bluuebunny/crossref_metadata_2025 huggingface dataset:
Slow Interactions of Gravity Waves and a Corrugated Sea Bed
Authors: Mitra A. , Greenberg M. D.
Published: July 2009

The effect of a corrugated sea bed on the linear theory of gravity water waves is considered. By straining the time variable, a perturbation solution is found in ε (the ratio of corrugation amplitude to mean water depth), through first order, for a wave system that is arbitrarily oriented with respect to the corrugations. That solution breaks down when the wave number k normal to the corrugation is a half-integer multiple of the wave number 2ω of the corrugations, i.e., when k = (ω, 2ω, .... Of these singularities, the first (k = ω) appears at the first order. To obtain a uniformly valid zeroth-order solution we include a zeroth-order reflected wave system, and obtain an alternation between incident and reflected waves on a time scale of order 0(ε−1). As representative of the other singular wave numbers, we consider k = 3ω, which singularity appears at the third order, and obtain a uniformly valid solution through second order (for the shallow water limit). Nonlinear effects are considered to the extent of noting that the zeroth-order linear and nonlinear results are identical, even for the first singular wave number k = ω.
The Permanent Deformation of a Cracked Cantilever Struck Transversely at Its Tip
Authors: Petroski H. J.
Published: July 2009

The presence of even a stable crack in a ductile cantilever can have a dramatic effect on the structural response of the beam. Not only can the magnitude of the permanent plastic deformation be significantly increased but also the final shape of the damaged beam can be dramatically affected by the size and location of the crack. Such effects are quantified by analyzing a simple model of the cracked beam with an attached tip mass.
Three-Dimensional Harmonic Vibrations of a Circular Beam
Authors: Panayotounakos D. E. , Theocaris P. S.
Published: July 2009

In this paper an analytical treatment for the determination of the natural frequencies of a circular uniform beam, subjected to three-dimensional harmonic loads, is presented. Each differential element of the beam has six degrees of freedom, i.e., three translations and three rotations. This problem, in the most general case of response, is associated with a partial linear differential system composed of four coupled 3 × 1 vectorial equations. The influences of transverse shear deformation and rotatory inertia are also included in the analysis. The aforementioned solution methodology is successfully demonstrated through several numerical results.
Influence of Geometric Imperfections and In-Plane Constraints on Nonlinear Vibrations of Simply Supported Cylindrical Panels
Authors: Hui David
Published: July 2009

This papers deals with the effects of initial geometric imperfections on large-amplitude vibrations of cylindrical panels simply supported along all four edges. In-plane movable and in-plane immovable boundary conditions are considered for each pair of parallel edges. Depending on whether the number of axial and circumferential half waves are odd or even, the presence of geometric imperfections (taken to be of the same shape as the vibration mode) of the order of the shell thickness may significantly raise or lower the linear vibration frequencies. In general, an increase (decrease) in the linear vibration frequency corresponds to a more pronounced soft-spring (hard-spring) behavior in nonlinear vibration.
The Study of Gravitational Nozzle Flows by Hodograph Transformations
Authors: Chan P. C. , Chow W. L.
Published: July 2009

The effect of gravity on two-dimensional imcompressible potential nozzle flows has been studied using the method of hodograph transformation coupled with numerical computation. It has been demonstrated that although hodograph transformation is an inverse technique, it has the ability to allow curved walls to be prescribed a priori. Calculations have been performed for flows discharging from symmetric nozzles with horizontal lips. The variation of total head versus discharge rate can only be obtained from detailed consideration of the gravitational effect. Some general features of nozzle flows, including the possibility of early flow separation from the top nozzle wall, have been observed.
The Incremental Strain Growth of Elastic-Plastic Bodies Subjected to High Levels of Cyclic Thermal Loading
Authors: Ponter A. R. S. , Cocks A. C. F.
Published: July 2009

