bluuebunny/crossref_metadata_2025 huggingface dataset:
Thin Inclusions and Cracks in Anisotropic Media
Authors: Mura T. , Lin S. C.
Published: November 2010

By using the solution of eigenstrain problems in anisotropic media, flat ellipsoidal inclusions and crack problems are investigated. When a dilatational misfit strain is defined in a flat ellipsoidal inclusion (i.e., disk-shaped precipitate), the elastic strain energy associated with the misfit becomes minimum when the plane of the inclusion coincides with one of the crystalline planes, where the matrix and the inclusion are assumed as two different cubic crystals having the same crystalline directions. The minimum value, however surprisingly, depends only on the elastic moduli of the inclusion. When crystalline directions of the inclusion are parallel to the principal axes of the ellipsoid, the elastic strain energy is independent of the orientation of the inclusion with respect to the crystalline directions of the matrix and the constant value is equal to the minimum value in the first case. If an inclusion is simply defined by giving a uniform dilatational misfit strain in an ellipsoidal domain in a homogeneous material (i.e., matrix and inclusion are same material), the condition for the minimum elastic strain energy is the same as that of the first case, namely the minimum occurs when the plane of the inclusion is parallel to one of the crystalline directions. The method employed here can be applied equally to generally anisotropic materials. The method is also applicable to fracture problems by taking the elastic moduli of the inclusion as zero. As examples, an elliptical crack is considered for a simple tension and a pure shear. The interaction energy between the applied stress and a crack is calculated. By using this result, the Griffith criterion for fracture is derived for the penny-shaped crack. Some numerical results for cubic crystals are shown.
Evaluation of Error Bounds in an Optimization Problem Using the Finite-Element Method
Authors: Buturla E. M. , McLay R. W.
Published: November 2010

Results of a numerical analysis completed in conjunction with the analytical development of a previous work are presented. The problem is an optimization study involving the thermal deflections of two parallel circular disks. The capability of choosing a mesh refinement to arbitrarily reduce approximation errors is illustrated and numerical convergence of the optimization process is demonstrated.
Dynamic Stability of Transverse Axisymmetric Waves in Circular Cylindrical Shells
Authors: Ginsberg J. H.
Published: November 2010

Previous experiments [1] have indicated that axisymmetric waves may be unstable and that nonsymmetric waves may result. To show that it is possible for such a phenomenon to occur even in perfectly cylindrical shells, a new mechanism for the coupling of the two types of waves is determined. Relationships for the phase velocity of steady-state waves as a function of the amplitude of transverse displacement are obtained. The stability of the system is shown to be defined by an equivalent nonlinear system with two degrees of freedom. It is found that the stability limits are the bifurcation points in the amplitude-phase velocity diagram for the axisymmetric and nonsymmetric waves. The solution is a uniform asymptotic expansion of the modal series for the displacement components and retains all effects significant to the first approximation of the nonlinearity.
The Elliptical Crack Subjected to Nonuniform Shear Loading
Authors: Smith F. W. , Sorensen D. R.
Published: November 2010

The equations of elasticity are solved for the problem of a flat elliptical crack which has nonuniform shear stresses applied to its surfaces. The shear stresses are prescribed independently in two directions on the crack surface and are expressed in the form of a third-degree polynomial. Mode two and mode three stress-intensity factors are presented in analytical and graphical form as functions of position along the crack border.
Stresses in a Transversely Isotropic Circular Cylinder Having a Spherical Cavity
Authors: Atsumi A. , Itou S.
Published: November 2010

This paper concerns the analysis of the stress distribution arising in a transversely isotropic infinite cylinder having a spherical cavity under longitudinal tension. Boundary conditions on the surface of the cylinder and the cavity are well satisfied by using the methods of Hankel transform and Schmidt-orthonormalization. Numerical calculations for some practical materials are carried out and the influence of transverse isotropy upon stress distribution is clarified.
Some Considerations on Timoshenko Bar Problem Subjected to Nonconservative Loading
Authors: Farshad Mehdi
Published: November 2010

The problem of a Timoshenko bar subjected to motion-dependent distributed and compressive axial end loading, is considered herein. The aim is the elaboration of the definition of follower-type loading in media with microstructure and with independent local motions which may be exemplified, to the first order, by a bar having independent lateral translation and rotation.
Dynamic Buckling of Complete Rigid-Plastic Spherical Shells
Authors: Jones Norman , Ahn C. S.
Published: November 2010

A theoretical investigation is undertaken into the dynamic instability of complete spherical shells which are loaded impulsively and made from a rigid-plastic material. The threshold velocities for the rigid-plastic spherical shells are larger than those for cylindrical shells having the same R/h ratios and material parameters, while the critical mode numbers are similar.
Plastic Waves of Combined Stress From Longitudinal Impact of a Pretorqued Tube, Analysis by Rate-Dependent Theory
Authors: Banerjee A. K. , Malvern L. E.
Published: November 2010

