bluuebunny/crossref_metadata_2025 huggingface dataset:
Lateral Structure Interaction With Seismic Waves
Authors: Scavuzzo R. J. , Bailey J. L. , Raftopoulos D. D.
Published: November 2010

The interaction of lateral structural inertia forces with horizontal seismic motion is formulated in terms of an integral equation of the Volterra type. By means of normal mode theory the inertia force at the base of the structure is expressed as a function of the foundation motion. After the motion of the two-dimensional elastic half space resulting from a uniform horizontal foundation force varying arbitrarily with time over a specified interval on the boundary of the half space has been determined, the interaction equation is derived. Numerical studies for two free-field acceleration inputs are made for different ground stiffnesses and structural characteristics. The first of these free-field inputs is a ramp sine function and the second is the east-west ground acceleration recorded at Golden Gate Park during the 1957 San Francisco earthquake. The interaction effects for structures similar to nuclear power plants prove to be significant.
Indentation of a Circular Membrane
Authors: Yang W. H. , Hsu K. H.
Published: November 2010

The problem of axisymmetric deformations of an elastic membrane has been formulated in terms of three first-order nonlinear ordinary differential equations. In this paper, the application of these equations is made to the problem of a circular flat membrane indented by a smooth sphere. The membrane is then deformed into an axisymmetric surface. The deformed membrane is divided into two regions: a region of contact with the sphere, and a region which is free of external load except at the boundaries. The common boundary of the two regions is not known a priori. The nonlinear membrane equations are applied specifically to each region and continuity of stress and deformation are required at the common boundary. Numerical solutions are obtained for the membrane of Mooney model material. Applications are pointed out in the discussion.
Hemodynamic Flow in Anisotropic, Viscoelastic Thick-Wall Vessels
Authors: Bulanowski E. A. , Yeh H.
Published: November 2010

Hemodynamic flow in anisotropic, viscoelastic thick-wall vessels is analyzed. For small amplitude harmonic waves, the wavelengths of which are large compared to the vessel radius, the fluid motion is governed by the linearized form of the Navier-Stokes equations and the vessel motion is described by the classical Navier equations for solids. Compressible and incompressible transversely isotropic vessels with frequency dependent material moduli are considered. Longitudinal constraints are also incorporated. The quantities calculated are: the velocities of propagation, transmission per wavelength, fluid impedance, and the displacements and stresses at the fluid-vessel interface. The results indicate that the earlier anisotropic analyses, which incorporate membrane or thick shell theories, agree qualitatively with the present thick-wall analysis. However, quantitative differences among the analyses do occur, especially as the compressibility of the vessel material decreases. For the thick-wall analysis, the effects of anisotropy on the various quantities of interest are established. In particular, it is shown that the fluid impedance is relatively insensitive to the degree of anisotropy, but the resistance and inductance are very sensitive to anisotropy at the high and low values of frequency respectively. In general, anisotropy significantly affects the first mode transmission per wavelength and second mode phase velocity. The displacements and stresses at the fluid-vessel interface are also altered by anisotropy. In addition, the arterial system was found to be essentially independent of moderate variations in the axial shear modulus of the material. Furthermore, it is demonstrated that the degree of viscoelasticity associated with the vessel material substantially alters the transmission per wavelength but affects the phase velocity to a much lesser degree. For the suggested value of the spring parameter associated with the longitudinal constraint, it is found that the additional mass and the viscous parameters have little effect on the system behavior. The overall effect of the longitudinal constraint is to completely subdue the second mode of transmission, increase the first mode phase velocity, decrease the first mode transmission per wavelength and axial displacement, and to increase the modulus and decrease the phase of the first mode fluid impedance. In addition to confirming the importance of anisotropy, viscoelasticity, and the longitudinal constraint, the investigation demonstrates that an appropriate thick-wall analysis is required in order to adequately describe the fluid-vessel behavior.
Wave Propagation in Viscoelastic Laminates
Authors: Stern M. , Bedford A. , Yew C. H.
Published: November 2010

For a simplified model of a laminated medium consisting of alternating layers of elastic and viscoelastic materials, the dispersion and attenuation characteristics for “plane,” longitudinal waves propagating in the direction of the layering are obtained. The dispersion and attenuation curves depend on a structure parameter involving the thickness of the layers and can deviate significantly from corresponding results for a continuum “effective-modulus” model. Curves are presented for a specific case with representative material parameters showing the effect of structure and of variations in the parameters of the composite.
Variational Equation of Motion for Coupled Flexure and Torsion of Bars of Thin-Walled Open Section Including Thermal Effect
Authors: Yu Yi-Yuan
Published: November 2010

