bluuebunny/crossref_metadata_2025 huggingface dataset:
Bounds on the Maximum Contact Stress of an Indented Elastic Layer
Authors: Pao Y. C. , Wu Ting-Shu , Chiu Y. P.
Published: November 2010

This paper is concerned with the plane-strain problem of an elastic layer supported on a half-space foundation and indented by a cylinder. A study is presented of the effect of the contact condition at the layer-foundation interface on the contact stresses of the indented layer. For the general problem of elastic indenter or elastic foundation, the integral equations governing the contact stress distribution of the indented layer derived on the basis of two-dimensional theory of elasticity are given and a numerical method of solution is formulated. The limiting contact conditions at the layer-foundation interface are then investigated by considering two extreme cases, one with the indented layer in frictionless contact with the half space and the other with the indented layer rigidly adhered to the half space. Graphs of the bounds on the maximum normal stress occurring in indented elastic layers for the cases of rigid cylindrical indenter and rigid half-space foundation are obtained for possible practical applications. Some results of the elastic indenter problem are also presented and discussed.
Entrance Development of the Weakly Interacted MHD Plane Channel Flow as Affected by Wall Conductances
Authors: Hsia Edward S.
Published: November 2010

Growth behavior of the weakly interacted laminar MHD flow in the entrance region of a plane channel with electrically conducting walls is investigated by the momentum integral method. In the developing region, the analysis shows that, with moderate magnetic Reynolds number, the nonuniformity of the magnetic field is found to be significant, and the effect of wall conductivity is found to shorten the growth history of the flow field. Numerical results, including local pressure gradient and skin-friction coefficient, are obtained over a range of Hartmann numbers of 0–10, and wall conductance parameter γ, defined as σwh/σa, of 0–20.
The Resistance to Rotation of Free and Enclosed Disks
Authors: Miloh T. , Poreh M.
Published: November 2010

A general analysis of the resistance to rotation of disks at high Reynolds numbers is presented. The theoretical calculations of the fluid-induced torque on free and enclosed, smooth and rough disks, as well as torque induced by the dilute polymer solutions, are found to be in good agreement with experimental results.
Combined Free and Forced Convection Through Vertical Rectangular Channels With Unequal Heating From Sides
Authors: Iqbal M. , Aggarwala B. D.
Published: November 2010

Fully developed laminar combined free and forced convection through vertical rectangular channels is studied. Uniform heat input per unit length is considered. All fluid properties are considered invariant with temperature except for the variation of density in the body-force term of the equation of motion. Broad sides of the duct are assumed at uniform temperature. The short sides have been treated for adiabatic condition; or under nonzero finite and even unequal heat fluxes. An exact solution of the problem has been presented. Nusselt numbers have been evaluated and their variation with respect to aspect ratios, buoyancy parameter, and short side heat fluxes have been studied.
Creep at Constant Stress in Isotropic Solids
Authors: Carroll M. M.
Published: November 2010

The admissible stress states for creep at constant stress in a particular viscoelastic solid are determined by the condition that they must give rise to strain histories which satisfy the equation of compatibility at every instant. Analysis of this condition is carried out for homogeneous, isotropic, compressible or incompressible linear solids, and also for compressible or incompressible nonlinear solids, under the assumption that the deformations involved are small.
Response of a Semi-Infinite Elastic Solid to an Arbitrary Line Load Along the Axis
Authors: Agrawal G. L. , Gottenberg W. G.
Published: November 2010

The axisymmetric problem of a line load acting along the axis of a semi-infinite elastic solid is solved using Hankel transforms. In this solution the line load is interpreted as a body force loading and by assuming the line load to be of the form of a Dirac delta function the solution of Mindlin’s problem of a point load within the interior of the half space is obtained. Solutions of this problem presented in the literature have been obtained using semi-inverse techniques whereas the solution given here is obtained in a systematic step-by-step manner.
Thermally Induced Stress Waves in a Laminated Composite
Authors: Sve C.
Published: November 2010

A solution is presented for the response of a periodically laminated elastic half plane subjected to rapid internal heating. The assumed temperature distribution has been used in previous investigations of electromagnetic absorption problems where thermal diffusion may be neglected. The laminations are perpendicular to the free surface of the half plane, and the incident flux is absorbed in each layer according to an exponential decay with depth. Since heal conduction is neglected on this time scale, the temperature distribution is discontinuous at the lamination interfaces. A microstructured continuum theory provides the dispersive model, and a solution is obtained for the composite stress in the far field. Limiting forms of the solution are included for the cases when the radiation is absorbed in the alternate layers only or when dispersion can be neglected. Several numerical examples are presented to illustrate the effect of dispersion.
A Numerical Method for Solving General MHD Duct Flow Problems
Authors: Chu Wen-Hwa
Published: November 2010

