bluuebunny/crossref_metadata_2025 huggingface dataset:
Response of an Elastic Half Space to Expanding Surface Loads
Authors: Gakenheimer D. C.
Published: November 2010

A class of elastic half-space problems involving axisymmetric, normally applied, surface loads is investigated. Each load is assumed to suddenly emanate from a point on the surface and expand radially at a constant rate. The cases of loads shaped like a ring and a disk are considered in detail. Exact solutions are derived for the displacements at every point in the half space in terms of single integrals. Each integral is identified as a specific wave. The integrals are evaluated analytically and numerically for different depths in the half space, for loads expanding at superseismic, transeismic, and subseismic rates, and for different values of Poisson’s ratio. Moreover, the interaction of the loads and the Rayleigh wave is described. Then solutions are obtained for loads of other shapes by convoluting the ring and disk load solutions.
The Response of Narrow-Mouthed Harbors in a Straight Coastline to Periodic Incident Waves
Authors: Carrier G. F. , Shaw R. P. , Miyata M.
Published: November 2010

The response to low-frequency periodic plane incident waves of a harbor connected by a narrow channel to the open sea is studied using linearized, constant depth, shallow water wave theory. Particular attention is paid to those frequencies close to the natural frequencies of the harbor basin and to those critical incident frequencies at which a maximum response is found. The theory developed is applicable as long as the width of the channel, and therefore, the harbor entrance is small compared to the incident wavelength and to the characteristic dimensions of the harbor basin. Significant amplifications are found at certain incident wavelengths which do not necessarily correspond to the natural frequencies of the harbor basin and a peculiar effect of the length of the entrance channel on the magnitude of the amplification; values of these critical incident wavelengths are noted.
Dynamics of a Submerged Ring-Stiffened Spherical Shell
Authors: Lou Y. K. , Klosner J. M.
Published: November 2010

The transient response of a ring-stiffened spherical shell to a sudden pressure increase in the surrounding acoustic medium is investigated. A modal expansion approach is used to analyze the shell, while the acoustic field equation is solved by invoking the Helmholtz integral. Coupling of the two fields occurs through the enforcement of continuity of the velocity components at the shell-fluid interface. Two solutions to the same problem are obtained by using plane and cylindrical wave approximations of the acoustic field. These approximate solutions fail to predict the transient behavior for the shell configuration analyzed. The result of this study indicates that a large dynamic factor must be assumed in the design of submerged, stiffened, spherical shell structures, if explosive loads are likely to be encountered.
Nonlinear Vibrations of a Buckled Beam Under Harmonic Excitation
Authors: Tseng W.-Y. , Dugundji J.
Published: November 2010

A buckled beam with fixed ends, excited by the harmonic motion of its supporting base, was investigated analytically and experimentally. Using Galerkin’s method the governing partial differential equation reduced to a modified Duffing equation, which was solved by the harmonic balance method. Besides the solution of simple harmonic motion (SHM), other branch solutions involving superharmonic motion (SPHM) were found experimentally and analytically. The stability of the steady-state SHM and SPHM solutions were analyzed by solving a variational Hill-type equation. The importance of the second mode on these results was examined by a similar stability analysis. The Runge-Kutta numerical integration method was used to investigate the snap-through problem. Intermittent, as well as continuous, snap-through behavior was obtained. The theoretical results agreed well with the experiments.
Optimal Thermoelastic Design for Given Deformation
Authors: Chern J.-M.
Published: November 2010

Optimal design of an elastic rod for given total elongation is discussed when both the axial loads and the steady-state temperature field in the rod depend on the design. Numerical results are presented for a rod that carries a given mass at the tip and rotates about an axis through the root that is perpendicular to the axis of the rod, while tip and root are kept at different temperatures and the lateral surface of the rod is thermally insulated.
The Free Vibrations of a Spinning Centrally Clamped Shallow Spherical Shell
Authors: Beckemeyer R. J. , Eversman W.
Published: November 2010

The results of a numerical analysis of the free-vibration characteristics of a thin shallow spherical shell spinning about its polar axis are presented. The shell is fully clamped by a central hub. The static equilibrium equations are formulated allowing for finite rotations. The free-vibration equations are derived by considering small perturbations about the spinning equilibrium configuration. Both flexural rigidity and membrane restoring forces due to spin are considered. Known techniques for the solution of stationary shell problems are extended to the more difficult case of the spinning shell. Plots of transverse frequency as a function of shell geometry are presented for the first two modes for shells with one and two nodal diameters for various values of inertia loading. Continuous transition from shell to flat disk results with increasing shell radius of curvature is shown.
Critical-Induced Acceleration for Shock Propagation in Polymethyl Methacrylate
Authors: Schuler K. W. , Walsh E. K.
Published: November 2010

