bluuebunny/crossref_metadata_2025 huggingface dataset:
Gravitational Flow Discharge From a Horizontal Duct
Authors: Chan P. , Han T. , Chow W. L.
Published: July 2009

The problem of a potential flow discharge through a two-dimensional horizontal duct under the influence of gravitation is examined by the method of hodograph transformation. The stream function is considered and established in the hodograph plane, and the solution in the physical plane is established through additional integrations. The unknown boundary functions of the free jet must be determined as part of the solution. The initial pressure level and the discharge characteristics between the total head and the flow rate, have been established. Results are compared with those obtained previously by other method.
Asymptotic Approximation and Perturbation Stream Functions in Viscous Flow Calculations
Authors: Berger B. S.
Published: July 2009

An asymptotic approximation technique is shown to substantially decrease the number of interations necessary for the accurate computation of steady solutions for viscous incompressible flows. A numerical study of flows exterior to a circular cylinder indicates that the technique reduces the required number of iterations by a factor of 10. The flux formulation of the vorticity stream function solution for the flow of a viscous incompressible fluid external to a circular cylinder requires the solution of the Poisson equation for the stream function. The use of the FACR (1), fast direct Poisson equation solver leads to serious errors in the computation of the stream function near the cylinder. However it is shown that these errors are eliminated through the introduction of a perturbation stream function.
Transient Buoyant Convection of a Contained Fluid Driven by the Changes in the Boundary Temperatures
Authors: Hyun J. M.
Published: July 2009

Finite-difference numerical solutions are obtained for transient buoyant convection at high Rayleigh numbers of a Boussinesq fluid in a closed cylinder. We consider the linear motions that occur due to a small change in the boundary temperature profiles linear in the vertical coordinate. Previous theoretical studies showed that the meridional circulation, driven by the sidewall boundary layer pumping, brings about the final state on a time scale th = Ra1/4 N−1, where N is the Brunt-Va¨isa¨la¨ frequency. By choosing th as the time scale of interest, the theory filters out the internal-gravity oscillations of time scale N−1. New details on the radial and vertical structures of the flow and temperature fields are presented. The impact of the internal-gravity oscillations on the temperature field is shown to be minor. However, the evolution of the velocities is highly oscillatory in time due to the dominant presence of the internal-gravity oscillations. Numerically calculated contour maps of the temperature and stream function are constructed, which illustrate the effect of Ra on the flow patterns and on the temperature adjustment process.
An Elastic-Plastic Finite Element Model of Rolling Contact, Part 1: Analysis of Single Contacts
Authors: Bhargava V. , Hahn G. T. , Rubin C. A.
Published: July 2009

This paper describes a two-dimensional (plane strain) elastic-plastic finite element model of rolling contact that embodies the elastic-perfectly plastic, cycle and amplitude-independent material of the Merwin and Johnson theory, but is rigorous with respect to equilibrium and continuity requirements. The rolling contact is simulated by translating a semielliptical pressure distribution. Both Hertzian and modified Hertzian pressure distributions are used to estimate the effect of plasticity on contact width and the continuity of the indentor-indentation interface. The model is tested for its ability to reproduce various features of the elastic-plastic indentation problem and the stress and strain states of single rolling contacts. This paper compares the results derived from the finite element analysis of a single, frictionless rolling contact at p0/k = 5 with those obtained from the Merwin and Johnson analysis. The finite element calculations validate basic assumptions made by Merwin and Johnson and are consistent with the development of “forward” flow. However, the comparison also reveals significant differences in the distribution of residual stress and strain components after a single contact cycle.
Use of Statical Indentation Laws in the Impact Analysis of Laminated Composite Plates
Authors: Tan T. M. , Sun C. T.
Published: July 2009

The low-velocity impact response of graphite/epoxy laminates was investigated theoretically and experimentally. A nine-node isoparametric plate finite element in conjunction with an empirical contact law was used for the theoretical investigation. Theoretical results are in good agreement with strain-gage experimental data. The results of the investigation indicate that the present theoretical procedure describes the impact response of laminate for low-impact velocities.
The Problem of Minimizing Stress Concentration at a Rigid Inclusion
Authors: Wheeler L.
Published: July 2009

With the objective of minimizing stress concentration, the plane-strain problem of the optimum shape for a rigid inclusion in an elastic matrix of unbounded extent is investigated. It is shown rigorously that the underlying variational problem is reducible to a more elementary problem which can be solved by conventional methods to arrive at the optimum shape, which is a suitably proportioned ellipse.
Antiplane Eigenstrain Problem of an Elliptic Inclusion in a Two-Phase Anisotropic Medium
Authors: Zhang H. T. , Chou Y. T.
Published: July 2009