A numerical method is successfully developed for solving general MHD duct flow problems, utilizing “machine transformation” and finite-difference technique with a new successive overrelaxation procedure. Examples are given to establish the method and to indicate the versatility of the associated computer program. The generality of the basic principle may help to solve many problems other than MHD flow in a general domain.
Moisture Transfer in Porous Elastic Solids
Authors: Mountfort M. V.
Published: November 2010

A theory is developed to cover the simultaneous moisture transfer and stress development in porous elastic solids. It is shown that this theory, small-strain, is analogous to that governing coupled heat transfer. As an example of the general solution method, the case of a porous elastic beam under simple load is examined.
Stresses in an Elastic Half Space Due to Surface Loads Progressing at the Speed of Rayleigh Waves
Authors: Sandler I. S. , Bleich H. H.
Published: November 2010

The nature of the singularity in the stresses produced near the front of a progressing step load of pressure on the surface of an elastic half space is investigated for the case when the velocity of the front coincides with that of Rayleigh waves in the elastic medium. The technique is based on the assumption of the basic form of the solution and the demonstration that this assumption is correct. It is found that for the particular velocity of the front considered here, unusually large stresses are produced in the medium.
Geometric Instabilities in Isotropic Plastic Solids Under Increasing Uniaxial Compression
Authors: Newman J. B.
Published: November 2010

This analysis seeks three-dimensional instabilities of uniaxial compressive flow in isotropic, strain-hardening, rigid-plastic materials of the Mises and maximum shear stress types. No instabilities are found for Mises materials. Maximum shear materials display axisymmetric, “deflectional”, and “higher-order” buckling. For increasingly slender specimens, the deflectional buckling process merges into that of the Shanley theory. The axisymmetric mode raises the possibility that instabilities contribute to the double axial bulging of ductile compression specimens reported by Na´da´i.
Surface-Roughness Effects in Rolling Contact
Authors: Nayak P. Ranganath
Published: November 2010

A theory of rolling contact is presented which deviates from past theories in two respects: (a) the contacting surfaces are not assumed to be topographically smooth, and (b) Coulomb’s law of friction is replaced by a law describing the behavior of interfacial friction junctions. Numerical results for the slip as a function of the normal and tangential loads are shown to depend on a roughness parameter D, which, in turn, depends on surface topography, the gross geometry of the contacting bodies and on the normal load. It is found that when D is large (i.e., the surfaces are very rough, or the normal load is small), the slip-force relationship differs considerably from that predicted by the smooth-surface (or classical) theory. When D tends to zero, the two theories coincide. The dependence of D on topographical parameters is shown explicitly. Numerical examples indicate that for cylinders of small radius, surface-roughness effects may be important. Their importance decreases as the cylinder radius or the maximum contact pressure is increased, or the surface is made smoother.
Large Deflections of a Linearly Viscoelastic Shallow Spherical Shell
Authors: Dea´k A. L.
Published: November 2010

Numerical solutions for the time history of motion of a shallow viscoelastic spherical shell are presented under large deformations. Axisymmetric motion is considered due to uniform pressure with arbitrary time variation. The dynamic viscoelastic buckling load is established by comparing long-time equilibrium states due to small changes in the applied pressure. The problem is formulated as a coupled pair of nonlinear integro-differential equations which is solved by Newton’s method.
On Obtaining Solutions for Almost Isochoric Finite Elastic Deformations
Authors: Faulkner M. G.
Published: November 2010

A method of solving inhomogeneous problems for slightly compressible elastic isotropic materials is outlined and illustrated using a two-parameter family of solutions.
Contact Pressure Between an Elastic Spherical Shell and a Rigid Plate
Authors: Updike D. P. , Kalnins A.
Published: November 2010

A theoretical analysis for the determination of the contact pressure between a uniform elastic spherical shell and a rigid plate is developed. The results are directly applicable to the theory of applanation tonometry which is concerned with the measurement of intraocular pressure. Numerical results are presented for a shell having a radius to thickness ratio of 30.
On the Laminar Two-Dimensional Free Jet of an Incompressible Pseudoplastic Fluid
Authors: Atkinson C.
Published: November 2010

A closed-form solution is obtained to boundary-layer equations given by Lemieux and Unny [1] for the free outflow of a non-Newtonian pseudoplastic fluid from a two-dimensional orifice into a mass of the same fluid. Results deduced from this solution are compared with numerical results given in [1]. The analytical solution given here contradicts some of these numerical results when the flow behavior index of the fluid is less than or equal to a half.
Plastic Behavior of Two-Layer Sandwich Structures
Authors: McLaughlin P. V.
Published: November 2010

Sandwich structures composed of two thin sheets separated by a core which can support only transverse shear are both statically and kinematically determinate “in-plane”, allowing in-plane elastic-plastic behavior of such structures to be found in terms of sheet material properties. Unlike homogeneous shells, the shear load-deformation relations separate from in-plane behavior, and all the usual difficulties associated therewith disappear. The method for deriving in-plane constitutive relations for thick (t/R terms not negligible compared to unity), doubly curved, nonsymmetric shells with arbitrary-known sheet elastic-plastic behavior is presented. The form of the equations for yield and limit behavior is discussed, including yield surfaces and flow laws. Comparison of thin versus thick shell theory shows that nonconservative strength predictions can result from neglecting t/R terms. Use of the theory is illustrated by an example which shows application to fibrous composite materials and the effect of shell thickness.
Limit Loads of Circular Plates Under Combined Loading
Authors: Haydl H. M. , Sherbourne A. N.
Published: November 2010