In a recent analysis, Chen and Gurtin have shown that whether a shock wave in a nonlinear viscoelastic material will grow, decay, or remain steady is directly related to whether the acceleration just behind the wave is greater than, less than, or equal to a certain critical acceleration. In this paper, we use the experimental results of Schuler and Barker to determine this critical-induced acceleration as a function of the strain behind the shock for polymethyl methacrylate.
Dynamic Stability of a Beam Carrying Moving Masses
Authors: Nelson H. D. , Conover R. A.
Published: November 2010

The dynamic stability of the lateral response of a simply supported Bernoulli-Euler beam carrying a continuous series of equally spaced mass particles is analyzed. The beam rests on a uniform elastic foundation and damping is considered by including a distributed viscous damping coefficient. The particles are restricted to constant speed. The Galerkin method is used to generate a set of approximate governing equations of motion possessing periodic coefficients. Floquet theory is utilized to study the parametric regions of stability which are displayed in graphical form.
The Application of the Finite-Element Technique to Potential Flow Problems
Authors: de Vries G. , Norrie D. H.
Published: November 2010

The finite-element method is applied to field problems governed by Laplace’s equation and, in particular, to potential flow in fluid mechanics. The conditions under which the variational method may be used are examined for Dirichlet, Neumann, and mixed boundary conditions, and for both singly and multiply connected regions. The discretization of the field, using finite elements of triangular form is developed, and the resulting equations are solved. A computer program based on this analysis has been developed, and will solve any two-dimensional potential fields for simple or mixed boundary conditions and for singly or multiply connected regions. It may be used for multiple-body flow fields, such as aerofoil cascades, with boundary constraints such as the Kutta condition.
A Two-Potential Model for the Equations of State of Gases at Moderate and High Densities
Authors: Yu J. S.
Published: November 2010

The isothermal compression, up to nearly half the liquid densities, of argon, nitrogen, and methane at three different temperatures ranging from 0–150 deg C are investigated by using the cell method originally developed by Lennard-Jones and Devonshire. A two-potential model is adopted in the evaluation of the classical partition function to partially take into account the contributions arising from the correlations of molecular motions. The Lennard-Jones 6–12 potential and the Kihara hard core model are used, respectively, for the calculation of the energy of the geometrically symmetric lattice and the energy of augmentation arising from molecular motions. The potential parameters used in the calculations are those derived from fitting the second virial coefficient of dilute gases. The resulting calculated isotherms are compared with experimental measurements; agreement obtained is good for the range of density considered. The Kihara hard-core model with parameters determined for dilute gases is found to be ineffective at very high densities. This agrees with the conclusion derived from the Monte Carlo and molecular dynamics calculations that the Lennard-Jones 12–6 potential is tolerably good in representing the effective pair potential at liquid densities.
Convergent Approximations of Problems of Impulsively Loaded Structures
Authors: Ho H.-S.
Published: November 2010

For a dynamically loaded system made of stable materials, it is found that a dynamically admissible solution, one that satisfies all but the initial conditions, is a definitely convergent solution in time, with geometry changes and discontinuities taken into account. A new and simpler definition for weak and strong discontinuities is proposed. Solutions using simple mode approximations or the more general time-dependent changing mode approximations are described. For rigid, perfectly plastic beams under impulsive loadings, the latter method indeed gives better results, as there are more parameters available to optimize the initial difference energy.
On the Plane Elastostatic Problem of a Loaded Crack Terminating at a Material Interface
Authors: Bogy D. B.
Published: November 2010

The plane problem of a crack that terminates at the interface of a bimaterial composite and is loaded on its faces is treated within the two-dimensional theory of elastostatics. The emphasis is placed on determining how the order of the singularity in the stress field at the crack tip depends on the material constants and the angle at which the crack meets the interface. Numerical results are presented through figures showing this dependence on the material parameters for several fixed angles. It is then shown by way of examples how to use these figures to obtain the dependence on the angle for any desired composite. For the two examples chosen, it is found that when the crack is in the weaker constituent the stress singularity is most severe if the crack is tangent to (lies in) the interface; whereas, when the crack is in the stronger constituent a particular angle is associated with the most severe stress singularity for each composite.
A Correlation Study of Formulations of Incremental Deformation and Stability of Continuous Bodies
Authors: Bazˇant Z. P.
Published: November 2010

In the past a number of different linearized mathematical formulations of the infinitesimal incremental deformations of continuous bodies under initial stress have been proposed. The best-known formulations are reviewed, tabulated, and subjected to a comparative study. It is demonstrated that they can be derived as special cases of a unified general formulation, and are all correct and mutually equivalent. In each formulation, the incremental elasticity constants and the incremental material stress tensor have a different significance. Their mutual relationships are established. Thus the analysis of a problem which has already been solved according to one formulation need not be repeated for another formulation. Furthermore, the connections to the various definitions of the objective stress rate are shown. The arbitrariness of choice between the infinitely many possible forms of incremental equilibrium equations corresponds to the arbitrariness in the definitions of (a) the finite strain tensor, (b) the material stress tensor, (c) the objective stress rates, (d) the stability criterion, and (e) the elastic material in finite strain. For demonstration of the differences, the problems of surface buckling of an orthotropic half space and a column with shear are studied. It is shown that the predicted buckling stresses can differ almost by a ratio of 1:2 if the proper distinction between various formulations is not made.
The Problem of an Elastic Stiffener Bonded to a Half Plane
Authors: Erdogan F. , Gupta G. D.
Published: November 2010