An antiplane eigenstrain problem of an elliptic inclusion in a two-phase anisotropic medium is analyzed based on the line-force concept. Explicit expressions for the stress field and strain energy are obtained under a given symmetry. The results are used to determine the stress singularity coefficient for a flat inclusion. When the tip of the inclusion is located at the interface boundary, the stress singularity coefficient S′ varies according to the formula S′ = (1 + K) S° where K is the elastic inhomogeneity factor and S° is the stress singularity coefficient for a homogeneous medium (K = 0).
Elastic Field of an Elliptic Inhomogeneity With Debonding Over an Arc (Antiplane Strain)
Authors: Karihaloo B. L. , Viswanathan K.
Published: July 2009

This paper describes the elastic field of an elliptic inhomogeneity that has debonded over an arc of its common boundary with a different elastic material in which it is embedded. Eshelby’s method of equivalent inclusion with a stress-free eigens train is employed. The solution is facilitated by the properties of Green’s functions. Only the antiplane strain case is treated for illustrating the procedure. Numerical results are presented for the stress intensity factors at the tips of the debonded arc, as well as for the relative displacements across the debond.
Hydrodynamic Disk Braking
Authors: Wang C. Y.
Published: July 2009

A viscous fluid separates a rotating disk and a parallel nonrotating disk. As the two disks are squeezed closer together, increased viscous torque is transmitted to the rotating disk. The Navier-Stokes equations are solved using a perturbation in the small squeeze number. Two cases of squeezing are studied: constant velocity approach and constant force approach.
A Stress Intensity Factor Tracer
Authors: Kim K.-S.
Published: July 2009

A new optical method, Stress Intensity Factor Tracer (SIFT), has been developed. The device measures continuously the real-time stress intensity factor variation, K1(t), of a moving crack tip using a single, stationary photodetector. The method uses the fact that any variation in K1(t) leads to a change in the intensity of light, I(t), impinging on a fixed finite area, Γ, on the focal plane. The focal plane is defined as the plane on which initially parallel light rays transmitted through a transparent fracture specimen (or reflected from the surface of an opaque specimen) are focused by a converging lens. Provided that the light detecting area, Γ, excludes the focal point, a simple relation, I(t) =B[K1(t)]4/3, has been obtained for a K1-dominant field. The constant, B, is a product of several experimental parameters including a “shape factor” of the sampling area, Γ, where I(t) is measured. A significant feature of this method is that I(t) is independent of the location of the crack tip in the illuminated zone on the specimen plane. The technique may therefore be applied to dynamic fracture studies without using high-speed photography. Only the constant, B, becomes a function of crack velocity for the dynamic K1-field. This paper presents the theoretical development of the SIFT method, including the wave optics of the system. Experimental results supporting the theory are included.
A Mixture Theory for Wave Propagation in Angle-Ply Laminates, Part 1: Theory
Authors: Murakami H.
Published: July 2009

In an effort to construct a continuum model with microstructure for elastic angle-ply laminates, an asymptotic mixture theory with multiple scales is presented in this two-part paper. The theory, which is in the form of a binary mixture, can simulate wave propagation in linearly elastic laminated composites with orthotropic lamina. Reissner’s new variational principle has been adopted to avoid the numerous solution procedures of microstructure boundary value problems (MBVP’s), which are required to find mixture properties in terms of the geometrical and material properties of the two constituents of the composite. For the special case of isotropic lamina the variational approach yields the same results as those derived by the asymptotic mixture theory with multiple scales [10] which requires the solution of the MBVP’s. The advantage of the variational approach over the alternative is that it makes the application of the technique feasible to wave propagation in fiber-reinforced and particulate composites. The application of the mixture model to angle-ply laminates is deferred to the second part of the paper, which also contains a study of dispersion of time harmonic waves in angle-ply laminates.
Linear Dynamic Poroelasticity With Microstructure for Partially Saturated Porous Solids
Authors: Berryman J. G. , Thigpen L.
Published: July 2009

Linear equations of motion are derived to describe the behavior of small disturbances in a porous solid containing both liquid and gas. Appropriate boundary conditions are derived to guarantee the uniqueness of the solutions of these equations.
Free Vibration of Rectangular Plates Stiffened With Viscoelastic Beams
Authors: Ohtomi K.
Published: July 2009

This investigation treats the free vibration of a simply supported rectangular plate, stiffened with viscoelastic beams. Using a convenient method in which the effects of beams are expressed with Dirac delta functions, the equation of motion can be expressed by only one equation. The frequency equation is obtained by applying the Laplace transformation to the equation of motion. The effects of the volume and the number of beams on the frequency and the logarithmic decrement are clarified.
Pretwist and Shear Flexibility in the Vibrations of Turbine Blades
Authors: Krenk S. , Gunneskov O.
Published: July 2009

A theory is developed for pretwisted beams with finite shear flexibility. The effect of pretwist is accounted for via the axial derivative of the St. Venant warping function. The shear flexibility relies on a decomposition of the shear stresses into torsion and shear contributions, and the normalized strain energy of the latter is expressed in terms of the shear flexibility tensor. An explicit approximation for the shear flexibility tensor is derived for cross sections of moderate wall thickness. A special Legendre transformation is used to obtain a consistent discretization, which is then cast in the form of a finite beam element. The accuracy of the method is illustrated by comparison with experimental results for a steam turbine blade, and the effects of pretwist and shear flexibility are discussed.
The Dynamics of a Harmonically Excited System Having Rigid Amplitude Constraints, Part 1: Subharmonic Motions and Local Bifurcations
Authors: Shaw S. W.
Published: July 2009

