bluuebunny/crossref_metadata_2025 huggingface dataset:
Elastic Moduli of Gray and Nodular Cast Iron
Authors: Speich G. R. , Schwoeble A. J. , Kapadia B. M.
Published: July 2009

The elastic moduli of both gray and nodular cast iron were measured by a pulse-echo elastic-wave technique at ambient and elevated temperatures up to 760°C. When compared at similar graphite contents, the elastic moduli of gray cast iron were much lower than those of nodular cast iron. These results are satisfactorily explained by theoretical models for the elastic moduli of two-phase solids which take into account not only the volume fraction but also the shape of the graphite particles. The temperature-dependence of the elastic moduli of both gray and nodular cast iron can also be correctly predicted from these same models.
Steady-State Vibrations of a Beam on a Pasternak Foundation for Moving Loads
Authors: Saito H. , Terasawa T.
Published: July 2009

The response of an infinite beam supported by a Pasternak-type foundation and subjected to a moving load is investigated. It is assumed that the load is uniformly distributed over the finite length on a beam and moves with constant velocity. The equations of motion based on the two-dimensional elastic theory are applied to a beam. Steady-state solutions are determined by applying the exponential Fourier transform with respect to the coordinate system attached to the moving load. The results are compared with those obtained from the Timoshenko and the Bernoulli-Euler beam theories, and the differences between the displacement and stress curves obtained from the three theories are clarified.
Asymptotic Integration Methods Applied to Rotating Beams
Authors: Steele C. R. , Barry K. E.
Published: July 2009

The in-plane vibrational characteristics of an off-axis clamped beam subjected to either compressive or tensile forces arising from steady rotation are studied. The differential equations of motion are cast into state vector form and solved using asymptotic matrix integration methods. The general theory of these methods is described in this paper and their application to the analysis of rotating beams is made. The advantages inherent in these methods with regard to accuracy, reduction of analytical complexity, and savings in computational costs are discussed.
The Steady-State Response of a Rotating Damped Disk of Variable Thickness
Authors: Irie T. , Yamada G. , Aomura S.
Published: July 2009

The stress distribution and steady-state response of a rotating damped annular disk of variable thickness are determined by means of the matrix method. The equation of equilibrium and the equations for the flexural vibration of the rotating disk are written as a respective coupled set of first-order differential equations by use of the matrices of the disk. The elements of the matrices are calculated by numerical integration of the equations, and the stress components and the driving-point impedance and force transmissibility of the disk are obtained by using these elements. The method is applied to free-clamped rotating disks with linearly, exponentially, and hyperbolically varying thickness driven by a harmonic force at the free outer edge, and the effects of the angular velocity and the variable thickness are studied.
A Stochastic Model for Predicting the Velocity Distribution of Warhead Fragments
Authors: Cohen E. A.
Published: July 2009

It has been the practice of those who study the velocity of fragments from a warhead to average the velocity of the fragment over its path rather than to examine in greater detail the underlying stochastic process. In this paper we present a more careful analysis of the pertinent statistical process by taking into account the correlations that exist along the trajectory of the fragment. One assumes that the fragments generally tumble uniformly and that drag coefficient depends only on presented area. This seems to be a good approximation in the supersonic regime (from Mach 3 to Mach 6, for example). A brief discussion of the case when drag, lift, and gravity effects are all assumed to be present is given. Also, we present a new family of “multivariate uniform distributions” geared to the physics of the problem.
Partitioned Transient Analysis Procedures for Coupled-Field Problems: Accuracy Analysis
Authors: Park K. C. , Felippa C. A.
Published: July 2009

Partitioned solution procedures for direct time integration of second-order coupled-field systems are studied from the standpoint of accuracy. These procedures are derived by three formulation steps: implicit integration of coupled governing equations, partitioning of resulting algebraic systems and extrapolation on the right-hand partition. It is shown that the combined effect of partition, extrapolation, and computational paths governs the choice of stable extrapolators and preservation of rigid-body motions. Stable extrapolators for various computational paths are derived and implementation-extrapolator combinations which preserve constant-velocity and constant-acceleration rigid-body motions are identified. A spectral analysis shows that the primary error source introduced by a stable partition is frequency distortion. Finally, as a guide to practical applications, the advantages and shortcomings of five specific partitions are discussed.
Some Results on the Nature of Eigenvalues of Discrete Damped Linear Systems
Authors: Inman D. J. , Andry A. N.
Published: July 2009

An analysis of the conditions under which the modes of a damped linear lumped parameter system are either all critically damped, overdamped or underdamped is presented. These conditions are derived from the definiteness of certain combinations of the coefficient matrices. Some results concerning the completeness of the eigenvectors are stated. The conditions are compared to previous results and their usefulness is illustrated by numerical examples.
An Unravelling Algorithm for Global Analysis of Dynamical Systems: An Application of Cell-to-Cell Mappings
Authors: Hsu C. S. , Guttalu R. S.
Published: July 2009