The contact problem of an elastic stiffener bonded to an elastic half plane with different mechanical properties is considered. The governing integral equation is reduced to an infinite system of linear algebraic equations. It is shown that, depending on the value of a parameter which is a function of the elastic constants and the thickness of the stiffener, the system is either regular or quasi-regular. A complete numerical example is given for which the strength of the stress singularity and the contact stresses are tabulated.
Electromagneto-Thermoelastic Plane Waves in Solids With Thermal Relaxation
Authors: Nayfeh A. H. , Nemat-Nasser S.
Published: November 2010

Perturbation techniques are used to study the influence of small thermoelastic and magnetoelastic couplings on the propagation of plane electromagneto-thermoelastic waves in an unbounded isotropic medium. The thermal relaxation time of heat conduction, and the electric displacement current are included in the analysis. It is found that the thermal field may affect transverse motions, and that the magnetic field may affect motions that occur parallel to its line of action.
On the Postbuckling Behavior of Imperfection-Sensitive Structures in the Plastic Range
Authors: Hutchinson J. W.
Published: November 2010

Aspects of postbuckling behavior are investigated for structures undergoing plastic deformation. The structures singled out are characterized by a highly imperfection-sensitive behavior where buckling takes place in the elastic range. A simple model study is carried out and is followed by an analysis of the plastic buckling of a complete spherical shell under external pressure. In both instances, the bifurcation behavior and subsequent deformation of the perfect structure as well as the influence which geometric imperfections have on buckling are studied.
Approximate Analyses of Thermally Induced Vibrations of Beams and Plates
Authors: Boley B. A.
Published: November 2010

A simple general formula is derived for the ratio of the maximum dynamic to static deflection of heated beams and plates. The formula, although approximate, is in good agreement with the exact results. The effects of damping and of axial or in-plane loads are then considered, and the pertinent generalizations of the previous approximate formula are derived.
Parametric Resonance of Stiffened Rectangular Plates
Authors: Duffield R. C. , Willems N.
Published: November 2010

This investigation is concerned with the onset of parametric instability of a simply supported stiffened rectangular plate subjected to in-plane sinusoidal dynamic forces. An analytical analysis is developed for the stiffened plate with the stiffeners treated as discrete elements. The results show that the location and size of the stiffeners have a significant effect on the location and contour of the boundaries of the parametric instability regions when compared with those of a flat unstiffened plate. Experimental verification is obtained for stiffened plates with a single centrally located stiffener transverse to an in-plane periodic force acting on two opposite edges.
An Analysis of Forces at the Pivot Bearing of a Compound Pendulum
Authors: Samson A.
Published: November 2010

Expressions for the maximum velocity and the magnitude and direction of the resultant force at the pivot bearing of a free swinging compound pendulum are developed. It is shown that the latter depend on the angle of launch, the position and the degree of compounding of the pendulum. An expression is found for the magnitude of the impulsive reaction at the pivot bearing of a compound pendulum upon impact at its perigee. It is shown that the reaction depends on the degree of compounding and place of strike of the impulse. Using a two spring analogy of stiffnesses of pendulum and impacted specimen, the maximum force on the pendulum for impact at its perigee is found to depend on the stiffnesses.
Initial Yield Surface of a Unidirectionally Reinforced Composite
Authors: Lin T. H. , Salinas D. , Ito Y. M.
Published: November 2010

This paper shows the calculation of the initial yield surface of a unidirectionally reinforced composite subjected to longitudinal normal, transverse normal, and longitudinal shear loadings. The composite is composed of boron filaments arranged in a periodic square array and embedded in a matrix of 6061 aluminum alloy. A finite-element method is employed to obtain solutions for stresses throughout the composite. The von Mises yield criterion is used to calculate the elastic limit of the local microscopic combined stresses in the composite.
Flows Between Stationary Surfaces of Revolution, Having Similarity Solutions
Authors: McAlister K. W. , Rice W.
Published: November 2010

Laminar flow of an incompressible, Newtonian fluid is considered, in a narrow space between two stationary surfaces of revolution having a common axis of symmetry. The method of free parameters is used to investigate the existence of similarity solutions. It is found that there are no surface shapes for which similarity solutions exist, when the full Navier-Stokes equations are used to describe the flow. After order-of-magnitude arguments are employed to reduce the equations surface shapes are found for which similarity solutions exist; the shapes are delineated and the similarity problems are formulated. Finally, a method for solving the similarity problem is discussed and the solution is tabulated from the results of calculations conducted on a digital computer.
The Hodograph Transformation in Plastic Waves With Discontinuous Loading Conditions
Authors: Bevilacqua L.
Published: November 2010

