is solved by a Laplace-transform-series-solution technique. The solution is obtained in the form of rational functions of the transform variable suitable for facilitating exact inverse transformation. The convergence and effectiveness of the series solution for accurate computation of the time history of the transient stress concentration at the cavity boundary are examined. It is found that, except in the immediate neighborhood of the defracted stress wave front, the series solution converges quite fast and it suffices to use only two (first and third) terms to calculate the maximum hoop stress due to the incidence of a step dilatational wave.
Pulse Propagation in Straight Circular Elastic Tubes
Authors: Goldsmith W. , Lee P. Y. , Sackman J. L.
Published: November 2010

An experimental investigation of elastic waves produced by the longitudinal impact of strikers with straight 2024 aluminum tubes of 1-in. dia and wall thicknesses of 0.035 in. (thin-walled), 0.095 in. (medium thick-walled), and 0.5 in. (solid bar) was performed by means of the Hopkinson bar technique. For most of the tests the strikers consisted of 1/2-in-dia steel balls; however, 1/4-in-dia, 3/16-in-dia and 1/8-in-dia steel balls were also used to permit variation in pulse duration. Both central and eccentric impact were achieved by firing the striker from an air gun at a predetermined pressure against the carefully positioned target; the initial velocity of the striker was measured whenever necessary. Longitudinal strain records of the resulting pulse from positions both on the inside and outside surfaces of the hollow specimens and on the outside of the solid bar were obtained by using strain gages of either foil or semiconductor type; some transverse strain histories were also measured concurrently. The transient longitudinal strains were predicted theoretically by solving the one-dimensional Rayleigh-Love equation of wave propagation in a semi-infinite tube with the aid of a computer program. The input to the program consisted of the measured strain record at the first gage station. Reasonable agreement between the data and the results of these calculations was obtained. An experimental investigation of the effect of shortening the pulse duration, the relation between the transverse and longitudinal strain at the same position, and the nature of the antisymmetrical component in the eccentric shots was also undertaken.
On the Determination of the Centers of Twist and of Shear for Cylindrical Shell Beams
Authors: Reissner E. , Tsai W. T.
Published: November 2010

We consider the problem on the basis of a definition of the centers of shear and of twist in terms of influence coefficients for end-loaded cantilever beams. We determine the influence coefficients approximately by combining the Saint Venant torsion and flexure solutions with an appropriate version of the principle of minimum complementary energy. We apply this method, considering the beam as a cylindrical shell. We find among other things a formula for closed-cross-section shells which includes as special cases the strength-of-materials formula for open-cross-section shells, as well as a formula for variable-thickness flat plates. Problems of particular theoretical interest for which solutions are given concern rectangular box beams and circular cylindrical shells with circumferentially varying properties.
Finite Fringe Holographic Interferometry Applied to a Right Circular Cone at Angle of Attack
Authors: Jagota R. C. , Collins D. J.
Published: November 2010

The successful application of holography to the study of three-dimensional flow fields due to phase objects has been reported in the literature. The present report extends this technique to the study of density fields around opaque bodies as would normally be encountered in wind tunnel experiments. The density field around a 10-deg half-angle cone at 0 and 10-deg angle of attack has been investigated by means of the finite fringe holographic interferometry. The three-dimensional density field obtained from the reduction of the interferograms was found to agree with that obtained from an analytical solution of the governing equations.
A Procedure for Applying the Extended Kantorovich Method to Nonlinear Problems
Authors: Soong Tsai-Chen
Published: November 2010

