bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Propagation of Bulges and Buckles
Authors: Chater E. , Hutchinson J. W.
Published: July 2009

Two examples illustrate the propagation of instability modes under quasi-static, steady-state conditions. The first is the inflation of a long cylindrical party balloon in which a bulge propagates down the length of the balloon. The second is the collapse of a long pipe under external pressure as a result of buckle propagation. In each example, there is a substantial barrier to the initiation of the instability mode. Once initiated, however, the mode will not arrest if the pressure is in excess of the quasi-static, steady-state propagation pressure. It is this critical pressure that is determined in this paper for each of the two examples.
On the Numerical Implementation of Elastoplastic Models
Authors: Yoder P. J. , Whirley R. G.
Published: July 2009

A closed-form solution is given for the way stresses evolve during an elastoplastic time step under conditions of purely kinematic hardening or softening. When isotropic effects are included, the analysis becomes more difficult, so a perturbation solution is developed. These solutions are then compared with various algorithms commonly used in finite element programs in order to assess the trade-offs between accuracy and computational efficiency.
The Elastic Inclusion With a Sliding Interface
Authors: Mura T. , Furuhashi R.
Published: July 2009

It is found that when an ellipsoidal inclusion undergoes a shear eigenstrain and the inclusion is free to slip along the interface, the stress field vanishes everywhere in the inclusion and the matrix. It is assumed in the analysis that the inclusion interface cannot sustain any shear traction. There exists a shear deformation that transforms an ellipsoid into the identical ellipsoid without changing its orientation (ellipsoid invariant transformation). This is not true, however, for a spheroidal inclusion. The amount of slip and the associated stress field are calculated for a spherical inclusion for a given uniform eigenstrain εij*.
The Subsurface Crack Under Conditions of Slip and Stick Caused by a Surface Normal Force
Authors: Chang F.-K. , Comninou Maria , Sheppard Sheri , Barber J. R.
Published: July 2009

A solution is given for the elastic stress field in a half plane containing a plane crack parallel to the surface and subjected to a uniform normal pressure and a concentrated normal load. Frictional slip according to Coulomb’s law is permitted between the crack faces. As the load is increased, a slip zone originates and grows either from a crack tip or from an intermediate point. Various arrangements of slip and stick zones can occur depending on the magnitude of the load and its location relative to the crack. At very high loads, the crack faces start to separate, but this case is not treated in the present paper.
Subsurface Crack Propagation Due to Surface Traction in Sliding Wear
Authors: Sin H.-C. , Suh N. P.
Published: July 2009

The mechanics of subsurface crack propagation in sliding wear of elastoplastic solids was investigated using the finite element method. The subsurface cracks, which experience both compressive and tangential loading, propagate along the direction of maximum shear stress and grow in a ductile manner due to plastic deformation of the crack tips. Based on the assumption that the crack growth rate is equal to the crack-tip sliding displacement, the wear rate was predicted for the case of crack propagation controlled delamination wear which compares favorably with the experimentally determined wear rates. According to the FEM results, linear elastic fracture mechanics (LEFM), which was previously used to determine the wear rate, is not an appropriate method of predicting the wear rate because of the large plastic deformation at the crack tip.
Analysis of Tube-Tubesheet Joint Loading Including Thermal Loading
Authors: Soler A. I. , Hong Xu
Published: July 2009

The tube-to-tubesheet rolling process is reexamined using a two-dimensional elastic plastic analysis. In addition to room temperature rolling, subsequent thermal cycling of the joint is considered. The development of a computer code based on an incremental analysis that includes finite deformation effects and the possibility of reversed yield is presented. Typical simulations are presented that indicate some of the influences of geometry, materials, and loading on final tube-to-tubesheet contact pressure.
Stability and Vibrations of Geometrically Nonlinear Cylindrically Orthotropic Circular Plates
Authors: Shilkrut D.
Published: July 2009

The stability analysis of axisymmetrical equilibrium states of geometrically nonlinear, orthotropic, circular plates that are deformed by multiparameter loading, including thermal influence, is presented. The dynamic method (method of small vibrations) is used to accomplish this purpose. The behavior of the plate in different cases is revealed. In particular, it is shown that two different types of snapping processes can occur. The values of frequencies of small eigenvibrations from various cases have been calculated. These investigations are realized by numerical and qualitative methods. Here only the numerical results are presented.
A Method for Reducing the Order of Nonlinear Dynamic Systems
Authors: Masri S. F. , Miller R. K. , Sassi H. , Caughey T. K.
Published: July 2009

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.
Javelin Dynamics With Measured Lift, Drag, and Pitching Moment
Authors: Hubbard M. , Rust H. J.
Published: July 2009