A rate-dependent theory for a strain-hardening material is used to interpret the experimental data of Lipkin and Clifton [6] for combined stress plastic waves. The numerical solution presented gives, as expected, a better qualitative explanation of the nonconstant-state regions than a rate-independent theory solution. The overall results show that, even for a relatively rate-insensitive material, such as the aluminum used in the experiments, a rate-dependent solution can be worked out that gives at least as good a representation of the complete dynamic plastic response of the tube as is given by a rate-independent theory solution.
Stress Analysis for Bonded Layers
Authors: Keer L. M.
Published: November 2010

The problem of a line bond between two layers is solved by techniques appropriate to the plane theory of elasticity. Integral transforms are used to reduce the problem to singular integral equations. Numerical results are obtained for the case of identical layers and the numerical scheme of Erdogan and Gupta proved to be effective for this case. Stress-intensity factors and bond stresses for several types of loading are calculated.
A Solution to the Contact of Two Rough Spherical Surfaces
Authors: Mikic B. B. , Roca R. T.
Published: November 2010

The influence of roughness on the interfacial pressure distribution in the contact of two spherical surfaces is considered. An approximate general solution is presented and it is shown that the pressure for all radii can be determined solely from a reference pressure which is, in turn, a function of two parameters—a dimensionless roughness and a dimensionless hardness. Values for the radius of contact are also presented.
Hiemenz Magnetic Flow of Power-Law Fluids
Authors: Djukic Dj. S.
Published: November 2010

The Galerkin approximative technique is used to solve the problem of stagnation in plane flow, the so-called “Hiemenz flow”, of a non-Newtonian power-law fluid in presence of a constant transverse magnetic field. The influence of the magnetic field strength on the wall shear stress is analyzed.
Growth of the Boundary Layer on a Spherical Gas Bubble
Authors: Chen J. L. S.
Published: November 2010

The unsteady flow of a pure viscous liquid past a gas bubble starting impulsively from rest is investigated theoretically. The Reynolds number is considered to be large so that boundary-layer ideas are applicable, but the bubble is nevertheless so small that it remains nearly spherical under the action of surface tension. This theory describes the growth of boundary layer due to an initial discontinuity in tangential stress at the bubble surface; the results also show how the flow changes from the irrotational motion to the steady-state boundary-layer flow described by Moore. The drag coefficient of the bubble is evaluated from the energy dissipation in the liquid; it is initially finite—by contrast with the case of flow with a boundary layer at a rigid wall, for which it is initially infinite—and, at a given instant, of smaller order than that for a solid sphere.
Application of Limit Analysis to Composite Materials and Structures
Authors: Majumdar S. , McLaughlin P. V.
Published: November 2010

The problem of determining a limit condition for a composite material in terms of average stresses by limit analysis is incompletely specified, and the limit condition so-obtained may be nonunique. Determination of average stress limit conditions in terms of properties of constituent phases is reviewed, and it is shown that under certain restrictions these limit conditions are single-valued and determinable by limit analysis. Applicability of average stress limit conditions to determining collapse loads on structures made of composite materials is then discussed.
The Applicability of Elastic/Viscoplastic Theory in Stress Wave Propagation
Authors: Fyfe I. M.
Published: November 2010

A viscoplastic constitutive model developed by Perzyna to describe stress wave propagation in rate-dependent materials is examined. The model is considered in terms of dislocation concepts and its ability to provide results which agree with those obtained from uniaxial stress, uniaxial strain, and biaxial strain experiments. It is proposed that the model may be a combination of a number of possible dislocation mechanisms, the dominant one depending on the strain rate. The theoretical model was found to be compatible with published experimental data in the three configurations for aluminum alloys with widely different rate-dependent characteristics. Some limiting conditions are also discussed.
Fluid Movement in a Channel With Permeable Walls Covered by Porous Media: A Model of Lung Alveolar Sheet
Authors: Tang H. T. , Fung Y. C.
Published: November 2010

The smallest microscopic blood vessels in the human lung are organized into sheet-like networks. These sheets form the walls of the 300 million alveoli in which air flows due to breathing. Each sheet may be idealized into a channel bounded by two thin layers of porous media. This paper is concerned with the blood flow in the channel and water movement in the porous wall. The Reynolds number in the lung alveolar sheets is very low, so creeping flow is assumed. Analytical and numerical results on the velocity and pressure distribution in the porous layers are presented.
On the Nature of Normality of Plastic Strain Rate and Convexity of Yield Surfaces in Plasticity
Authors: Naghdi P. M. , Trapp J. A.
Published: November 2010