The Kantorovich method as extended by Kerr is an elegant iterative technique applicable to some multivariable problems in applied mechanics. Kerr has shown, in a clamped rectangular plate example, that a one-term solution agreed closely with existing results obtained by more elaborate means. However, the analyzed problems were limited to linear formulations only. The present paper suggests a general purpose nonlinear method, which follows the iterative procedure of the extended Kantorovich technique, to derive approximate solutions of problems that involve simultaneous, multifunctional nonlinear partial differential equations. The solutions are analytic and require much less numerical efforts than, for instance, a corresponding nonlinear finite-difference equation method for comparable accuracy. An example is given for the deflection solutions of a plate under lateral pressure, by using von Karman’s large-deflection plate equations. Numerical calculations showed that a one-term solution of the present method agreed within 0.03 percent with the result of a nonlinear finite-difference method extrapolated to infinite nodes. A highly accurate one-term solution which is continuous and differentiable, sometimes expressible in closed forms, would be valuable in nonlinear analysis as well as in linear problems mixed with local nonlinear, postbuckled regions.
Large Axisymmetric Deformation of a Nonlinear Viscoelastic Membrane Due to Spinning
Authors: Wineman A. S.
Published: November 2010

The problem of a viscoelastic membrane undergoing large planar deformation due to spinning is solved. The membrane, rigidly bonded at its inner boundary and traction-free at the outer, consists of a nonlinear viscoelastic solid whose behavior is modeled by a nonlinear single integral constitutive equation. The model includes the possibility that the relaxation time is influenced by the amount of stretching. Spinning is considered to be sufficiently slow so that shear effects can be neglected. The formulation uses radial and circumferential stretch ratios as dependent variables. These satisfy a system of first-order nonlinear partial-differential integral equations. The numerical procedure at each time step obtains the current spatial derivatives of the stretch ratios in terms of the current and previously determined stretch ratios. This gives essentially a first-order nonlinear system of differential equations, of the same structure as that obtained in the elastic version of the problem [1], which is integrated numerically. Solutions are obtained for both strain-dependent and strain-independent relaxation times.
Determination of the Unloading Boundary in Transverse Impact of an Elastic-Plastic String
Authors: Tuschak P. A. , Schultz A. B.
Published: November 2010

When a thin, elastic-plastic wire is transversely impacted, both longitudinal and transverse loading waves propagate. For certain types of excitation, unloading waves also propagate, and they overtake and interact with the loading waves. These interactions occur on moving boundaries, and a knowledge of the locations of these boundaries is needed for the solution of wave-propagation problems of this kind. An analytical technique and a numerical technique for the solution of such problems in long wires is presented. Examples, including response to impact by a finite mass, are given to illustrate the techniques. For finite length wires, the techniques will determine the initial portion of the solution.
Torsional Waves in an Infinite Elastic Solid Containing a Spheroidal Cavity
Authors: Datta S. K.
Published: November 2010

A low-frequency analysis is presented here for the axisymmetric problem of diffraction of torsional waves by an oblate spheroidal cavity in an isotropic homogeneous elastic medium. The method used gives a complete low-frequency expansion of the scattered field in terms of associated Legendre functions, instead of spheroidal wave functions that one gets by the method of separation of variables. This makes the numerical computation much simpler. Graphs and tables are presented for the displacement distribution on the cavity surface and the nonzero shear stress at the end of the major axis of the spheroid. It is found that for low frequencies and for the values of the ratio (b/a) of the minor and major axes of the spheroid considered here the absolute value of the ratio of the nonzero dynamic and static shear stress evaluated at the end of the major axis is independent of b/a for confocal spheroids. An estimate is also given for the radius of convergence of the low-frequency expansion.
The Stress and Deformation in Mild Steel During Axisymmetric Necking
Authors: Kaplan M. A.
Published: November 2010

Closed-form solutions for the stress and deformation fields near the minimum section of the neck are obtained for a mild steel rod subject to axial extension by tensile loads. The procedure involves the use of an experimental result together with the incompressibility and symmetry conditions to find the deformations independently of the stresses. The stresses are then determined with the Levy-Mises flow equations without the use of a specific work-hardening rule. The solution, because of a simplifying assumption, is not valid throughout the entire plastic flow region. Experimental evidence indicates, however, that the region of validity extends well beyond the fracture region. The results enable the tensile test to be used to provide a complete description of material behavior until fracture. To accomplish this, it is necessary to measure the axial load and the radius and radius of curvature at the minimum section. As an example, the work-hardening characteristics of mild steel are determined under the usual work or strain-hardening hypothesis. The application of the results to ductile metals, other than mild steel, is briefly discussed.
Continuous Bond Failure Due to a Moving Force
Authors: Jahanshahi A.
Published: November 2010