A simple model for the response of mechanical systems having two-sided amplitude constraints is considered. The model consists of a piecewise-linear single degree-of-freedom oscillator subjected to harmonic excitation. Encounters with the constraints are modeled using a simple impact rule employing a coefficient of restitution, and excursions between the constraints are assumed to be governed by a linear equation of motion. Symmetric double-impact motions, both harmonic and subharmonic, are studied by means of a mapping that relates conditions at subsequent impacts. Stability and bifurcation analyses are carried out for these motions and regions are found in which no stable symmetric motions exist. The possible motions that can occur in such regions are discussed in the following paper, Part 2.
Analysis of Wire Ropes With Internal-Wire-Rope Cores
Authors: Phillips J. W. , Costello G. A.
Published: July 2009

Stresses in the individual wires of complex wire rope are determined for rope constructions having an internal-wire-rope (IWRC). The ropes may be pulled, twisted, and bent over a sheave or drum. The effects of friction are neglected. Specific results for a 6 × 25 filler-wire IWRC rope that is prevented from twisting indicate that the maximum stresses (exclusive of contact stresses) are typically 1.5 to 3 times as large as the nominal rope stress based on rope load and total metallic area.
Thermal Effect on the Transverse Vibration of High-Speed Rotating Anisotropic Disk
Authors: Ghosh N. C.
Published: July 2009

An attempt has been made to consider the thermal effect on the transverse vibration of a high-speed rotating disk in a steady-state heat conduction. The material of the disk, in this case, is assumed to be thermomechanically anisotropic. The present attempt is made with an objective to provide some theoretical studies on the problem that may serve as a base from which more detailed investigations with regard to the usage of composite material may be attempted to gain new and needed design information regarding turbine disks and thereby to reduce the chances of turbine failure. In this connection a new critical speed of disk rotation has been obtained and consequently this critical speed is found to depend on central temperature, thermomechanical anisotropy, and so forth.
Influence of Cavity Shape on Damage Parameter
Authors: Jansson S. , Stigh U.
Published: July 2009

The relation between cavity shape and damage parameter is analyzed for a cavitated material. The matrix consists of isotropic, incompressible power law creeping material. The cavities are assumed to be either cylindrical or spheroidal in shape and to be well separated. Damage is defined here from the creep rate equation postulated by Rabotnov. The result shows that the damage parameter is virtually independent of the creep exponent for penny-shaped cracks and for spherical cavities. It is also observed for elongated cavities aligned to the tensile direction, that the damage parameter approaches the Kachanov-Rabotnov damage measure, equal to the area fraction of cavities in a section of a specimen. However, for all other cases the Kachanov-Rabotnov damage measure underestimates the effect of cavities on strain rate. For a plane stress or strain problem with elliptical cavities, the effect of cavity orientation on the damage parameter is shown to be severe. This indicates the need for taking cavity orientation into account when formulating creep laws for multiaxial stress states.
A Physically Based Constitutive Equation for Creep-Damaging Solids
Authors: Levy A. J.
Published: July 2009

Uniaxial and multiaxial forms of a constitutive equation, characterizing the creep-damaging behavior of metals at elevated temperatures, are developed based on Dyson’s constrained cavity growth mechanism. The model employs a single scalar internal variable which can be identified with the area fraction of cavitated boundaries. This variable, together with the power law creep model is capable of describing steady creep, tertiary creep, and dilatation arising from the nucleation and growth of grain boundary cavities.
An Incremental Constitutive Relation of Unilateral Contact Friction for Large Deformation Analysis
Authors: Cheng J.-H. , Kikuchi N.
Published: July 2009

An incremental constitutive relation of friction contact is presented for large deformation analysis. After a brief review of published explanations of friction, a model is constructed following the established concepts of plasticity theory. Extensive studies are laid on how the theory closely simulates the nature of friction and how the unknown parameters in the equation are to be determined from the existing experimental results. Possible extensions to allow considerations of temperature and nonlocal effects are discussed. Formulations of a quasistatic boundary value problem based on the updated Lagrangian approach are summarized. The elastoplastic material is assumed to behave according to the generalized Prandtl-Reuss constitutive equation. Finite element methods are employed to solve the problem. Two examples are selected to demonstrate the capability and adequacy of the proposed model.
Acoustoelastic Response of a Polycrystalline Aggregate With Orthotropic Texture
Authors: Johnson G. C.
Published: July 2009

