bluuebunny/crossref_metadata_2025 huggingface dataset:
Growth Instability During Nonuniform Directional Solidification of Pure Metals
Authors: Richmond Owen , Hector Louis G. , Fridy Joseph M.
Published: April 2008

Solidification of a pure metal against a flat mold surface is examined using a nonuniform thermohypoelastic beam. Heat is removed with a spatially periodic heat flux superimposed onto uniform cooling, which leads to irregular growth of the casting. The associated nonuniform temperature field also produces nonuniform deformation in the casting which in time may lead to air gap nucleation along the mold/casting interface. Air gap nucleation is defined as the circumstance where the local mold/casting interface pressure falls to zero. Unstable growth occurs when such air gaps nucleate beneath thickness minima, thus further reducing heat transfer at these positions, and dramatically amplifying the existing thickness nonuniformity. The time to onset of instability depends upon material properties such as density, latent heat, thermal conductivity, elastic constants, and coefficient of thermal expansion as well as upon process parameters such as cooling rate, fluid pressure, and wavelength of the periodic heat flux.
A Finite Deformation Theory of Viscoplasticity Based on Overstress: Part I—Constitutive Equations
Authors: Nishiguchi I. , Sham T.-L. , Krempl E.
Published: April 2008

The viscoplasticity theory based on overstress (VBO) is extended to finite deformation (FVBO). Yield surfaces and loading/unloading conditions are not part of this theory which represents creep, relaxation, and rate sensitivity in a “unified” way. Additive decomposition of the rate of deformation into the elastic and the inelastic parts is assumed. For the elastic part, the hypoelastic relation is used. For the inelastic part, the flow law of VBO is augmented by a term quadratic in the overstress together with a modified Jaumann stress rate which jointly or separately allow the modeling of second-order effects.
An Incremental Plastic Analysis of Multiphase Materials
Authors: Li Y. Y. , Chen Y.
Published: April 2008

The determination of the elastoplastic behavior of multiphase materials such as metallic alloys or steels during phase transformation is a complex problem. This incremental method is aimed at applications for composites having several phases each with different plastic behaviors and also materials undergoing phase transformation. We assume the decomposition of all strain, in the inclusion as well as in the matrix, into elastic and plastic components. Relations between various incremental stresses and strains are established through the use of the elastic moduli of the matrix and inclusions. The elastic components of the incremental stress-free strain and perturbed strain are related by an effective tangent tensor. A sample calculation was performed for a composite of epoxy matrix reinforced by silica particles. Comparisons made with experimental results existing in the literature show reasonable agreements.
The Singularity Strength at the Apex of a Wedge Undergoing Finite Deformations
Authors: Duva J. M.
Published: April 2008

Herein we establish general formulae for characterizing the singular behavior at the apex of a wedge of nonlinear material of arbitrary size undergoing plane-strain finite deformation. Two sets of boundary conditions are considered: (a) both wedge flanks are clamped, and (b) one flank is clamped and the other free. The mode of deformation is obtained in one simple case for illustration.
Modifications of Series Expansions for General End Conditions and Corner Singularities on the Semi-Infinite Strip
Authors: Kim Yoon Young , Steele Charles R.
Published: April 2008

Modified series expansions are used to study semi-infinite isotropic elastic strip problems for general end conditions and corner singularities. The solutions of strips with mixed lateral edges are used as the expansion sets of the end displacement and stress, and an end stiffness matrix, the relation of harmonics of the end displacement and stress, is formed. The present end stiffness matrix approach, an extension to static strip problems of the method by Kim and Steele (1989, 1990) for time-harmonic wave propagation in a semi-infinite cylinder, is effective due to the asymptotic behavior of the stiffness matrix. Also presented is a technique for handling the corner singularities, which is based on the asymptotic analysis of the expansion coefficients of the end stresses. With this, the order and strength of the singularities are determined, local oscillations are virtually suppressed, and converging solutions are obtained. Some numerical examples are given to demonstrate the effectiveness of the approach.
Delamination Specimens for Orthotropic Materials
Authors: Suo Zhigang
Published: April 2008

A semi-infinite crack in an infinite strip of orthotropic material is analyzed. Analytic expressions for mixed-mode stress intensity factors are derived with only parameter undetermined, which is then extracted from numerical solutions to integral equations. The results are relatively simple and complete, and provide the flexibility to simulate a wide range of practical problems, such as fracture specimens and edge delamination phenomena of woods and fiber-reinforced composites. As an illustration, specimens with transverse splitting from notches are analyzed based on the general solution. The validity of using solutions for an isotropic material to calibrate some testing geometries of orthotropic materials is discussed.
Axisymmetric Stress Analysis of a Broken, Debonded Fiber
Authors: Mbanefo U. , Westmann R. A.
Published: April 2008