A new method is offered here for global analysis of nonlinear dynamical systems. It is based upon the idea of constructing the associated cell-to-cell mappings for dynamical systems governed by point mappings or governed by ordinary differential equations. The method uses an algorithm which allows us to determine in a very effective manner the equilibrium states, periodic motions and their domains of attraction when they are asymptotically stable. The theoretic base and the detail of the method are discussed in the paper and the great potential of the method is demonstrated by several examples of application.
The Contact Problem for a Rigid Inclusion Pressed Between Two Dissimilar Elastic Half Planes
Authors: Gladwell G. M. L.
Published: July 2009

Paper concerns the plane-strain problem of a rigid, thin, rounded inclusion pressed between two isotropic elastic half planes with different elastic constants. Required to find the extents of the contact regions between each plane and the inclusion, and the contact stress distributions. The governing integral equations are solved approximately by using Chebyshev expansions. Numerical results are presented.
Some Considerations on Thermal Shock Problems in a Plate
Authors: Takeuti Y. , Furukawa T.
Published: July 2009

Manson has given a well-known conventional approach to thermal shock problems in a plate. In his investigation, however, the inertia term and the thermomechanical coupling term were neglected in the governing field equations. As a result, the treatment became quasi-static, and then it was inadequate to model thermal shock problems having a steep time-gradient in the thermal and mechanical fields. In the present paper, we examine a rigorous treatment to find the exact solution for thermal shock problems in a plate when the following two effects are taken into account: (a) Dynamic treatment due to the presence of an inertia term. (b) A coupled thermal stress problem in the presence of a thermoelastic coupling term. Thus we can determine the significance of these effects on the thermal stress distribution when a sudden change of temperature occurs.
Theoretical and Experimental Investigation of Stress Waves at a Junction of Three Bars
Authors: Desmond Thomas P.
Published: July 2009

When a longitudinal stress wave impinges on a junction of three elastic bars (where two bars are collinear and a third is noncollinear to the others), six separate stress waves are produced. A longitudinal stress wave and a flexural wave are reflected back along the first bar, and a stress wave of each type is transmitted into the second and third bars. For the theoretical treatment of these waves, the simple one-dimensional theory is used to describe the propagation of longitudinal (or axial) waves, and the Timoshenko beam theory is used to describe the propagation of transverse (or bending) waves. The method of characteristics is used to transform the partial differential equations into total differential equations. The total differential equations are then solved by a forward differencing finite-difference scheme. For solution at the junction, the junction is modeled as a rigid-body element. Impact experiments were performed to verify the analysis, and agreement between theory and experiment is very satisfactory.
Free Vibration of Thin-Walled Open Section Beams With Unconstrained Damping Treatment
Authors: Narayanan S. , Verma J. P. , Mallik A. K.
Published: July 2009

Free-vibration characteristics of a thin-walled, open cross-section beam, with unconstrained damping layers at the flanges, are investigated. Both uncoupled transverse vibration and the coupled bending-torsion oscillations, of a beam of a top-hat section, are considered. Numerical results are presented for natural frequencies and modal loss factors of simply supported and clamped-clamped beams.
Note on the Energy-Release Rate for a Crack Starting From the Apex of a Wedge
Authors: Yatomi C.
Published: July 2009

We show that for a Mode III crack starting from the apex of a wedge, the initial value of the energy-release rate is zero, although the stresses at the crack tip are unbounded.
Numerical and Experimental Simulations of Pseudoplastic Transient Pipe Flows
Authors: de Saint Victor X. , Ly D. P. , Bellet D.
Published: July 2009

The purpose of this work is to develop and to compare different methods for the determination of startup flows of a pseudoplastic fluid in pipes under a varying pressure gradient. Three methods are proposed: 1. A method involving a finite-difference calculation. 2. A method using an approximation of the acceleration term in the equation governing the phenomenon. 3. An experimental method based on measurements of local velocities by means of Laser-Doppler anemometry. The most interesting point of this work is the good agreement observed between the three methods in the non-Newtonian case.
Creep of 2618 Aluminum Under Side-Steps of Tension and Torsion and Stress Reversal Predicted by a Viscous-Viscoelastic Model
Authors: Findley W. N. , Lai J. S.
Published: July 2009

Combined tension and torsion creep experiments are reported in which (A) one stress component was increased or decreased while the other remained constant; (B) one stress component was removed while the other remained constant; (C) torsion was partially or fully reversed with or without simultaneous constant tension. Among the observed features of the experimental results were the following: when one stress component was removed the creep from the other component was unaffected; upon small reductions in stress there was no recovery-type behavior; and when torsion was fully reversed, all prior strain was wiped out. A nonlinear viscous-viscoelastic model was used for which the material constants were derived from constant-stress creep and recovery data and previously reported. This model, together with certain necessary modifications, was used to compute the creep resulting from the complex stress histories described. Most features of the experimental results were predicted reasonably well by the modified theory.
An Isoparametric Finite Element With Nodal Derivatives
Authors: Webster W. D.
Published: July 2009