A linearized method of analysis proposed in an accompanying paper [1] is used to obtain the ratchet rate for two types of thermal loading problems where parts of the structure experience reversed plastic straining. For structures that can shakedown plasticially it is found that for a given increment of load beyond the plastic shakedown boundary, the rate of ratchet increases with increasing level of thermal loading. When a structure is unable to shakedown plastically it ratchets at low mechanical loading as the result of a localized mechanism that involves some reversed plasticity. It is shown that the ratchet rate in such situations can be substantial but its value is very dependent on the local curvature of the yield and not the accuracy of the yield surface itself.
Optimal Forms of Shallow Shells With Circular Boundary, Part 1: Maximum Fundamental Frequency
Authors: Plaut R. H. , Johnson L. W. , Parbery R.
Published: July 2009

Thin, shallow, elastic shells with given circular boundary are considered. We seek the axisymmetric shell form which maximizes the fundamental frequency of vibration. The boundary conditions, material, surface area, and uniform thickness of the shell are specified. We employ a bimodal formulation and use an iterative procedure based on the optimality condition to obtain optimal forms. Results are presented for clamped and simply supported boundary conditions. For the clamped case, the optimal forms have zero slope at the boundary. The maximum fundamental frequency is significantly higher than that for the corresponding spherical shell if the boundary is clamped, but only slightly higher if it is simply supported.
Effects of Mode Interaction on Collapse of Short, Imperfect, Thin-Walled Columns
Authors: Hui David
Published: July 2009

The present paper deals with the design of beneficial geometric imperfections of short, thin-walled columns in order to maximize their energy absorption. The investigation was motivated by the experimental finding that under axial compressive load, the symmetric mode (which has a higher buckling load than the antisymmetric mode) actually has a much higher energy absorption than the antisymmetric mode as measured by the area under the curve of applied load versus end-shortening curve. Thus, an attempt is made to introduce imperfections in the beneficial symmetric mode so that the mode shapes of extremely large deflection in plastic collapse will also be of the symmetric type. The two-mode stability problem is studied using Koiter’s theory of elastic stability.
Vibrations of Thick Free Circular Plates, Exact Versus Approximate Solutions
Authors: Hutchinson J. R.
Published: July 2009

An exact solution for the natural frequencies of a thick free circular plate is compared to approximate solutions. The exact solution is a series solution of the general linear elasticity equations that converges to the correct natural frequencies. The approximate solutions to which this exact solution is compared are the Mindlin plate theory and a modification of a solution method proposed by Pickett. The comparisons clearly show the range of applicability of the approximate solutions as well as their accuracy. The choice of a best shear coefficient for use in the Mindlin plate theory is considered by evaluating the shear coefficient that would make the exact and modified Pickett method match the Mindlin plate solution.
A Consistent Theory for Elastic Deformations With Small Strains
Authors: Shield R. T.
Published: July 2009

A consistent theory is developed for linear elastic behavior in which the strains are small but in which no restriction is placed on the magnitudes of the displacements or the rotations of elements of the body. The theory reduces to the classical theory for infinitesimal deformations when the rotations are small. Pure torsion of a long cylinder and the bending of a beam by a terminal load are treated in order to illustrate the application of the theory. The bending solution agrees with the St. Venant flexure solution when the deflections are small and with the theory of the elastica when the deflections are large.
On the Effect of Dislocation Loop Curvature on Elastic Precursor Decay
Authors: Markenscoff X. , Ni L.
Published: July 2009

The exact solution for the fields radiated from a circular dislocation loop expanding in its own plane with constant velocity is obtained in terms of elliptic functions of different kinds. The solution is used to obtain the contribution of small disloction loops to the decay of the leading wave front of a wave propagating in an elastic solid containing dislocations. It is found that the loop curvature can contribute to the decay in the leading term.
The Generation of Waves in a Semi-Infinite Plate by a Smooth Oscillating Piston
Authors: Gregory R. D. , Gladwell I.
Published: July 2009