Within the scope of the purely mechanical theory of plasticity, in a previous paper we have derived two inequalities which place restrictions on the constitutive equation for the rate of plastic strain in a finitely deformed elastic-plastic material. Here we take up the matter further, elaborate on the nature of the previously derived restrictions and obtain some additional results pertaining to the normality of the plastic strain rate and convexity of yield surfaces. Although in the main our discussions are carried out in the context of finite deformation, the nature of the restrictions for infinitesimal deformation is also examined. A special case of an elastic-plastic material in which the stress response is characterized by the stress rate and that of a rigid-plastic material are given detailed attention.
Experimental Study of Pressure Vessel Models Having Fabrication Flaws
Authors: Sendelbeck R. L. , Ljungstro¨m O. , Ljungstro¨m B. , Hoff N. J.
Published: November 2010

Experiments were carried out with 22 thin-walled circular cylindrical shells provided with localized inaccuracies representing weld flaws. It was found that along a girth weld a misalignment of the midsurfaces of the curved sheets of which the shell is welded together causes little reduction in the bursting pressure of the shell even if the misalignment amounts to three or four times the wall thickness.
An Analytical Study of an Experimentally Verified Hardening Law
Authors: Phillips A. , Weng G. J.
Published: November 2010

A previously obtained experimentally verified hardening law is analytically expressed. This analytical representation is applied to experimental data and an excellent agreement between analysis and experiment is shown. A comparison with other previously proposed hardening laws is presented.
An Improved Stiffly Stable Method for Direct Integration of Nonlinear Structural Dynamic Equations
Authors: Park K. C.
Published: November 2010

The behavior of linear multistep methods has been evaluated for application to structural dynamics problems. By examining the local stability of the currently popular methods as applied to nonlinear problems, it is shown that the presence of historical derivatives can cause numerical instability in the nonlinear dynamics even for methods that are unconditionally stable for linear problems. Through an understanding of the stability characteristics of Gear’s two-step and three-step methods, a new method requiring no historical derivative information has been developed. Superiority of the new method for nonlinear problems is indicated by means of comparisons with currently popular methods.
Package Cushioning for the Human Head—1: Analytical Considerations
Authors: Liu Y. King , Chandran K. B.
Published: November 2010

The closed head impact problem was idealized as a fluid-filled cylinder attached to a spring-dashpot element striking a rigid wall. The rigid cylinder represents the skull, the fluid denotes the brain, and the cerebrospinal fluid (CSF) and spring-dashpot simulate the composite elastic and dissipative properties of the helmet, hair, skin, skull, and the real wall. The exact closed-form wave-propagation solution was obtained by exploiting the hyperbolic nature of the Laplace transformed equations. The infinite series solution suitable for all values of time was also obtained via the residue theorem. The system response was found to be dependent on 4 dimensionless ratios: 1. The brain to skull mass. 2. The skull to closed brain stiffness. 3. The damping factor of the skull. 4. The impact velocity to the brain wave speed. Results were presented for a range of parameter values realistic to the head injury problem. The severity of the impact was evaluated by the ratio between the cavitation duration at contrecoup and the contact duration between the head and the wall.
Estimation From Censored, Interval Data of the Median Breaking Point of Polyethylene Subjected to Stress-Cracking Tests: A Monte Carlo Study
Authors: Denby L. , Fowlkes E. B. , Roe R. J.
Published: November 2010

A Monte Carlo study has been carried out in order to study the properties of various alternative estimators for median breaking point of polyethylene specimens subjected to an environmental stress cracking test. Tables of bias, variance, and mean square error have been derived for different sample sizes, interval sizes, and levels of censoring data with the lognormal distribution as a model. These tables will aid in the design of experiments for efficient estimation of median breaking point.
Radial Expansion of Impacted Helical Springs
Authors: Costello G. A.
Published: November 2010

A theory is presented which will predict the radial expansion of impacted helical springs. This becomes important in cases where the spring is surrounded by a cylindrical constraint because of the possibility of excessive wear. The results show that the dynamic radial expansion can be much larger than that predicted by statical methods.
Theoretical and Experimental Studies of Transient Elastic-Plastic Large Deflections of Geometrically Stiffened Rings
Authors: Wu R. W. H. , Witmer E. A.
Published: November 2010

Finite-element formulations have been derived for the large-deflection elastic-plastic dynamic responses of arbitrarily curved two-dimensional beam structures which may consist of hard-boned, multilayer, geometrically stiffened configurations. Experiments have been conducted for structural responses of geometrically stiffened, freely suspended, circular rings of 6061-T6511 aluminum alloy to intense explosive loading which induces large-deflection elastic-plastic transient and permanent deformations of the structure. Very good correlation of the measured permanent deformation and transient strain with theoretical predictions is demonstrated.
Magnetoelastic Buckling and Vibration of a Rod Carrying Electric Current
Authors: Chattopadhyay S. , Moon F. C.
Published: November 2010