Optimal release conditions for the javelin are studied using computer simulation. Included are two important and realistic assumptions: (1) initial velocity attainable by the thrower is dependent on the throwing angle, and (2) the aerodynamic center of pressure moves as a function of angle of attack. Aerodynamic forces and moments, previously measured in wind tunnel tests, are incorporated in the simulation. Range contours are presented in the two-space of initial angle of attack–initial flight path angle, assuming zero initial angular velocity.
Interactions Between Self and Parametrically Excited Motions in Articulated Tubes
Authors: Bajaj A. K.
Published: July 2009

The nonlinear dynamics of a two-segment articulated tubes system conveying a fluid is studied when the flow is harmonically perturbed. The mean value of the flow rate is near its critical value when the downward vertical position gets unstable and undergoes Hopf bifurcation into periodic solutions. The harmonic perturbations are assumed to be in parametric resonance with the linearized system. The method of Alternate Problems is used to obtain the small nonlinear subharmonic solutions of the system. It is shown that, in addition to the usual jump response, the system also exhibits stable and unstable isolated solution branches. For some parameter combinations the stable solutions can become unstable and can then bifurcate into aperiodic or amplitude-modulated motions.
Another Theorem for Determining the Definiteness of Sign of Functions and Its Applications to the Stability of Permanent Rotations of a Rigid Body
Authors: Ge Z.-M. , Wu Y.-J.
Published: July 2009

A new theorem for determining the definiteness of sign of functions is presented. As the examples illustrate, it is applied to the stability of permanent rotations of a rigid body about a fixed point in five cases.
On Asymptotic Approximations to Beam Model Shapes
Authors: Dowell E. H.
Published: July 2009

Recently the author had occasion to investigate inter alia the asymptotic character of the mode shapes of uniform beams. These results do not seem to have been presented before in the literature and so are given here as they appear to be of general interest. Clamped-free and free-free beams are considered, although other beam boundary conditions may be treated in a similar manner.
Laminar Wall Jet of a Non-Newtonian Fluid Over a Curved Surface
Authors: Gorla Rama Subba Reddy
Published: July 2009

An analysis is presented for the flow of a laminar, two-dimensional, incompressible, non-Newtonian fluid jet flowing over a curved surface. A unique similarity solution is obtained for both concave and convex surfaces. The similarity solution requires a special shape of the curved surface which is also determined. Numerical results are presented for the details of the velocity field and skin friction coefficient as a function of the curvature parameter.
The Estimation of Large Deflections of a Portal Frame Under Asymmetric Pulse Loading
Authors: Raphanel J. L. , Symonds P. S.
Published: July 2009

Modifications of a simple elastic-plastic technique [1-4] are shown which allow estimation of local deformation in the loaded column of a portal frame as well as the side-sway deflections of the frame. A wholly elastic response stage provides input to a simplified rigid-plastic solution, in which velocity patterns first of local and then of modal (side-sway) type occur, and which furnishes estimates of final plastic deflections. Maximum (elastic plus plastic) deflections are estimated by adding displacements corresponding to the elastic strain field defined by the stresses of the closing rigid-plastic mode. The method is described for perfectly plastic and for strain-rate sensitive material, and comparisons are shown here with values computed3 for both types of material by a finite element program. Emphasis in this paper is put on the inclusion of elastic and vicoplastic effects.
Impact and Bending of a Rigid-Plastic Fan Blade
Authors: Stronge W. J. , Shioya T.
Published: July 2009

A rigid-plastic fan blade is subjected to a transverse impact force at the tip in addition to radial centrifugal forces caused by fan rotation. Large and small deflection formulations for inplane bending of the cantilevered blade are calculated and compared. If the effects of centrifugal force are completely considered, the difference between these calculations is shown to be small within the beam. Most of the deflection originates from plastic deformation far from the tip so the large deflection effects near the tip have little influence. The largest curvature is inversely proportional to the centrifugal force, directly proportional to the third power of impact force, and always occurs near the point of impact.
Dynamic Characteristics of Large Repetitive Framelike Structures
Authors: Nayfeh Adnan H. , Hartle Michael S.
Published: July 2009

Using a building block approach and starting with a single element, expressions for the energy of various two-dimensional frametype gridwork configurations are derived. These are then used to develop energy equivalent continua for the grid-works. Equations of motion and associated boundary conditions are obtained for the continua. Some dynamic characteristics of these continua are investigated and compared with corresponding results obtained from finite element codes and also with some available theoretical predictions.
Optimal Forms of Shallow Shells With Circular Boundary, Part 2: Maximum Buckling Load
Authors: Plaut R. H. , Johnson L. W.
Published: July 2009