A finite element using the nodal point values of the first partial derivatives of the unknown function with respect to the coordinates to increase the order of the resulting interpolating polynomial is formulated as an isoparametric element. The shape functions in local coordinates are given and then to satisfy requirements for the transformation of derivatives are modified for use with the global coordinates. Examples of a cantilever beam, a curved cantilever beam, and a flat bar with a hole demonstrate the high-order capabilities of the element. The advantages of the element over other isoparametric elements are discussed.
A Perturbation Analysis of Fluid-Structure Interactions in a Model Test System
Authors: Kalumuck K. M. , Huber P. W.
Published: July 2009

A perturbation analysis of fluid-structure interactions in a model test system of controlled flexibility excited by a complex hydrodynamic transient is presented. The analysis demonstrates the important features of the perturbation method and its implementation. Comparison of predictions with experiment provides a test of the analytical procedure and its underlying assumptions. The results illustrate the important effect of transient liquid mass redistribution on the flexible system response.
An Embedded Elliptical Crack, in an Infinite Solid, Subject to Arbitrary Crack-Face Tractions
Authors: Vijayakumar K. , Atluri S. N.
Published: July 2009

In this paper, following a critical assessment of earlier work of Green and Sneddon, Segedin, Kassir, and Sih (who obtained solutions for specific cases of normal loading on the crack face and the cases of constant and linear shear distribution on the crack face), Shah and Kobayashi (whose work is limited to the case of third-order polynomial distribution of normal loading on the crack face), and Smith and Sorensen (whose work is limited to the case of a third-order polynomial variation of shear loading on the crack face), a general solution is presented for the case of arbitrary normal as well as shear loading on the faces of an embedded elliptical crack in an infinite solid. The present solution is based on a generalization of the potential function representation used by Shah and Kobayashi. Expressions for stress-intensity factors near the flaw border, as well as for stresses in the far-field, for the foregoing general loadings, are given.
Dispersion in Laminar Flow Through Tubes by Simultaneous Diffusion and Convection
Authors: Yu J. S.
Published: July 2009

The dispersion of a small quantity of a solute initially injected into a round tube in which steady-state laminar flow exists is critically examined. It is shown that the mean solute concentration profile is far from being symmetric at small dimensionless times after injection. The mean concentration and the axial location at the peak of the profile are presented in detail as functions of time for flow with various Peclet numbers. It is suggested that such results may be useful for determining either the molecular diffusion coefficient or the mean flow velocity or both from experimental measurements. A previously established criterion in terms of the Peclet number for determining the minimum dimensionless time required for applying Taylor’s theory of dispersion is graphically illustrated. Although the complete generalized dispersion equation of Gill’s model is exact, the truncated two-term form of it with time-dependent coefficients is exact only asymptotically at large values of time; however, at small Peclet numbers, the two-term approximation is shown graphically to be reasonably satisfactory over all values of time. The exact series solution is compared with the solution of Tseng and Besant through the use of Fourier transform.
Droplet Dynamics in Creeping Flows
Authors: Stewart M. B. , Morrison F. A.
Published: July 2009

The accelerated motion of a liquid droplet is investigated analytically. The equation of motion is developed through an analysis of the internal and external fluid motions. Response to step changes in applied force and external fluid velocity are determined. Oscillating forces and velocities are treated and frequency response characteristics found. In the appropriate limits, the results reduce to the known behavior of bubbles or rigid particles.
Stress-Intensity Factor for a Three-Dimensional Rectangular Crack
Authors: Kassir M. K.
Published: July 2009

An integral transform solution is developed to reduce the problem of determining the stress-intensity factor of a narrow three-dimensional rectangular crack to the solution of a Fredholm integral equation of the second kind. The crack is assumed to be embedded in an infinite elastic solid subjected to normal loading. Numerical results are presented to indicate a reduction in the value of the stress-intensity factor from the plane strain case. For an elongated rectangular crack the plane-strain stress-intensity factor is recovered.
Thickness Effects Are Minor in the Energy-Release Rate Integral for Bent Plates Containing Elliptic Holes or Cracks
Authors: Simmonds J. G. , Duva J.
Published: July 2009

The exact value of Sanders’ path-independent, energy-release rate integral I for an infinite, bent elastic slab containing an elliptic hole is shown to be approximated by its value from classical plate theory to within a relative error of O(h/c)F(e), where h is the thickness, c is the semimajor axis of the ellipse, and F is a function of the eccentricity e. This result is based on Golden’veiser’s analysis of three-dimensional edge effects in plates, as developed by van der Heijden. As the elliptic hole approaches a crack, F(e)~In (1−e). However, this limit is physically meaningless, because Golden’veiser’s analysis assumes that h is small compared to the minimum radius of curvature of the ellipse. Using Knowles and Wang’s analysis of the stresses in a cracked plate predicted by Reissner’s theory, we show that the relative error in computing I from classical plate theory is only O(h/c)In(h/c), where c is the semicrack length. Our results suggest that classical plate and shell theories are entirely adequate for predicting crack growth, within the limitations of applying any elastic theory to an inherently inelastic phenomenon.
Large Plane-to-Surface Deformations of Membranes With Inclusion
Authors: Fenner W. J. , Wu C. H.
Published: July 2009