Literature on flexure and torsion of bars of thin-walled open section is reviewed. The use of the variational equation of motion in solving problems of structural dynamics is further advocated. The variational equation of motion, together with the associated stress-displacement relations, is then derived for coupled flexure and torsion of the open section. Thermal effect is included, leading to a thermal twisting moment in addition to the usual thermal bending moments. For the special case of an open section with one axis of symmetry and with symmetrical heat input, only flexure is shown to be thermally inducible. The general result then reduces to the simple variational equation of flexural motion used in a separate study of the thermal flutter of a spacecraft boom.
Slip Phenomenon for a Circular Inclusion
Authors: Hussain M. A. , Pu S. L.
Published: November 2010

In many contact problems when friction is not to be neglected the slip phenomenon has not been well understood. The purpose of this paper is to study the slip phenomenon by focusing on a special contact problem; namely, an unbonded circular inclusion in an infinite medium, subjected to a uniaxial tension. The interface between the inclusion and the exterior material is partitioned into regions of rigid linkage, slip, and separation. Determination of these regions leads to a coupled system of three sets of dual-series relations. Solutions have been obtained by using variational techniques. The regions of slip and the separation are simultaneously determined from the condition that the normal and shearing components of stress are finite throughout the interface. It is found that the regions of slip are quite sensitive to the coefficient of friction, but the effect of friction on the contact angle is rather small.
Spherically Symmetric Vibration of an Elastic Spherical Shell Subject to a Radial and Time-Dependent Body-Force Field
Authors: McKinney J. M.
Published: November 2010

A solution, exact within the framework of linear elastokinetics, is obtained for a vibrating, elastic, arbitrarily thick spherical shell subject only to a spherically symmetric body force field of the form FR(r, τ) = Fr(r)Ft(τ). Fr(r) is taken in the form of a polynomial whereas Ft(τ) is restricted only to being a sectionally continuous function of time.
The Equivalence of Two Classical Problems of Free Spinning Gyrostats
Authors: Roberson R. E.
Published: November 2010

Two problems of a torque-free body with a fixed point are considered. In both the body is rigid but for an internal rotor symmetric about its axis of rotation. In one the rotor is driven at a constant angular velocity, in the other the interaction torque between body and rotor has a zero component on the axis of relative rotation. The dynamical equations are shown to have exactly the same structure. A brief literature summary on the torque-free gyrostat is appended.
Shakedown of Steel Plates
Authors: Muspratt M. A.
Published: November 2010

Standard mathematical programming techniques are used for obtaining the shakedown load and stochastic shakedown load of a simply supported axisymmetric plate subjected to uniform pressure. The yield criteria of Tresca, von Mises, and Hill are all invoked.
Slow Particulate Viscous Flow in Channels and Tubes—Application to Biomechanics
Authors: Tong P. , Fung Y. C.
Published: November 2010

A formulation of the finite-element method for both two-dimensional and axisymmetric slow viscous flow is presented. Its application to flow of large particles in a channel or a circular cylindrical tube is discussed. The particles are assumed to be disk-shaped and are disposed axisymmetrically in the tube. The velocity profiles, the pressure gradient, and the shear stress on the wall are determined as functions of kinematic parameters. The conditions are selected to represent an idealization of the motion of red blood cells and plasma in capillary blood vessels.
Deflected Turbulent Jet Flows
Authors: Platten J. L. , Keffer J. F.
Published: November 2010

An experimental investigation of an axisymmetric turbulent jet discharging into a uniform crosswind has been performed for a range of jet to free-stream velocity ratios.
A Solution of Shock-Induced Boundary-Layer Interaction Problems by an Integral Method
Authors: Murdock J. W.
Published: November 2010

An integral technique is developed to solve a general class of shock-induced boundary-layer interaction problems. Included in this class is the boundary layer which grows downstream of the leading edge of a semi-infinite flat plate with a shock wave propagating over it, and the boundary-layer region in a shock tube that is dependent upon both the shock wave and the expansion wave. The integral equations used to solve the Howarth transformed (incompressible) momentum equation are formulated in terms of a general two-parameter family of velocity profiles. These equations are solved for a velocity profile which is a linear combination of the two exact solutions valid at either end of the interaction region. The relative proportion of these two solutions is controlled by a shape factor similar to the Karman-Pohlhausen one in that it is controlled by the degree of unsteadiness in the boundary layer rather than by the pressure gradient. The solutions generated are in excellent agreement with published exact solutions, and all discontinuities in the slope of the shear stress present in earlier similar integral solutions are eliminated. The momentum and displacement thicknesses and the wall shear stress are predicted to within one percent of the exact values.
A Systematic Exposition of the Conservation Equations for Blast Waves
Authors: Oppenheim A. K. , Lundstrom E. A. , Kuhl A. L. , Kamel M. M.
Published: November 2010