The effect of high electric currents on the stability and dynamics of a circular rod is investigated. A uniform current distribution in the undeformed rod is assumed. The perturbed magnetic field due to bending deformation is shown to set up a system of destabilizing forces. For long wavelength vibrations, a frequency-current dispersion relation is obtained which shows a continuous decrease in the natural frequency of the rod as the current in the rod is increased. At a critical value of current the natural frequency of the rod goes to zero and the rod buckles, which is the solid analog to the “kink instability” in plasma physics. The critical current criteria is applied to find the minimum support distance for a superconducting coil for magnetic levitation of trains. Experiments were conducted on a copper rod to observe the destabilizing effect of the electric currents of up to 400 A. Dynamic tests show that the natural frequencies decrease as the current in the rod increased. The frequency-current dispersion and the estimated critical current agree reasonably with the corresponding theoretical values.
Lower Bounds to the Gravest and All Higher Frequencies of Homogeneous Vibrating Plates of Arbitrary Shape
Authors: Pnueli D.
Published: November 2010

A method is presented by which lower bound can be calculated for the gravest and all higher frequencies of both clamped and simply supported plates of arbitrary shape. The results have the form of simple algebraic formulas which depend on the plate’s area only. Numerical examples are presented for rectangular, triangular, and elliptical configurations.
On the Use of Beam Functions for Problems of Plates Involving Free Edges
Authors: Bassily S. F. , Dickinson S. M.
Published: November 2010

The inadequacy of beam vibration mode shapes when used in the Ritz method to obtain approximate solutions for flexural problems concerning plates involving free edges is demonstrated. A new set of functions, related to beam mode shapes, is postulated which allows considerably more accurate treatment of such plates. Several numerical examples concerning static deflection and free vibration of plates involving free edges are examined and serve to illustrate the applicability and accuracy of the new functions and to further demonstrate the inadequacy of the ordinary beam functions.
Stress-Intensity Factors for an Insulated Half-Plane Crack
Authors: Kassir Mumtaz K.
Published: November 2010

This paper is concerned with determining the stress-intensity factors due to disturbance of a uniform flow of heat by an insulated half-plane crack in an elastic solid. The spatial thermoelastic problem is formulated in terms of Papkovich-Neuber displacement potentials and is solved by the application of Kontorovich-Lebedev integral transform and certain singular solutions of Laplace equation in three dimensions. The analysis reveals that four distinct displacement potentials are needed to satisfy the finite displacement and inverse square root stress-singularity at the edge of the crack. Closed-form expressions are obtained for the stress-intensity factors (k2 and k3) and their variations along the crack border are shown in curves.
Transient Response of Viscoplastic and Viscoelastic Shells Submerged in Fluid Media
Authors: Duffey T. A.
Published: November 2010

The transient fluid-shell interaction problem is investigated for thin shells constructed of other than linearly elastic materials. Specifically, solutions are developed in terms of elementary functions for the transient responses of impulsively loaded, fluid-surrounded spherical shells constructed of either viscoplastic or viscoelastic materials. In all cases the fluid medium surrounding the shell is taken as inviscid and compressible and only spherically symmetric shell motions and radiation of sound into the surrounding medium are considered. It is found that the influence of material strain hardening and strain-rate sensitivity can be significant in reducing fluid-shell displacement responses. Further, limited investigations for viscoelastic materials indicate that for higher loss materials, displacement response of the shell is significantly altered by the inclusion of the viscoelastic behavior.
Mean-Square Response of Thermoviscoelastic Medium to Nonstationary Random Excitation
Authors: Mosberg W. , Yildiz M.
Published: November 2010

The mean-square wave response of a lightly damped thermoviscoelastic medium to a special type of nonstationary random excitation is determined. The excitation function on the thermoviscoelastic medium is taken in the form of a product of a well-defined, slowly varying envelope function, and a part which prescribes the statistical characteristics of the excitation. Both the unit step and rectangular step functions are used for the envelope function, and both white noise and noise with an exponentially decaying harmonic correlation function are used to prescribe the statistical property of the excitation. By taking into consideration the slow variation envelope function and the wave characteristics of the lightly damped thermoviscoelastic medium, the mean-square response (as a function of temperature, excitation, and damping parameters with the aid of reversible and irreversible thermodynamics) is evaluated.
Multiple Fracture of Plates Under Localized Impulsive Loading
Authors: Colton J. D.
Published: November 2010

An investigation was performed to determine the fracture patterns produced by localized impulsive loading on brittle plates and their dependence on the intensity and area of the load. Experiments were performed on effectively infinite plates loaded over a finite area with sheet explosive. The mechanisms, location, and time sequence of deformation and fracture were determined by terminal observation, high-speed framing camera photographs, and strain gages. It was found that all fractures were initiated by bending stress; two different fracture patterns in plates were produced experimentally. The plate response was also predicted analytically by numerically integrating the characteristic equations of Mindlin plate theory. It was found analytically that, depending on loading intensity and duration, a total of five fracture patterns in plates, including both those observed experimentally, can be produced by localized impulsive loads.
An Investigation of the Steady Creep of a Spherical Cavity in a Half Space
Authors: Anderson C. A.
Published: November 2010