The study of a single broken fiber embedded in an infinite elastic matrix subjected to a uniform far-field strain is presented. The solution, which accounts for the presence of interface debonding in the neighborhood of the fiber fracture, is carried out within the framework of classical elastostatics. The boundary value problem is reduced first to a pair of dual integral equations, and then to a Cauchy singular integral equation which is solved numercially. Results are presented illustrating the dependence of the fiber axial force and the interface shear stress upon the geometrical and material parameters.
Axisymmetric Vibrations of Circular Plates on Tensionless Elastic Foundations
Authors: Celep Zekai , Turhan Dogˇan
Published: April 2008

The present study deals with the axisymmetric vibrations of a circular plate subjected to a concentrated dynamic load at its center. The plate is assumed to be supported on an elastic foundation that reacts in compression only. At first the static solution is obtained and contact radius is determined. Later, this is used as an initial configuration of the forced vibrations. The forced vibrations are assumed to be due to the time dependency of the load. The solution is carried out by Galerkin’s method and by using modal functions of the completely free plate. Numerical results are illustrated in figures for stepwise change of the loading.
Random Vibrations of Viscoelastic Laminated Plates
Authors: Cederbaum G.
Published: April 2008

The response of viscoelastic laminated plates subjected to random excitation is investigated. The Fourier transform of the Boltzmann representation of the viscoelastic phases is incorporated into a micromechanical analysis, which establish the five frequency-dependent functions, characterizing the effective behavior of unidirectional fiber composites. This enables to express the governing equation, using the first-order shear deformation theory, in the frequency domain. The inversion of the response function into the time domain is performed by the Fast Fourier Transform algorithm. Two stationary random fields are considered: (i) ideal white noise, and (ii) band-limited white noise. In both cases analytical expressions for the mean squares are derived. Furthermore, the complex eigenvalues are investigated and the ratio between the imaginary part and the real one, η, is shown to relate to the damping ratio. The influence of the temperature, length-to-thickness ratio, and the fibers’ orientation on η is studied.
Anisotropic Plates With Various Openings Under Uniform Loading or Pure Bending
Authors: Hwu Chyanbin
Published: April 2008

In the case when an anisotropic plate contains a triangular, oval, or square opening, the only solution available in the literature is an approximate solution for orthotropic plates with openings, which was obtained by Lekhnitskii using the complex variable formulation. Solutions for any kind of anisotropic plates with various openings are presented in this paper by applying the Stroh formalism and using the technique of conformal mapping. Unlike the former results, which have different orders of approximation for different openings, the solutions presented here have only one simple unified expression for various openings such as the ellipse, circle, crack, triangle, oval, and square. Two special loading conditions are considered: one is uniform loading, the other is pure bending. Through the use of identities developed in the literature, the hoop stress along the opening boundary is obtained in real form. The results show that the effect of anisotropy on the stress concentration is totally determined through the fundamental elasticity matrices N1 and N3 introduced by Stroh.
Nonlinear Finite Element Formulation for the Large Displacement Analysis of Plates
Authors: Chang Bilin , Shabana A. A.
Published: April 2008

In this investigation a nonlinear total Lagrangian finite element formulation is developed for the dynamic analysis of plates that undergo large rigid body displacements. In this formulation shape functions are required to include rigid body modes that describe only large translational displacements. This does not represent any limitation on the technique presented in this study, since most of commonly used shape functions satisfy this requirement. For each finite plate element an intermediate element coordinate system, whose axes are initially parallel to the axes of the element coordinate system, is introduced. This intermediate element coordinate system, which has an origin which is rigidly attached to the origin of the deformable body, is used for the convenience of describing the configuration of the element with respect to the deformable body coordinate system in the undeformed state. The nonlinear dynamic equations developed in this investigation for the large rigid body displacement and small elastic deformation analysis of the rectangular plates are expressed in terms of a unique set of time invariant element matrices that depend on the assumed displacement field. The invariants of motion of the deformable body discretized using the plate elements are obtained by assembling the invariants of its elements using a standard finite element procedure.
Inverse Dynamics of Constrained Multibody Systems
Authors: Wang J. T.
Published: April 2008

A method for analyzing constrained multibody systems is presented. The method is applicable to a class of problems in which the multibody system is subjected to both force and kinematic constraints. This class of problems cannot be solved by using the classical methods. The method is based upon the concept of partial velocity and generalized forces of Kane’s method to permit the choice of constraint forces for fulfilling both kinematic and force constraints. Thus, the constraint forces or moments at convenient points or bodies may be specified in any desired form. For many applications, the method also allows analysts to choose a constant coefficient matrix for the undetermined force term to greatly reduce the burden of repeatedly computing its orthogonal complement matrix in solving the differential algebraic dynamic equations. Two examples illustrating the concepts are presented.
Optimization of Self-Acting Gas Bearings for Maximum Static Stiffness
Authors: Robert Michel P.
Published: April 2008