Limit loads of circular plates under combined transverse and in-plane loading are given for the von Mises yield condition. Ivanov’s approximation to the Ilyushin yield surface is used. Collapse load interaction curves and stress fields are given for simply supported and clamped plates. The results are compared with existing solutions for the title problem based on the Tresca yield criterion.
A Class of General Solutions to the Nonlinear Dynamic Equations of Elastic Strings
Authors: Lee Shiang-Yu , Ames W. F.
Published: November 2010

A class of general solutions to the nonlinear dynamic equations for large deflections of an elastic string is developed. These solutions, obtained under a condition of decoupling, are valid for transverse waves traveling in one direction on semi-infinite or infinite regions. An example is given and the results demonstrate clearly the effect of transverse wave distortion.
Elastic Wave Propagation in Inhomogeneous Bars of Several Sections
Authors: Wade J. E. , Torvik P. J.
Published: November 2010

An approximate method is given for analyzing the propagation of low-frequency wave trains in prismatic bars of cross sections which can be approximated through subdivision into rectangular elements. The method may be applied to inhomogeneous (composite) bars, for it is not required that each such element have the same properties. Results from the new method compare favorably with results previously obtained for a rectangular bar. Frequency spectra for several composite bars, including a bar of thick angle section, are given.
Analysis of the Vibra-Lo
Authors: Brower W. B.
Published: November 2010

A recently invented land-locomotive device called the Vibra-Lo, which employs an oscillating driving force, is analyzed. It is shown that the ratio of the device static weight to the magnitude of the oscillating driving force is a basic design parameter which depends only on the value of the static friction coefficient. It is indicated that if it were possible to achieve bidirectional friction it might be advantageous in a practical device.
Flow in Turbulent Wall Layer Over Uniform Roughness
Authors: Wu Jin
Published: November 2010

A boundary-layer survey has been conducted on a rough plate consisting of uniform spherical particles arranged in a random and compact fashion. Strong turbulent mixing was observed in a region within a quarter of the particle size from the top of the particles. Such mixing is important to transfer or transport processes near a rough wall. The data of the normal axis of the present rough surface are found to be located at a distance of 1/50 of the particle diameter below the top of the particles. This reference data are different from that used by Nikuradse, indicating a possible modification of some numerical constants determined by Nikuradse.
The Morley-Koiter Equations for Thin-Walled Circular Cylindrical Shells: Part 1—General Solution for Symmetrical Shells of Uniform Thickness
Authors: Mangelsdorf C. P.
Published: November 2010

Modified Donnell equilibrium equations are solved in Part 1 for the case of symmetrical loading and supports, using Fourier series. An evaluation procedure for simple, fixed, and relaxed simple conditions is suggested. In Part 2, an application of the general solution is made for a shell with small circumferential grooves (or ribs) subjected to a longitudinal line load after approximations to allow for such grooves are introduced. The solution is completed for the boundary conditions of classical simple supports and relaxed simple supports and the results compared with experimental data.
The Load Transfer Problem in Shafts Coupled Through a Sleeve
Authors: Erdogan F. , Gupta G. D.
Published: November 2010

The following load transfer problems are considered in this paper: torque transfer between an elastic shaft and a finite elastic disk or sleeve of different materials, torque transfer between two identical shafts coupled through a finite sleeve, and torque transfer between two dissimilar shafts coupled through a finite sleeve. In all cases it is assumed that the contact between the sleeve and the shafts is one of perfect adhesion accomplished through bonding or shrink-fit. The problems are shown to reduce to singular integral equations with generalized Cauchy kernels. Some numerical examples are worked out and the stress-intensity factors and distribution of contact stresses are given.
The Prediction of Axisymmetric Turbulent Boundary Layer in Conical Nozzles
Authors: Au S. B.
Published: November 2010

A theoretical axisymmetric model of flow through conical Venturimeters, capable of solution by digital computer, has been developed to predict the development of the turbulent boundary layer along the convergent and throat section where the flow is subjected to a favorable pressure gradient. A computation method was developed to solve the momentum, auxiliary, continuity, and state equations simultaneously step-by-step. For a given inlet condition the throat condition can be predicted. Theoretical predictions were compared with experimental results obtained from two 10-in-dia Venturimeters of area ratios 0.25 and 0.5. The agreement between the theory and detailed boundary-layer surveys is good.
Influence of Enveloping Water Layer on the Rise of Air Bubbles in Newtonian Fluids
Authors: Mercier J. L. , da Cunha F. M. , Teixeira J. C. , Scofield M. P.
Published: November 2010