For large deformations, the strain-energy density function for a neo-Hookean membrane is dominated by the sum of squares of the two principal stretch ratios. This property reduces the displacement equations of equilibrium for the class of problems considered to three uncoupled linear equations. The nonlinear coupling appears only in the algebraic stress calculations. In light of the scarcity of exact solutions to nontrivial problems, the approximate but explicit solutions obtained here should be of some practical value.
Dynamic Stability of Truncated Conical Shells Under Pulsating Torsion
Authors: Tani J.
Published: July 2009

The dynamic stability of clamped, truncated conical shells under periodic torsion is analyzed by the Galerkin method in conjunction with Hsu’s results. The instability regions of practical importance are clarified for relatively low frequency ranges. Numerical results indicate that under the purely periodic torsion only the combination instability region exists but that with an increase in the static torsion the principal instability region becomes most significant. The relative openness of the instability regions is found to depend sensitively on the circumferential phase difference of two vibration modes excited simultaneously at the resonance with the same circumferential wave number.
Arrest of Mode III Fast Fracture by a Transition From Elastic to Viscoplastic Material Properties
Authors: Aboudi J. , Achenbach J. D.
Published: July 2009

The transient problem of arrest of a rapidly propagating Mode III crack has been investigated for a crack which initially propagates in an elastic solid, and then enters a region of viscoplastic material properties. The transition to the viscoplastic behavior is modeled by a gradual process which starts at a certain time at which the constitutive relations change in a timewise manner from elastic to elastic-viscoplastic. Both deceleration and complete arrest of the crack have been treated. The solution has been obtained numerically by a finite-difference procedure. Arrest of a crack in a perfectly elastic material has been treated as a special case. Several field quantities such as the effective plastic strain, plastic work, total strain, and crack surface displacement have been computed, and their relation to arrest criteria have been explored.
Stress Concentrations in Cylindrically Orthotropic Composite Plates With a Circular Hole
Authors: Hoff N. J.
Published: July 2009

The equations governing the distribution of the stresses in a cylindrically orthotropic plate with a circular hole are solved for the case when the plate is subjected to uniform uniaxial traction. Closed-form solutions are given for the circumferential stresses along the edge of the hole.
Equilibrium of Heavy Elastic Cylindrical Shells
Authors: Wang C.-Y. , Watson L. T.
Published: July 2009

An originally circular, heavy elastic shell rests on a horizonal surface. The equilibrium shape is governed by the heavy elastica equations. The solutions depend heavily on the parameter B, which represents the relative importance of density and perimeter length to flexural rigidity. There are four distinct cases. A perturbation analysis is obtained for small B while a similarity solution exists for large B. The general solution is obtained by accurate numerical integration using a least change secant update quasi-Newton method and a new homotopy method.
Nonlinear Harmonic Oscillations of Gyroscopic Structural Systems and the Case of a Rotating Ring
Authors: Maewal A.
Published: July 2009

Two related problems are investigated in order to study via a simple example the influence of gyroscopic forces on nonlinear harmonic oscillations of rotationally symmetric shell structures. First, the amplitude frequency equations are calculated for circumferentially traveling waves in a circular ring rotating about its geometrical axis. The results show that in the range of rotational speeds considered the backward traveling waves exhibit hardening type of response, whereas for the forward traveling waves there is a transition from hardening to softening type of behavior as the rotational speed increases. The second part of the paper is devoted to an analysis of interaction between the two traveling waves which is expected at low angular speeds. The results, valid for arbitrary shells of revolution, reveal the existence of secondary bifurcation points on the branches corresponding to the traveling waves, and the response on the secondary branches is found to be close to standing waves which do not appear at all as solutions of the linear free-vibration problem for the rotating shell.
Application of the Method of Integral Relations to the Calculation of Two-Dimensional Incompressible Turbulent Boundary Layer
Authors: Yeung W.-S. , Yang R.-J.
Published: July 2009

The orthonormal version of the Method of Integral Relations (MIR) was applied to solve for a two-dimensional incompressible turbulent boundary layer. The flow was assumed to be nonseparating. Flows with favorable, unfavorable, and zero pressure gradient were considered, and comparisons made with available experimental data. In general, the method predicted very well the experimental results for flows with favorable or zero pressure gradient; for flows with unfavorable pressure gradient, it predicted the experimental data well only up to a certain distance from the initial station. This result is due to the flow not being in equilibrium beyond that distance. Finally, the scheme was shown to be efficient in obtaining numerical solutions.
The Plane Parallel Flow of a Binary Mixture of Fluids
Authors: Srivastava L. M. , Srivastava V. P.
Published: July 2009