The gap profile of a two-dimensional self-acting gas bearing is determined such that the static stiffness it can achieve is maximum. Three fundamental profiles are obtained according to the stiffness mode to be considered: normal, pitch, or roll. The optimization process takes place within the framework of the compressible lubrication theory among all the profiles having a given minimum film thickness. The method proposed here is based on the calculus of variations and uses a finite element technique coupled with an iterative mapping to converge to the final solution. As an example, the case of a square bearing is treated and the three fundamental gap profiles, along with their optimum characteristics, are plotted to illustrate the solutions.
Mixing in a Closed Room by the Action of Two Fans
Authors: Lichter Seth , Dagan Arie , Underhill William B. , Ayanle Hassan
Published: April 2008

The mixing induced by two constant flow rate fans, which vary periodically in direction, is studied as a function of the period of oscillation of the fans. The three-dimensional equations of motion are integrated to determine the particle trajectories. As first shown by Aref’s work on a two-dimensional map, mixing may be greatly enhanced by unsteadiness. It is found that trajectories can be trapped in a restricted region by surfaces which function similarly to KAM tori in two dimensions. Results are presented for the largest Lyapunov exponent and the correlation dimension as a function of oscillation period. These results may be used to determine the conditions for good mixing.
Cumulant Neglect Closure of Nonstationary Solutions of Stochastic System
Authors: Pawleta Marian , Socha Leslaw
Published: April 2008

The comparison of the exact nonstationary solution of stochastic dynamic system with the corresponding one obtained by the cumulant closure technique is presented in this paper. The solutions of linear system with colored noise will be considered.
The Effect of Wall Motions on the Governing Equations of Contained Fluids
Authors: Ohayon Roger , Felippa Carlos A.
Published: April 2008

The equations of motion for an acoustic fluid enclosed in a moving or flexible container are studied. It is shown that the determination of the reference state must account for the surface-integrated effect of the wall motions. The governing equation of transient motions about this state in the displacement potential does not generally reduce to the classical wave equation unless special adjustments are made. The results are relevant to finite elements formulations based on the displacement potential.
Near-Tip Fields for Quasi-Static Crack Growth Along a Ductile-Brittle Interface
Authors: Drugan W. J.
Published: April 2008

As an analytical first study of the mechanics of ductile-brittle interfacial crack growth, I derive the stress and deformation fields near the tip of a crack that is growing quasi-statically along an interface joining material phases idealized as being rigid on one side and homogeneous, isotropic, elastic-ideally plastic on the other. Both the cases of antiplane strain and plane strain are treated, since it is some combination of these that pertains near an interface crack under general three-dimensional conditions. In the antiplane strain case, a family of solutions for the growing crack fields is found covering all admissible crack line shear stress ratios except for the case when the shearing is parallel to the crack; the Mode III homogeneous material solution is shown to be a limiting member of this family. Two distinct solution families are shown to exist for the growing crack fields in the plane strain case. One of these contains the Mode I homogeneous material solution and is characterized by large crack line stress triaxialities (up to 39 percent higher than that in homogeneous material solutions), while the other family has a limiting member that closely resembles (but is not identical to) the Mode II homogeneous material solution and is characterized by small and even negative crack line stress triaxialities. These solutions, which appear to constitute all possible that involve traction-free crack faces, are shown to cover large portions, but not the entire admissible range, of crack line near-tip shear/normal stress ratios (“mixities“).
A Thermal Elastica Theory of Piston-Ring and Cylinder-Bore Contact
Authors: Sun D. C.
Published: April 2008

The contact between piston-ring and cylinder-bore is generally nonuniform, due to mechanical and thermal distortion of the bore and manufacturing imperfection in the shape of the free ring. This nonuniform contact problem is treated in the present work that features arbitrarily specified bore shape and free ring shape, and also includes the thermal deformation of the ring and the effect of gas pressure. The problem is solved with the elastica theory, incorporating thermal elasticity, and a complementarity formulation. Solutions are computed using dimensions, material values, and operating parameters representative of those found in automotive engines.
Free Vibration of Helical Springs
Authors: Jiang W. , Jones W. K. , Wang T. L. , Wu K. H.
Published: April 2008

This paper presents a theoretical investigation of the coupled extensional-torsional vibration of helical springs. The study shows that two types of periodic wave will propagate through the spring, one characterizing the extensional-compressive deformation and the other one, the torsional deformation. The shapes of the individual waves are simple, but the oscillation of the spring is complex due to the interaction and superposition of the component waves.
Stability of Linear Conservative Gyroscopic Systems
Authors: Walker J. A.
Published: April 2008

Sufficient conditions are obtained for the stability and instability of linear conservative gyroscopic systems. The conditions are nonspectral, involve only the definiteness of certain combinations of the coefficient matrices, and may yield useful design constraints. An example is employed to compare these results with earlier results of the same type.
A Modified, Slowly Varying Parameter Approach for Systems With Impulsive Loadings
Authors: Jones Nicholas P. , Shenton Harry W.
Published: April 2008