The rise of air bubbles in five Newtonian fluids is compared for two different cases of bubble formation and release: (a) directly into the five homogeneous fluids and (b) directly into a layer of distilled water underlying each one of the five liquids. It was found in Case (b) that medium-sized bubbles rise steadily through the upper liquid with an enveloping water layer of variable thickness. The influence of this water layer on the trajectory, shape, and terminal velocity of bubbles is particularly significant in low viscosity upper phases. The resulting water mass transfer per bubble through the lower density upper phase depends on viscosity and was markedly greater for the higher viscosity fluids. The behavior and the nature of the detachment of the water layers from the larger size bubbles are also presented and discussed.
Radial Propagation of Axial Shear Waves in a Finitely Deformed Elastic Solid
Authors: Kurashige M.
Published: November 2010

A study is made of the radial propagation of axial shear waves in an incompressible elastic solid under finite radial deformation. Basic equations are derived on the basis of Biot’s mechanics of incremental deformations, and analysis is made by the method of characteristics. Numerical examples are given by specializing the initial deformation to two cases: (a) an infinite solid with a cylindrical bore is inflated by all-around tension, and (b) a cuboid is rounded into a ring and its ends are bonded to each other. The influence of the inhomogeneities of such deformations upon the laws of shear wave propagation is presented in the form of curves.
The Role of Articular Facets During +Gz Acceleration
Authors: Prasad P. , King A. I. , Ewing C. L.
Published: November 2010

Experimental evidence is presented to document the load-bearing capability of the articular facets which join the vertebrae of the spine together posteriorly. Contrary to the general opinion that these facets carry no vertical load, this paper gives qualitative as well as quantitative data to show that there exists a dual load path along the vertebral column. Extensively instrumented human cadavers were used as test subjects. Strain gages were used to provide qualitative evidence of facets load while a unique intervertebral load cell supplied quantitative information of the load-bearing role of the facets. The results of this study led to a clearer understanding of the mechanism of injury to the vertebral column during +Gz impact acceleration.
Thermal Stresses in Chemically Hardening Elastic Media With Application to the Molding Process
Authors: Levitsky Myron , Shaffer Bernard W.
Published: November 2010

A method has been formulated for the determination of thermal stresses in materials which harden in the presence of an exothermic chemical reaction. Hardening is described by the transformation of the material from an inviscid liquid-like state into an elastic solid, where intermediate states consist of a mixture of the two, in a ratio which is determined by the degree of chemical reaction. The method is illustrated in terms of an infinite slab cast between two rigid mold surfaces. It is found that the stress component normal to the slab surfaces vanishes in the residual state, so that removal of the slab from the mold leaves the remaining residual stress unchanged. On the other hand, the residual stress component parallel to the slab surfaces does not vanish. Its distribution is described as a function of the parameters of the hardening process.
The Contract Problem for an Elastic Layer Supported by Two Elastic Quarter Planes
Authors: Erdogan F. , Ratwani M.
Published: November 2010

The frictionless contact problem for an elastic layer supported by two elastic quarter planes is considered. It is shown that as in the layer-half-space problem, the width of the contact area is dependent on the relative distribution of the applied load and is independent of its amplitude. At the corner of the support the contact pressure has an integrable singularity with its power α (0 < α < 0.5) depending on a single bielastic constant. The problem is reduced to a singular integral equation with a generalized Cauchy kernel and with the unknown contact pressure as the density function. The calculated results include the power and the strength of the stress singularity, the width of the contact area, and the contact pressure for various geometries, external loads, and material combinations.
Accumulated Slip of a Friction-Controlled Mass Excited by Earthquake Motions
Authors: Crandall S. H. , Lee S. S. , Williams J. H.
Published: November 2010

A rigid mass driven by Coulomb friction from a randomly moving foundation is used as a simple model of a possible earthquake isolation system for a stiff compact structure. The structure is protected from accelerations greater than that produced by the limiting friction at the expense of a residual relative displacement with respect to the foundation. The RMS residual displacement is predicted approximately, both analytically and by computer simulation. The analytical approximation makes use of equivalent linearization applied to a nonstationary response problem. The computer simulation marches out exact response histories for an ensemble of independent earthquake realizations. There is good agreement between the two predictions. The trade-off between peak accelerations and residual displacements for typical earthquake intensities is displayed.
The Inflation and Contact Constraint of a Rectangular Mooney Membrane
Authors: Feng W. W. , Tielking J. T. , Huang P.
Published: November 2010

This paper presents a minimum energy solution for the deformed configuration of an edge-bonded rectangular membrane loaded with uniform pressure and contacting a frictionless rigid constraint. A technique borrowed from optimization theory is employed to derive a potential energy functional which contains the contact constraint condition with no increase in the number of independent functions. This energy functional is minimized by a series of geometrically admissible, continuous, coordinate functions with constant coefficients determined by the Ritz procedure. The variable-metric method, as generalized by Fletcher and Powell, is used to find the coefficients in the energy minimizing series solutions. The results presented show the contact boundary and the distortion of a square gridwork laid on the undeformed membrane.
Limit Cycle Oscillations of Parametrically Excited Second-Order Nonlinear Systems
Authors: Hsu C. S.
Published: November 2010