Within the framework of the two-dimensional theory of elastodynamics a closed-form, quasi-stationary, solution is given to the problem of continuous failure of bond between an elastic half space and a rigid body. The bond failure is due to a line force moving at the interface.
Ellipsoidlike Deformations of Tubelike Balloons—Asymptotic Solution With Boundary Layer
Authors: Wu Chien-Heng
Published: November 2010

A family of axially symmetrical balloons characterized by a small slenderness parameter ε is considered. The balloons are inflated by pressures proportional to ε−1. It is shown that as ε tends to zero the inflated balloon approaches to an ellipsoidal surface of revolution.
A Numerical Study of Rotationally Symmetric Flow of Second-Order Fluid
Authors: Balaram M. , Luthra B. R.
Published: November 2010

This is a numerical investigation of the steady flow produced by an infinite rotating disk when the second-order fluid at infinity is in a state of solid rotation. The flow field is determined when the fluid at infinity is rotating in the same sense as that of the disk. The use of this viscometric representation limits the result to weakly viscoelastic fluids. The numerical computations obtained indicate that the question of increased or decreased total (radial plus tangential) wall stresses due to the presence of elasticity depends on the flow parameter S(S > 1 or S < 1, indicate that the fluid at infinity having a faster or slower angular velocity compared with that of the disk). We found that the total wall stress is higher or lower when compared with a Newtonian fluid depending on S > 1 or S < 1, respectively. With increasing |α| (as the fluid becomes more non-Newtonian), the total wall stress is increased or decreased when S < 1 or S > 1.
Propagation of Stress Gradient Through an Inclusion—Part 2
Authors: Ting T. C. T. , Chou Shun-Chin
Published: November 2010

This is the second of a two-part study on the propagation of stress gradient in composite materials. In this paper the propagation of stress gradient behind the wave front in an elastic medium is investigated. It is shown that the stress gradient does not maintain the same sign as the wave front is propagated. The implication of this result is that the plastic yield can occur at places behind the wave front before it occurs at the wave front even if the initial wave has a discontinuous rise in stress at the wave front followed by a gradual decrease in magnitude behind the wave front. Numerical examples are presented for plane and circular pressure waves propagated through an inclusion of various shapes.
Application of the Generalized Airy Stress Function to Problems on Elastic Vibrations of Hollow Cylinders
Authors: Bourgois R. A.
Published: November 2010

This Note concerns the use of the generalized Airy stress function, introduced by Radok [1], for dynamic plane-stress and plane-strain problems with axial symmetry. The solution of the basic equations for stress waves may be accomplished by Laplace transformation. The case of the dynamic elastic response of a thick cylinder to internal axial symmetric impact loads will be studied.
Work Bounds and Associated Deformation of Cyclically Loaded Creeping Structures
Authors: Ponter A. R. S. , Williams J. J.
Published: November 2010

In this paper the deformations of a beam subject to cyclic bending moment and a thick-walled cylinder subject to cyclic internal pressure are investigated for an elastic/time hardening/perfectly plastic material. Bounds [1, 2] are computed on the work done by the applied loads over a cycle when the material has reached a cyclic state of stress. The bounds provide the extreme states when the cycle time is either large or small compared with a characteristic time of the material. It is found that the difference between the bounds is generally very small. This result is discussed in relation to recent work by Williams and Leckie [3].
Refinements in the Approximate Analysis of Web-Stiffened Sandwich Structures
Authors: Chen Y. N. , Cicero F. , Kempner J.
Published: November 2010