Many oscillating systems in practice are subject to periodic, impulsive loads during their motion. For nonlinear systems traditional methods, such as the slowly varying parameter technique, have been used to study the response of such systems by “smearing“ the effect of the impulse over one cycle of the oscillation. Unfortunately, in many instances this approach violates the basic assumption used in the application of the averaging technique, resulting in limited predictive capability. This paper presents a modification to the standard slowly varying parameter technique for nonlinear systems which addresses this problem by assuming a solution form which admits a discontinuity in velocity at the time the impulse is applied. Examples are given which outline the improvement in accuracy of the new technique.
Inertia Effects in Thin Film Flow With a Corrugated Boundary
Authors: Serbetci Ilter , Tichy John A.
Published: April 2008

An analytical solution is presented for two-dimensional, incompressible film flow between a sinusoidally grooved (or rough) surface and a flat surface. The upper grooved surface is stationary whereas the lower, smooth surface moves with a constant speed, The Navier-Stokes equations were solved employing both mapping techniques and perturbation expansions. Due to the inclusion of the inertia effects, a different pressure distribution is obtained than predicted by the classical lubrication theory. In particular, the amplitude of the pressure distribution of the classical lubrication theory is found to be in error by over 100 percent (for modified Reynolds number of 3–4).
Stability of Liquid Film Flow Down an Oscillating Wall
Authors: Bauer Ronald J. , von Kerczek C. H.
Published: April 2008

The stability of a liquid film flowing down an inclined oscillating wall is analyzed. First, the linear theory growth rates of disturbances are calculated to second order in a disturbance wave number. It is shown that this growth rate is simply the sum of the same growth rate expansions for a nonoscillating film on an inclined plate and an oscillating film on a horizontal plate. These growth rates were originally calculated by Yih (1963, 1968). The growth rate formula derived here shows that long wavelength disturbances to a vertical falling film, which are unstable at all nonzero values of the Reynolds number when the wall is stationary, can be stabilized by sufficiently large values of wall oscillation in certain frequency ranges. Second, the full time-dependent stability equations are solved in terms of a wall oscillation amplitude expansion carried to about 20 terms. This expansion shows that for values of mean flow Reynolds number less than about ten, the wall oscillations completely stabilize the film against all the unstable disturbances of the steady film.
Stress-Focusing Effect in a Uniformly Heated Solid Sphere
Authors: Hata Toshiaki
Published: April 2008

The ray theory is applied to the stress-focusing effects in a uniformly heated solid sphere. The stress-focusing effect is the phenomenon that, under an instantaneous heating, stress waves reflected from the free surface of the sphere result in very high stresses at the center. Using the ray theory, the Laplace transformed solution of stress waves in the sphere is sorted out into rays according to the ray path of multiply-reflected waves. Inverse transform of each ray gives rise to the exact solution of the transient response up to the arrival time of the next ray. The numerical results reveal that stresses peak out periodically at a constant period and, unlike the case of cylinder, the radial stress at the center of the sphere is bounded.
Thermal Shock in a Hollow Sphere Caused by Rapid Uniform Heating
Authors: Hata Toshiaki
Published: April 2008

This paper is concerned with a method for calculating the dynamic stress distribution in a hollow sphere. Adopting the Goodier’s concept, the dynamic thermoelastic problem in a sphere is decomposed into a particular form of dynamic stress problem corresponding to the thermoelastic displacement potential and the homogeneous form of dynamic stress problem corresponding to the stress functions. Applying the ray theory to the homogeneous form, we obtain the general solution for transient waves induced by sudden heating. When a hollow sphere is subjected suddenly to a uniform temperature rise throughout the sphere, stress waves occur at the internal and external surfaces the moment thermal impact is applied. During instantaneous heating, the interfering effects of these waves can cause a very high dynamic stress at the internal surface of a sphere. The numerical results show that, as the ratio of the internal radius to the external one increases, the tangential stress on the internal surface becomes higher.
Creasing Singularities in Compressible Elastic Materials
Authors: Silling S. A.
Published: April 2008

The deformation and stress fields near a crease in the surface of an isotropic, compressible elastic body in equilibrium are in general singular. The order of the singularity depends on the constitutive behavior in the limit of zero volume. In this paper the problem of the creasing of a semicircular cylinder folded about its axis is solved exactly for a family of materials that includes the Blatz-Ko material (a foam rubber). Conditions under which strong ellipticity is lost are derived.
An Edge Dislocation in a Three-Phase Composite Cylinder Model
Authors: Luo H. A. , Chen Y.
Published: April 2008