A second-order nonlinear system subjected to parametric excitation is investigated. The nonlinear factors included are nonlinear damping and a cubic term in displacement. The primary purpose of the paper is to study the limiting effects of these nonlinear factors on the growth of motion for those systems which are otherwise unstable and have an exponential growth. Through an asymptotic analysis formulas are found for evaluating the limit cycle response amplitude in the first and second instability regions of the Ince-Strutt chart. Some results calculated from these formulas for the important case of velocity square damping are compared against those obtained by direct numerical integration in order to assess their accuracy.
Differentiation of Moire´ Patterns by Optical Spatial Filtering
Authors: Chiang F. P. , Khetan R. P.
Published: November 2010

By placing a moire´ pattern behind the first field lens of an optical spatial processor its diffraction spectrum will be formed at the first image plane of the system. This diffraction spectrum is filtered to give two images only along a selected direction. The third field lens collects the selected orders to form the Moire´ pattern at the second image plane. However, if a recording photographic plate is placed at a certain distance away from the second image plane, a double image occurs which is shifted along the selected direction. The resulting moire´-of-moire´ pattern depicts the partial derivative contours of the model.
An Analysis of the Deformation and Stresses in an Endless Belt Passing Over Cylindrical Rollers
Authors: Salathe Eric P.
Published: November 2010

The theory of finite elasticity is used to describe the large elastic deformation of a circular cylindrical tube into an endless belt which passes over two cylindrical rollers. A perturbation solution is obtained applicable when the thickness of the tube is small. It is found that the solution breaks down where the belt leaves the rollers, and the method of matched asymptotic expansions is used to obtain the deformation in those regions.
Dynamic Plastic Pulse Buckling Beyond Strain-Rate Reversal
Authors: Lindberg H. E. , Kennedy T. C.
Published: November 2010

A large deflection, elastic-plastic numerical theory (SABOR/DRASTIC 6) is used to investigate dynamic buckling motion beyond strain-rate reversal in cylindrical shells under radial impulse. It is found that the mode number of the most amplified harmonic is smaller than predicted by the simple analytic tangent modulus theory because of the increased stiffness after strain-rate reversal, neglected in the simple theory. Nevertheless, the simple theory gives reasonable estimates for threshold buckling impulses. In buckling well beyond threshold (about three times the threshold impulse in a thin shell, radius-to-thickness ratio of 120) plastic deformation becomes more localized at the buckle crests, but compressive strain continues to dominate so that a simple plastic hinge postbuckling analysis would be inadequate. Accuracy of the numerical theory is confirmed by comparison with experiment (asymmetric loading below buckling threshold and symmetric loading above) and with the tangent modulus theory prior to strain-rate reversal.
Multiparameter Quadratic Eigenproblems
Authors: Taylor D. L. , Kane T. R.
Published: November 2010

This paper contains an analytical theory for the study of the eigensystem of a multi-parameter quadratic eigenproblem. Previous work in this general area has focused mainly on first order eigenproblems. In the present work, eigenvalues and eigenvectors are expressed in the form of infinite series in which parameters entering the elements of various matrices play the roles of independent variables, and it is shown how the coefficients may be evaluated. The methods of derivation are given in sufficient detail to allow extension to either higher derivatives or higher order eigenproblems. Among the results presented are formulae for the second derivatives of eigenvectors, which have not been presented previously. Formulae applicable to special cases of first order eigenproblems are given also.
Time Series Methods for the Synthesis of Random Vibration Systems
Authors: Gersch W. , Liu R. S-Z.
Published: November 2010

A least-squares method procedure for synthesizing the discrete time series that is characteristic of the uniform samples of the response of linear structural systems to stationary random excitation is described. The structural system is assumed to be an n-degree-of-freedom system that is representable by a set of ordinary differential equations excited by a vector white noise force. It is known that the discrete time series of uniformly spaced samples of a scalar white noise excited stationary linear differential equation can be represented as an autoregressive-moving average (AR-MA) time series and that the parameters of the AR-MA model can be computed from the covariance function of the differential equation model. The contributions of this paper are (i) the result that a scalar input scalar output AR-MA model duplicates the scalar output covariance function of a regularly sampled linear structural system with a multivariate white noise input, (ii) a computationally efficient method for computing the covariance function of a randomly excited structural system, and (iii) a demonstration of the theory and the numerical details of a two-stage least-squares procedure for the computation of the AR-MA parameters from the output covariance functions data.
On the Determination of Stresses and Deflections for Anisotropic Homogeneous Cantilever Beams
Authors: Nair S. , Reissner E.
Published: November 2010