In this paper the theory of the hodograph transformation is developed in a systematic way for one-dimensional wave propagation in elastic-plastic solids. The material is assumed to have isotropic strain-hardening characteristics with no Bauschinger effect. It is shown that in the hodograph plane it is possible to obtain a Riemann solution for the Cauchy problem. The mappings of different kinds of shock fronts and the elastic-plastic boundary onto the hodograph plane are derived. Two problems are solved using the hodograph method. The first one is related to a long rod subjected to a square pulse loading in stress at the free end. Although this problem is well known it provides a good illustration for the method. The second is related to a square pulse loading in stress followed by loading in reversal at the free end of a long rod. It is shown that under certain conditions the shock wave originated by loading in reversal penetrates the progressing plastic waves indefinitely. The region behind the shock front is plastic again but does not belong to the class of simple waves as the region ahead of the shock. The characteristics with positive slope in the region behind the shock in the X-t plane are concave toward the X-axis. The hodograph method is used to investigate if the condition of plastic loading is satisfied behind the shock and to find the first part of the elastic-plastic boundary.
Shakedown in Elastic-Plastic Systems Under Dynamic Loadings
Authors: Ho Hwa-Shan
Published: November 2010

Following the derivations of Koiter, who gave a general proof of Melan’s shakedown theorem for elastic-plastic systems under quasi-static reversible parametric loadings, it is shown here that the inclusion of the inertia force due to dynamic loadings does not change the basic tendency for the system to shakedown, if it can. Because of the validity of this shakedown theorem, the problem of designing a system under dynamic loadings and with only a finite amount of allowable plastic work can be transformed into a quasi-static, elastic counterpart. For the case of proportional loadings, two methods for solving the “compounded” shakedown load are proposed. One is called the “Method of Zero Work;” the other, involving a systematic numerical procedure, is called the “Method of Direct Search.” The concept of “optimum preloading” is also introduced.
On the Stability of Continuous Media
Authors: D’Souza A. F.
Published: November 2010

The stability of a basic stationary motion is investigated. The problem is posed as an initial boundary-value problem of partial differential equations in the perturbations. The spectral representation of the Green’s function matrix for the linearized problem is obtained and employed to generate a generalized energy function which is then used for the stability investigation of linearized and certain nonlinear problems. The results are applied to the stability of linearized aerodynamic panel flutter problem and to a nonlinear equation with conic nonlinearity.
Creeping Viscous Flow Through a Circular Tube of Nonuniform Cross Section
Authors: Langlois W. E.
Published: November 2010

Creeping viscous flow in a nonuniform pipe is analyzed by taking the local velocity profile and pressure gradients to be those of flow in a cone-shaped region. With this approach it is not necessary to assume that the pipe radius is a slowly varying function of distance along the axis.
Shear Waves Guided by a Cylindrical Hole in a Finitely Deformed Elastic Solid
Authors: Kurashige M.
Published: November 2010

The present paper deals with the propagation of unattenuated axisymmetric waves of small amplitude guided by a cylindrical bore through a neo-Hookean solid of infinite extent, which is finitely deformed by an all-around tension at infinity. The basic equations for the axisymmetric case are derived on the basis of Biot’s mechanics of incremental deformations, and applied to the problem by using Galerkin’s method. The influence of nonhomogeneous initial stresses upon the phase velocity of shear waves is presented in the form of curves.
On Natural Vibrations and Waves in Laminated Orthotropic Plates
Authors: Dong S. B. , Nelson R. B.
Published: November 2010

A solution method is presented for studying the vibrations of a laminated plate composed of an arbitrary number of bonded elastic, orthotropic layers. The analysis is carried out within the framework of linear elasticity for plane-strain behavior. The essence of the method is a discretization of the plate into arbitrarily large number of laminas, each of which comprise a separate entity. An approximate displacement field is assumed for each lamina and is characterized by a discrete number of generalized coordinates at the laminar bounding planes and at its midsurface. An algebraic eigenvalue problem results, whose solution yields the frequencies and modal displacement patterns, the 10 lowest which are determined. Stresses are calculated in a straightforward manner from eigenvectors. A homogeneous isotropic plate is studied to ascertain the accuracy and effectiveness of this method and examples on homogeneous and laminated orthotropic plates are given to offer some insight on their physical behavior.
The Bending and Stretching of a Uniform Elastic Strip Around a Cylindrical Drum
Authors: Meier J. H. , Lee H. C. , Raider J. W. , Conway H. D.
Published: November 2010