An exact solution is given for the stress field due to an edge dislocation embedded in a three-phase composite cylinder. The force on the dislocation is then derived, from which a set of simple approximate formulae is also suggested. It is shown that, in comparison with the two-phase model adopted by Dundurs and Mura (1964), the three-phase model allows the dislocation to have a stable equilibrium position under much less stringent combinations of the material constants. As a result, the so-called trapping mechanism of dislocations is more likely to take place in the three-phase model. Also, the analysis and calculation show that in the three-phase model the orientation of Burgers vector has only limited influence on the stability of dislocation. This behavior is pronouncedly different from that predicted by the two-phase model.
Convex Models of Vehicle Response to Unknown but Bounded Terrain
Authors: Ben-Haim Yakov , Elishakoff Isaac
Published: April 2008

This study presents a nonprobabilistic set theoretical approach to analyzing uncertainty in vehicle vibrations arising from motion along imperfectly known terrain. The uncertainty in the substrate is described by a set of allowed substrate profile functions. The analysis of the vehicle response consists in determining the range of variation of performance parameters, as the substrate profile varies over the set of allowed functions. This enables characterization of the uncertain but bounded motion of the vehicle as well as optimization of the vehicle design with respect to uncertainty in the substrate. Maximum acceleration during motion on an imperfectly known surface is determined and related to standard design guidelines for limiting exposure to vibrational acceleration. A method is developed for determining the greatest lower bound of the number of sign changes per second of the vibrational acceleration when moving over an irregular and incompletely specified substrate. Motion along uniformly bounded substrates is studied, as well as traversal of barriers.
The In-Plane Loading of a Rigid Disk Inclusion Embedded in an Elastic Half-Space
Authors: Selvadurai A. P. S. , Singh B. M. , Au M. C.
Published: April 2008

The paper examines the problem of the in-plane loading of a rigid disk inclusion which is embedded in bonded contact with an isotropic elastic half-space region. The governing coupled integral equations, derived via a Hankel transform technique, are evaluated numerically to generate results for the in-plane stiffness of the rigid disk inclusion and the rotation which accompanies the lateral translation.
Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part III—Large-Scale Yielding
Authors: Shih C. F. , Asaro R. J. , O’Dowd N. P.
Published: April 2008

In Parts I and II, the structure of small-scale yielding fields of interface cracks were described in the context of small strain plasticity and J2 deformation theory. These fields are members of a family parameterized by the plastic phase angle ξ which also determines the shape or phase of the plastic zone. Through full-field analysis, we showed the resemblance between the plane-strain interface crack-tip fields and mixed-mode HRR fields in homogeneous material. This connection was exploited, to the extent possible, inasmuch as the interface fields do not appear to have a separable form. The present investigation is focused on “opening” dominated load states (| ξ | ≤ π/6) and the scope is broadened to include finite ligament plasticity and finite deformation effects on near-tip fields. We adopt a geometrically rigorous formulation of J2 flow theory taking full account of crack-tip blunting. Our results reveal several surprising effects, that have important implications for fracture, associated with finite ligament plasticity and finite strains. For one thing the fields that develop near bimaterial interfaces are more intense than those in homogeneous material when compared at the same value of J or remote load. For example, the plastic zones, plastic strains, and the crack-tip openings, δt, that evolve near bimaterial interfaces are considerably larger than those that develop in homogeneous materials. The stresses within the finite strain zone are also higher. In addition, a localized zone of high hydrostatic stresses develops near the crack tip but then expands rapidly within the weaker material as the plasticity spreads across the ligament. These stresses can be as much as 30 percent higher than those in homogeneous materials. Thus, the weaker material is subjected to large stresses as well as strains—states which promote ductile fracture processes. At the same time, the accompanying high interfacial stresses can promote interfacial fracture.
On Energy Rate Theorems for Linear First-Order Nonholonomic Systems
Authors: Papastavridis John G.
Published: April 2008

Starting with the Boltzmann/Hamel equations of motion of mechanical systems subject to general linear and first-order nonholonomic and rheonomic constraints, and in nonholonomic coordinates, this paper derives the general (reactionless) energy rate, or power, equation for such systems, in a straightforward and physically clear fashion. A power (reaction-containing) equation for these systems, but in holonomic coordinates, is also derived for completeness. An example of a sphere rolling on a uniformly spinning plane serves to illustrate these power theorems. The paper extends and corrects the recent work by Kane and Levinson (1988) on the same topic.
Nonlinear Transient Analysis of Large Rotordynamic Systems
Authors: Shiau T. N. , Jean A. N.
Published: April 2008

A solution technique based on implicit numerical integration combined with a condensation technique is presented to predict the transient response of large flexible rotor systems with nonlinear characteristics. The analysis directly tackles the nonlinear second-order differential equations which describe the system motion. The condensation technique can lead to a reduced model in which only the coordinates associated with nonlinear components of the system are considered. Thus, a substantial reduction of computation can be expected if the nonlinear components of system are sparse. A flexible rotor system is studied to illustrate the merits of the procedures. The results show that, if the system is of a small number of coordinates associated with nonlinear components compared to that of entire system degrees-of-freedom, the computational time can be considerably reduced using this technique.
Void Growth in Plastically Deformed Free-Cutting Brass
Authors: Worswick M. J. , Pick R. J.
Published: April 2008