The stability of a spherical cavity in a half space of a creeping material is investigated. The finite-element method with a nearly incompressible formulation and a stable method of time stepping is used to predict the steady creep state from an initial elastic state. Applications are made to thermal creep problems involving pure halite which obeys a well-documented creep law of the Weertman form. For a spherical cavity in a half space of halite various steady motions are observed depending on the depth, the temperature field, and the internal pressurization of the cavity.
The Fundamental Solution for a Shallow Shell With an Arbitrary Quadratic Midsurface
Authors: Simmonds J. G. , Bradley M. R.
Published: November 2010

The complex-valued differential operator associated with the linear Marguerre equations for a constant thickness, elastically isotropic shallow shell with an arbitrary quadratic midsurface consists of the biharmonic operator minus the imaginary unit i times a constant coefficient second-order differential operator. The fundamental solution of this differential operator is denoted by g(r, θ; κ), where r and θ are polar coordinates and κ is the (dimensionless) Gaussian curvature of the midsurface at the origin. Via a double Fourier transform, a plane wave or Whittaker representation is obtained for g(r, θ; κ). From this is extracted a series representation for g(r, θ; κ) in powers of r2, with coefficients depending on ln r, θ, and κ. The results are shown to agree with the known special cases for κ = 1, 0, and −1.
Work Bounding Functions for Plastic Materials
Authors: Carter P. , Martin J. B.
Published: November 2010

The minimum work and maximum complementary work potentials for both time-independent and time-dependent plasticity are reconsidered from the viewpoint of internal variable theories. It is shown that the minimum work and maximum complementary work can be bounded in a simple and direct manner. The bounds provide the minimum work and maximum complementary work under certain limitations.
The Practical Use of Gauss’ Principle of Least Constraint
Authors: Vujanovic B.
Published: November 2010

In this paper Gauss’ principle of least constraint is used to obtain approximate solutions of conservative and nonconservative dynamical systems. The main feature of the method is that every particular problem is reduced to an algebraic problem of minimizing a quadratic form with respect to the physical components of the acceleration vector of the system, or with respect to the components of a generalized force. The method is illustrated by solving several problems. The method is equally applicable to ordinary as well as partial differential equations. A brief criticism of the least-squares method, as a method of solving differential equations, is given.
The Boundary Layer Inside a Conical Surface Due to a Swirling Flow With Throughflow
Authors: Fabian J. M. , Oates G. C.
Published: November 2010

The problem of describing the boundary layer existing inside a conical surface due to the presence of a swirling flow passing through the cone is considered. Approximate solutions based upon the Karman-Polhausen method are obtained for both the laminar and the turbulent cases. The results obtained are in close agreement with known solutions previously obtained in the limits of swirl with no throughflow and throughflow with no swirl. The present results appear to be valid over the entire range of swirl to throughflow ratios.
Recursive Least-Squares Time Domain Identification of Structural Parameters
Authors: Caravani P. , Watson M. L. , Thomson W. T.
Published: November 2010

A method of identifying structural parameters such as damping and stiffness of a building from its time response under dynamic excitation is presented. A least-squares recursive computer algorithm which requires no matrix inversion is developed and tested with the response of a two-degree-of-freedom structure including Gaussian white noise. The algorithm provides means to account for both the model uncertainty and the investigators’ confidence in the initial guess of the parameters. These statistical quantities can be updated with passage of time. The study indicates that rapid convergence to the correct values of the parameters takes place even under severe noise in the response data.
A Simple Bound on the Asymptotic Pressure in a Spherical Cavity, Surrounded by an Infinite Elasto-Plastic Medium
Authors: Durban D. , Baruch M.
Published: November 2010

A simple formula is suggested for the upper bound on the asymptotic pressure in a spherical cavity surrounded by an infinite elasto-plastic medium. The uniaxial stress-strain curve is assumed to be represented by the Ramberg-Osgood equation. Comparison of the proposed upper bound with the exact asymptotic pressure, for a few metals, shows that the average overestimation is around 16 percent.
The Near-Field Disturbance Created by a Body in a Stratified Medium With a Free Surface
Authors: Murdock J. W.
Published: November 2010

The inviscid equations of motion for a slender body in a stratified fluid are formulated in a way which illustrates the relationship between the vorticity in the flow and the internal wave behavior. This formulation makes it clear that the problem admits a singular perturbation expansion of the solution if the density variation is small (large Vaisala length). Analytic solutions valid in the near field are obtained for the case of a finite-thickness constant thermocline. The slender body approximation is found to be invalid near the body; the use of this approximation results in a singularity behind the body which extends to infinity. The reason for the appearance of the singularity is given, and a technique for eliminating it is outlined. The effect of the singularity on the solution at the surface is found to be small. Typical behavior of the near-field surface current is presented in graphical form. The near-field surface disturbance is found to result primarily from the basic body potential flow field with corrections made as a result of the stratification.
Effects of Fluctuating Moisture and Temperature on the Mechanical Response of Resin-Plates
Authors: Weitsman Y.
Published: November 2010