The investigation covers a flat strip bent into a circular ring and a cylindrical drum expanding inside the ring. The resulting anticlastic deformations of the strip and the contact patterns are representative of a flat strip being bent around a rigid, frictionless, cylindrical drum and then put under tension. The analysis shows that three contact patterns are possible and their respective regions are delineated in terms of the geometric and tension parameters. Expressions for anticlastic deformations and some numerical solutions are also presented.
On the Solution of Plane, Orthotropic Elasticity Problems by an Integral Method
Authors: Benjumea R. , Sikarskie D. L.
Published: November 2010

The present paper is concerned with the application of integral equation techniques to problems in plane orthotropic elasticity. Two approaches for solving such problems are outlined, both of which are characterized by embedding the real body in a “fictitious” body for which the appropriate influence functions are known. Fictitious tractions are then introduced such that the boundary conditions on the real body are satisfied. This results in a coupled set of integral equations in the fictitious traction components. Once these are found the unknowns, i.e., stresses, etc., are found in a straightforward manner. The difficulty is in introducing the fictitious traction field such that the resulting integral equations are useful computationally, i.e., are Fredholm equations of the second rather than the first kind. A sufficient condition for this is that the fictitious traction field is applied to the boundary of the real body. The two approaches just mentioned differ in the choice of influence function used, in one case the influence function being singular in the field and the other singular on the boundary. A solution method already exists in the isotropic case using the boundary influence function [3]. An alternate formulation is presented using an internal influence function which is shown to have computational advantages in the anisotropic (orthotropic) case. To illustrate the methods, the stress field is found in a “truncated” orthotropic quarter space, under the condition of a given traction on the truncated surface, traction-free elsewhere. This problem is of interest in certain Rock Mechanics calculations, e.g., to a first approximation the stress field is that due to a rigid wedge penetrating a brittle, orthotropic elastic solid (prior to chip formation).
The Plane Solution for Anisotropic Elastic Wedges Under Normal and Shear Loading
Authors: Bogy D. B.
Published: November 2010

The plane traction problem for an anisotropic wedge is solved within the theory of linear elastostatics. The technique employs the complex function representation of the plane solution in conjunction with the Mellin transform. Special attention is given to the orthotropic wedge; the uniform load solution is given in terms of elementary functions for wedge angles less than π, the logarithmic singularities in the stress field resulting from discontinuous loads on the half plane are studied, and the stress singularity at the apex is investigated for the reentrant wedges. Simplified results for the anisotropic half plane and cracked full plane are also presented.
Problems Involving a Receding Contact Between a Layer and a Half Space
Authors: Keer L. M. , Dundurs J. , Tsai K. C.
Published: November 2010

The work reconsiders the smooth receding contact between an elastic layer and a half space when the two bodies are pressed together. The analysis leads to a Fredholm integral equation of the second kind for an auxiliary function that is directly related to the contact pressure. An unexpected result is that the integral equation is homogeneous, and that finding the extent of contact can be viewed as an eigenvalue problem. The integral equation can be solved numerically to any required degree of accuracy, and the extent of contact and the contact pressure are computed for concentrated and uniformly distributed loads in both plane and axisymmetric problems. The present analysis confirms the results of Weitsman rather than Pu and Hussain over a wide range of mismatch in the elastic constants.
Two Mixed Problems for a Semi-Infinite Layer
Authors: Keer L. M. , Silva M. A. G.
Published: November 2010

Two mixed boundary-value problems for a semi-infinite layer are studied. The first is that of a uniformly loaded layer resting on a smooth, rigid foundation and lifted at its end. The second problem concerns a semi-infinite layer with an end crack parallel to and midway between the two surfaces that is opened by end loads. Physical quantities of interest appropriate to both problems are calculated.
On the Analysis of Asymmetric Stress
Authors: Stokes V. K.
Published: November 2010

An attempt has been made to analyze asymmetric stress. Bounds for the principal stresses have been established in terms of the principal stresses corresponding to the symmetric part of the stress tensor. Sufficient conditions for the existence of one or three principal stresses have been established. Bounds have also been established for the maximum shear stress. Detailed results have been given for the case of a quasi two-dimensional stress distribution.
An Analysis of Peristaltic Pumping
Authors: Tong P. , Vawter D.
Published: November 2010

A finite-element method has been adopted for the detailed analysis of peristaltic pumping. It is found that both wavelengths and wave amplitudes influence the flow field strongly. When there is no net flow, reflux occurs on the axis of the tube for short wavelengths, whereas reflux occurs off the axis for longer wavelengths.
Liapunov Analysis of the Generalized Pfluger Problem
Authors: Walker J. A.
Published: November 2010

A pin-ended column under an arbitrary tangential loading is considered. It is proved by the direct method of Liapunov that the mode of instability in all such problems is by divergence in the presence or absence of viscous damping, and an exact and simple criterion is given for the critical loadings. Two independent Liapunov functionals are also given for any such problem in the presence of arbitrary velocity-dependent loadings. These functionals are shown to provide exact stability results for a wide variety of such problems, and are believed to be the first ever found for the generalized Pflu¨ger problem.
Void Growth in an Elastic-Plastic Medium
Authors: Needleman A.
Published: November 2010