In order to provide a rational background for the analysis of experimental observations of blast wave phenomena, the conservation equations governing their nonsteady flow field are formulated in a general manner, without the usual restrictions imposed by an equation of state, and with proper account taken, by means of source terms, of other effects which, besides the inertial terms that conventionally dominate these equations, can affect the flow. Taking advantage of the fact that a blast wave can be generally considered as a spatially one-dimensional flow field whose nonsteady behavior can be regarded, consequently, as a function of just two independent variables, two generalized blast wave coordinates are introduced, one associated with the front of the blast wave and the other with its flow field. The conservation equations are accordingly transformed into this coordinate system, acquiring thereby a comprehensive character, in that they refer then to any frame of reference, being applicable, in particular, to problems involving either space or time profiles of the gas-dynamic parameters in the Eulerian system, or time profiles in the Lagrangian system.
Velocity Distribution in the Liquid Film During Draining on a Cylindrical Surface
Authors: Chawla T. C. , Fauske H. K.
Published: November 2010

The solution of the momentum equation describing unsteady creeping flow of the liquid film during its initial period of drainage on a cylindrical surface has been obtained by the method of finite Hankel transform. The steady-state solution describing the later stages of the drainage process [1, 2] has been deduced by letting the time since the start of motion to be infinite. For completeness, the derivation of the velocity distribution for the vertical plane case applying finite sine transform (equivalent of finite Hankel transform for a cylindrical surface) has also been included.
A Qualitative Study of Gas Bearings Operating at High Subsonic and Supersonic Tangential Speeds
Authors: Constantinescu V. N. , Hsing F. C.
Published: November 2010

The work presented here is a preliminary study of the Mach number effect based on the usual lubrication assumptions except, for the retention of convective terms in the equations of motion. The essential step in this analysis is to adopt the momentum integral method, i.e., to assume a velocity profile satisfying the prescribed boundary conditions. The first attempt is to assume a second-order polynomial for the velocity profile. Although this may not be able to give a sufficient detail of the velocity field. Nevertheless, the results should, hopefully, give us some more insight into this problem. Analytical results based on perturbation theory are presented for journal, slider, and step bearings. Numerical results for a plane slider are also presented here. All results indicate that when a dimensionless mean speed parameter, namely, the modified Mach number, approaches to unity the pressrue field converges very quickly to the limiting solution ph = constant even at moderate values of the compressibility number. In addition, both small perturbation analysis and numerical results reveal that under some circumstances, e.g., in a plane slider, the pressure boundary condition at the trailing edge should be modified in order to obtain a physically meaningful solution.
The Fluctuating Flow of a Gas Near a Stagnation Point on a Hot Wall
Authors: Gribben R. J.
Published: November 2010

Solutions are given in series, valid for low and high frequencies, for the two-dimensional flow in the vicinity of a stagnation point due to an incident stream, assumed incompressible, which is fluctuating in amplitude about a steady mean. The wall is assumed to be hot so that compressibility effects may not be neglected within the laminar boundary layer itself. Numerical computations are carried out for the case of the wall-mainstream temperature ratio, χ, equal to unity (a warm wall) and χ = 2.003 (a typical hot wall). Calculation of the fluctuations in the skin-friction and heat-transfer rate at the wall support previous approximate results at low frequencies for these two values of χ and the effect of the hot wall is seen to enhance the phase lead (skin friction) over, and decrease the phase lag (heat transfer) behind, the main stream. The possibility of covering the whole frequency range by the two series is discussed.
Dynamic Stresses in a Plate With Circular Holes
Authors: Cheng S. L.
Published: November 2010

The formal solution of the problem of defraction of a plane, time-harmonic, compressional wave by a group of cavities in a thin elastic plate is obtained by the method of multiple scattering. The cavities are circular and their geometry of distribution is arbitrary. Numerical results of two identical holes at a finite separation are presented in detail.
Postbuckling Analysis of a Magnetoelastic Beam
Authors: Popelar C. H.
Published: November 2010

The initial postbuckling behavior of an elastic ferromagnetic beam in a transverse magnetic field is studied. The cantilever beam is found to be imperfection-sensitive. Imperfections due to deviations from straightness of the beam and due to misalignment of the field with the normal to the beam are investigated. Reductions of the buckling field due to initial curvature of the beam are not sufficient to account for the two-to-one discrepancy between recorded theoretical and experimental results. However, reductions of 50 percent or more are readily produced by misalignment.
An Experimental and Numerical Study of Elastic Strain Waves on the Center Line of a 6061-T6 Aluminum Bar
Authors: Habberstad J. L. , Hoge K. G. , Foster J. E.
Published: November 2010

The elastic strain waves resulting from the impact of two 3/4-in-dia 6061-T6 aluminum bars are studied experimentally and analytically. Experimental data are obtained from strain gages on the center line and outer surface of the bar, located at various distances from the impact end of the bar. Experimental data are compared to numerical results obtained from integrating the exact equations of two-dimensional motion. In general, agreement between the numerical and experimental results is very good.
Sudden Twisting of a Penny-Shaped Crack
Authors: Sih G. C. , Embley G. T.
Published: November 2010