This paper concerns the stress-response of a geometrically constrained resin-slab under externally fluctuating moisture and temperature conditions. The response of the resin is described by a rheologically complex viscoelastic behavior and is analyzed on the basis of the best data that is available at present. The results indicate that the stresses can undergo a change in sign when a test coupon is subjected to a “thermal spike”. This observation may explain the fracture and cracking that has been detected experimentally. In addition, sample results are provided for the residual stresses that develop upon cool-down. It is shown that in this case a subsequent exposure to moisture may contribute to the reduction of such stresses. A brief discussion is provided concerning the diffusion of moisture under fluctuating temperatures.
A High-Order Theory of Plate Deformation—Part 1: Homogeneous Plates
Authors: Lo K. H. , Christensen R. M. , Wu E. M.
Published: November 2010

A theory of plate deformation is derived which accounts for the effects of transverse shear deformation, transverse normal strain, and a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate. The theory is compared with lower-order plate theories through application to a particular problem involving a plate acted upon by a sinusoidal surface pressure. Comparison is also made with the exact elasticity solution of this problem. It is found that when the ratio of the characteristic length of the load pattern to the plate thickness is of the order of unity, lower-order theories are inadequate and the present high-order theory is required to give meaningful results. The present work treats homogeneous plates while Part 2 involves laminated plates.
On Harmonic Waves in Layered Composites
Authors: Minagawa S. , Nemat-Nasser S.
Published: November 2010

For harmonic waves propagating in a layered elastic composite, approximate dispersion relations are developed. Both waves propagating in the direction of the layers, and those propagating obliquely to this direction, are considered. The layer problem is treated as a special case of fiber-reinforced elastic composites. For illustration, the approximate results are compared with the exact ones for the special case of homogeneous layers.
Determination of Transient Responses of a Thick-Walled Spherical Shell by the Ray Theory
Authors: Pao Yih-Hsing , Ceranoglu Ahmet N.
Published: November 2010

The dynamic response of a thick-walled elastic spherical shell subject to radially symmetric loadings is studied by applying the theory of rays. The Fourier transformed solution of the waves in the shell is sorted out into rays by following the ray-path of the multiply reflected waves at both surfaces. Inverse transform of each ray, which is obtainable in closed form, gives rise to the exact solution of the transient response up to the arrival time of the next ray. Numerical results are shown for internally applied pressure with a step or a square-time function. The radial stresses are found to be critically large in tension due to multiple reflections at both surfaces of a thick shell.
The Acceleration of Thin Cylindrical Bodies in a Viscous Fluid
Authors: Lugt H. J. , Haussling H. J.
Published: November 2010

The start from rest of a thin cylindrical body with elliptic cross section in a viscous incompressible fluid is studied numerically for various acceleration models. Force and moment coefficients are computed. The role of the starting vortices behind the leading and trailing edges in the generation of lift is investigated.
The Behavior of Gas Bubbles in the Casson Fluid
Authors: Shima A. , Tsujino T.
Published: November 2010

In the present paper, the equation of motion for the bubble and the pressure equation at the bubble wall in a Casson fluid were obtained. Then by using the derived equations, the behavior in the case where a gas bubble in human blood grows or collapses by the difference between the inside and the outside pressure of the bubble were numerically clarified.
An Elastic Strip Pressed Against an Elastic Half Plane by a Steadily Moving Force
Authors: Adams G. G.
Published: November 2010

An infinite elastic strip is pressed against an elastic half plane of a different material by a steadily moving concentrated force. Using the plane strain theory of elasticity, it is shown that the problem can be decomposed into its symmetric and antisymmetric parts. These mixed boundary-value problems are then solved by reduction to Fredholm integral equations subject to certain other conditions. For various material combinations, and a range of speed, the extent and location of the contact region as well as the contact pressure will be computed and illustrated graphically.
On the Uniqueness and Stability of Endochronic Theories of Material Behavior
Authors: Sandler I. S.
Published: November 2010

A stability and uniqueness analysis of endochronic models without internal barriers has been performed by means of the construction of certain simple dynamic problems. It has been shown that serious difficulties can arise when such models are used and that they are unsuitable for the numerical solution of mechanical problems. The deficiencies in the endochronic models may be circumvented by the introduction of internal barriers, but these have much the same features as the yield condition of classical plasticity.
Analysis of Closure in Fatigue Crack Growth
Authors: Budiansky B. , Hutchinson J. W.
Published: November 2010

A theoretical study is made of the implications of a Dugdale-Barenblatt model for fatigue crack growth under steady cyclic loading. Residual plastic stretches and the effects of crack closure on crack opening and closing loads are calculated by complex function methods for a range of loading ratios. An assessment is made of the influence of cyclic strain hardening and softening.
Low Frequency Bloch Waves for Wave Equations Whose Speed Is a Deterministic, or Randomlike, Periodic Function
Authors: Balanis G. N.
Published: November 2010