Presented in this work is a method of construction of approximate functions in connection with the energy formulation of certain eigenvalue problems of web-stiffened sandwich structures. The construction is based upon the method of Young together with a group of fundamental functions deduced from Timoshenko’s flexural equations for elastic beams. The analysis is exemplified and numerically tested by the eigenvalue problems of free vibrations and buckling of one-dimensional sandwich structures. Results indicate that the present method possesses advantages over similar constructions oriented from the classical flexural normal modes of Bernoulli-Euler.
Reflection and Refraction of Weak Elastic-Plastic Waves
Authors: Jahsman W. E.
Published: November 2010

The method of singular surfaces is used to obtain expressions for the amplitudes of weak discontinuities reflected from or transmitted across interfaces between solids of dissimilar elastic-plastic properties. Here weak discontinuities are taken to mean discontinuities in derivatives of stress, strain, and velocity components. These discontinuities occur across singular surfaces which propagate at characteristic wave speeds and are referred to as weak waves. Analogous to elastic wave propagation results, two reflected and two refracted fronts satisfy stress and velocity continuity conditions in media prestressed into the plastic range. However, the speeds of these fronts are generally less than the elastic dilatational and shear wave speeds, and the amplitudes of the reflected and refracted discontinuities can differ dramatically from their elastic counterparts. Numerical examples are considered in which weak waves are reflected from rigid and stress-free surfaces. The medium through which the waves pass is prestressed in the direction parallel to the reflecting surface. Results are presented which show the dependence of the reflected velocity and stress discontinuity amplitudes on the angle of incidence of the oncoming wave. As compared to elastic wave propagation, the presence of plastic deformation reduces the amplitude of the reflected front which travels at the speed of the incident front and raises the amplitude of the other reflected front. The most pronounced effect of plastic deformation is found when the incident front travels at the slow wave speed (SV-type wave). In this case, the critical angle of incidence (beyond which reflected weak waves alone cannot satisfy the boundary conditions) decreases to 22.5 deg from the elastic value of 30 deg when Poisson’s ratio is 1/3. It is conjectured that elastic-plastic surface waves may be needed to satisfy the interface conditions at incidence angles beyond this critical value.
Plane Solutions for Traction Problems on Orthotropic Unsymmetrical Wedges and Symmetrically Twinned Wedges
Authors: Kuo M. C. , Bogy D. B.
Published: November 2010

The plane traction problem for a composite wedge formed from two identical orthotropic wedges is solved by use of the complex function representation of the plane solution for anisotropic materials in conjunction with the Mellin transform. As a preliminary to this solution the traction problem for a single unsymmetrical orthotropic wedge is also studied. For both problems the stress concentration at the wedge apex is examined and the dependence of the order of the singularity on the wedge angle and material constants is exhibited graphically.
Boundary Conditions for the Turbulent Mixing Layer Between Two Parallel Streams
Authors: Unny T. E. , Hayakawa Norio
Published: November 2010

The boundary conditions of the boundary-layer problem between two parallel turbulent streams are investigated solving higher-order terms of the inner and outer boundary-layer expansion. It is shown that the assumption that the eddy viscosity is proportional to longitudinal distance x fails to yield the third boundary condition of the boundary-layer problem. In this paper this boundary condition has been derived based on the consideration that the eddy viscosity attains a constant value at large but finite distance. The result applies to compressible as well as incompressible flow.
A Numerical Method for Predicting the Dynamic Performance of Electromechanical Relays
Authors: Elliott G. L.
Published: November 2010

This paper describes a method for estimating the dynamic characteristics of electromagnetic relays. The equations of motion are formulated based on a constant core reluctance model magnetic circuit and then solved using an extended de Vogelaere method. Good agreement is found between the predicted values and those measured in practice.
Time Base Errors in Video Tape Packs
Authors: Mukherjee S.
Published: November 2010