A transient stress analysis for the problem of a torque applied suddenly to the surface of a penny-shaped crack in an infinite elastic body is carried out. The singular solution is equivalent to that of the sudden appearance of a crack in a body under torsion. Using an integral transform technique developed for this class of transient problems, the dynamic stresses near the periphery of the crack are found to have the same angular distribution and inverse square root singularity as in the static case. This character of the local solution prevails for all time only in a toroidal region extremely close to the crack border. Within this region, the stress intensity is found to vary with time, reaching a peak greater than the static value and subsequently oscillating about that value with decreasing amplitude. The dynamic crack-opening displacement field is also given for any instant of time after loading.
The Effect of Initial Imperfections on the Buckling Load of Shallow Circular Arches
Authors: Schreyer H. L.
Published: November 2010

This paper presents an exact analysis for the buckling value of a concentrated load applied to a shallow circular arch. The effects of load offset and initial imperfections with the same form as the buckling mode are included. The results are displayed graphically and a comparison is made with experimental values that are available in the literature.
Response of a Ring-Reinforced Cylindrical Shell, Immersed in a Fluid Medium, to an Axisymmetric Step Pulse
Authors: Crouzet-Pascal J. , Garnet H.
Published: November 2010

The dynamic response of a ring-stiffened circular cylindrical shell, immersed in a fluid and subjected to a suddenly applied radial load, is investigated. The shell is infinitely long, the stiffening rings are periodically spaced and identical, and the applied load is uniformly distributed. In the analysis, the authors employ a technique involving the superposition of steady-state solutions which they have found, in previous applications, to be more suitable for problems involving complex interaction conditions than the customary transform approaches. The shell response is computed for an applied step pulse. Displacements and stress histories, and variations in their peak levels, are presented for values of ring flexibility, mass, and spacing, varying over a broad range. The response to the dynamic load is also compared to the response obtained for a static load of equal amplitude. It is found, for example, that for a given ring spacing and flexibility, increase in ring mass above a certain level can lead to dynamic stresses and displacements that exceed their static counterparts by large amounts. Such a situation also makes the existence of an oscillating response more likely. When the ring mass has a negligible influence of the shell response, the trends followed by the peak dynamic displacement and stress with ring flexibility are not appreciably different from those followed by the corresponding static quantities. A similar observation can be made concerning the variation of the peak dynamic displacement with ring spacing.
Dynamic Scattered Light Photoelasticity in Two-Dimensional Problems
Authors: Hemann J. H. , Becherer R. J.
Published: November 2010

The individual normal stresses in a two-dimensional plane-stress wave-propagation problem can be determined directly by using scattered light photoelasticity. The applicability of the method is shown by subjecting a rectangular plate to an explosive load.
Deflection and Moment Data for Rectangular Plates of Variable Thickness
Authors: Petrina P. , Conway H. D.
Published: November 2010

Numerical values of deflections and moments are given for uniformly loaded rectangular plates with a pair of opposite sides simply supported and the others either simply supported or clamped. The plates are tapered in a direction parallel to the simply supported sides. Data are given for two tapers and for plate aspect ratios equal to 1 (square plates), 1.5 and 2.
Large Deformation of Very Thin Shells—The Inverse Problem
Authors: Flu¨gge W. , Chou S.-C.
Published: November 2010

This paper deals with the inverse problem of large deformation of very thin shells. An inflated shell of known shape is considered and the differential equations are derived for the case that the inflation pressure is decreased or entirely removed. They are applied to a toroid which is circular in cross section when fully inflated. It is found that under decreasing pressure the shell cannot remain smooth, but develops wrinkles on part of its surface.
On Elastic Line Contact
Authors: Kalker J. J.
Published: November 2010

Two-dimensional elastic half-space contact theory suffers from the defect that the surface displacement with respect to infinity becomes infinitely large when the total force carried by the half space is different from zero. Several authors removed this defect by altering the geometry so that the depth of the elastic body becomes finite. In the present paper another approach is chosen by considering contact areas which are many times as long as they are wide, but which still are small as compared with a characteristic dimension of the body which is approximated by the half space. As one of the examples, the Hertz problem is considered, and the asymptotic results are compared with the exact theory. It is found that errors of 10–15 percent are found when the contact ellipse is twice as long as wide, and errors of 2–3 percent are encountered when the ratio of the axes is five.
Flow Patterns of a Circular Vortex Ring With Density Difference Under Gravity
Authors: Chen C.-J. , Chang L.-M.
Published: November 2010

The evolution of a circular vortex ring with a density 1.5 times of the ambient fluid under gravity was investigated. Three distinct patterns, namely, laminar, wavy, and turbulent, were observed. It is found that approximately as Nre > 2000, the vortex becomes turbulent, as Nre < 1500, laminar but to disintegrate into subrings. The stability curve was determined.
Mode Responses of Dynamically Loaded Structures
Authors: Lee L. S. S.
Published: November 2010