This paper examines the low frequency behavior of the Bloch wave solution to wave equations whose sound speed is a three-dimensional periodic or almost-periodic function of position. The case where the sound speed is a randomlike function of position is also considered. The low frequency dependence of the Bloch wave phase velocity is obtained as a power series in the frequency. The frequency independent term is related to the average value of the inhomogeneities and is independent of the direction of propagation. The first dispersive term, which is also independent of the direction of propagation, is quadratic in frequency. Its coefficient is related to the spatial correlation of the inhomogeneities.
Experimental and Theoretical Study on Magnetoelastic Buckling of a Ferromagnetic Cantilevered Beam-Plate
Authors: Miya K. , Hara K. , Someya K.
Published: November 2010

When a cantilever of magnetically soft material is inserted with its wide face normal to a uniform magnetic field and the magnetic field is increased to a critical value the cantilever will buckle. The experimental magnetoelastic buckling fields and the theoretical ones differ by a factor of two. A magnetic field distortion near an edge of the specimen is here evaluated based on the finite-element method and the results are applied to the experimental results so as to explain the discrepancy between the experiment and the theory. The corrected experimental values are within 15 percent of the theoretical values. The effect of demagnetization on the buckling field is here demonstrated as well as the effect of specimen dimensions.
Axial Impact Buckling of a Column With Random Initial Imperfections
Authors: Elishakoff I.
Published: November 2010

Axial impact buckling of perfectly elastic bars with initial imperfections is considered in a probabilistic setting. It is assumed that the initial imperfection function involved a single parameter, which in turn is a continuous random variable with given probability distribution function. The structure is said to buckle if the absolute value of the total displacement exceeds a prescribed value. The probabilistic nature of the random, critical time when such a failure occurs for the first time, is studied.
Influence of Unequal Pedestal Stiffness on the Instability Regions of a Rotating Asymmetric Shaft
Authors: O¯ta H. , Mizutani K.
Published: November 2010

This paper treats unstable vibrations of a rotating asymmetric shaft supported by upper and lower flexible bearing pedestals each of which has a directional inequality in stiffness and a concentrated mass. The position, width and number of the instability regions and a dynamic behavior of the shaft are analytically obtained by approximation. As a result, it is determined simply by one parameter that each unstable region which is caused only by asymmetry of the rotating shaft is split up into several parts (one, two, three, or four regions) by the directional stiffness inequality of bearing pedestals. Instability regions derived from approximation were found to agree well with those obtained by analog computer.
Transition Behavior of a Blasius-Type Boundary Layer Subjected to Uniform Blowing or Suction
Authors: Sokolov M. , Karpati G.
Published: November 2010

The momentum integral equation is used to study the transient behavior of a Blasius-type boundary layer which is suddenly subjected to uniform blowing or suction. The time required for the boundary layer to adjust itself from one steady state (Blasius) to the other (constant blowing or suction) was found to be proportional to the distance from the leading edge. Boundary-layer thickness of intermediate states and skin friction coefficients are also reported.
Steady Flow in Tubes of Slowly Varying Cross Section
Authors: MacDonald D. A.
Published: November 2010

This paper studies steady incompressible viscous fluid motion in axisymmetric tubes of slowly varying cross section. Theory, which is independent of the actual shape of tube wall profile, is developed and a number of illustrative examples are studied. Results which portray the behavior of pressure drop (pressure rise, in some cases) and wall shear stress are presented.
Creep and Recovery of 2618 Aluminum Alloy Under Combined Stress With a Representation by a Viscous-Viscoelastic Model
Authors: Findley W. N. , Lai J. S.
Published: November 2010

Creep and recovery data are presented for combined tension and torsion of 2618 Aluminum at 200°C (392°F). These data are represented by a mechanical-mathematical model in which the strain is resolved into five components: elastic, time-independent plastic, recoverable viscoelastic, time-dependent nonrecoverable viscous (positive) and time-dependent nonrecoverable viscous (negative). By using recovery data the recoverable component is separated from the nonrecoverable creep strain. Results show that the time-dependence may be represented by a power of time (independent of stress) and that the time-dependence of the recoverable and nonrecoverable strains are the same. It is also shown that the proportion of recoverable versus nonrecoverable strain may be taken to be independent of stress. The mathematical expressions developed describe quite well the creep and recovery under tension and/or torsion. Results are presented in a form which may prove suitable for predicting creep or relaxation under variable input using the modified superposition simplification of the multiple integral representation for the recoverable strain component and strain hardening for the nonrecoverable component. Comparison between predicted strain or stress and actual tests under different variable stress or strain histories will be presented in subsequent papers.
Measurement of the Elastic-Plastic Boundary Around Coldworked Fastener Holes
Authors: Poolsuk S. , Sharpe W. N.
Published: November 2010