We analyze the effect of anisotropy on beam flexibility by the derivation of upper and lower bounds, through use of the principles of minimum potential and complementary energy, for the load-deflection ratios of narrow rectangular cross-section cantilever beams. The basic assumption is a class of stress-strain relations of such nature that normal strains are caused not only by normal stresses but also by shearing stresses, and shearing strains are caused not only by shearing stresses but also by normal stresses.
Elastic-Plastic Response of 6061-T6 Aluminum Beams to Impulse Loads
Authors: Forrestal M. J. , Wesenberg D. L.
Published: November 2010

The elastic-plastic response of 6061-T6 aluminum beams is examined experimentally and analytically. Simply supported beams are loaded with half-sine wave, short-duration magnetic pressure pulses and the response is monitored with a framing camera and strain gages. A closed-form elastic-plastic approximate theory for peak displacement is derived and compared with measurements and a numerical analysis. Measured displacement-time and strain-time histories are also compared with numerical predictions. Good agreement is shown between measurements and predictions.
Dynamics of Initially Stressed Plates
Authors: Reismann H. , Tendorf Z. A.
Published: November 2010

A formalism is presented for the solution of supported plates of bounded extent, subjected to time-dependent transverse forces and boundary conditions. Initially, and during the course of the motion, the plate is assumed to be in an arbitrary (stable) state of membrane stress. An example of a suddenly loaded, simply supported rectangular plate is presented. The membrane prestress, in the example problem, is assumed to be constant and parallel to two opposite edges of the plate.
Identification of Viscous Damping in Structures From Modal Information
Authors: Be´liveau Jean-Guy
Published: November 2010

The identification of damping, stiffness, and mass parameters from modal information is formulated within a general Bayesian framework. A modified Newton-Raphson scheme is used to modify parameter estimates, given natural frequencies, associated damping constants, mode shapes, and phase angles. Actual data from a nine-story steel structure are used in an application of the method.
Approximate Solutions of the Unsteady Boundary-Layer Equations
Authors: Bianchini A. , de Socio L. , Pozzi A.
Published: November 2010

An approximate integral method is proposed for solving the unsteady laminar boundary-layer equations. The essence of the method is to assume a similar solution for the velocity profile even in those situations where similar solutions do not exist, and then to find a suitable scale function for the similarity variable. The scale function is the solution to a simple first-order linear partial differential equation. This solution is determined in closed form. Satisfactory results were obtained in comparison with more sophisticated and time-consuming procedures.
Buckling of an Elliptical Plate With Simply Supported Edge Under Uniform Compression
Authors: Sato Kenzo
Published: November 2010

On the basis of the ordinary thin plate theory, the stability of a simply supported elliptical plate subjected to uniform compression in its middle plane is considered by the use of circular functions, hyperbolic functions, Mathieu functions, and modified Mathieu functions which are solutions of the equilibrium equation of the buckled plate. The first five eigenvalues for the buckling mode symmetrical about both axes are calculated numerically for a variety of aspect ratios of the ellipse. The limiting cases of a circular plate and of an infinitely long strip are also discussed.
The Squeezing of a Fluid Between Two Plates
Authors: Wang C.-Y.
Published: November 2010

A viscous fluid lies between two parallel plates which are being squeezed or separated. If the normal velocity is proportional to (1 − αt)−1/2 the unsteady Navier-Stokes equations admit similarity solutions. The resulting nonlinear ordinary differential equation is governed by a parameter S which characterizes unsteadiness. Asymptotic solutions for small S and for large positive S are found which compare well with those obtained by numerical integration. It is found that the resistance is proportional to (1 − αt)−2 but is not necessarily opposite to the direction of motion.
Transient Filtration in a Porous Elastic Cylinder
Authors: Kenyon D. E.
Published: November 2010

The time-dependent filtration of liquid through the wall of a soft, porous tube can be quite unlike that of a hard, porous tube. Under conditions described, the seepage is limited to thin layers near each surface, and in one of these layers, liquid seepage proceeds in a direction opposite to the sense of the applied pressure drop across the tube wall. This occurs because it is impossible to produce isotropic contact stress in the solid if kept at constant volume by the slowness of seepage. The liquid must then bear the entire isotropic stress.
Contact Between Viscoelastic Bodies
Authors: Comninou Maria
Published: November 2010

Similarly to elasticity, it is useful to classify contacts between viscoelastic bodies by comparing the regions of contact in the loaded and load-free states. General properties are obtained for the class of contacts in which the contact region does not exceed the natural (load-free) contact. The displacements, strains, and stresses in such problems are proportional to the level of the loading history, but the scaling of load histories leaves the contact region unaltered. The results are valid within linear viscoelasticity, either quasi-static or dynamic. Additional properties are derived for plane contact problems in quasi-static viscoelasticity when the contact is monotonically receding.
On the Problem of a Spherical Cavity in an Infinite Elasto-Plastic Medium
Authors: Durban D. , Baruch M.
Published: November 2010