Instantaneous mode responses of dynamically loaded elastic, viscous, ideally plastic and rigid, viscoplastic structures are defined and characterized by variational criteria with isometric constraints. Under some loading conditions, the instantaneous mode responses would coincide with the natural mode solutions of those problems. For the case of a rigid, perfectly plastic problem, it is believed that the criterion for an instantaneous mode response would yield simultaneously the true limit load and the true collapse mechanism of the limit analysis. Examples of beams and plates of various materials subjected to uniformly distributed, rectangular pulse load or impulsive loading are given to illustrate the instantaneous mode responses which are then compared with exact solutions.
On Uniqueness in Ideally Elastoplastic Problems in Case of Nonassociated Flow Rules
Authors: Bleich H. H.
Published: November 2010

It is known that in the quasi-static treatment of ideally elastoplastic solids, lack of uniqueness may occur unless associated flow rules are used. This has been illustrated by a simple example in reference [3]. The present study shows that the uniqueness difficulties in the foregoing and in similar situations disappear, if inertia forces are included in the analysis. As inertia forces in nature are unavoidable there may therefore be nothing improper in the use of nonassociated flow rules. One is simply not permitted to replace the actual dynamic situation in the limit by a quasi-static one. It is shown, however, that an entirely arbitrary selection of yield condition and flow rules is not permissible, but that the combination must satisfy a requirement which is derived. No general proof of uniqueness of dynamic problems for material prescriptions satisfying this requirement is as yet available. It is the purpose of the paper to induce interested investigators to search for such a general proof.
On the Response of a Two-Degree-of-Freedom Rigid Disk With a Moving Massive Load
Authors: Stahl K. J. , Iwan W. D.
Published: November 2010

An analysis of the dynamic response of an elastically supported two-degree-of-freedom rigid circular disk excited by a moving massive load is presented. The equations of motion of the system are solved by transforming a set of coupled Hill-Mathieu equations into an ordinary eigenvalue problem. Two types of system instability are observed. A stiffness instability region exists above the critical speed of the disk and a terminal instability region exists for all load speeds exceeding a certain limiting value. The introduction of viscous damping may destabilize the system.
Bifurcation of Circular Rings Under Normal Concentrated Loads
Authors: Seide P. , Albano E. D.
Published: November 2010

The deformation in bending of a circular ring loaded in its plane by concentrated forces is studied. The ring is assumed to be an elastica. The loads are of equal magnitudes and are equally spaced about the ring. Values of loading at which bifurcation of the symmetrical finite distortion shape occurs are determined for forces which remain normal to the ring. It is found that no bifurcation point exists for a ring under three loads. Buckling of a ring under two loads can occur only when the prebuckling configuration is an extremely distorted one. If the number of loads is five or greater, the critical average pressure does not differ greatly from the result for the ring under uniform pressure.
Beam on Bilinear Foundation
Authors: Johnson W. H. , Kouskoulas V.
Published: November 2010

This paper develops and applies a methodology for the solution of the problem of a beam on bilinear foundation. The nonlinear ordinary differential equation of the response is linearized by partitioning the beam at points of zero deflection as determined from the known or assumed linear solution and the problem is reduced to the solution of a system of nonlinear transcendental equations. The method of solution of these equations, which are characteristic of the problem in question, is formalized and applied.
Liapunov Functional for a Rectangular, Nonuniform Density Membrane
Authors: Dixon M. W.
Published: November 2010

The question of stability of equilibrium of a general rectangular, nonuniform density membrane adjacent to a supersonic airstream arbitrarily directed with respect to the edges of the membrane is considered using the direct method of Liapunov. The governing equation of the system, derived using piston theory, is used with the developed Liapunov functional to show that the equilibrium of the system is stable in the absence of structural damping, or for structural damping of a certain form.
Pyrotechnic Shock Synthesis Using Nonstationary Broad Band Noise
Authors: Bucciarelli L. L. , Askinazi J.
Published: November 2010

Various techniques are currently used to simulate a shock environment. The authors investigate the validity of simulating the shock environment due to a pyrotechnic firing by means of a nonstationary transient formed by modulating a stationary broad band random signal with an exponentially decaying pulse.
Nonlinear Vibration of a Rectangular Plate Arbitrarily Laminated of Anisotropic Material
Authors: Bert C. W.
Published: November 2010

A new simplified approach is presented for calculating the flexural frequencies of a composite-material plate undergoing moderately large, normal deflections. The plate may be arbitrarily laminated with respect to the midplane, so that bending-stretching coupling is present. The approach used is a generalization of the work of Wah for homogeneous, isotropic plates. In the case of orthotropic plates, it differs from various orthotropic extensions of the popular Berger hypothesis. The present theory is applied to the practical case of a clamped rectangular plate with finite in-plane restraint. The results are compared satisfactorily with those of previous analyses for various special cases.
Large Amplitude Forced Vibrations of Simply Supported Thin Cylindrical Shells
Authors: Ginsberg J. H.
Published: November 2010