Estimates of the effective second-order and third-order elastic constants of a polycrystalline aggregate exhibiting texture are presented for the case of orthotropic sample symmetry and cubic crystalline symmetry. The nature of the texture is brought into the analysis through the crystallites’ orientation distribution function which is written in a series of generalized spherical harmonics. The effective response is evaluated using a Voigt-type procedure in which the crystal stiffnesses are averaged over the orientation distribution function. In evaluating the results, it is found that only seven terms in the expansion for the orientation distribution function are required for the exact representation of the effective properties.
A Change in Wave Type Modeled by the Variable Coefficient Korteweg-deVries Equation
Authors: Cramer M. S. , Nguyen S. H. , Bowman M. E. , McCown B. E.
Published: July 2009

Strongly shoaling solutions to the variable coefficient Korteweg-deVries equation have been obtained for arbitrary initial or off-shore waveforms and depth variations. Although the solutions were capable of exhibiting dispersive behavior off-shore, the near-shore behavior was always found to be governed by a variable coefficient Burger equation. Conditions under which the wave slope became infinite were given in terms of the initial shape of the wave and the depth variation. These solutions are valid when α < < δ < < 1, where α is the ratio of the initial wave amplitude to the depth and δ is the ratio of the initial length of the wave to the length scale associated with the depth variation. Numerical solutions of this equation were also found; these were in excellent agreement with the asymptotic results.
On the Comparison Between Microscopic and Macroscopic Instability Mechanisms in a Class of Fiber-Reinforced Composites
Authors: Triantafyllidis N. , Maker B. N.
Published: July 2009

To investigate the relation between the macroscopic and microscopic instability predictions for certain microstructured media, we study the stability of an axially stretched fiber-reinforced composite under plane strain conditions. The microstructural instability is attributed to a bifurcation buckling of the fibers while the corresponding macroscopic one occurs at the loss of ellipticity in the homogenized incremental equilibrium equations of the material. The effects of geometry and material properties on those phenomena are analyzed. The macroscopic approach consistently and sometimes considerably overestimates the stable region of the composite. The attractive feature in this work is that all the investigations can be done by using analytical solutions instead of the numerical ones employed in similar investigations so far.
Reduction of Free-Edge Stress Concentration
Authors: Heyliger P. R. , Reddy J. N.
Published: July 2009

A quasi-three dimensional elasticity formulation and associated finite element model for the stress analysis of symmetric laminates with free-edge cap reinforcement are described. Numerical results are presented to show the effect of the reinforcement on the reduction of free-edge stresses. It is observed that the interlaminar normal stresses are reduced considerably more than the interlaminar shear stresses due to the free-edge reinforcement.
Thermal Expansion Coefficients and Thermal Stresses in an Aligned Short Fiber Composite With Application to a Short Carbon Fiber/Aluminum
Authors: Takao Y. , Taya M.
Published: July 2009

A formulation to compute the effective thermal expansion coefficients (αc) of an anisotropic short fiber-reinforced composite and the thermal stress (σ) induced in and around the fiber is developed. The formulation is based on the Eshelby’s equivalent inclusion method. Main emphasis is placed on short Carbon fiber/Aluminum. The thermal stress due to a uniform temperature rise ΔT is computed at points just outside the fiber. The effects of various parameters on αc and σ are also investigated.
Characteristics of the Elastic Field of a Rigid Line Inhomogeneity
Authors: Wang Z. Y. , Zhang H. T. , Chou Y. T.
Published: July 2009

Explicit expressions are obtained for the stress and displacement fields near the tip of a rigid line inhomogeneity subjected to an inclined loading. It is shown that the tip stress field, with a square-root singularity, differs in characteristics from that of a slit crack. New designations for the mode of deformation based on the fracture concept are presented and the inhomogeneity extension forces are calculated and discussed.
The Crack Problem for Bonded Nonhomogeneous Materials Under Antiplane Shear Loading
Authors: Erdogan F.
Published: July 2009

The main objective of this paper is the investigation of the singular nature of the crack-tip stress field in a nonhomogeneous medium having a shear modulus with a discontinuous derivative. The problem is considered for the simplest possible loading and geometry, namely the antiplane shear loading of two bonded half spaces in which the crack is perpendicular to the interface. It is shown that the square-root singularity of the crack-tip stress field is unaffected by the discontinuity in the derivative of the shear modulus. The problem is solved for a finite crack and extensive results are given for the stress intensity factors.
The Dynamic, Steady-State Propagation of an Antiplane Shear Crack in a General Linearly Viscoelastic Layer
Authors: Walton J. R.
Published: July 2009

In a previous paper, the dynamic, steady-state propagation of a semi-infinite antiplane shear crack was considered for an infinite, general linearly viscoelastic body. Under the assumptions that the shear modulus is a positive, nonincreasing continuous and convex function of time, convenient, closed-form expressions were derived for the stress intensity factor and for the entire stress distribution ahead of and in the plane of the advancing crack. The solution was shown to have a simple, universal dependence on the shear modulus and crack speed from which qualitative and quantitative information can readily be gleaned. Here, the corresponding problem for a general, linearly viscoelastic layer is solved. An infinite series representation for the stress intensity factor is derived, each term of which can be calculated recursively in closed form. As before, a simple universal dependence on crack speed and material properties is exhibited.
An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading, Part 2: Applications
Authors: Ponter A. R. S. , Karadeniz S.
Published: July 2009