A semi-infinite plate is set into plane strain, time-harmonic vibration by a rigid oscillating piston, which is in smooth contact with the edge of the plate. The exact (linearized) solution to this problem is obtained as a series expansion involving the Rayleigh-Lamb modes of the plate, the coefficients being determined by a biorthogonality relation. We compute the amplitude of the resultant force exerted by the piston, the mean total rate of working of the piston, and the proportion of outgoing energy in each of the available propagating modes; resonances are observed at certain of the cut-off frequencies.
Creep and Creep Recovery of 2618-T61 Aluminum Under Variable Temperature
Authors: Cho U. W. , Findley W. N.
Published: July 2009

Creep and creep recovery data are reported for pure tension of 2618-T61 aluminum alloy under variable temperature between 200° C and 230° C. Varying temperature experiments involved an abrupt temperature increase and a linearly increasing and decreasing temperature at a constant stress of 137.9 MPa (20 ksi). A temperature-compensated time by Sherby and Dorn was employed to represent the effect of temperature. A temperature-history-dependent theory using data from constant stress creep and creep recovery together with the apparent activation energy was used to predict the creep under variable temperature. The predictions agreed quite well with the observed data. The apparent activation energy of this alloy was found to be 49,000 cal/mole°K.
Statics and Geometry of Underconstrained Axisymmetric 3-Nets
Authors: Kuznetsov E. N.
Published: July 2009

A 3-net is a system formed by three intersecting arrays of linear flexible members such that every intersection involves one member of each array. The subject of this study is an axisymmetric 3-net where the first array is meridional and the other two are inclined to a meridian at equal but opposite angles. If the net intersections are not fixed the system is underconstrained and, generally, does not possess a unique configuration. However, such systems allow exceptional configurations in which they lack kinematic mobility and admit prestress. Pertinent equations governing the intricately interrelated statics and geometry of axisymmetric 3-nets are developed and some closed-form solutions are obtained. On this basis, two particular classes of immobile (static) 3-nets are synthesized and two corresponding sets of feasible geometric shapes are investigated.
Exact Displacement Analysis of Four-Link Spatial Mechanisms by the Direction Cosine Matrix Method
Authors: Huang T. C. , Youm Y.
Published: July 2009

A method of displacement analysis of the four-link spatial mechanism is developed. The results through this analysis will be exact solutions that can be obtained without resorting to numerical or iteration schemes. In the analysis, the position of a link in a mechanism can be fully defined if its direction and length are known. Therefore, this analysis involves the calculation of the unknown direction cosines and length of each link for a given configuration of the mechanism. In finding the direction cosines of the unknown unit vectors involved for each link and rotating axis, two types of coordinates, the global and the local, are generally used. Then, a direction cosine matrix between each local coordinate system and the global coordinates is established. Thus, the unknown direction cosines of the local coordinates, the links, and the rotating axes are obtained in global coordinates. In this development, direction cosine matrices are used throughout the analysis. As an illustration, the application of this method to the study of four-link spatial mechanisms, RGGR, RGCR, RRGG, and RRGC will be presented.
Engineering Formulas for Fractures Emanating From Cylindrical and Spherical Holes
Authors: Nilson R. H. , Proffer W. J.
Published: July 2009

Generalized integral formulas based on the weight-function technique are used to calculate stress intensity and opening displacements for planar or axisymmetric fractures emanating from a cylindrical or spherical hole in an elastic medium. These approximate formulas reduce to known exact solutions in the limits of very short (notch) fractures or very long [penny-shaped or Griffith) fractures. In the intermediate range, where fracture length is comparable to hole size, the approximation is generally accurate within a few percent, as demonstrated by comparison with available numerical results for the planar problem of a circular hole with an arbitrary number of radial cracks as well as the axisymmetric problems of a cylindrical or spherical hole with a disk-shaped circumferential fracture. The generalized integral formulas provide a fast, simple, and reasonably accurate method for solving a broad class of engineering problems, including hydraulic and explosive fracturing applications, in which the following features are important: cavity pressurization, stress concentration around the cavity due to in situ compressive stresses, arbitrary pressure distribution along fracture, varying fracture length, and multiple fracturing.
Wave-Front Approximations in a Moving Coordinate System
Authors: Harris J. G.
Published: July 2009