This is a study of time base errors in video tape packs. The tape is viscoelastic. If a wound pack is stored at a constant temperature or subjected to environmental temperature cycles, the stresses relax and the tape creeps. Consequently, inelastic strains in the tape during playback cause distortion in the pictures. Time base error is a measure of inelastic longitudinal strain in the tape at playback. In this paper a mathematical model is developed to predict the effect of storage time, winding pattern, and pack size on time base error. Both the tape and hub are assumed elastic under hydrostatic loading and viscoelastic in shear. A four element fluid model is used for the tape and a Maxwell fluid model is used for the hub. Some comparison with experiments shows reasonable correlation.
On the Buckling of Axially Compressed Imperfect Cylindrical Shells
Authors: Arbocz J. , Sechler E. E.
Published: November 2010

A theoretical investigation of the buckling behavior of imperfect isotropic shells with edge constraints and under axial compression was carried out. The nonlinear Donnell equations for imperfect isotropic shells have been reduced to an equivalent set of nonlinear ordinary differential equations. The resulting two-point boundary-value problem was solved numerically by the “shooting method.” The use of this method made it possible to investigate how the axial load level at the limit point is affected by the following factors: the rigorous enforcing of the experimental boundary conditions, the prebuckling growth caused by the edge constraint, the overall symmetry of the response pattern, and the orientation and shape of the axisymmetric and asymmetric imperfection components.
On the Inflation of a Plane Nonlinear Membrane
Authors: Feng W. W. , Huang P.
Published: November 2010

The deformed configurations of an inflated flat nonlinear membrane are obtained by the minimum potential energy principle. The deformed configurations of the membrane are assumed to be represented by a series of geometric admissible functions with unknown coefficients. The unknown coefficients that minimize the total potential energy of the deformed membrane are determined by Fletcher and Powell’s [1] method. The strain-energy-density function for the numerical calculations is assumed to have the Mooney form. The results for a particular case when the Mooney membrane reduces to the neo-Hookean membrane, agree with the previous results obtained by numerical integration of the corresponding equilibrium equations.
A Rigid Punch in Contact With a Nonhomogeneous Elastic Solid
Authors: Kassir M. K. , Chuaprasert M. F.
Published: November 2010

This paper treats the axisymmetric problem of a rigid punch in contact with a nonhomogeneous elastic isotropic solid whose modulus of rigidity is a continuous function of the depth while the other elastic parameter, Poisson’s ratio, is assumed to be constant. An integral transform solution is given which reduces the formulation of the problem to a Fredholm integral equation of the second kind which is amenable to numerical treatment. The physical quantities of interest are studied in detail and illustrative numerical results for several punch profiles are obtained and exhibited in tabulated and graphical form.
Elastodynamic Stress-Intensity Factors for Tearing of a Half Plane
Authors: Achenbach J. D. , Varatharajulu V. K.
Published: November 2010

This paper is concerned with the propagation of a crack which emanates under an arbitrary angle from a free surface, when that surface is subjected to antiplane mechanical disturbances. The elastodynamic problem is solved by the method of homogeneous solutions, which is based on the observation that for the externally applied disturbances that are considered here the particle velocity is self-similar. The shear stress in the vicinity of the crack tip is determined, and a stress-intensity factor is computed. For various values of the crack propagation velocity the dependence of the stress-intensity factor on the angle of crack propagation is studied. As the velocity of crack propagation increases, the maximum value of the stress-intensity factor is still obtained for symmetrical crack propagation. The singularities at the corners of the wedge-shaped regions neighboring the propagating crack are also examined. It is shown that for small values of the crack propagation velocity, the elastodynamic results reduce to corresponding quasi-static solutions.
Bounding Solutions for a Plate Subjected to Variable Surface Temperature
Authors: Ponter A. R. S. , Leckie F. A.
Published: November 2010