In an accompanying paper an extended shakedown theory was described for structures subjected to constant mechanical loads and cyclically varying thermal loads, a circumstance of interest in Fast Reactor design. In this paper the upper bound theorem is used to construct interactive diagrams for a sequence of sample problems. These examples imply that for many shell problems, where the temperature variations occur along the surface, ratchetting occurs in two distinct ways. For low thermal loading the structure deforms in the same mechanism that occurs at plastic collapse when only the mechanical loads are applied. For high levels of thermal loading the mechanism changes to a local concentration of strain. This behavior differs significantly from that of the Bree problem. In one example this mechanism involves through-thickness shear deformation of a plate; as a consequence the use of thin shell theory which ignores shear deformation in numerical solutions of problems of this type is likely to result in nonconservative estimates of inelastic deformations.
Point-Force Excitation of an Elastic Plate With an Embedded Cavity
Authors: Bostro¨m A. , Karlsson A.
Published: July 2009

The propagation of elastic waves in a thick plate containing an embedded cavity is considered. The full elastodynamic equations are solved and both time-harmonic and pulse propagations are treated. The time-harmonic problem is solved using the null field approach, a method whose main characteristics are surface integral representations and expansions in spherical and planar vector wave functions. To obtain the pulse response, a Fourier integral in frequency is employed. Numerical examples are given showing the fields in both the time and frequency domains at a few selected locations on the plate surfaces when the plate is excited by a point force. Only low and intermediate frequencies are included and the pulse width is thus somewhat larger than the dimensions of the spheroidal cavity.
Singular Value Decomposition for Constrained Dynamical Systems
Authors: Singh R. P. , Likins P. W.
Published: July 2009

The method of singular value decomposition is shown to have useful application to the problem of reducing the equations of motion for a class of constrained dynamical systems to their minimum dimension. This method is shown to be superior to classical Gaussian elimination for several reasons: (i) The resulting equations of motion are assured to be of full rank. (ii) The process is more amenable to automation, as may be appropriate in the development of a computer program for application to a generic class of systems. (iii) The analyst is spared the responsibility for the selection of specific coordinates to be eliminated by substitution in each individual case, a selection that has no physical justification but presents abundant risk of mathematical contradiction. This approach is shown to be very efficient when the governing dynamical equations are derived via Kane’s method.
The Elastic Field of an Elliptic Inclusion With a Slipping Interface
Authors: Tsuchida E. , Mura T. , Dundurs J.
Published: July 2009

The paper analyzes the elastic fields caused by an elliptic inclusion which undergoes a uniform expansion. The interface between the inclusion and the matrix cannot sustain shear tractions and is free to slip. Papkovich–Neuber displacement potentials are used to solve the problem. In contrast to the perfectly bonded interface, the solution cannot be expressed in closed form and involves infinite series. The results are illustrated by numerical examples.
Harmonic Wave Propagation in Nonhomogeneous Layered Composites
Authors: Duan Z. P. , Eischen J. W. , Herrmann G.
Published: July 2009

A new method for analyzing plane wave propagation in a periodically layered, elastic, nonhomogeneous composite body is proposed. The nonhomogeneity considered is a variation of the material properties within each composite layer. Results from probability theory are used to arrive at the two fundamental solutions of the governing second order ordinary differential equations. Floquet’s wave theory is combined with a Wronskian formula to yield the dispersion relationship for this nonhomogeneous composite. Numerical results show that the presence of material nonhomogeneity affects the range of frequencies which can pass through the composite unattenuated.
Direct Measurement of Flexural Strains in Plates by Shearography
Authors: Takezaki J. , Hung Y. Y.
Published: July 2009

Strains in a flexed plate are directly related to the second derivatives of the plate deflections. A technique is developed which enables shearography to measure second derivatives of deflection directly. The technique is based on generating fictitious carrier fringes in the form of periodic linear fringes of uniform spacing. The carrier fringes are distorted when the plate is deformed. The change in the pitch of the carrier fringes due to deformation yields the flexural strain directly. The pitch of the carrier fringes is equivalent to gage length.
Rectangular Plates on Unilateral Edge Supports: Part 2—Implementation; Concentrated and Uniform Loading
Authors: Dempsey J. P. , Li Hui
Published: July 2009

Rectangular plates in unilateral contact with sagged and unsagged supports laterally loaded by centrally concentrated loads and uniform pressure are examined. The loss of contact and the redistribution of deflections, moments, and support reactions are presented. Computer implementation aspects are discussed.
Transient Gas or Liquid Flow Along a Preexisting or Hydraulically-Induced Fracture in a Permeable Medium
Authors: Nilson R. H. , Morrison F. A.
Published: July 2009