The void growth occurring during tensile testing of uniaxial and notched specimens of free-cutting brass has been determined experimentally. This material contains a globular lead phase which tears or bursts to nucleate voids during deformation. Using quantitative metallographic data from specimens whose deformation was interrupted prior to failure, histories of void volume fraction and void aspect ratio were determined. The measured stress-strain response from the tensile tests was shown to be close to predictions from a finite element model incorporating Gurson’s constitutive model for a porous plastic solid. Predicted void growth rates agreed well with experiment for uniaxial specimens but were less than the measured growth rates in notched, high triaxiality specimens.
Viscoelastic Multilayered Cylinders Rolling With Dry Friction
Authors: Kalker J. J.
Published: April 2008

Two circular cylinders consisting of a rigid core which is covered by an arbitrary number of homogeneous, isotropic, viscoelastic coats of arbitrary, but uniform thickness are pressed together so that a contact area in the form of a strip forms between them, and subsequently rolled in the presence of dry friction. A Maxwell model of viscoelasticity is employed; the friction is finite and modeled by Coulomb’s law; partial slip in the contact area is allowed. It is required to find the viscoelastic field in the cylinder, notably in the contact strip, when the compressive force and the creepage in rolling direction are specified. The proposed method works almost equally fast in the case of pure elasticity and of viscoelasticity. It is akin to the method of Bentall et al. (1968), but automated, modernized, and extended.
Axisymmetric Scattering of a Plane Longitudinal Wave by a Circular Crack in a Transversely Isotropic Solid
Authors: Kundu T. , Bostro¨m A.
Published: April 2008

The scattering of elastic waves by a circular crack situated in a transversely isotropic solid is studied here. The axis of material symmetry and the axis of the crack coincides. The incident wave is taken as a plane longitudinal wave propagating perpendicular to the crack surface. A Hankel transform representation of the scattered field is used, and after some manipulations using the boundary conditions this leads to an integral equation over the crack for the displacement jump across the crack. This jump is expanded in a series of Legendre polynomials which fulfill the correct edge condition and the integral equation is projected on the same set of Legendre polynomials. The far field is computed by the stationary phase method. A few numerical computations are carried out for both isotropic and anisotropic solids. Results for the isotropic solid compare favorably with those available in the literature.
Vibrations of Moderately Elliptic Clamped Plates: A Perturbation Scheme for Eigenvalues
Authors: Parnes R.
Published: April 2008

Frequencies of vibration of an elliptic plate, clamped along the edge, are determined by means of a perturbation scheme based on a boundary perturbation method (B.P.M.). Eigenvalues are obtained corresponding to higher modes of vibration containing elliptic nodes, in addition to the fundamental mode. Comparison with previously derived values in the fundamental mode reveals that the present scheme leads to accurate results for moderately elliptic plates.
The Effect of Plasticity on Resonant Pipe Vibration
Authors: Beaney E. M.
Published: April 2008

An understanding of the response of pipework systems to high levels of seismic excitation is required to enable aseismic design methods to be securely based. Theoretical and experimental modeling of simple systems and components demonstrate that plasticity in the pipe wall controls the vibration response level and that, because of an unexpected level of material strain hardening, in pressurized pipes, simple elastic modal and frequency analysis are satisfactory. Given the correct material properties an energy balance approach correctly predicts the steady.
Free Fall of a Sphere in a Partially Lubricated Cylinder
Authors: Gans Roger F.
Published: April 2008

The entrainment of lubricant at the entrance of a lubrication zone, such as that of a partially starved slider bearing, is analyzed in a closed system using the method of matched asymptotic expansions. A sphere falling together with a small lens of lubricant in a closely fitting tube is shown to fall under gravity at a speed V=(Mg−Fc)√[(RC−RS)/RC]/(16π2μRC), where M denotes the total mass of the system, sphere plus lubricant, g the acceleration of gravity, Fc the differential contact force, μ the viscosity of the lubricant, and RC and RS the radii of the tube and the sphere, respectively. Potential biological applications and experimental verification are discussed.
Stress Field Around a Rounded Crack Tip
Authors: Chiang C. R.
Published: April 2008

A method based on the eigenfunction (Williams stress functions) expansion is developed to examine the stress distribution around the tip region of a macrocrack which has some specific micro configuration. In particular, a macrocrack running into a micro hole under mode I condition is analyzed in detail. The coefficients associated with each eigenfunction are determined by a collocation procedure and the convergence of the numerical results is shown to be quite satisfactory.
Formulas for Generating Prescribed Residual Stress Distributions in Center-Wound Rolls
Authors: Boutaghou Zine-Eddine , Chase Thomas R.
Published: April 2008