The paper considers the problem of a plate subjected to constant average in-plane stresses and temperature variations through the thickness of the plate. The material is described by a linear elastic/time-hardening viscous/perfectly plastic idealization. We show that the pertinent phenomenon which occurs due to a variable cyclic temperature history may be exhibited by computing bounding solutions which correspond to very fast and very slow cycling. This problem is typical of the situation which occurs in design of nuclear fuel cans and pressure vessels.
The Wrinkled Axisymmetric Air Bags Made of Inextensible Membrane
Authors: Wu Chien H.
Published: November 2010

The wrinkling phenomenon is a consequence of the presence of a negative principal stress resultant. This condition, together with certain geometric compatibility conditions, is used to determine the locations and geometry of wrinkled zones. The governing equation is nonlinear but can be reduced to a quadrature. The shape of the air bag without azimuthal stress resultant is determined in terms of an elliptic integral.
Bearing Capacity of a Coulomb Plate on Elastic Foundation
Authors: Mohaghegh M. M. , Coon M. D.
Published: November 2010

The bearing capacity of an infinite plate resting on elastic foundation is determined assuming that the plate material is rigid-plastic satisfying the Coulomb yield criterion. The sandwich idealization of the plate is utilized and the Coulomb criterion is developed for this plate. The bearing capacity is determined using the method of limit analysis. The analysis shows that the plastic bending of the Coulomb plate is associated with the development of compressive forces which increase the limit moment and therefore the bearing capacity. An example of applying the analysis results is given by determining the bearing capacity of floating ice sheets.
Propagation of SH-Waves Through a Fiber-Reinforced Composite-Elliptic Cylindrical Fibers
Authors: Datta S. K.
Published: November 2010

Propagation of SH-waves through a fiber-reinforced composite has been considered. Fibers are taken to be elliptic in cross section and are assumed to be randomly distributed. It has been shown that the medium behaves like a homogeneous orthotropic one if the major axes of the ellipses are oriented in a particular direction. Elliptic cavities and Griffith cracks have been treated as special cases. Numerical results are presented for the average rigidities and also shear stresses on a cavity.
Elastodynamic Near-Tip Stress and Displacement Fields for Rapidly Propagating Cracks in Orthotropic Materials
Authors: Achenbach J. D. , Bazˇant Z. P.
Published: November 2010

The near-tip angular variations of elastodynamic stress and displacement fields are investigated for rapid transient crack propagation in isotropic and orthotropic materials. The two-dimensional near-tip displacement fields are assumed in the general form rp T(t, c) K(θ, c), where c is a time-varying velocity of crack propagation, and it is shown that p = 0.5. For isotropic materials, K(θ, c) is determined explicitly by analytical considerations. A numerical procedure is employed to determine K(θ, c) for orthotropic materials. The tendency of the maximum stresses to move out of the plane of crack propagation as the speed of crack propagation increases is more pronounced for orthotropic materials, for the case that the crack propagates in the direction of the larger elastic modulus. The angular variations of the near-tip fields are the same for steady-state and transient crack propagation, and for propagation along straight and curved paths, provided that the direction of crack propagation and the speed of the crack tip vary continuously.
Dynamic Stability of Cylindrical Shells Under Step Loading
Authors: Tamura Y. S. , Babcock C. D.
Published: November 2010

A study has been made to determine the dynamic stability of an imperfect circular cylindrical shell subject to a step loading in the axial direction. In the analysis, the radial displacement of the shell is approximated by a finite degree-of-freedom system. The dynamic analysis includes not only the effect of the radial inertia, but also, in an approximate manner, that due to the axial inertia. The critical loads are determined by numerical integration of the equation of motion. Compared with the static case, there is a significant reduction of the dynamic buckling load for the high wave number range of the radial modes. It is concluded that due to frequency coupling between axial and radial motions, the axial inertia plays an essential role in characterizing the dynamic instability of a finite length shell.
On the Constitutive Equations of Biological Materials
Authors: Demiray H.
Published: November 2010

This paper deals with a simple possible form of the strain-energy function for biological tissues which are assumed to be transversely isotropic. Also the solution of a problem is studied and the result is compared with experiments.
The Plane Solution for Joined Dissimilar Elastic Semistrips Under Tension
Authors: Bogy D. B.
Published: November 2010