Similarity solutions are derived for the transient two-dimensional flow of a gas or liquid along an isolated fracture in a permeable medium. The driving pressure at the fracture inlet is constant, and the confining stress is uniform. Two different cases are considered, preexisting fractures with uniform aperture as well as hydraulic fractures with a variable aperture proportional to the local overpressure (fluid pressure less confining stress). The evolution of the pressure distribution is described by a set of four asymptotic solutions, each having a self-similar form. At early times the flow in the fracture is turbulent, and Darcian seepage losses into the porous surroundings are negligible. At late times the flow in the fracture is laminar, and seepage losses become a dominant consideration. At intermediate times there are two alternative asymptotes, depending upon the physical parameters. The mathematical model also describes the flow along a fracture which is filled with high-permeability porous material as well as the flow in an assemblage of porous blocks.
The Effect of the Earth’s Rotation on Channel Flow
Authors: Speziale C. G.
Published: July 2009

The influence that the rotation of the earth has on laminar channel flow is investigated theoretically. The full nonlinear Navier-Stokes equations relative to a reference frame rotating with the earth are solved numerically for laminar flow in a rectangular channel whose axis is aligned east-west: the orientation which yields the most drastic effect. It is demonstrated that for channels of moderate width (less than 1 ft for the flow of most liquids), the rotation of the earth can give rise to a roll instability which has a severe distortional effect on the classical parabolic velocity profile. Consequently, the usual assumption made of neglecting the effect of the earth’s rotation in the calculation of channel flow can lead to serious errors unless the channel is substantially smaller than this size. It is briefly shown that similar effects would be expected for turbulent channel flow when the channel width is approximately an order of magnitude larger.
Impact With Friction
Authors: Keller J. B.
Published: July 2009

A theory of the impact or collision of two rigid bodies, taking account of friction, is presented. It determines how the direction of sliding varies during the impact, which must be known to calculate the direction of the frictional force and thence the frictional impulse. This is accomplished by analyzing the equations of motion of the bodies during the collision. The normal impulse is determined by using a coefficient of restitution. When the direction of sliding is constant throughout the collision, the theory agrees with that given by Whittaker, which is correct only in this case.
On the Singularities in Reissner’s Theory for the Bending of Elastic Plates
Authors: Burton W. S. , Sinclair G. B.
Published: July 2009

Wedge-shaped elastic plates under bending, with the edges forming the wedge vertex being either stress-free, clamped or simply supported, are characterized as to possible singular behavior within the context of Reissner’s plate theory.
Point Control of a One-Link Flexible Manipulator
Authors: Skaar S. B. , Tucker D.
Published: July 2009

An alternative approach to the control of nonrigid, distributed parameter systems is presented. Transfer functions that relate the response of points on the system to a controlling force or torque are used in place of ordinary differential equations, which represent an approximation to the system dynamics. The implications of this “point control” approach are discussed with regard to plant modeling accuracy, uncontrolled regions, open-loop and closed-loop control strategies, system identification, and feedback estimation. Sample optimal control histories are illustrated for a single-link manipulator member with end load.
Free Vibration of a Rectangular Parallelepiped Using the Theory of a Cosserat Point
Authors: Rubin M. B.
Published: July 2009

Free vibration of a rectangular parallelepiped composed of a homogeneous linear elastic isotropic material is studied. The parallelepiped is modeled as an isotropic Cosserat point and simple formulas are developed to predict the lowest frequencies of vibration. Within the context of the theory, extensional and shear vibrations are uncoupled. The lowest extensional frequency predicted by the Cosserat theory is compared with available exact solutions and with predictions of thin rod theory. Finally, by introducing a simple modification of the director inertia coefficient it is shown that the Cosserat predictions of the extensional frequencies are correct.
Invariance Considerations in Large Strain Elasto-Plasticity
Authors: Dashner P. A.
Published: July 2009

This paper addresses a number of issues in the ongoing debate over the relevance and/or appropriateness of the rotational invariance requirement which is generally associated with the intermediate unstressed configuration. In particular, it is argued that the principle of material frame invariance has been “misapplied” by the proponents of full rotational invariance. Insistence on a strictly “kinematic” interpretation of the deformation gradient (F = FeFp) constituents Fe and Fp justifies elimination of the plastic rotational component Rp(Fp = RpUp) based on the principle of determinism for stress — not invariance of frame. However, simple physical considerations, including a physical example involving a “structurally anisotropic” crystal, suggest that a more intricate definition of the gradient constituents is required in order to adequately account for microstructural characteristics. These considerations suggest alternative definitions for the gradient constituents Fe and Fp with associated constitutive invariance requirements.
Determination of Dynamic Forces From Wave Motion Measurements
Authors: Michaels J. E. , Pao Yih-Hsing
Published: July 2009

An experimental method has been developed for generating oblique forces with known orientations and time histories. Recorded signals from several forces were analyzed by an iterative deconvolution method to determine their orientations and time histories. The recovered values agree closely with the exact ones for these controlled sources. These experiments are a valuable test of source characterization methods that may be applied to seismic data from earthquake sources or to signals recorded from the acoustic emission of cracks.
Study of a Three-Dimensional Crack Terminating at an Interface
Authors: Lee J. C. , Keer L. M.
Published: July 2009