The uniaxial deformation of an elastic-plastic medium containing a doubly periodic square array of circular cylindrical voids is studied under plane-strain conditions. Both the effects of geometrical nonlinearities resulting from large deformation and physical nonlinearities arising from plastic material behavior are included in formulating the problem. A variational principle is used as the basis for implementing a finite-element solution. Results are obtained for the change in void shape and size under increasing overall strain, the overall tensile behavior of the material with voids, and the development of the plastic zone about a void.
Another Look at Nonholonomic Systems
Authors: Passerello C. E. , Huston R. L.
Published: November 2010

The relative advantages and disadvantages of various analytical methods for nonholonomic systems are briefly presented and discussed. The techniques of Kane’s method are then used to develop a derivation of a general method which consolidates and employs the advantages of the various classical methods. These advantages include the automatic elimination of nonworking constraint forces while avoiding the computation of vector components of acceleration. The method also provides for the arbitrary choice of dependent variables so that it may be adapted to a variety of nonholonomic systems. Two special cases are considered and the method is then illustrated in the classical problem of the rolling coin.
Attenuation of Harmonic Waves in Layered Media
Authors: Christensen R. M.
Published: November 2010

The effective attenuation of harmonic waves propagating through periodically layered elastic media is studied. The waves are taken to be propagating in the direction normal to that of the layering of the media, which has alternate layers of like material. The main restriction of the derivation is that the wavelength of the waves must be long compared with the periodic spacing of the layering. An explicit formula for the attenuation is derived by a perturbation method of analysis. The analysis reveals the basic cause of the attenuation effect in terms of the scattering properties of the medium. Specific examples are studied.
A Continuum Approach Toward Dynamics of Gridworks
Authors: Sun C. T. , Yang T. Y.
Published: November 2010

A two-dimensional continuum model with couple stress is established for a gridwork which consists of orthogonally intersecting beams rigidly connected at the joints. Equations of motion, boundary conditions, and the constitutive equations are derived, which can be employed to analyze the dynamic as well as static responses of the gridwork. Transverse vibrations and wave propagation are, in particular, investigated by the continuum theory. For the sake of comparison, the finite-element method is employed to calculate the frequencies for several specific gridworks. It is found that the results obtained from the continuum theory agree very well with the finite-element solutions, particularly in the range of long wavelengths.
Incremental Deformations in Orthotropic Laminated Plates Under Initial Stress
Authors: Sun C. T.
Published: November 2010

Plate equations for the incremental deformation in composite plates with orthotropic constituent layers are derived according to Trefftz’s formulation for elastic bodies under initial stress. The plate theory thus derived includes the microdeformation which can account for the heterogeneity of the plate. Flexural wave propagation under initial stress and buckling of a simply supported rectangular composite plate are investigated. In a special case of harmonic wave propagation in a free composite plate dispersion curves predicted by the plate equations are compared with the exact curve. Good agreement is observed for the complete plate theory and Approximation I, while the adequacy of the other two sets of simplified equations, Approximations II and III, depends vitally on the ratio of the transverse shear rigidities of the constituent materials.
Stress Redistribution and Rupture Due to Creep in a Uniformly Stretched Thin Plate Containing a Circular Hole
Authors: Hayhurst D. R.
Published: November 2010

A uniaxial theory of low-stress, high-temperature creep rupture has been shown to predict the results of uniaxial creep rupture tests. By including the creep rupture relationships into the accepted multiaxial deformation laws and following the numerical procedure outlined in a previous publication, a lower bound on the rupture time has been obtained for the case of a biaxially loaded plate containing a small hole at its center. It has been shown that the rupture behavior of the structure is controlled by a single stress whose magnitude is independent of the form of the constitutive relationship. The results of the prediction method agreed well with the experimentally determined values for aluminum plates tested at elevated temperatures.
On the Dynamic Stability of Fluid-Conveying Pipes
Authors: Weaver D. S. , Unny T. E.
Published: November 2010

This paper presents a general analysis of the dynamic stability of a finite-length, fluid-conveying pipe. The Flu¨gge-Kempner equation is used in conjunction with classical potential theory so that circumferential modes as well as the usual beam modes may be considered. The cylinders are found to become unstable statically at first but flutter is predicted for higher velocities. The critical flow velocities for short, thin shells are associated with a number of circumferential waves. This number reduces for thicker and longer shells until the instability is in a beam mode. When the limiting case of a long thin shell is taken, it is found to agree with previous results obtained using a simpler beam approach.
On the Reciprocal Form of Hamilton’s Principle
Authors: Elias Z. M.
Published: November 2010