The flow of a binary mixture of chemically inert incompressible, Newtonian fluids over an infinite plate, set into motion in its plane by impulse and by oscillation, is studied. The binary mixture consists of (i) two different viscous density nonstratified fluids, and (ii) two different viscous density stratified fluids. The exact solutions are obtained using two methods, (i) Laplace transform and (ii) Hankel transform. To further study the velocities and the wall shear stress, asymptotic expansion are found for small and large times. Some other results of physical importance such as results for noninteracting fluids, strongly interacting fluids, and extremely different fluids are also derived and compared analytically with other results. Finally, to gain an insight into the patterns of the flow, numerical study of the results has been made in detail using digital computer. A strong motivation of the present analysis has been the hope that such a theory of fluids is useful in providing some insight in rheological properties of complex fluids as polymers, liquid crystals and, in particular, blood in the vessels of small diameter. Also the theory of fluids might provide an improved understanding of such diverse subjects as diffusion of proteins, swimming of micro-organism and particle deposition in respiratory tract.
Direct Approach to Aerodynamic Design Problems
Authors: Chin W. C.
Published: July 2009

“Direct” small disturbance approaches to inviscid aerodynamic “inverse” or “design” problems in two and three-dimensional, subsonic, supersonic, and transonic flow, are given which extend the stream function method of Chin and Rizzetta. Our shape solutions generally involve nonlinear differential equations of mixed type for scalar “streamlike” functions Ψ which are solved with Neumann conditions related to prescribed surface pressure and “Kutta-type” constraints on edge closure or included angle specified using jumps in ψ or its streamwise derivative. Because edge constraints are enforced automatically the methods are direct. They resemble “analysis” potential function (φ) methods for flows past fixed shapes where the jumps [φ] are chosen “directly” to insure smooth trailing edge flow; thus computational methods for analysis apply with minor change to design. Dualities relating the analysis problem for camber to the design problem for thickness, and the design problem for camber to the analysis problem for thickness, are given for planar flow; both closed trailing edges, and cusped ones, generally opened, which model the displacement effects of viscous wakes, are considered. These are extended to three dimensions and consequences of an inverse analogy to Prandtl’s lifting line for analysis problems are explored. Transonic inverse formulations for airfoils, wings, fans, cascades, inlets, and nacelles are discussed and preliminary numerical results are presented.
On the Radial Oscillations of Multiple Gas Bubbles in an Incompressible Liquid
Authors: Foody B. E. , Huber P. W.
Published: July 2009

The radial oscillations of multiple gas bubbles in an incompressible liquid bounded by plane solid or free surfaces are analyzed. Derivation of the normal mode frequencies and mode shapes of two, three, and four bubble configurations in an unbounded liquid illustrate the method of analysis. Expressions for the oscillation frequencies of bubbles near free and solid surfaces are derived.
Gas-Driven Fracture Propagation
Authors: Nilson R. H.
Published: July 2009

A one-dimensional gas-flow drives a wedge-shaped fracture into a linearly elastic, impermeable half space which is in uniform compression, σ∞, at infinity. Under a constant driving pressure, p0, the fracture/flow system accelerates through a sequence of three self-similar asymptotic regimes (laminar, turbulent, inviscid) in which the fracture grows like an elementary function of time (exponential, near-unity power, and linear, respectively). In each regime, the transport equations are reducible under a separation-of-variables transformation. The integro-differential equations which describe the viscous flows are solved by iterative shooting methods, using expansion techniques to accomodate a zero-pressure singularity at the leading edge of the flow. These numerical results are complemented by an asymptotic analysis for large pressure ratio (N = p0/σ∞ → ∞) which exploits the disparity between the fracture length and penetration length of the flow. Since the seepage losses to a surrounding porous medium are shown to be negligable in the late-time long-fracture limit, the results have application to geologic problems such as: containment evaluation of underground nuclear tests, stimulation of oil and gas wells, and permeability enhancement prior to in situ combustion processes.
A Self-Consistent Scheme for the Relaxation Behavior of Metals
Authors: Weng G. J.
Published: July 2009

We identify in this paper that stress relaxation in metals is a “strain-free” process. The corresponding self-consistent relations between the strain, and stress variations of a grain and of its aggregate are derived from Eshelby’s solution of an ellipsoidal inclusion. It is shown that, under such a process, the strain in a more favorably oriented grain continues to rise and that its stress decreases more drastically than that of the aggregate; conversely, for a less favorably oriented grain, its strain decreases and its stress relaxes less. The self-consistent relations are supplemented with a temperature-dependent, physically consistent constitutive equation for the slip system. Such an equation enables us to determine the single crystal constants at one temperature from the polycrystal data at another temperature; it also makes the self-consistent scheme applicable to the varying-temperature environment. The established theory was finally applied to predict the relaxation behavior of an RR-59 aluminum alloy under combined stress; the results showed reasonably good agreement with the experimental data.
A Critical Appraisal of Static Hardness Measurements
Authors: Rubenstein C.
Published: July 2009