In this study the stress intensity factors for a three-dimensional crack perpendicular to and terminating at a bimaterial interface are calculated. It is assumed that the crack is pressurized by a uniform pressure. The method of solution used here is based upon the body-force method and requires the analytical results from the elasticity point-force solution for a bimaterial interface. The solution technique leads to the reduction of the problem to a two-dimensional singular integral equation, which can be solved numerically for the crack opening displacement. Numerical examples of a semi-circular, semi-elliptical crack and growth of circular crack are given.
The Transient Field Under a Point Force Acting on an Infinite Strip
Authors: Brock L. M.
Published: July 2009

As a prelude to studying the transient stresses in a notched bar under impact, the transient stress and velocity field in the cross-section under a point force acting on one surface of an infinite elastic strip is examined. The point force is suddenly applied and normal to the surface. By transform methods, closed-form expressions for the transient field are obtained and used to study the multiple wave reflection process noticeably affects the field. In particular, the normal stress on the cross-section, tensile for the most part before the arrival of reflections, subsequently becomes essentially compressive.
Interaction Between an Edge Dislocation and a Rigid Elliptical Inclusion
Authors: Santare M. H. , Keer L. M.
Published: July 2009

A solution is presented for the two-dimensional elastic field created by the interaction of an edge dislocation with a rigid elliptical inclusion. The complex potential approach by Muskhelishvili is used and a closed-form solution is obtained. Contour plots for the glide component of the Peach–Koehler forces are presented. Particular attention is paid to the rigid body of the inclusion with respect to the dislocation.
Several Elliptical Punches on an Elastic Half Space
Authors: Fabrikant V. I.
Published: July 2009

A general theorem is established which relates the resulting forces, acting on a set of arbitrary punches, with their generalized displacements through a system of linear algebraic equations. The theorem is applied to the case of arbitrarily located elliptical punches. Several specific examples are considered.
Transient Response of a Support Structure Excited by an Accelerating Unbalanced Rotor
Authors: Ellyin F. , Wolanski Z.
Published: July 2009

The transient vibration of a beam supporting an unbalanced rotor is investigated using finite element discretization techniques. The rotor speed is time dependent to simulate transients at startup. The beam is low-tuned relative to the rotor operating speed. A rigid rotor shaft mounted in an oil-film bearing is considered. The “short-bearing” approximation and nonlinear performance of the journal bearing are assumed. The method of solution for transient response is based on direct integration of the system equations of motion using finite element in time formulation. The results of numerical anlaysis are presented in graphical form and discussed. One notes significant effects of the journal bearing on the system response.
Whirl Instabilities in Pressure Step Bearings
Authors: Brindley J. , Elliott L. , McKay J. T.
Published: July 2009

The effect on the stability of a dynamically loaded journal bearing of introducing a pressure step is examined by calculating numerically the whirl orbits described by the journal for a range of values of physical effects. In all full film cases the configuration is unstable in that the orbits spiral outwards to the bearing case; the tightness of the spiral is, however, much influenced by parameter values. The presence of appropriate cavitation permits a degree of stability, with the existence of stable whirl orbits. Cavity position and extent are vitally important to the stability characteristics, a result one would expect to be true of more realistic cavitation models than the single one used here.
Transient Temperature Distribution in Partially Filled Rotating Horizontal Cylinders
Authors: Blech J. J. , Green I. , Kopelman J.
Published: July 2009

The transient temperature distribution in an infinitely long horizontal rotating cylinder which is partially filled by a viscous fluid is calculated. Thermal boundary and initial conditions are such that the fluid starts from a uniform temperature, and that the outer boundary (cylinder surface) is isothermal at a different temperature. Nondimensional analysis shows that the problem can be fully described by a properly defined Fourier modulus and a normalized bubble eccentricity.
Hydrodynamic Lubrication in Hemispherical Punch Stretch Forming
Authors: Chen Kuo-Kuang , Sun D. C.
Published: July 2009

The existence and consequence of hydrodynamic lubrication in sheet metal forming is demonstrated using a model problem of hemispherical punch stretch forming. The problem is solved by incorporating a lubrication analysis into an incremental plasticity analysis. The sheet material is assumed to be elastic plastic with strain hardening, and the lubricant is assumed isoviscous. The study identifies two dimensionless parameters controlling the condition of lubrication. The resulting variable friction at the punch-sheet interface is found to affect significantly the distribution of strains in the sheet metal and its formability.
On the Relation Between Kinematic Mappings of Planar and Spherical Displacements
Authors: McCarthy J. M.
Published: July 2009