A complementary energy principle for dynamic analysis due to Toupin is critically examined. It is found that the variational principle is a necessary but not a sufficient condition for geometric compatibility and that consequently it allows the occurrence of spurious solutions. A necessary and sufficient condition of compatibility is obtained through the reciprocal form of Hamilton’s principle which is derived for discrete and continuous systems. Additional terms appearing in the derived principle insure that spurious solutions cannot occur. The derived variational principle can be expressed in terms of stresses and velocities or in terms of impulses.
Stability of the General Plane Membrane Adjacent to a Supersonic Airstream
Authors: Walker J. A. , Dixon M. W.
Published: November 2010

The stability of equilibrium of an arbitrarily shaped, multiply connected, nonuniform-density, plane membrane adjacent to a supersonic airstream is studied using the direct method of Liapunov. In the piston theory regime it is found that plane membranes cannot flutter in the absence of structural damping, regardless of shape or mass distribution. Linear and nonlinear structural damping are then studied and the possibility of destabilization by damping is noted. Means of extending the present analysis to cover the effects of small nonlinearities and time-varying parameters are also discussed.
Parametric Resonance of Skew Stiffened Plates
Authors: Merritt R. G. , Willems N.
Published: November 2010

An investigation of the region of principal resonance of low-order spatial modes of an in-plane loaded, skew stiffened plate is considered. Hamilton’s principle is used to arrive at the equation of motion in which plate stiffening is accounted for through discrete representation. The method of averaging in the first approximation reduces the equation of motion to two independent equations which are subsequently solved by a perturbation technique in order to determine boundary curves for the principal region of resonance. Selected numerical examples indicate the effect of variation of skew angle and stiffening on the principal region of resonance. A brief discussion of problems inherent in this consideration of simply supported skew plates is included.
A Continuum Theory for Wave Propagation in Laminated Composites—Case 1: Propagation Normal to the Laminates
Authors: Hegemier G. A. , Nayfeh Adnan H.
Published: November 2010

A continuum theory is developed for wave propagation normal to the layers of a laminated composite with elastic, periodic, microstructure. Construction is based upon an asymptotic scheme in which dominant signal wavelengths are assumed large compared to typical composite microdimensions. A hierarchy of models are defined by the order of truncation of the asymptotic sequence obtained. To estimate system accuracy, the phase velocity spectrum is investigated. Retention of all terms in the asymptotic sequence is found to yield the exact spectrum of Rytov. Based upon spectral collation of the lowest-order dispersive model, accuracy superior to several existing theories is observed. In addition, treatment of transient pulse cases show good correlation with exact data. Finally, the lowest-order dispersive theory is cast in a standard mixture form.
On the Buckling of Cylinders in Axial Compression
Authors: Dym C. L.
Published: November 2010

The paper presents for the first time buckling results for cylinders in axial compression based upon shell equations advanced by Koiter and Budiansky. The numerical results are compared to those of Flu¨gge and of Donnell, and limiting results for the infinitely long shell are also given. The principal conclusion is that the Flu¨gge buckling results are in excellent agreement with those obtained from the highly refined Koiter-Budiansky equations.
Influence of Bed Size on the Flow Characteristics and Porosity of Randomly Packed Beds of Spheres
Authors: Beavers G. S. , Sparrow E. M. , Rodenz D. E.
Published: November 2010

Experiments were performed to investigate the flow characteristics and porosity of randomly packed beds of glass spheres for conditions where the bed size cannot be regarded as infinitely large compared with the sphere size. The operating conditions of the flow experiments extended over a Reynolds number range for which the flow was governed by the Forchheimer extension of the linear Darcy law. The influence of the bed bounding walls on the permeability, on the coefficient of the Forchheimer inertia term, and on the porosity, was studied by using beds of rectangular cross section. It was found that the permeability was not apparently influenced by the bounding walls when the equivalent diameter of the bed was greater than 12 times the sphere diameter, whereas the coefficient of the inertia term was affected by the presence of the walls for bed equivalent diameters as high as 40 sphere diameters. The porosity of the beds was not influenced by the bed size for values of the bed equivalent diameter greater than 15 sphere diameters. When the large-bed porosity value was used with the Carman-Kozeny relationship for the permeability as a function of sphere diameter, an excellent representation of accumulated experimental data was attained.
The Formation of Chips in the Penetration of Elastic-Brittle Materials (Rock)
Authors: Sikarskie D. L. , Altiero N. J.
Published: November 2010

An analysis is presented for the formation of chips in a two-dimensional, isotropic, elastic-brittle solid, due to the penetration of a rigid wedge. The analysis can be viewed in three parts. It is first necessary to obtain the static stress field due to a prescribed traction on the boundary. An integral method is used for this which is particularly convenient for the present problem. With the stresses known the field is searched to determine where fracture is initiated. Fracture is assumed to satisfy a Coulomb-Mohr fracture criterion. It is found that for certain realistic parameter ranges fracture initiation is somewhat insensitive to the details of traction distribution and wedge angle but is dependent on the material parameters. An approximate fracture path is proposed for stable fracture growth based on a certain fracture function. It is further proposed that the transition from stable to unstable fracture growth takes place at the inflection point of the fracture function versus fracture path length plot. Arguments are based on the Griffith theory of fracture and experimental data on crack velocity. Ratios of chip formation wedge forces to incipient fracture wedge forces are calculated from the theory and are of the order of 4. The results appear to be in reasonable quantitative agreement with some wedge penetration experiments on charcoal grey granite.
On the Propagation of One-Dimensional Acceleration Waves in Laminated Composites
Authors: Chen P. J. , Gurtin M. E.
Published: November 2010