Altmann’s equations for describing the residual stresses in center-wound rolled webs are solved to determine the winding stress necessary to produce prescribed residual stress distributions in the finished roll. A solution for constant circumferential stress is expanded to control the peak winding stress. Two example winding problems are discussed.
Matrix Cracking in Fiber-Reinforced Composite Materials
Authors: Luo H. A. , Chen Y.
Published: April 2008

Matrix cracking is a major pattern of the failure of composite materials. A crack can form in the matrix during manufacturing, or be produced during loading. Erdogan, Gupta, and Ratwani (1974) first considered the interaction between an isolated circular inclusion and a line crack embedded in infinite matrix. As commented by Erdogan et al., their model is applicable to the composite materials which contain sparsely distributed inclusions. For composites filled with finite concentration of inclusions, it is commonly understood that the stress and strain fields near the crack depend considerably on the microstructure around it. One notable simplified model is the so-called three-phase model which was introduced by Christensen and Lo (1979). The three-phase model considers that in the immediate neighborhood of the inclusion there is a layer of matrix material, but at certain distance the heterogeneous medium can be substituted by a homogeneous medium with the equivalent properties of the composite. Thus, for the problems of which the interest is in the field near the inclusion, it can reasonably be accepted as a good model. The two-dimensional version of the three-phase model consists of three concentric cylindrical layers with the outer one, labeled by 3, extended to infinity. The external radii a and b of the inner and intermediate phases, labeled by 1 and 2, respectively, are related by (a/b)2 =c, where c is the volume fraction of the fiber in composite.
The Maggi or Canonical Form of Lagrange’s Equations of Motion of Holonomic Mechanical Systems
Authors: Papastavridis John G.
Published: April 2008

This paper formulates the simplest possible, or canonical, form of the Lagrangean-type of equations of motion of holonomically constrained mechanical systems. This is achieved by introducing a new special set of n holonomic (system) coordinates in terms of which the m ( < n) holonomic constraints are expressed in their simplest, or uncoupled, form: the first m of these new coordinates vanish; the remaining (n-m) (nonvanishing) new coordinates of the (n-m) degree-of-freedom system are then independent. From the resulting equations of motion: (a) The last (n-m) are reactionless canonical equations (the holonomic counterpart of the linear or nonlinear equations, either of Maggi (in the old variables), or of Boltzmann/Hamel (in the new variables)) whose solution yields the motion, while (b) the first m supply the system reactions, in the old or new coordinates, once the motion is known. Special forms of these equations and a simple example are also given. The geometrical interpretation of the above, in modern vector/linear algebra language is summarized in the Appendix.
Equivalence of Stochastic Averaging and Stochastic Normal Forms
Authors: Namachchivaya N. S. , Leng Gerard
Published: April 2008

The equivalence of the methods of stochastic averaging and stochastic normal forms is demonstrated for systems under the effect of linear multiplicative and additive noise. It is shown that both methods lead to reduced systems with the same Markovian approximation. The key result is that the second-order stochastic terms have to be retained in the normal form computation. Examples showing applications to systems undergoing divergence and flutter instability are provided. Furthermore, it is shown that unlike stochastic averaging, stochastic normal forms can be used in the analysis of nilpotent systems to eliminate the stable modes. Finally, some results pertaining to stochastic Lorenz equations are presented.
Gravity-Driven Granular Flows of Smooth, Inelastic Spheres Down Bumpy Inclines
Authors: Richman M. W. , Marciniec R. P.
Published: April 2008

We employ a kinetic constitutive theory that includes the effects of particle transport and collisions to analyze steady, fully developed, gravity-driven flows of smooth, inelastic spheres down bumpy inclines. By replacing the solid fraction by its depth-averaged value wherever it occurs in the balance equations, we obtain a closed-form solution for the granular temperature profile, which when employed in the constitutive relations for the normal and shear stresses determines the solid fraction and mean velocity profiles. The solutions ensure that the stresses and energy flux vanish at the free surface and that the balance of momentum and energy are satisfied at the base. We also determine for fixed flow rates the ranges of inclinations within which steady flows are possible, and for fixed inclinations the depths of the resulting flows. Most striking are the inclinations and flow rates at which both a dilute, fast flow and a dense, slow flow are possible.
Flows Inside and Around a Vaporizing/Condensing Drop Translating in an Electric Field
Authors: Nguyen H. D. , Chung J. N.
Published: April 2008

The flow behavior inside and around a translating liquid drop that simultaneously experiences a large interfacial radial mass flux as a result of evaporation or condensation, and the influence of a uniform electric field is analyzed in this paper. The steady-state equations of continuity and momentum of both continuous and drop phases are transformed, by a perturbation technique, into a series of systems of linear partial differential equations which are then solved analytically. The flow structure and the drag force are computed to the first order in ε( =U∞R/ν), the perturbed parameter. Interfacial velocity profiles are represented by Legendre polynomials up to second order to accommodate the electric-field-induced shear stress. It is found that the presence of an electric field does not contribute to the total drag force, but greatly modifies the flow patterns. The droplet internal flow is dominated by the electric field such that the double loop Taylor flow appears at relatively high field strength. The outside flow is dominated by the interfacial mass flux and the recirculation zone only shows up for an evaporating drop under a negative electric field. The electric field also moves the dividing streamline toward to or away from the surface depending on the direction of the electric field and the velocity direction at the interface. Also the effects of an electric field on the flow field are more pronounced for a drop with outward interfacial mass flux because the electric field helps restore the strength of internal circulation weakened by the outward interfacial mass flux.
Transient Stokes Flow in a Channel Driven by Moving Sleeves
Authors: Carbonaro P. , Hansen Erik B.
Published: April 2008