The problem is reduced to a system of two singular integral equations for determining the interface slope and shear stress. The dominant part of the system is analyzed to determine the order of the stress singularly and its dependence on the elastic constants. The equations are then solved numerically for several chosen composites, and the interface slope and traction are exhibited graphically. The solution should be relevant in studying adhesive joints by means of the simple tension test.
Stress Analysis for a Double Lap Joint
Authors: Keer L. M. , Chantaramungkorn K.
Published: November 2010

The problem of a double lap joint is analyzed and solved by using integral transform techniques. Singular integral equations are deduced from integral transform solutions using boundary and continuity conditions appropriate to the problem. Numerical results are obtained for the case of identical materials for the cover and central layers. Stress-intensity factors are calculated and presented in the form of a table and contact stresses are shown in the form of curves for various values of geometrical parameters.
Thermoelastic Vibration and Damping for Circular Timoshenko Beams
Authors: Shieh R.-C.
Published: November 2010

Within the framework of the theories of coupled linear thermoelasticity and Timoshenko beams, the vibration and thermoelastic damping (with emphasis on the transverse ones) of circular cross-section beams are studied. The governing equations are derived for the case of general mechanical boundary conditions and special thermal boundary conditions that follow the Newton surface heat transfer law. A variational principle governing the eigenfunctions associated with an eigenvalue is formulated. An exact solution, together with the thermoelastic damping coefficient, is obtained for the case of transverse vibrations of a simply supported beam with lateral surfaces thermally insulated and end surfaces kept at constant temperature. Numerical results, together with the discussion for the first two eigenvalues and the thermoelastic damping coefficients, are also presented.
A Modal Analysis for the Response of Linear Gyroscopic Systems
Authors: Meirovitch L.
Published: November 2010

This paper presents a new modal analysis that permits the derivation of closed-form response of linear gyroscopic systems in a manner similar to that in which the classical modal analysis permits the derivation of the response of natural elastic systems. The method has important implications in the dynamics and control of rotating systems. As an illustration, the response of a spinning rigid body containing flexible parts is derived. This represents the first time that the response of a linear gyroscopic system to external excitation is derived in closed form.
Nonlinear Spatial Instability of a Film Coating on a Plate
Authors: Agrawal S. K. , Lin S. P.
Published: November 2010

The problem of nonlinear hydrodynamic stability of a film coating on a surface subject to spatially varying disturbances is formulated and solved. The characteristics of the wavy surface of the film resulting from the nonlinear stability are predicted and compared with the known experimental observations.
Flow Through a Deformable Porous Material
Authors: Beavers G. S. , Wilson T. A. , Masha B. A.
Published: November 2010

A model is presented to describe the one-dimensional flow of an incompressible fluid through a deformable porous material. The model is based on the Forchheimer extension of the Darcy law for flows through incompressible media, where the Forchheimer coefficients are functions of the local stress. Experiments to determine the stress-dependence of the coefficients for polyurethane foam specimens are described. The coefficients are then used in the model to predict the mass flow rate through long polyurethane specimens as a function of the applied pressure difference across the material. The predictions of the model are compared with experimental observations.
Macroscopic Streamline Integral Relations for Two-Phase Flows
Authors: Drew D. A.
Published: November 2010

A spout-fluidized bed is an example of a situation where a nonuniform fluid flow through a bed of particles causes particle circulation. Several integral relations are derived from a steady, two-dimensional two-phase flow model. The vorticity of the particle motion enclosed by a particle streamline is shown to be equal to the fluid vorticity enclosed by that streamline. The net flux of fluid vorticity through a particle streamline is shown to be equal to zero. The pressure drop along a fluid streamline is related to the net drag force along that streamline. The net flux of particle vorticity through a fluid streamline is given in terms of the pressure drop. Implications of these relations to the mechanics of particle-fluid flows are discussed. Relations giving the particle vorticity in terms of an integral of the fluid vorticity, and vice versa, are presented. A possible numerical scheme for calculation of the flow fields is discussed.
On the Unconditional Stability of an Implicit Algorithm for Nonlinear Structural Dynamics
Authors: Belytschko T. , Schoeberle D. F.
Published: November 2010