In Part 1, optimal forms were determined for maximizing the fundamental vibration frequency of a thin, shallow, axisymmetric, elastic shell with given circular boundary. Our objective in this part is to maximize the critical load for buckling under a uniformly distributed load or a concentrated load at the center. Again, the shell form is varied and the material, surface area, and uniform thickness of the shell are specified. Both clamped and simply supported boundary conditions are considered for the case of uniform loading, while one example is presented involving a concentrated load acting on a clamped shell. The optimality condition leads to forms that have zero slope at the boundary if it is clamped. The maximum critical load is sometimes associated with a limit point and sometimes with a bifurcation point. It is often substantially higher than the critical load for the corresponding spherical shell.
Optimal Forms of Shallow Shells With Circular Boundary, Part 3: Maximum Enclosed Volume
Authors: Plaut R. H. , Johnson L. W.
Published: July 2009

In Parts 1 and 2, we determined optimal forms of shallow shells with respect to vibration and stability, respectively. In this final part, we consider a given load and find the shell form for which the volume between the base plane and the deflected shell is a maximum. As before, the shell is assumed to be thin, elastic, and axisymmetric, with a given circular boundary that is either clamped or simply supported. The material, surface area, and uniform thickness of the shell are specified. Both uniformly distributed loads and concentrated central loads are treated. In the numerical results, the maximum enclosed volume is on the order of 10 percent higher than that for the corresponding spherical shell.
Bounds for Elastic Moduli of Multiphase Short-Fiber Composites
Authors: Nomura S. , Chou T.-W.
Published: July 2009

This paper examines upper and lower bounds of the effective elastic modulus of unidirectional short-fiber composites. The short-fibers are modeled by aligned ellipsoidal inclusions of the same aspect ratio but not necessarily the same size. We adopt a perturbation expansion of the composite local strain field by using the Green function tensor. Explicit expressions of the effective elastic modulus are derived up to the third-order term by use of the information on the correlation functions. The variational method is then employed to optimize the bounds of the effective modulus in a closed form. Numerical examples of the bounds as functions of the fiber aspect ratio and the fiber volume fraction are given for a glass/epoxy system. The present approach predicts narrower bounds than those of Hashin and coworkers for the limiting cases of spherical particles and continuous fibers since their bounds corresponds to a model that take the correlation functions up to the second order into account.
An Elastic Potential for the Nonlinear Response of Unidirectional Graphite Composites
Authors: Pindera M.-J. , Herakovich C. T.
Published: July 2009

An elastic potential is proposed that is capable of modeling the reversible portion of the observed nonlinear response of unidirectional graphite fiber composites. The model includes both the stiffening stress-strain behavior as well as the softening Poisson’s response for loading in the fiber direction. The model is compared with experimental results for Celion 6000/PMR-15 graphite-polyimide.
A Laminated Beam Theory With Interlayer Slip
Authors: Murakami H.
Published: July 2009

A Timoshenko beam theory with built-in interlayer slip is developed to facilitate analytical means of simulating the effect of interlayer slip on the stiffness degradation of laminated beam structures. The proposed theory is unique in the sense that any well-structures interlay slip law can be adopted in the beam model. Based on the principle of virtual work, well-posed boundary value problems of the proposed beam theory are defined. It is shown that the proposed theory reduces to the existing Bernoulli-Euler beam theory with interlayer slip by introducing the kinematic constraint of zero transverse shear strain. As a demonstration of the theory the load-deflection curves of a simply supported sandwich beam subjected to a concentrated load at the center are computed for several characteristic interlayer slip laws. It is found that the proposed model has the capability of simulating the deformation of beams with wide range of interlayer bond qualities, from interface with perfect bond to interface without connectors.
An Elastic Punch Moving Across the Surface of a Semi-Infinite Solid
Authors: Adams G. G. , Zeid I.
Published: July 2009

An elastic punch, modeled as a semi-infinite strip, moves with constant speed over the surface of a semi-infinite elastic body. Using the plane strain theory of elasticity, we obtain the resulting stress distribution along the interface of the contacting bodies for different material combinations and a range of sliding velocity and frictional coefficients. It is found that both the stress intensity factor and the order of the singularity depend on sliding velocity as well as on the other parameters. Speed-dependent composite material parameters are defined which determine the orders of the singularities.
Thermoelastic Displacements and Stresses Due to a Heat Source Moving Over the Surface of a Half Plane
Authors: Barber J. R.
Published: July 2009

A solution is given for the surface displacement and stresses due to a line heat source that moves at constant speed over the surface of an elastic half plane. The solution is obtained by integration of previous results for the instantaneous point source. The final results are expressed in terms of Bessel functions for which numerically efficient series and asymptotic expressions are given.
Propagation and Scattering of SH-Waves in Semi-Infinite Domains Using a Time-Dependent Boundary Element Method
Authors: Rice J. M. , Sadd M. H.
Published: July 2009

The propagation and scattering of SH-waves of general form is investigated using the boundary element method. Attention is focused on semi-infinite regions containing subsurface cavities. The analysis is carried out within the context of linear elastodynamic theory formulated as an integral equation. Using a time-dependent Green’s function for the half space, the boundary integral equation is developed and is discretized into a finite set of algebraic relations. A time-stepping algorithm is constructed for the solution of general boundary value—initial value problems. Results of this solution technique are presented for the two-dimensional case of transient waves scattering off of buried stress-free cavities.
The Improved Frequency Response Function and its Effect on Modal Circle Fits
Authors: Elliott K. B. , Mitchell L. D.
Published: July 2009