The response of a thin circular cylindrical shell to resonant harmonic excitation is examined by a modal expansion approach. The nonlinear strain-displacement relations lead to a nonlinear boundary condition, as well as nonlinear equations of motion. The solution, which retains tangential inertia effects, is obtained by a perturbation technique that yields a consistent first approximation of the nonlinear response. The results are applicable for a wide range of parameters and to cases of excitation near any of the three lowest natural frequencies corresponding to given axial and circumferential wavelengths. For situations where shallow shell theory is valid, the results of previous studies, which were based upon such a theory, are in close agreement.
Bifurcation of Rings Under Concentrated Centrally Directed Loads
Authors: Albano E. D. , Seide P.
Published: November 2010

The stability of the large symmetrical deformations of circular rings under equal and equally spaced centrally directed loads is examined. It is found that for 5 or more loads the critical average pressure (the load divided by the distance between loads) does not differ significantly from the result for uniform pressure. The results for 2, 3, and 4 centrally directed or normal loads are identical.
Postbuckling of Orthotropic Annular Plates
Authors: Uthgenannt E. B. , Brand R. S.
Published: November 2010

The postbuckling behavior of orthotropic annular plates due to in-plane compressive loads applied at the outer edge is considered. The governing differential equations are derived by extending von Karman’s nonlinear plate theory to include orthotropic material properties. It is then assumed that the deformations are restricted to axisymmetric forms and the equations are specialized on the basis of this restriction. The equations are given in nondimensional form and are solved by a numerical technique originally employed by Keller and Reiss. Parameters of interest are the membrane and bending stresses, deflections, and slopes. The curves illustrate the importance of including the orthotropicity of the material in analyses.
Steady-State Responses of a Beam on Idealized Strain-Hardening Foundations for a Moving Load
Authors: Mulcahy T. M.
Published: November 2010

The steady-state responses to a point load moving with constant velocity on an elastic beam which rests on two types of idealized strain-hardening foundations are considered. The one-dimensional elastic-rigid foundation problem is shown to be equivalent to an elastic foundation with two traveling point loads. The opposing loads produce deflections which remain bounded for all load velocities and less than the corresponding elastic foundation results. The deflections of a one-dimensional elastic-perfectly plastic foundation are shown to be bounded for all load velocities. However, deflections significantly larger than the corresponding elastic foundation results occur over a wide range of velocities which are less than the elastic foundation critical velocity.
Transient Response of a Buried Foundation to Antiplane Shear Waves
Authors: Thau S. A. , Umek A.
Published: November 2010

A rigid rectangular foundation, embedded at an arbitrary depth below the surface of an elastic half space is subjected to a plane, transient SH-wave. The Laplace and Kantorovich-Lebedev transforms are applied to derive the equation of motion for the foundation during the initial time period required for an SH-wave to traverse the base width. The peak impulse response is found to occur during this time and the response there-after appears to be valid based on a comparison with the known, long-time limit. Consequently, the results presented here can be convolved with an earthquake accelerogram to yield an accurate foundation earthquake response.
Scattering of Compressional Waves by a Rigid Spheroidal Inclusion
Authors: Oien Michael A. , Pao Yih-Hsing
Published: November 2010

The scattering of an axial plane harmonic compressional wave by a mobile rigid spheroidal inclusion in an elastic medium is investigated. A solution valid for low frequencies is obtained using the eigenfunction expansion method. Numerical results are presented for the excited translational motion of the spheroid and for dynamic stress-concentration factors.
Transient Response of a Point-Excited Submerged Spherical Shell
Authors: Lou Y. K. , Klosner J. M.
Published: November 2010

The transient responses of a submerged spherical shell to a concentrated impulse and Heaviside load are obtained by using the classical mode method and the Laplace transform. For long time solutions, only a relatively small number of modes are sufficient, while for the short time response, a large number of modes must be used in order to achieve acceptable accuracy. For the lower modes, the inversion integral involves only simple poles and can be evaluated by Cauchy’s residue theorem. For the higher modes it is necessary to use asymptotic approximations and the inversion involves branch points and poles. A spherical wave approximation, similar to Haywood’s cylindrical wave approximation, is also used to solve the transient problem. It is found that the approximation accurately predicts the maximum peak response for the impulse load, while it underestimates the response for the Heaviside load.
Elastic Analysis of a Skull
Authors: Hardy C. H. , Marcal P. V.
Published: November 2010

A finite-element elastic analysis is made of a skull. Measurements were made of the geometry and thickness of a skull. The skull was then idealized with a doubly curved and arbitrary triangular shell element. Results suggest that the skull is well built for resistance to front loads. The importance of using a composite material through the thickness of the shell was established. On the basis of tensile cracking at maximum elastic stress, loads of 3500 lb and 1400 lb were predicted for the first cracking of the skull due to front and side loading, respectively.
Moving Load on a Fluid-Solid Interface: Subsonic and Intersonic Regimes
Authors: Kennedy T. C. , Herrmann G.
Published: November 2010

The steady-state response of a semi-infinite solid, with an overlying semi-infinite fluid, subjected at the plane interface to a moving point load is determined for subsonic and intersonic load velocities. Some numerical results for the displacements at the interface are presented and compared to the results obtained in the absence of the fluid.
Thermal Fracturing of Hard Rock
Authors: Lauriello P. J. , Chen Y.
Published: November 2010