The nonlinear problem of a spherical cavity surrounded by an infinite elasto-plastic medium, and subjected to uniform radial loads, is considered. The material is assumed to be incrementally elasto-plastic. No restriction on the magnitude of the deformation and stress is imposed. For the cases of internal or external pressure, the governing nonlinear differential equations are solved in terms of closed integrals. Numerical results obtained for some metals are also shown.
Singular Parabolic Partial-Differential Equations That Arise in Impulsive Motion Problems
Authors: Ingham D. B.
Published: November 2010

The thermal boundary layer over a semi-infinite flat plate is investigated. For time t < 0 there is the Blasius boundary layer and no thermal boundary layer. At t = 0, a temperature boundary layer is initiated without altering the velocity and the subsequent temperature boundary layer is studied for all time. The resulting linear, singular parabolic partial differential equation is solved using an efficient numerical method. Numerical results for several values of the Prandtl number are compared with analytical and numerical results obtained by previous authors. Because of the large interest shown recently in impulsive problems which result in the solution of singular parabolic equations the method is extended to study some of these problems. In two of the examples considered the governing equations are nonlinear.
Integrable Generalized Wave Equations Exhibiting a Hypoelastic Compressible Rate-Sensitive Material Flow
Authors: Ziv M.
Published: November 2010

Numerically integrable wave (characteristic) equations governing quasi-linear material motion are derived in generalized spatial curvilinear coordinates. The material under consideration is assigned an isentropic hypoelastic/compressible visco-perfectly plastic flow behavior where geometrical nonlinearities prevail throughout, while finite strains correspond only to the anelastic component of the constitutive equation. The characteristics formulation for the flow is derived under a tensor approach, based on those discontinuity relations that are compatible with the geometric description of hyperbolic partial differential equations. Results for spatial multidimensional integration schemes are presented in the form of nonlinear characteristic equations along their orthogonal path of integration (bicharacteristic curves) varying according to wave speed.
Plane Thermoelastic Problem in a Multiply Connected Orthotropic Body
Authors: Takeuti Y. , Noda N.
Published: November 2010

In this paper, we describe a general treatment for plane thermoelastic problems in multiply connected orthotropic bodies, and provide an example of its application to be a practical problem. In the first part of the paper, the modified Michell’s conditions are derived for the finite domain of orthotropic bodies with many holes. In the second part, the new transient thermal stress solution method is illustrated by application to an orthotropic hollow circular disk under an instantaneous point heat source.
Water Waves in a Nonhomogeneous Incompressible Fluid
Authors: Green A. E. , Naghdi P. M.
Published: November 2010

After a brief discussion of some undesirable features of a number of different partial differential equations often employed in the existing literature on water waves, a relatively simple restricted theory is constructed by a direct approach which is particularly suited for applications to problems of fluid sheets. The rest of the paper is concerned with a derivation of a system of nonlinear differential equations (which may include the effects of gravity and surface tension) governing the two-dimensional motion of incompressible in-viscid fluids for propagation of fairly long waves in a nonhomogeneous stream of water of variable initial depth, as well as some new results pertaining to hydraulic jumps. The latter includes an additional class of possible solutions not noted previously.
Aerodynamic Characteristics of a Rectangular Wing With a Tip Clearance in a Channel
Authors: Sugiyama Y.
Published: November 2010

Aerodynamic characteristics of a single, stationary wing, whose tip is in an end-wall boundary layer, are studied experimentally to determine the effects of aspect ratio, tip clearance, angle of attack and end-wall boundary layer. Spanwise distributions of the lift and drag coefficient are derived and interpreted from the data obtained by chordwise pressure measurements on the wing surface. The results indicate that the slope of the lift curve, the angle of zero lift and the drag coefficient reach a maximum at an optimum value of the tip clearance in a certain range of the aspect ratio. Interesting information is also obtained for effects of the end-wall boundary layer on the lift and drag of the wing with a slot.
Crack Problem for a Semi-Infinite Solid With Heated Bounding Surface
Authors: Sekine H.
Published: November 2010

On the basis of the stationary two-dimensional theory of thermoelasticity, the thermal stresses near the tips of a thermally insulated line crack situated in a semi-infinite solid which is heated on a part of the bounding surface is considered. The crack is replaced by continuous distributions of temperature dislocations and edge dislocations. Then the integral equations are obtained as a system of singular integral equations with Cauchy kernels. By means of this method, the singular behavior of the thermal stresses around the crack tips is easily examined and the stress-intensity factors can be readily evaluated. Numerical results for the stress-intensity factors are plotted in terms of the geometrical parameters.
Experiments on Buckling and Vibration of Superconducting Coils
Authors: Moon F. C. , Swanson C.
Published: November 2010