When structures are excited by random force excitation the circle fits of the data around resonance are usually poor. The structural parameter estimates, which result from this fit, are usually erroneous. No matter how elegant the circle or the multimodal fit, the results will be poor if the frequency response function (FRF) is a poor representation of the actual structural response. In general for the random excitation case, this is the case. The conventional fast Fourier transform (FFT) method which is used to estimate the frequency response function, is given by H1 (f) = Gxy/Gxx. This produces poor results when the coherence of the data falls in the resonance region. A drop in the coherence usually indicates noise at the input of the structure for this case. H1 (f) is quite sensitive to such noise giving erroneous estimates. This paper investigates an alternative method for computing the frequency response function, H2 (f) = Gyy/Gyx, and its impact on the accuracy of the circle fit procedure used in modal analysis. This new estimator is not sensitive to input noise like the currently used H1 (f). H2(f) provides the best estimate at or around resonance even in the presence of noise on the input signal. If one defines the average percentage fit error in the circle fit operation as 100 times the average radial deviation of the data points from the radius of the statistically fit circle divided by the fit circle radius, one can compute the circle fit accuracy for each of the proposed methods of data treatment. Typically, the percentage fitting error for H1 (f) might be 10 percent while the fitting error for H2 (f) using exactly the same data will be 0.5 percent. Thus, the proposed method eliminates long-standing system analysis errors through the use of a simple revision of the way the data are treated in the FFT processor around the resonance regions.
Wheelset Mechanics During Wheelclimb Derailment
Authors: Karmel A. , Sweet L. M.
Published: July 2009

An analysis of the mechanics and dynamics of a railroad vehicle wheelset during flange contact and wheelclimb derailment is presented. The theoretical model includes wheelset lateral, vertical, roll, yaw, and axle rotation degrees of freedom, plus lateral displacement of the truck frame. The equations of motion are based on the kinematics and dynamics of the wheelset subject to constraints imposed by wheel/rail contact geometry. These constraints are used to compute creepages and normal forces at the wheel/rail contact points, needed as inputs to the Kalker Simplified Theory of rolling contact. Computational methods for simulation of the nonlinear dynamic model are discussed. Results of the simulation demonstrate the significance of the various degrees of freedom on wheelset motion and on predicted values of the derailment quotient (Q/P).
A Simple Higher-Order Theory for Laminated Composite Plates
Authors: Reddy J. N.
Published: July 2009

A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano [6], but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.
Neck Propagation in Tensile Tests: A Study Using Rate-Independent, Strain Hardening Plasticity
Authors: Nimmer R. P. , Miller L. C.
Published: July 2009

A J2 yield criterion and time and temperature-independent flow theory of plasticity have been applied to study characteristic phenomena observed in tensile tests of some ductile polymers: namely a load drop immediately after yield and stable propagation of a neck along the entire length of the specimen. A trilinear stress-strain curve is used to quantify the effect of material model data on these physical observations.
Dynamic Stresses and Displacements Around Cylindrical Cavities of Arbitrary Shape
Authors: Datta S. K. , Wong K. C. , Shah A. H.
Published: July 2009

Dynamic stresses and displacements around cylindrical cavities of various shapes, namely, circular, triangular, and square cavities are presented in this paper. Also presented are results for a pair of circular cavities of equal radii and a pair of circular and square cavities. These results are of interest in estimating the effects of corners and multiple scattering on the distribution of dynamic displacements and stresses around cylindrical holes or openings. Since exact analytical solutios are not available in these cases (except for a single circular hole) a numerical technique combining the finite element method (FEM) and the method of eigenfunction expansions is used here.
Indentation of a Penny-Shaped Crack by an Oblate Spheroidal Rigid Inclusion in a Transversely Isotropic Medium
Authors: Tsai Y. M.
Published: July 2009

The stress distribution produced by the identation of a penny-shaped crack by an oblate smooth spheroidal rigid inclusion in a transversely isotropic medium is investigated using the method of Hankel transforms. This three-part mixed boundary value problem is solved using the techniques of triple integral equations. The normal contact stress between the crack surface and the indenter is written as the product of the associated half-space contact stress and a nondimensional crack-effect correction function. An exact expression for the stress-intensity is obtained as the product of a dimensional quantity and a nondimensional function. The curves for these nondimensional functions are presented and used to determine the values of the normalized stress-intensity factor and the normalized maximum contact stress. The stress-intensity factor is shown to be dependent on the material constants and increasing with increasing indentation. The stress-intensity factor also increases if the radius of curvature of the indenter surface increases.
Nonlinear Vibration of Thin Elastic Plates, Part 1: Generalized Incremental Hamilton’s Principle and Element Formulation
Authors: Lau S. L. , Cheung Y. K. , Wu S. Y.
Published: July 2009