Thermal fracturing of hard crystalline in situ rock has been studied by solving the quasistatic uncoupled thermoelastic equations for a semi-infinite medium subjected to transient surface heating over a circular area by a constant flux or constant temperature convective heat source. The thermoelastic stress state is related to brittle fracture in rock according to an appropriate form of the Griffith and the modified Griffith theories. The predicted zone of weakening has been experimentally investigated by lasing samples of Barre granite. Measurements of the size of the in-depth fractures correlated well with the predicted results.
Upper and Lower Bounds for Deflections of Laminated Cantilever Beams Including the Effect of Transverse Shear Deformation
Authors: Reissner E.
Published: November 2010

We state a method for obtaining upper and lower-bound results for the end deflection of a narrow rectangular cantilever beam, treated as a problem in plane stress. Reference is made to well-known earlier approximate results for this problem, using elementary polynomial solutions of Airy’s differential equation, and using approximate, rather than exact boundary conditions, without the establishment of bounds for the error in the approximate solution. Application of the bound method is here limited by the use of simple polynomial approximations for stresses and displacements, with the possibility remaining to obtain improved bounds by more elaborate choices of approximation functions.
A General Continuum Theory With Microstructure for Wave Propagation in Elastic Laminated Composites
Authors: Hegemier G. A. , Bache T. C.
Published: November 2010

A continuum theory with microstructure for wave propagation in laminated composites, proposed in previous works concerning propagation normal and parallel to the laminates, is extended herein to the general two-dimensional case. Continuum model construction is based upon an asymptotic scheme in which dominant signal wavelengths are assumed large compared to typical composite microdimensions. A hierarchy of models is defined by the order of truncation of the obtained asymptotic sequence. Particular attention is given to the lowest order dispersive theory. The phase velocity spectrum of the general theory is investigated for one-dimensional wave propagation at various propagation angles with respect to the laminates. Retention of all terms in the asymptotic sequence is found to yield the exact elasticity spectrum, while spectral collation of the lowest order dispersive theory with the first three modes of the exact theory gives excellent agreement.
Shock Pressure in Oblique Impact—A Theoretical Analysis
Authors: Persson C. A˚ke
Published: November 2010

The variation of shock pressure with the angle between the colliding surfaces in an oblique impact between two plane plates is analyzed theoretically. The analysis is carried out for small impact angles and the plate materials are assumed to behave like fluids (Case 1) and linear elastic media (Case 2). In the latter case the two extreme assumptions concerning the friction at the interface, no friction and no sliding, are treated. The results show that the shock pressure increases quadratically with the impact angle (except for some of the no sliding cases, where decreasing pressure can occur) and that the pressure rise is strongly dependent upon the ratio between the impact velocity and the shock wave velocities for the plate materials.
On Approximations of the Buckling Stresses of Axially Compressed Cylinders
Authors: Dym C. L.
Published: November 2010

An uncoupled eighth-order equation for the buckling of axially compressed cylinders, within the framework of the Koiter-Budiansky shell equations, is derived for the first time herein. A solution of this equation is then used to generate some different types of approximations for the buckling stresses of a circular cylinder. Comparisons to previous solutions are given, as are some remarks on the nature of the approximations and their relationships to the limiting cases of infinitely short and infinitely long shells. Also given is a summary of the uncoupled system of equations of Sanders’ linear shell theory.
On Pure Bending and Stretching of Orthotropic Laminated Cylindrical Shells
Authors: Reissner E. , Tsai W. T.
Published: November 2010

The paper considers pure bending and stretching of axially uniform, orthotropic nonhomogeneous (laminated) thin-walled beams, as a problem of the theory of thin shells. In analyzing this problem, it is found that the stretching and bending stiffness factors for such shells are generally different for closed-cross-section shells and for longitudinally slit shells. While an analogous result for torsion of (homogeneous) shells is well known, the significance of the present results for the problems of bending and stretching of laminated shells lies in the fact that no such effect exists for homogeneous shells.
Thermal Stresses in an Orthotropic Elastic Slab Due to Prescribed Surface Temperatures
Authors: Tauchert T. R. , Ako¨z A. Y.
Published: November 2010

The stresses in an orthotropic, elastic slab resulting from a stationary, two-dimensional temperature field are examined. A general method of solution based upon displacement potentials is presented for the case of prescribed surface temperatures. Both the plane-strain and plane-stress problems are discussed. As an illustrative example, the stresses resulting from a uniform temperature rise over a portion of one face of the slab are computed; numerical results are given for a fiber-reinforced composite material.
On the Friction Reducing Non-Newtonian Flow Around an Enclosed Disk
Authors: Bilgen E. , Vasseur P.
Published: November 2010