A semiempirical analysis of the indentation process is made as a result of which the hardness indentation data obtained with ball, cone and square-based pyramid indenters are related to the uniaxial stress-strain curve of the indented material. It is shown that deductions from the analysis are valid only for annealed materials. The factors liable to result in erroneous hardness readings are considered and the influence of residual stresses in the surface and the subsurface layers of the material under examination are shown to explain (i) the dependence of cone and pyramid hardness on the applied load and (ii) the anomalous influence of cone angle on the measured hardness when large angle indenters are pressed into materials which have been strain-hardened prior to the hardness measurement.
Heat Conduction Through a Flat Punch
Authors: Comninou Maria , Barber J. R. , Dundurs John
Published: July 2009

An elastic half plane is indented by a perfectly conducting rigid flat punch, which is maintained at a different temperature from the half plane. It is found that, depending on the magnitude and direction of the total heat flux, one of the following states occurs: separation at the punch corners, perfect thermal contact throughout the punch face, or an imperfect contact region at the center with adjacent perfect contact regions.
A Diagonally Dominant Solution for the Cylinder End Problem
Authors: Gerhardt T. D. , Cheng Shun
Published: July 2009

An improved elasticity solution for the cylinder problem with axisymmetric torsionless end loading is presented. Consideration is given to the specification of arbitrary stresses on the end of a semi-infinite cylinder with a stress-free lateral surface. As is known from the literature, the solution to this problem is obtained in the form of a nonorthogonal eigenfunction expansion. Previous solutions have utilized functions biorthogonal to the eigenfunctions to generate an infinite system of linear algebraic equations for determination of the unknown expansion coefficients. However, this system of linear equations has matrices which are not diagonally dominant. Consequently, numerical instability of the calculated eigenfunction coefficients is observed when the number of equations kept before truncation is varied. This instability has an adverse effect on the convergence of the calculated end stresses. In the current paper, a new Galerkin formulation is presented which makes this system of equations diagonally dominant. This results in the precise calculation of the eigenfunction coefficients, regardless of how many equations are kept before truncation. By consideration of a numerical example, the present solution is shown to yield an accurate calculation of cylinder stresses and displacements.
On the Nonlinear Intrinsic Dynamics of Doubly Curved Shells
Authors: Libai A.
Published: July 2009

The field equations of motion and compatibility for the nonlinear dynamics of doubly curved shells are recast in an intrinsic form, in terms of the metric and curvature functions of their reference surfaces. For appropriate input, the motion of the shell is described without the need for an external reference coordinate system or the use of vector quantities such as position, velocity, and acceleration. The equations are shown to be readily applicable to time integration schemes. Such cases, as the (spatially) constant load problem and the inextensional dynamics problem, are also considered. The need for further work in the area is emphasized.
Harmonic Waves in Fiber-Reinforced Orthotropic Elastic Composites
Authors: Nemat-Nasser S. , Yamada M.
Published: July 2009

The dispersive property of fiber-reinforced elastic composites consisting of orthotropic materials is studied. Based on a new quotient recently proposed by one of the authors, approximate dispersion curves are obtained, and the influence of anisotropy is illustrated.
Rotating Flow Over a Disk Sector
Authors: Toren M. , Solan A. , Ungarish M.
Published: July 2009

The rotating boundary layer flow over a plane sector of angle θs and infinite radius is solved. For sufficiently large radius the radial coordinate is eliminated by a Von Karman transformation, leaving a nonaxisymmetric flow in (θ,z), which cyclically changes over the full circle, from a Blasius boundary layer, to a Bodewadt flow, and to a rotating wake. Leading terms of the three-dimensional perturbation of the Blasius flow, and of the rotating wake are given, and the matching over the full circle is outlined for limiting values of θs.
Dynamic Behavior of a Buried Pipe in a Seismic Environment
Authors: Datta S. K. , Shah A. H. , El-Akily N.
Published: July 2009

Axisymmetric dynamic response of a buried pipe due to an incident compressional wave is the subject of this investigation. The pipe has been modeled as a thin cylindrical shell of linear homogeneous isotropic elastic material embedded in a linear isotropic homogeneous elastic medium of infinite extent. The response characteristics of the pipe due to changes in the material properties of the surrounding medium have been carefully studied. It is found that even at long wavelengths and low frequencies, the dynamic response is significantly altered by the changes in the Poisson’s ratio and the rigidity modulus of the surrounding medium. Further, it is found that there are real resonant frequencies of the pipe that are also significantly dependent on these quantities, as well as on the wavelength.
Stress Wave Propagation in a Bar of Arbitrary Cross Section
Authors: Nagaya K.
Published: July 2009