The finite element method has been widely used for analyzing nonlinear problems, but it is surprising that so far only a few papers have been devoted to nonlinear periodic structural vibrations. In Part 1 of this paper, a generalized incremental Hamilton’s principle for nonlinear periodic vibrations of thin elastic plates is presented. This principle is particularly suitable for the formulation of finite elements and finite strips in geometrically nonlinear plate problems due to the fact that the nonlinear parts of inplane stress resultants are functions subject to variation and that the Kirchhoff assumption is included as part of its Euler equations. Following a general formulation method given in this paper, a simple triangular incremental modified Discrete Kirchhoff Theory (DKT) plate element with 15 stretching and bending nodal displacements is derived. The accuracy of this element is demonstrated via some typical examples of nonlinear bending and frequency response of free vibrations. Comparisons with previous results are also made. In Part 2 of this paper, this incremental element is applied to the computation of complicated frequency responses of plates with existence of internal resonance and very interesting seminumerical results are obtained.
Nonlinear Vibration of Thin Elastic Plates, Part 2: Internal Resonance by Amplitude-Incremental Finite Element
Authors: Lau S. L. , Cheung Y. K. , Wu S. Y.
Published: July 2009

The simple amplitude-incremental triangular plate element derived in Part 1 of this paper is applied to treat the large-amplitude periodic vibrations of thin elastic plates with existence of internal resonance. A simply supported rectangular plate with immovable edges (b/a = 1.5) and having linear frequencies ω13 = 3.45 ω11 is selected as a typical example. The frequency response of free vibration as well as forced vibration under harmonic excitation are computed. To the best knowledge of the authors, these very interesting results for such plate problems have not appeared in literature previously. Some special considerations to simplify and to speed up the numerical process are also discussed.
Flow Between Eccentric Rotating Cylinders
Authors: San Andres A. , Szeri A. Z.
Published: July 2009

In this numerical study of flow between eccentric cylinders, the size of the separation eddy and the position of the points of separation and reattachment are found to be Reynolds number dependent. The separation point moves in the direction of rotation upon increasing the Reynolds number, in contradiction to the first-order inertial perturbation theory of Ballal and Rivlin [1]. The numerical methods employed in this study include Galerkin’s procedure with B-spline test functions.
Dynamics of Constrained Multibody Systems
Authors: Kamman J. W. , Huston R. L.
Published: July 2009

A new automated procedure for obtaining and solving the governing equations of motion of constrained multibody systems is presented. The procedure is applicable when the constraints are either (a) geometrical (for example, “closed-loops”) or (b) kinematical (for example, specified motion). The procedure is based on a “zero eigenvalues theorem,” which provides an “orthogonal complement” array which in turn is used to contract the dynamical equations. This contraction, together with the constraint equations, forms a consistent set of governing equations. An advantage of this formulation is that constraining forces are automatically eliminated from the analysis. The method is applied with Kane’s equations—an especially convenient set of dynamical equations for multibody systems. Examples of a constrained hanging chain and a chain whose end has a prescribed motion are presented. Applications in robotics, cable dynamics, and biomechanics are suggested.
Sufficient Conditions for Small Particles to Hold Together Because of Adhesion Forces
Authors: Fichman M. , Pnueli D.
Published: July 2009

An elastic-plastic collision between two small particles or between a small one and a larger one is considered. Adhesion forces are included. It is found that the elastic limit of the particles material is quite frequently reached, sometimes even without initial velocity at all. Conditions for the particles not to have enough energy to overcome the adhesion forces are formulated, and used to calculate conditions for the particles to stick together.
Postbuckling Analysis for the Bending of a Long Beam With a Thin, Open, Circular Cross Section
Authors: Benson R. C.
Published: July 2009

A longitudinal bending moment applied to a thin, open section beam induces limit point buckling, due to a second-order effect that flattens the leaves of the cross section. It is shown here, for the case of a circular cross section, that the leaves themselves may exhibit multiple equilibrium configurations. Thus, the postbuckling behavior of the beam is not uniquely defined, and perturbations may shift the system to an unexpected loading path. In this paper, the various equilibrium configurations are examined and judged for stability. A “perfect” bifurcating geometry is identified, and a form of imperfection sensitivity is observed.
Free Vibrations of Noncircular Cylindrical Shells Having Circumferentially Varying Thickness
Authors: Suzuki K. , Leissa A. W.
Published: July 2009

An exact method using power series expansions is presented for solving free vibration problems for noncircular cylindrical shells having circumferential thickness variation. The method is used to obtain the first known results for this class of problems. Frequencies and mode shapes are presented for a set of elliptical cylindrical shells having second degree thickness variation in each quadrant.
Chute Flows of Granular Material: Some Computer Simulations
Authors: Campbell C. S. , Brennen C. E.
Published: July 2009