The decrease in lateral stiffness with increase in current and subsequent buckling of a flexible superconducting coil in a three coil partial torus is reported. The instability was observed for both clamped and clamped-pinned constraints on circular coils. Tests on the in-plane stability show an increase in stiffness with current in contrast with the out of plane or lateral buckling behavior. Along with the decrease in lateral natural frequencies of the coils, a significant increase in damping was observed. The critical buckling current was found to be in good agreement with theoretical calculations based on the authors’ previous work.
Experimental Studies on the Buckling Under Axial Compression of Integrally Stringer-Stiffened Circular Cylindrical Shells
Authors: Weller T. , Singer J.
Published: November 2010

An experimental study of the buckling of closely spaced integrally stringer-stiffened circular cylindrical shells under axial compression was carried out to determine the influence of stiffener and shell geometry, as well as mechanical properties of shell material, on the applicability of linear theory. Tests included 84 shells made of two different kinds of steel with completely different mechanical properties and 74 shells made of 7075-T6 Aluminum alloy. Agreement between linear theory and experiments was found to be governed primarily by shell geometry, Z, where for Z > 1000 values of “linearity” (ratio of experimental buckling load to the predicted one) of 70 percent and considerably above were obtained. Correlation with linear theory was also found to be affected by stringer area parameter (A1/bh) where for (A1/bh) > 0.45 the values of linearity obtained exceeded 65 percent and usually were much higher. No significant effect of other stiffener and shell parameters on the applicability of linear theory could be discerned for the specimens tested. The boundary conditions were found to be of importance and for some steel shells the inelastic behavior of the shell material was found to have a considerable effect on the linearity. Predictions of imperfection sensitivity studies could not be correlated with test results. By a conservative structural efficiency criterion all the tested stringer-stiffened shells were found to be more efficient than equivalent weight isotropic shells.
Lower Bounds to the Collapse Load of a Thick Circular Cylinder Subjected to Internal Pressure and Shear
Authors: Inoue N. , Nakagawa H. , Nakayama T. , Shimono M. , Tanaka T.
Published: November 2010

A new method for obtaining statically admissible states of stress in plane strain in the mathematical theory of plasticity is presented. After deriving a general solution, the proposed procedure is exemplified by a known solution of a thick circular cylinder subjected to internal pressure. The method is applied to a thick circular cylinder subjected to internal pressure and shear, and a lower-bound solution is given.
Quasi-Bifurcation of Rods Within an Axial Plastic Compressive Wave
Authors: Lee L. H. N.
Published: November 2010

A quasi-bifurcation criterion for determining certain infinitesimal disturbances which may amplify with time in an elastic-plastic body subject to prescribed initial, kinematic and time-dependent traction boundary conditions is employed to explain the onset of buckling of rods by axial impact. The experimental results of Abrahamson and Goodier indicate that rods impacting a rigid target at velocities sufficient to produce finite axial strains are found to buckle plastically with fairly reproducible final buckling modes. The predicted quasi-bifurcation modes at the onset of instability are in qualitative agreement with the observed final buckling modes.
Waves From Suddenly Punched Hole in Finitely Stretched Elastic Sheet
Authors: Mioduchowski A. , Moodie T. Bryant , Haddow J. B.
Published: November 2010

The method of characteristics is used to obtain numerical solutions for the plane stress problem of propagation of unloading waves from a suddenly punched circular hole in an elastic sheet subjected to finite, isotropic, tensile, biaxial strain. It is shown that, for instantaneous punching of a sheet of Mooney-Rivlin material, a shock is formed initially. Also an expression is obtained for the time when a shock forms if there is a linear reduction with time, from the initial value to zero, of the nominal tensile stress at the hole boundary. Numerical results are presented for the Mooney-Rivlin material and these results are compared with those obtained from the linear theory of elasticity, significant differences being found for stretches greater than about 1.05.
One Dimensional, Linear Dynamic Electromechanical Responses of Ferroelectric Ceramics
Authors: Amos D. E. , Chen P. J.
Published: November 2010

In this paper we consider the coupled electromechanical responses of poled ferroelectric ceramics. Our considerations are linear as well as one dimensional. The constitutive relations which characterize the stress and the electric field in terms of the strain and the electric displacement reflect the fact that the responses of such a material are time dependent. These time dependent processes arise principally because domain switching, due to mechanical loadings and the application of external electric fields, does not occur instantaneously as well as due to other mechanical and electrical relaxation effects. We then formulate the boundary-initial value problems which correspond to the voltage mode, finite resistance, and pulse poling and depoling experiments. These problems are solved using Laplace transform technique, and numerical inversions of the transform solutions are obtained by utilizing the method outlined by Luke and Salzer.
Dynamics of Multirigid-Body Systems
Authors: Huston R. L. , Passerello C. E. , Harlow M. W.
Published: November 2010

New and recently developed concepts and ideas useful in obtaining efficient computer algorithms for solving the equations of motion of multibody mechanical systems are presented and discussed. These ideas include the use of Euler parameters, Lagrange’s form of d’Alembert’s principle, quasi-coordinates, relative coordinates, and body connection arrays. The mechanical systems considered are linked rigid bodies with adjoining bodies sharing at least one point, and with no “closed loops” permitted. An explicit formulation of the equations of motion is presented.