Kinematic mappings, which transform the parameters specifying a rigid displacement into a point in a higher dimensional space, have been the focus of recent study for the purpose of classifying rigid motion, aiding mechanism design, and automating robot task planning. Presented here is the procedure which demonstrates that the particular mapping introduced by Blaschke and Mu¨iller (1956) to study planar kinematics, and used subsequently by other researchers, is a limiting case of a mapping based on the Euler parameters of an orthogonal matrix used by Ravani (1982) for spherical kinematics.
Explicit Approximate Solutions Associated With the Mechanics of Hydraulic Fracturing
Authors: Advani S. H. , Torok J. S. , Lee J. K.
Published: July 2009

Governing equations, based on a Lagrangian formulation, for the assumed case of a hydraulically induced vertial elliptic fracture propagating in a uniformly confined, linear, elastic, homogeneous medium are derived. Explicit solutions for the generalized coordinates designating the time-dependent crack width, major axis, and minor axis are obtained for one-dimensional fracture fluid flow with and without leak-off effects.
On Material Forces in Elementary Beam Theory
Authors: Kienzler R. , Herrmann G.
Published: July 2009

Material conservation and balance laws of elementary elasto-static beam theory are derived and a complete duality between the description in physical and in material space is established.
A Finite Element Approach to Interface Cracks
Authors: van der Zande H. D. , Grootenboer H. J.
Published: July 2009

To investigate the behavior of cracks at the interface of materials with different elastic properties, a finite element model to calculate the Mode II stress-intensity factors was developed. The interface crack was considered to have locally closed tips, the size of which was determined from the finite element results. Numerical results of the integral equation for an interface crack were derived by M. Comninou for different applied loads. Comparing her results with our finite element calculations, some interesting differences have been discussed.
Stresses in Bi-Metal Thermostats
Authors: Suhir E.
Published: July 2009

The magnitude and the distribution of stresses in bi-metal thermostats subjected to uniform heating or cooling are determined. The suggested approach enables one to evaluate the normal stresses in the thermostat plates, as well as the shearing and normal (“peeling”) stresses in the interface. The developed approach is applicable, generally speaking, to any elongated lap shear assembly.
Dynamic Plastic Analysis of Impulsively Loaded Viscoplastic Rectangular Plates With Finite Deflections
Authors: Hui David , de Oliveira J. G.
Published: July 2009

An energy balance method for the dynamic plastic analysis of thin rectangular plates made of a strain-rate sensitive material, taking into account the influence of finite-deflections, is proposed. The particular case of a fully clamped plate under uniformly distributed dynamic pressure pulse or blast loading is studied in some detail. In addition to the nonaxisymmetric and dynamic nature of the problem, the analysis considers important nonlinearities in the strains, equilibrium equations, and constitutive equations. Nonlinear ordinary differential equations in various regimes of plate deflections and loading histories are derived and solved using a Runge–Kutta method. Comparisons are made with existing experimental data.
A Cell Mapping Method for Nonlinear Deterministic and Stochastic Systems—Part II: Examples of Application
Authors: Chiu H. M. , Hsu C. S.
Published: July 2009

In this second part of the two-part paper we demonstrate the viability of the compatible simple and generalized cell mapping method by applying it to various deterministic and stochastic problems. First we consider deterministic problems with non-chaotic responses. For this class of problems we show how system responses and domains of attraction can be obtained by a refining procedure of the present method. Then, we consider stochastic problems with stochasticity lying in system parameters or excitation. Next, deterministic systems with chaotic responses are considered. By the present method, finding the statistical responses of such systems under random excitation also presents no difficulties. Some of the systems studied here are well-known. New results are, however, also obtained. These are results on Duffing systems with a stochastic coefficient, the global results of a Duffing system shown in Section 4, the results on strongly nonlinear Duffing systems under random excitations reported in Section 7.2, and the strange attractor results for systems subjected to random excitations.
Effect of Fiber Anisotropy on Thermal Stresses in Fibrous Composites
Authors: Avery W. B. , Herakovich C. T.
Published: July 2009

An elasticity solution is utilized to analyze an orthotropic fiber in an isotropic matrix under uniform thermal load. The analysis reveals that stress distributions in the fiber are singular in the radial coordinate when the radial fiber stiffness (Crr) is greater than the hoop stiffness (Cθθ). Conversely, if Crr < Cθθ the maximum stress in the composite is finite and occurs at the fiber-matrix interface. In both cases the stress distributions are radically different than those predicted assuming the fiber to be transversely isotropic (Crr=Cθθ). It is also shown that fiber volume fraction greatly influences the stress distribution for transversely isotropic fibers, but has little effect on the distribution if the fibers are transversely orthotropic.
One-Dimensional Softening With Localization
Authors: Schreyer Howard L. , Chen Z.
Published: July 2009

The relationship between material softening and structural softening is investigated through the use of a model problem in one dimension. If the size of the softening zone is large the structural softening response is stable under displacement-prescribed loading. For a small size, the softening response is unstable and the loading regime is sensitive to imperfections in stiffness. A nonlocal constitutive equation in which the limit stress is a function of strain and strain gradient is introduced to provide an approach for simulating softening with localization. Implications for the numerical modeling of softening phenomena are given.