A computer simulation has been developed to describe unidirectional flows of granular materials. Results are presented for a simulation of the two-dimensional flow of disks or cylinders down an inclined plane or chute. Velocity and solid fraction profiles were measured from the simulated systems and compared with theoretical analyses and are compared with the limited experimental results now available. The behavior is shown to be critically dependent on a third field quantity—the “granular temperature”—a measure of the kinetic energy contained in the random motions of the particles.
Reflection and Transmission of Elastic Waves by a Periodic Array of Cracks
Authors: Angel Y. C. , Achenbach J. D.
Published: July 2009

The interaction of elastic waves with a planar array of periodically spaced cracks of equal length is investigated. For normal incidence, reflection and transmission of longitudinal and transverse wave has been considered. Application of finite Fourier transform techniques reduces the solution of the mixed-boundary value problem for a typical strip to that of a singular integral equation. The solution has been obtained numerically. The reflected and transmitted far-field displacements are shown to be superpositions of a finite number of propagating body-wave modes. The numerical results have been checked by an application of the balance of rates of energies. The reflection coefficients have been plotted versus both the frequency and the ratio of crack length to crack spacing. The results according to exact elastodynamic theory have been compared with two approximations. Good agreement is observed at low frequencies.
The Generation of Internal Gravity Waves in a Multilayered Moving Fluid by a Flap-Type Wave Maker
Authors: Mu¨ller M. R. , Shang P. C.
Published: July 2009

Experiments have examined the waveforms generated by a flap-type wave maker in a moving, three-layer fluid. Results show that the observed modulating waveforms could be predicted accurately for low frequencies and that if the two interfaces are sufficiently close together, both mode-one waves (whose amplitude vary in the vertical such that there is only one maximum) and mode-two waves (with a vertical amplitude structure that contains two relative maxima) are generated of similar amplitude. This results in downstream shifts from sinuous to varicose modes of oscillation.
A Finite Element Study of Low Reynolds Number Two-Phase Flow in Cylindrical Tubes
Authors: Shen E. I. , Udell K. S.
Published: July 2009

A finite element solution to the steady-state problem of an inviscid bubble flowing at low Reynolds number in a cylindrical tube occupied by a second viscous phase was obtained. Interfacial tension forces were balanced against the viscous and pressure forces in order to locate the position of bubble-liquid interface. Velocities, pressures, and film thicknesses were obtained as a function of the capillary number. Specific applications of these results include the description of multiphase flow in tubes and porous media, and blood cell movement in small capillaries. The numerical results are compared with published theories and experiments.
Nonuniqueness in Steady-State Heat Transfer in Prestressed Duplex Tubes—Analysis and Case History
Authors: Srinivasan M. G. , France D. M.
Published: July 2009

More than one steady-state solution is shown to exist for the problem of steady-state heat transfer across the walls of a duplex tube when the initial prestress between the inner and outer tubes is sufficiently low. This determination was used in explaining the apparently erratic heat-transfer performance of prestressed duplex tubes in the steam generating system of the Experimental Breeder Reactor II. The importance of the results lies not only in showing that nonuniqueness of steady-state solution applies to more complex geometries than heretofore analyzed, but also in demonstrating that such multiple steady-state conditions appear in practical situations.
The Role of Axial Edge Effects and Cavitation in Lubrication for Short Journal Bearings
Authors: Buckholz R. H. , Lin J. , Pan C. H. T.
Published: July 2009

Questions concerning the role of axial edge effects in short bearing theory are investigated using the method of matched asymptotic expansion applied to Reynolds lubrication equation. Attention was initially directed to this problem by other studies that indicate regions of nonconformity in the short bearing solution (i.e., small length to diameter ratio). In the present theory a matched asymptotic expansion method—using the bearing slenderness ratio as the small parameter—is appied to journal bearings. The axial inlet fluid film edge and axial cavitation boundary layers are examined. The axial boundary layers are shown to scale on the bearing slenderness ratio; these boundary layers are necessary to adjust the pressure to the prescribed boundary value. Cavitation boundary shapes, as determined from Reynolds’ free surface condition, are shown to be independent of the bearing eccentricity ratio. A reduction in load capacity—relative to previous theories—is shown. Pressure profiles obtained by the present theory are compared to previously reported short bearing results.
The Mechanics of High-Speed Rolling of Viscoplastic Materials
Authors: Tirosh J. , Iddan D. , Pawelski O.
Published: July 2009