In this paper we study one-dimensional wave propagation in (nonlinear) elastic and viscoelastic composites. We derive an expression for the amplitude of an acceleration wave; when confined to the junction points of the cells, this expression has exactly the same form as that for a single nonlinear viscoelastic material. We use this fact to derive effective moduli for composites.
Analysis for the Dynamic Response of Stiffened Shells
Authors: Harari A. , Baron M. L.
Published: November 2010

The natural frequencies and mode shapes for the vibrations of stiffened cylindrical shells with, or without, hemispherical end caps are evaluated. The approach utilizes a theory in which the shell elements and the circumferential stiffeners are considered as separate structures and compatibility is enforced at their junctures. The results are compared with those from orthotropic theory in which the stiffener effects are smeared over the shell. Numerical results are presented for frequencies and mode shapes for several cases of interest. The theoretical results have been compared with a set of experimental results from the Ordnance Research Laboratories and excellent agreement has been found. Comparisons of theory and experiment are presented in this paper.
A Procedure for Investigating the Liapunov Stability of Nonautonomous Linear Second-Order Systems
Authors: Jones S. E. , Robe T. R.
Published: November 2010

Utilizing Liapunov’s direct method a procedure is presented which generates sufficient conditions for the stability of the null solution of the nonautonomous differential equation x¨ + b(t)x˙ + a(t)x = 0. This procedure systematically leads to the construction of a Liapunov function for a given differential equation and thus eliminates the normally ad hoc nature of the direct method. Four examples illustrating the procedure are discussed.
A Simplified Theory of the Constitutive Equations of Metal Plasticity at Finite Deformation
Authors: Wang Y.-S.
Published: November 2010

Derivation of the constitutive equations of elastic-plastic and elastic-viscoplastic solids at finite deformations is discussed. The deformation is uncoupled by using the Lee-Freund three-configuration deformation model. By assuming elastic properties to be independent of plastic deformation, the elastic and plastic (or viscoplastic) constitutive equations are essentially uncoupled. The normality condition of the plastic strain-rate vector to the yield surface in stress space is obtained by incorporating the concept of internal variables in the energy equation.
A Method for Approximate Stability Analysis and Its Application to Circular Cylindrical Shells Under Circumferentially Varying Edge Loads
Authors: Libai A. , Durban D.
Published: November 2010

A procedure is presented which relates the solution of the stability problem for an elastic structure subjected to a complex prebuckling stress distribution, to that of a solved stability problem for the same structure but with a “simple” stress distribution. The procedure reduces to obtaining the characteristic roots of a symmetric matrix. It is then applied to the buckling problem of a circular cylindrical shell subjected to a circumferentially varying compressive stress field and boundary conditions of the SS1-2 types. The main result is that for the boundary conditions and number of harmonic terms in the edge load taken, the buckling parameter approaches, as h/R → 0, that of a cylinder uniformly subjected to the maximum circumferential stress.
Postbuckling Behavior of Unsymmetrically Layered Anisotropic Rectangular Plates
Authors: Chia C. Y. , Prabhakara M. K.
Published: November 2010

An analysis for the postbuckling behavior of unsymmetrically layered rectangular anisotropic plates is presented. Each layer is assumed to have arbitrary thickness, elastic properties, and orientation of orthotropic axes with respect to the plate axes. The governing nonlinear differential equations in the sense of von Karman are solved in conjunction with boundary conditions for clamped edges by use of the multiple Fourier method. In the case of simply supported edges, a solution based on the method is also obtained for unsymmetrical angle-ply plates. In the examples, a nine-term approximation to each series is used and load-deflection relations, bending moments, membrane forces are presented for clamped cross-ply and angle-ply and simply supported angle-ply plates with various aspect ratios. Numerical results obtained from the present solution are, in special cases, compared with available data.
On the Derivation of Shell Theories by Direct Approach
Authors: Green A. E. , Naghdi P. M.
Published: November 2010

A constrained theory of shells by a direct approach, based on a general theory of a Cosserat surface, is derived and its relation to other recent developments obtained by direct procedures is indicated.
On Steady and Pulsatile Flow of Blood
Authors: Ariman T. , Turk M. A. , Sylvester N. D.
Published: November 2010

The steady and pulsatile flow of blood through small rigid, circular tubes has been analysed by a microcontinuum approach. The exact solutions for velocity and cell rotational velocity are obtained. A comparison of the theoretical velocity profiles with the experimentally determined profiles for both steady and pulsatile blood flow is quite encouraging.