In this paper an implicit Newmark β-method with iterations for nonlinear structural dynamics is described; the algorithm is identical to standard algorithms except that a new convergence criterion is employed. A discrete energy is defined and it is shown that this discrete energy is bounded regardless of the size of the time step; this is a sufficient condition for the unconditional stability of the algorithm for nonlinear material problems. Numerical examples are given for problems with both geometric and material nonlinearities.
Axially Symmetric Stress Distributions in Elastic Solids Containing Penny-Shaped Cracks Under Torsion
Authors: Pasha M. L.
Published: November 2010

We present the axially symmetric stress distributions in elastic solids containing a pair of axially symmetric penny shaped cracks when the infinite elastic medium is kept under torsion. We derive the integral representation formula for the torsion function and the expressions for the stress-intensity factors.
Thermoelasticity of Cylindrically Anisotropic Generally Laminated Cylinders
Authors: Padovan J.
Published: November 2010

The effects of cylindrically curvilinear mechanical and thermal material anisotropy on the stationary thermoelastic fields of generally laminated cylinders are studied. To model the stated problem, each individual ply of the cylinder is considered to be composed of both mechanically and thermally cylindrically anisotropic media whose governing fields satisfy the 3-D elasticity and conduction equations. Based on finite and infinite Fourier integral transforms together with the use of complex adjoint differential operators and complex power series expansions, a nonhomogeneous pseudo-stiffness procedure is used to develop the general solution form for the stated problem. Through the use of the model and its solution, several numerical experiments are presented which emphasize the significant effects of cylindrical material anisotropy on the governing fields of several different types of laminate configuration.
A Parametric Approach to Cyclic Creep
Authors: Radhakrishnan V. M.
Published: November 2010

Investigations have been carried out to study the effect of oscillating stress on the strain accumulation in pure aluminum at elevated temperature. The creep rate under the oscillating stress has been found to increase with increasing value of the alternating component of the stress and is somewhat higher than the steady-state creep rate corresponding to the maximum stress, in the range of temperature used. The rupture time is inversely proportional to the cyclic creep rate. A model for obtaining the reference stress has been proposed and based on the data obtained, a parametric approach is presented.
The Effects of Main-Flow Radial Velocity on the Stability of Developing Laminar Pipe Flow
Authors: Shen F. C. T. , Chen T. S. , Huang L. M.
Published: November 2010

In studying the stability due to axisymmetric disturbances of the developing flow of an incompressible fluid in the entrance region of a circular tube, a generalized version of the Orr-Sommerfeld equation was derived which takes account of the radial velocity component in the main flow. The new terms in the generalized Orr-Sommerfeld equation are inversely proportional to the Reynolds number. The resulting eigenvalue problem consisting of the disturbance equation and the boundary conditions was solved by a direct numerical integration scheme along with an iteration procedure. Neutral stability curves and critical Reynolds numbers at various axial locations are presented. A comparison of the present results with those from the conventional Orr-Sommerfeld equation in which the effect of the main-flow radial velocity is neglected, shows that inclusion of the radial velocity contributes to a destabilization of the main flow.
Potential Flow Model for an Impulsively Started Circular Cylinder
Authors: Yang H. T. , Bar-Lev M.
Published: November 2010

The initial phase of the flow field around an impulsively started circular cylinder is modelled by a pair of symmetric potential vortices in the wake. The rate of increase of the vorticity and of the separation angle are related to the unsteady laminar boundary layer adjacent to the cylinder. The resulting system of three ordinary differential equations with proper initial and matching conditions are solved numerically. The computed flow configuration and time history of drag are compared with available experiments.