In the present work a consideration is given to the speed effect on the mechanical performance of strip rolling process with time-dependent materials. The speed-governing dimensionless groups (Euler number and Bingham number) are identified. The suggested approach includes, in an upper bound sense (mixed with stress-equilibrium solutions), the dynamic stress distribution of a Bingham-like viscoplastic material, the speed-dependent energy dissipations, the self-heated surface temperature, and the associated material softening. All these effects are coupled and contributed for explaining the apparently puzzling empirical evidence showing reduction in the roll torque and separation force while increasing the rolling speed. For a relativelyl slow speed, the predicted roll separtion force matches very well an available experimental data as well as Kobayashi’s rigid-plastic finite element analysis. The predicted torque, however, is somewhat higher than the experiments, in particular when the roll-flatness correction is incorporated. The capability of forecasting the variation of roll force with various speeds (reaching high speeds), was checked versus Ford’s measurements and a satisfactory agreement is demonstrated.
On the Numerical Solution of One-Dimensional Continuum Problems Using the Theory of a Cosserat Point
Authors: Rubin M. B.
Published: July 2009

The theory of a Cosserat point is specialized to describe the motion of a one-dimensional continuum. Attention is focused on two problems of an elastic bar. Vibration of a linear-elastic bar is considered in the first problem and static deformation of a nonlinear-elastic bar subjected to a uniform body force is considered in the second problem. A closed-form solution is derived for each problem by dividing the bar into two elements, each of which is modeled as a Cosserat point. The predictions of the two-element approximation are shown to be very accurate.
Groove Bottom Contours of Minimum Stress Concentration for Antiplane Shear Deformation
Authors: Eldiwany B. H. , Wheeler L. T.
Published: July 2009

Results from free streamline hydrodynamics are exploited in order to solve optimization problems for antiplane shear deformation, in which the stress concentration is to be minimized. These problems pertain to the optimum shapes for grooves cut into a half-space. We obtain results, which from the standpoint of the hydrodynamics problem, complement those presently in the literature. The solution is given in an integral form which in general must be evaluated by numerical methods, but that reduces to elliptic integrals for the special case of a notch whose faces meet the half-space boundary at right angles.
Dynamics and Stability of Coaxial Cylindrical Shells Conveying Viscous Fluid
Authors: Paidoussis M. P. , Misra A. K. , Chan S. P.
Published: July 2009

In this paper the dynamics and stability characteristics of coaxial cylindrical shells containing incompressible, viscous fluid flow are examined in contrast to previous studies where the fluid has been considered to be inviscid. Specifically, upstream pressurization of the flow (to overcome frictional pressure drop) and skin friction on the shell surfaces are taken into account, generating time-mean normal and tangential loading on the shells. Shell motions are described by Flu¨gge’s thin shell equations, suitably modified to incorporate the time-mean stress resultants arising from viscous effects. The fluctuating fluid forces, coupled to shell vibration, are determined entirely by means of linearized potential flow theory and formulated with the aid of generalized-force Fourier-transform techniques. It is found that the effect of viscosity in the annular flow generally tends to destabilize the system, vis-a`-vis inviscid flow, whereas viscous effects in the inner flow stabilize the system. These effects can be quantitatively very important, so that, generally, neglect of viscous effects cannot be justified.
A Beam Theory for Anisotropic Materials
Authors: Bauchau O. A.
Published: July 2009

Beam theory plays an important role in structural analysis. The basic assumption is that initially plane sections remain plane after deformation, neglecting out-of-plane warpings. Predictions based on these assumptions are accurate for slender, solid, cross-sectional beams made out of isotropic materials. The beam theory derived in this paper from variational principles is based on the sole kinematic assumption that each section is infinitely rigid in its own plane, but free to warp out of plane. After a short review of the Bernoulli and Saint-Venant approaches to beam theory, a set of orthonormal eigenwarpings is derived. Improved solutions can be obtained by expanding the axial displacements or axial stress distribution in series of eigenwarpings and using energy principles to derive the governing equations. The improved Saint-Venant approach leads to fast converging solutions and accurate results are obtained considering only a few eigenwarping terms.
Edge Vibrations in Laminated Composite Plates
Authors: Dong S. B. , Huang K. H.
Published: July 2009

Plane strain edge vibrations or end modes in laminated composite plates are investigated by means of finite elements. This method is capable of modeling the behavior of any laminate construction whose properties are completely anisotropic within the plane. Two eigenvalue problems involving nonsymmetric matrices are derived. The form of each eigenvalue problem depends on the parameter chosen for the eigenvalue, i.e., either the frequency or the axial wave number. Orthogonality relations are discussed. Examples on two four-ply composite plates are given as illustrations. The analogy of the analysis procedure as the dynamic counterpart of the quantitative measure of Saint-Venant’s principle is called to attention.
Dynamic Rate Effects on Timoshenko Beam Response
Authors: Ross T. J.
Published: July 2009