In this paper a method for solving wave propagation problems of an infinite bar of arbitrary cross section has been presented. The frequency equation for finding phase velocites for longitudinal, torsional, and flexural waves have been obtained by making use of the Fourier expansion collocation method which has been developed by the author on the vibration and dynamic response problems of membranes and plates. As a numerical example, the phase velocities versus wave numbers are calculated for elliptical and truncated elliptical cross-section bars.
Simultaneous Stress Relaxation in Tension and Creep in Torsion of 2618 Aluminum at Elevated Temperature
Authors: Lai J. S. , Findley W. N.
Published: July 2009

Experiments are reported for stress relaxation and simultaneous stress relaxation and creep with proportional and nonproportional loading and unloading. Results were compared with predictions of a viscous-viscoelastic theory, and modifications, and strain hardening. Predictions were calculated from results of combined constant-stress tension and torsion creep and recovery tests only, which were reported previously. Results showed that a modified viscous-viscoelastic theory predicted all the observed features and predicted the creep and relaxation rates reasonably well.
Incompressible Flow Between Finite Disks
Authors: Adams M. L. , Szeri A. Z.
Published: July 2009

Solutions were developed and are shown here for the primary laminar steady flow field that occurs in an incompressible, isoviscous, Newtonian fluid which is contained between two finite parallel disks. One of the disks is made to rotate at constant velocity and the other is held stationary, and either a source or a sink is located concentric to the axis of rotation. The analysis is general, containing all terms of the Navier-Stokes equations for rotationally symmetric flows, and produces a four-parameter family of solutions. The high Reynolds number flow contains multiple cells, arranged along the radius, and the flow appears to be uniquely defined by the boundary condition and the Reynolds number.
A Linear Algebra Approach to the Analysis of Rigid Body Displacement From Initial and Final Position Data
Authors: Laub A. J. , Shiflett G. R.
Published: July 2009

The location and orientation of a rigid body in space can be defined in terms of three noncollinear points in the body. As the rigid body is moved through space, the motion may be described by a series of rotations and translations. The sequence of displacements may be conveniently represented in matrix form by a series of displacement matrices that describe the motion of the body between successive positions. If the rotations and translations (and hence the displacement matrix) are known then succeeding positions of a rigid body may be easily calculated in terms of the initial position. Conversely, if successive positions of three points in the rigid body are known, it is possible to calculate the parameters of the corresponding rotation and translation. In this paper, a new solution is presented which provides explicit formulas for the rotation and translation of a rigid body in terms of the initial and final positions of three points fixed in the rigid body. The rotation matrix is determined directly whereupon appropriate rotation angles and other information can subsequently be calculated if desired.
Large Deflections of Circular Plates of Variable Thickness
Authors: Banerjee B.
Published: July 2009

The large deflection of a clamped circular plate of variable thickness under uniform load has been investigated using von Karman’s equations. Numerical results obtained for the deflections and stresses at the center of the plate have been given in tabular forms.
Asymmetric Contact Problem Including Wear for Nonhomogeneous Half Space
Authors: Sankar T. S. , Fabrikant V.
Published: July 2009

Contact problem with wear for asymmetric rigid die acting on a half space whose elastic modulus is a power function of depth is considered for the case when the die is rotating according to an arbitrary law. Zone of contact is taken to be a circle, and the wear is proportional to the work done by the tangential stresses obeying Coloumb’s law. Integral equation of the problem is derived and an exact solution of the equation is obtained in closed form. The case of inclined flat die is discussed as an illustrative example of the general method of solution that is proposed.
An Educational Elasticity Problem With Friction, Part 2: Unloading for Strong Friction and Reloading
Authors: Comninou Maria , Dundurs John
Published: July 2009

This paper examines the case of unloading with strong friction, and also treats reloading of the unbounded solid with a semi-infinite cut. The solid is compressed uniformly normal to the cut, and a concentrated force acts on the tip of the cut causing localized separation and frictional slip.
Natural Convection Past Inclined Porous Layers
Authors: Rudraiah N. , Wilfred V.
Published: July 2009

This paper describes a study of combined Rayleigh-Be´nard convection and Tollmien-Schlichting type of instability of a fluid in an inclined layer bounded by two permeable beds. Several types of flows, depending on the value of the Prandtl number, Pr, are studied using a fast convergent power series technique. Two different convective movements, longitudinal and transverse rolls, based on different Prandtl numbers, are reported. The effect of slip at the nominal surface is to augment the instability and change the critical Grashof number, Gr, and critical Rayleigh number, Ra, markedly for small permeability parameter σ, being independent of Gr and Ra for large σ. The effect of inclination φ is to inhibit the onset of instability in the case of air and to augment it in the case of mercury. It is shown that at maximum inclination (i.e., φ = π/2), the instability sets in as transverse rolls, irrespective of the value of Pr. In the case of mercury, the transverse rolls exist for all φ, whereas in the case of air, they are limited only to certain φ. The cell pattern changes dramatically in the range φ = π/6–π/4.
Calculation of Unsteady Transonic Pressure Distributions by the Indicial Method
Authors: Kerlick G. D. , Nixon D.
Published: July 2009