The turbulent flow characteristics of non-Newtonian dilute polymer solutions around an enclosed rotating disk have been studied both theoretically and experimentally. In the theoretical analysis, the momentum equations of the boundary layers on both rotating disk and housing have been solved numerically using appropriate velocity profiles. It is shown that the theoretical predictions for minimum resistance conditions are in good agreement with the experimental results of this study and with those in the literature.
Capillary Flow in Triangular Grooves
Authors: Ayyaswamy P. S. , Catton I. , Edwards D. K.
Published: November 2010

Solutions to the two-dimensional equations of motion for steady laminar flow in grooves are obtained by the Galerkin boundary method. The two independent parameters which characterize the flow configuration are the half angle of the liquid-filled triangular groove and the contact angle of the shear-free meniscus. The analytical results include dimensionless velocity contours, average velocity, hydraulic diameter, and area. The friction factor coefficient K, where f = K/Re and Re is Reynolds number based upon hydraulic diameter, is also found. Results are reported for channel half angles from 5–60 deg and contact angles from 0.1 deg to the complementary angle (full groove condition). Comparisons with analysis and experimental data for the full groove are made and found to be excellent.
The Swirling Turbulent Plume
Authors: Narain J. P. , Uberoi M. S.
Published: November 2010

An entrainment model for an axisymmetric buoyant swirling turbulent plume in a quiescent homogeneous density surrounding medium has been developed. The streamwise similarity of the mean axial velocity, swirl velocity, turbulent Reynolds stresses, and the density difference between the plume and the ambient fluid are assumed. Consistent with various integrated conservation equations, the entrainment is found to be a function of the Reynolds stress, the form of various similarity profiles, the local densimetric Froude number, and the swirl ratio of the swirling plume. While the swirl alone always increases the rate of entrainment across the boundaries of the plume, it also interacts with the buoyancy forces to cause a slight detrainment of the fluid from the plume. The numerical results for the decays of axial and swirling velocities and the spread of the jet agree reasonably well with the existing experimental investigations.
Steady-State Response of a Dynamical System Under Combined Parametric and Forcing Excitations
Authors: Hsu C. S. , Cheng W.-H.
Published: November 2010

A linear dynamical system subjected to combined parametric and forcing excitations of periodic nature is governed by a system of inhomogeneous differential equations with periodic coefficients. Presented here is an explicit expression for the steady-state periodic response of such a system, given in terms of the fundamental matrix of the homogeneous system. Based upon this expression, specific analytic formulas of the steady-state response can be derived for some physical systems. For a general system where such an analytical determination is not feasible, the derived expression allows us to devise a straightforward numerical procedure which is particularly suited for computer evaluation and which is equally suited for high-order systems.
Slip Line Field of Anisotropic Soil
Authors: Greenstein J. , Livneh M.
Published: November 2010

This paper is concerned with anisotropic material in the two-dimensional case. A general yield function is postulated, and it is shown that both the equilibrium equations and the velocity equations are hyperbolic. Moreover, in the perfectly plastic-rigid media the velocity characteristics coincide with the stress characteristics. Thus, for practical applications, once the parameters of the yield function have been found for the anisotropic material, the conventional method of the isotropic case may be adopted, using the relevant relationships along the characteristics. An illustrative example is given.
Numerical Solution of Non-Hertzian Elastic Contact Problems
Authors: Singh Krishna P. , Paul Burton
Published: November 2010

A general method for the numerical analysis of frictionless nonconformable non-Hertzian contact of bodies of arbitrary shape is developed. Numerical difficulties arise because the solution is extremely sensitive to the manner in which one discretizes the governing integral equation. The difficulties were overcome by utilizing new techniques, referred to as the method of redundant field points (RFP) and the method of functional regularization (FR). The accuracy and efficiency of the methods developed were tested thoroughly against known solutions of Hertzian problems. To illustrate the power of the methods, a heretofore unsolved non-Hertzian problem (corresponding to the case of rounded indentors with local flat spots) has been solved.
Minimal Weight Design for Conical Shells
Authors: Reiss R.
Published: November 2010

The statical method for solving the problem of minimum volume design of sandwich conical shells obeying the Tresca criterion is presented. By employing variational techniques, necessary and sufficient conditions for an absolute minimum are obtained. The form of the solution is shown to be geometry as well as load-dependent. Conditions for uniqueness are established and a nonunique example is presented. Examples are presented for conical shells with a rigidly attached central boss.
Propagation of a Shock Wave Front Through a Lens-Shaped Elastic Body
Authors: Ting T. C. T. , Herrmann G.
Published: November 2010

Ray theory is used to solve the problem of a plane pressure pulse with a discontinuous pressure front striking an elastic body whose cross section has the shape of a lens. Both plane-strain and axisymmetric motions are considered. The front and back surfaces of the lens are assumed to be circular. The velocity and acceleration at the P-wave front and the discontinuity in acceleration at the S-wave front are obtained explicitly for points along the axis of the lens and at the center of the back surface where reflections occur. The purpose of this study is to assess the effect of the curvatures of the lens on the velocity-time history at the center of the back surface of the lens which can be measured experimentally. Comparison with a laboratory test shows excellent agreement between analytical and experimental results.