The problem of a viscoelastic Timoshenko beam subjected to a transversely applied step-loading is solved using the Laplace transform method. It is established that the support shear force is amplified more than the support bending moment for a fixed-end beam when strain rate influences are accounted for implicitly in the viscoelastic constitutive formulation.
The Dynamics of a Harmonically Excited System Having Rigid Amplitude Constraints, Part 2: Chaotic Motions and Global Bifurcations
Authors: Shaw S. W.
Published: July 2009

The simple model described in [1] was shown to exhibit nonlinear behavior such as subharmonic responses. In this paper parameter regions are examined in which no simple stable motions exist. In such regions complicated bifurcation sequences are encountered which result in long period and chaotic motions. These motions are irregular, bounded responses to periodic excitation and have not been previously considered in systems having two-sided amplitude constraints.
A Note on Numerical Analysis of Dynamic Coupled Thermoelasticity
Authors: Liu W. K. , Chang H.-G.
Published: July 2009

A method of computation for dynamic coupled thermoelasticity is developed. This approach has the advantage of applying an implicit algorithm to the elasticity equation and an unconditionally stable explicit algorithm to the heat conduction equation. As a result, the coupled matrix equations are “symmetric” and “profiled.” In addition, unconditional stability is sought.
A New Displacement Form for the Nonlinear Equations of Motion of Shells of Revolution
Authors: Simmonds J. G.
Published: July 2009

In the theory of shells of revolution undergoing torsionless, axisymmetric motion, an extensional and a bending hoop strain are introduced that are linear in the displacements, regardless of the magnitudes of the strains and the meridional rotation. The resulting equations of motion and boundary conditions are derived and some common conservative surface loads are listed along with their potentials. The governing equations appear to be the simplest possible in terms of displacements.
Large-Amplitude Oscillations of Unsymmetrically Laminated Anisotropic Rectangular Plates Including Shear, Rotatory Inertia, and Transverse Normal Stress
Authors: Sivakumaran K. S. , Chia C. Y.
Published: July 2009

This paper is concerned with nonlinear free vibrations of generally laminated anisotropic elastic plates. Based on Reissner’s variational principle a nonlinear plate theory is developed. The effects of transverse shear, rotatory inertia, transverse normal stress, and transverse normal contraction or extension are included in this theory. Using the Galerkin procedure and principle of harmonic balance, approximate solutions to governing equations of unsymmetrically laminated rectangular plates including transverse shear, rotatory inertia, and transverse normal stress are formulated for various boundary conditions. Numerical results for the ratio of nonlinear frequency to linear frequency of unsymmetric angle-ply and cross-ply laminates are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, and aspect ratio and for different boundary conditions. Present results are also compared with available data.
Eigenfunctions at a Singular Point in Transversely Isotropic Materials Under Axisymmetric Deformations
Authors: Ting T. C. T. , Jin Yijian , Chou S. C.
Published: July 2009

When a two-dimensional elastic body that contains a notch or a crack is under a plane stress or plane strain deformation, the asymptotic solution of the stress near the apex of the notch or crack is simply a series of eigenfunctions of the form ρδf (ψ,δ) in which (ρ,ψ) is the polar coordinate with origin at the apex and δ is the eigenvalue. If the body is a three-dimensional elastic solid that contains axisymmetric notches or cracks and subjected to an axisymmetric deformation, the eigenfunctions associated with an eigenvalue contains not only the ρδ term, but also the ρδ+1, ρδ+2… terms. Therefore, the second and higher-order terms of the asymptotic solution are not simply the second and subsequent eigenfunctions. We present the eigenfunctions for transversely isotropic materials under an axisymmetric deformation. The degenerate case in which the eigenvalues p1 and p2 of the elasticity constants are identical is also considered. The latter includes the isotropic material as a special case.
First-Order Variation in Elastic Fields Due to Variation in Location of a Planar Crack Front
Authors: Rice J. R.
Published: July 2009

The problem explained in the title is formulated generally and given an explicit solution for tensile loadings opening a half-plane crack in an infinite body. For the half-plane crack, changes in the opening displacement between the crack surfaces and in the stress-intensity factor distribution along the crack front are calculated to first order in an arbitrary deviation of the crack-front position from a reference straight line. The deviations considered lie in the original crack plane. The results suggest that in the presence of loadings that would induce uniform conditions along the crack front, if it were straignt, small initial deviations from straightness should reduce in size during quasistatic crack growth if of small enough spatial wavelength but possibly enlarge in size if of longer wavelength. The solution methods rely on elastic reciprocity, in terms of a three-dimensional version of weight function theory for tensile cracks, and on direct solution of elastic crack problems. The weight function is derived for the half-plane crack by solving for the first-order variation in the elastic displacement field associated with arbitrary variations of the crack front from a straight reference line. Also, a new three-dimensional weight function theory is developed for planar cracks under general mixed-mode loading involving tension and shears relative to the crack, the connection between weight functions and the Green’s function for crack problems is shown, and some results are given for the half-plane crack on the variations of elastic fields for variation of crack-front location in the presence of general loadings including shear.