A two-dimensional, nonstationary Stokes flow in an infinite channel with plane, parallel walls is considered. The flow is driven by two sleeves forming parts of the walls and moving with a constant velocity starting at t = 0. The exact Laplace transform of the stream function is determined and an approximate inversion, valid for t small, is performed. The resulting approximate formula for the stream function is used to study numerically the nonstationary flow as it approaches the stationary state in which an infinite system of Moffatt eddies is fully developed. The results are presented as a series of streamline plots.
Monte Carlo Simulation of Coupled Nonlinear Oscillators Under Random Excitations
Authors: Li Wenlung , Ibrahim R. A.
Published: April 2008

The main objectives of this note are to examine the random response of nonlinear three degree-of-freedom systems in the neighborhood of combination internal resonance by using Monte Carlo simulation and to compare the results with those obtained by first-order non-Gaussian closure. The numerical simulation is found to support the main features of the nonlinear interaction in the neighborhood of internal resonance conditions. For example, the nonlinear interaction takes place in the form of a randomly continuous energy exchange between the modes involved. In addition, the results verify the existence of energy absorbing effect as predicted by the non-Gaussian closure method. While the non-Gaussian closure exhibits regions of multiple solutions in the neighborhood of exact internal resonance, the numerical simulation gives only one solution depending on the assigned initial conditions. This observation requires further investigation to establish the domains of attraction in stochastic nonlinear dynamics.
Diffusion of Self-Equilibrating End Loads in a Stretched Elastoplastic Circular Cylinder
Authors: Durban D. , Stronge W. J.
Published: April 2008

Low rates of axial diffusion are discovered for asymmetric instantaneous self-equilibrating disturbances imposed at the end of an initially stretched circular cylinder. The diffusion rates are evaluated within the framework of continuum plasticity for materials represented by the isotropic J2 flow theory. Over most of the initial stress range, a lower bound on the decay rate is provided by an eigenvalue associated with flexure. There is almost no decay for this component of a disturbance when the axial stretch is small in comparison with the stretch at necking.
Finite, Dynamic Motions of Thin Rate-Dependent Sheets
Authors: Blume J. A.
Published: April 2008

The transient response of a thin sheet comprised of a rate-dependent solid is determined. The material is assumed to be incompressible, and the constitutive response is governed by a nonlinearly viscous power-law model. The sheet has axially symmetry, but an otherwise arbitrarily varying thickness. Axially symmetric, finite, dynamic motions of the sheet are identified.
A Mechanism for Shear Band Formation in the High Strain-Rate Torsion Test
Authors: Burns Timothy J.
Published: April 2008

A numerical study of a one-dimensional model of the high strain-rate torsion test shows that a moving boundary of rigid unloading, starting from the ends of the thin-walled tubular specimen, is a plausible mechanism for adiabatic shear band formation during the test. Even though the dimensionless thermal diffusivity parameter is very small, the moving boundary is due to heat transfer from the specimen through its ends, which are assumed to be isothermal heat sinks. The mathematical model is based on a physical model of thermoelastic-plastic flow and a phenomenological Arrhenius model for the plastic flow surface. The numerical technique used is the semi-discretization method of lines.
On Bonded Inclusions With Circular or Straight Boundaries in Plane Elastostatics
Authors: Honein T. , Herrmann G.
Published: April 2008

It is shown that the solution, in plane elastostatics, for an infinite domain with a bonded circular inclusion (heterogeneous problem), may be obtained from the solution of the corresponding homogeneous problem merely by substitution into a simple algebraic expression (heterogenization). This relation is universal in the sense of being independent of the loading considered. The case of two half-planes occupied by two dissimilar materials and bonded along a straight boundary is obtained as a limiting case.
Analysis of Branched Interface Cracks
Authors: Mukai D. J. , Ballarini R. , Miller G. R.
Published: April 2008

A solution is presented for the problem of a finite length crack branching off the interface between two bonded dissimilar isotropic materials. Results are presented in terms of the ratio of the energy release rate of a branched interface crack to the energy release rate of a straight interface crack with the same total length. It is found that this ratio reaches a maximum when the interface crack branches into the softer material. Longer branches tend to have smaller maximum energy release rate ratio angles indicating that all else being equal, a branch crack will tend to turn back parallel to the interface as it grows.