Coldworking the material near the edge of a fastener hole is one important means of increasing fatigue life. The stresses, strains, and location of the boundary between elastic and plastic regions have been analyzed by various theoretical studies. The purpose of this research is to experimentally evaluate the theories’ capabilities of predicting the boundary location. Specimens of 7075-T6 aluminum 6.35 mm and 3.18 mm thick with a 6.60 mm hole were coldworked various amounts by an industrial process. The elastic-plastic boundary was located by foil gage and thickness change measurements; both techniques gave similar results. Theories based on plane stress agreed well for the thinner specimens.
Finite Elasticity Solutions Using Hybrid Finite Elements Based on a Complementary Energy Principle
Authors: Murakawa H. , Atluri S. N.
Published: November 2010

The possibility of deriving a complementary energy principle, for the incremental analysis of finite deformations of nonlinear-elastic solids, in terms of incremental Piola-Lagrange (unsymmetric) stress alone, is examined. A new incremental hybrid stress finite-element model, based on an incremental complementary energy principle involving both the incremental Piola-Lagrange stress, and an incremental rotation tensor which leads to discretization of rotational equilibrium equations, is presented. An application of this new method to the finite strain analysis of a compressible nonlinear-elastic solid is included, and the numerical results are discussed.
Initial Response of a Rock Penetrator
Authors: Longcope D. B. , Grady D. E.
Published: November 2010

An analysis based on elastic rod theory is given for the early-time axisymmetric response of pointed penetrators. Results of measurements by laser interferometry of the back surface particle velocity of laboratory scale penetrators impacted by sandstone targets are presented. Values of the initial pressure on the penetrator tip are determined which give good agreement between the analytical and experimental results. These initial tip pressures are found to be approximated by the stress-particle velocity Hugoniot for the target material.
Computational Aspects of Time Integration Procedures in Structural Dynamics—Part 1: Implementation
Authors: Felippa C. A. , Park K. C.
Published: November 2010

A unified approach for the implementation of direct time integration procedures in structural dynamics is presented. Two key performance assessment factors are considered, viz., computational effort and error propagation. It is shown that these factors are strongly affected by details in the reduction of the second-order equations of motion to a system of first-order equations, and by the computational path followed at each time step. Part 1 is primarily devoted to the study of the organization of the computational process. Specific implementation forms derivable from the unified approach are studied in detail, and rated accordingly. An analysis of the computational error propagation characteristics of these implementations is presented in Part 2.
Response of a Multidegree-of-Freedom System to Nonstationary Random Excitation
Authors: Masri S. F.
Published: November 2010

This paper presents an analytical study of the covariance kernels of a damped linear two-degree-of-freedom system that is subjected to spatially correlated nonstationary stochastic excitation consisting of modulated white noise. A unit-step intensity function and an exponential function, resembling the envelope of a typical earthquake, are considered in conjunction with a propagating disturbance. Results of the analysis are used to determine the dependence of the peak transient mean-square response of the system on the uncoupled frequency ratios, mass ratios, wave propagation speed, shape of the intensity function, and system damping.
Stress Concentration in a Stretched Cylindrical Shell With Two Elliptical Holes
Authors: Hansen E. B.
Published: November 2010

The circumferential membrane and bending stresses at the edges of two identical elliptical holes in a circular cylindrical shell loaded by axial tension are computed by means of an integral equation method. Pairs of holes of which the center line is along a generator of the shell, along a directrix, or in a direction forming an angle of 45° with the generators are considered. For each of these hole configurations results are presented for a number of hole distances, hole sizes, and axis ratios.
Stationary Response of a Randomly Parametric Excited Nonlinear System
Authors: Ibrahim R. A.
Published: November 2010

This paper presents a review of three truncation schemes for the problem of the infinite hierarchy of moment equations and an investigation of the stationary response of a nonlinear system under a broad band random parametric excitation. The validity of the truncation methods is discussed together with the conditions for preservation of moment properties. One of these schemes is employed to truncate the dynamic moment equations of a nonlinear single-degree-of-freedom system subject to a broad band random parametric excitation. The influence of inertia, stiffness, and damping nonlinearities is discussed and closed-form solutions are obtained for each case. The preservation of the response moment properties is confirmed for certain solutions while it fails for the remaining ones. The invalidity of these solutions is not necessarily attributed to the inaccuracy of the used truncation method as it may be due to the fact that the system may not be able to achieve a stationary response.
A Steadily Moving Load on an Elastic Beam Resting on a Tensionless Winkler Foundation
Authors: Choros J. , Adams G. G.
Published: November 2010

An infinitely long Euler-Bernoulli beam resting on a tensionless Winkler foundation is considered. Steady-state solutions are obtained for a downward directed concentrated force moving with constant speed. First, the critical load necessary to initiate separation of the beam from the foundation is determined for a range of speed. For loads greater than critical, one or more regions of noncontact can be expected to occur. Closed-form solutions of the differential equations are obtained in terms of local coordinate systems which significantly reduces the coupling among the various regions. The extent and location of the noncontact regions, as well as the corresponding beam deflections, are then determined for a range of force and speed. The results show that many solutions are possible and the final determination is based on an energy criterion.