A method for the rapid estimation of complete unsteady transonic pressure distributions is developed. The two key elements of this method are (1) the indicial method and (2) the strained coordinate technique. The indicial method permits the determination of the response of a system to an arbitrary schedule of perturbations once the response of the system to a step change in one of the perturbing variables (the indicial response) is known. The strained coordinate permits the movement of discontinuities in the solution (e.g., shock waves) to occur as the solution develops in time. Together, these two techniques provide detailed information on the time development of pressure distributions over an airfoil that is of use in aeroelastic applications such as control surface flutter and active control design. Examples of both oscillatory and transient perturbations are given, as well an example that demonstrates the potential of this method for aeroelastic tailoring and active control. In all cases, the agreement with more expensive finite-difference calculations is good, and the time savings is about an order of magnitude.
The Growth of Localized Disturbances in Unstable Flows
Authors: Craik A. D. D.
Published: July 2009

The development of three-dimensional localized disturbances in unstable flows was recently studied by Craik [1] using a model dispersion relation. The adoption of such an approximate formula for the linear dispersion relation allows a dramatic reduction in computational effort, in comparison with more precise calculations (e.g., Gaster [3], [5]), yet may still yield quite accurate results. Craik [1] gives simple analytical solutions for various limiting cases of his chosen model. Here, this model is further investigated. Numerical results are given which are free of previous scaling assumptions and the accuracy of the proposed model is assessed by comparison with known exact computations for plane Poiseuille flow. Certain improvements are made by including further terms in the model dispersion relation and the influence of these additional terms is determined. A further model is investigated which yields “splitting” of the wave packet into two regions of greatest amplitude, one on either side of the axis of symmetry. Such behavior may be characteristic of many flows at sufficiently large Reynolds numbers. Extension of this work to three-dimensional and slowly varying flows seems a practical possibility.
A Nonlinear Constitutive Model for Granular Materials: Application to Gravity Flow
Authors: McTigue D. F.
Published: July 2009

The form of the dissipative part of the stress in flowing granular materials is motivated by considering momentum exchange due to intergranular collisions. Both shear and normal stresses are predicted that are quadratic in the rate of deformation. The equilibrium part of the stress is assumed to include a thermodynamic pressure and a term compatible with the Coulomb failure criterion in the limit of vanishing deformation. Solutions for the volume fraction and velocity fields in steady gravity flow down a slope are found. The volume fraction increases linearly downward through the shearing layer at a rate that decreases with increasing slope. The velocity profile develops an inflection near the lower boundary at smaller slopes, and becomes fully convex downstream as it approaches a critical maximum slope for steady flow. The results are in qualitative agreement with available experimental measurements.
Creep and Plastic Strains of 304 Stainless Steel at 593°C Under Step Stress Changes, Considering Aging
Authors: Cho U. W. , Findley W. N.
Published: July 2009

Nonlinear constitutive equations for varying stress histories are developed and used to predict the creep behavior of 304 stainless steel at 593°C (1100°F) under variable tension or torsion stresses including reloading, complete unloading, step-up, and step-down stress changes. The strain in the constitutive equations (a viscous-viscoelastic model) consists of: linear elastic, time-independent plastic, time-dependent-recoverable viscoelastic, and time-dependent-nonrecoverable viscous components. For variable stressing, the modified superposition principle, derived from the multiple integral representation, and the strain hardening theory were used to represent the recoverable and nonrecoverable components, respectively, of the time-dependent strain. Time-independent plastic strains were described by a flow rule of similar form to that for nonrecoverable, time-dependent strains. The material constants of the theory were determined from constant stress creep and creep recovery data. Considerable aging effects were found and the effects on the strain components were incorporated in each strain predicted by the theory. Some modifications of the theory for the viscoelastic strain component under step-down stress changes were made to improve the predictions. The final predictions combining the foregoing features made satisfactory agreements with the experimental creep data under step stress changes.
An Integral Equation Approach to the Inclusion Problem of Elastoplasticity
Authors: Johnson W. C. , Lee J. K.
Published: July 2009

An integral equation approach is derived for the calculation of the elastoplastic strain field associated with a transformed inclusion of constant stress-free transformation strain and for an inhomogeneity when the far stress field remains elastic. The assumptions of a coherent precipitate and the deformation theory of plasticity are employed although any yield condition and flow rule can be chosen. The complexity of the integral equation is such that an iterative solution scheme is necessary. The technique is applied to a spherical precipitate in a uniform elastic stress field where associated stress and strain fields and plastic zone are calculated. The nature of the plastic relaxation process compares qualitatively with two-dimensional plane stress behavior. Extension of this technique to the nonaxisymmetric problem is also examined.