A wave-front approximation to the wave emitted when a propagating mode III crack abruptly slows it speed of advance is calculated. Of particular interest is the approximation of the Cagniard-deHoop inversion integral when it is expressed in terms of the variables of a moving coordinate system.
On the Ergodicity Assumption in an Applied Mechanics Problem
Authors: Scheurkogel A. , Elishakoff I.
Published: July 2009

A deformation of a thin uniform cylindrical shell is considered under random axisymmetric loading. Mathematically this is equivalent to the study of a quasi-linear differential equation with random inhomogeneous term and random coefficient. The approximate method of solution, based on the assumption of ergodicity of the shell slope, is first described. It is shown that sometimes this assumption is valid but when not, it may yield non-negligible errors. In particular, it is shown via the exact solution that assumption of ergodicity of the shell slope is correct if the loading is ergodic in correlation. However, this assumption may yield an error of about 20 percent if the loading in ergodic in mean-square but not in correlation.
Transverse Impact of a Hyperelastic Stretched String
Authors: Beatty M. F. , Haddow J. B.
Published: July 2009

Governing equations are derived for the plane motion of a stretched hyperelastic string subjected to a suddenly applied force at one end. These equations can be put in the form of a quasilinear system of first-order partial differential equations, which is totally hyperbolic for an admissible strain energy function. There are, in general, two wave speeds and two corresponding shock speeds. Special consideration is given to the jump relations across the shocks. Similarity solutions for a string moved at one end in loading or unloading are obtained for a general hyperelastic solid. The results are applicable to the familiar neo-Hookean or Mooney-Rivlin material, and the nature of the solution for another special hyperelastic material is discussed. These solutions are valid for a semi-infinite string, or until the first reflection occurs. It is shown that a special case of the similarity solution is valid for the normal impact of a stretched string by a constant speed, point application of load. Exact solution to the equations for the neo-Hookean model is derived in terms of elliptic integrals, and some numerical results are provided.
The Acoustic Response of a Periodically Rough Elastic Plate (Ice) in Contact With Water
Authors: Lakhtakia A. , Varadan V. K. , Varadan V. V.
Published: July 2009

The plane wave scattering matrix theory is applied to formulate a T-matrix which characterizes the acoustic response of an infinite solid plate bounded by semi-infinite vacuum and fluid half spaces on either side. Individual T-matrices for the periodically rough vacuum/solid and solid/fluid interfaces are used in this derivation. Using the computed results, the anomalies in the scattering response of the rough solid plate are explained in terms of the Rayleigh, the Scholte, and the Lamb waves.
Effects of Geometric Imperfections on Frequency-Load Interaction of Biaxially Compressed Antisymmetric Angle Ply Rectangular Plates
Authors: Hui David
Published: July 2009

The present paper deals with the influence of small geometric imperfections on the vibration frequencies of rectangular, simply supported, angle ply, thin composite plates subjected to inplane uniaxial or biaxial compressive preload. Depending on the amount of preload, the frequencies of laminated plates with different imperfection shapes may be significantly higher than those for perfect plates, especially in a certain range of fiber angles. Interaction curves between frequency and applied preload are plotted for various fiber angles and imperfection amplitudes for both the uniaxial and equal biaxial loading cases.
Nonlinear Forced Vibrations of Beams
Authors: Countryman M. , Kannan R.
Published: July 2009

An iterative procedure for computing periodic solutions of nonlinear vibrating beams is presented. The nonlinear partial differential equation is replaced by a coupled system of equations. The contraction mapping principle is then applied to generate a method of successive approximations. The coupled equations are then approximated by discrete equations that are solved by matrix-theoretic techniques and numerical quadrature procedures. Some numerical examples are provided to illustrate the method.
Clearing Maximum Height With Constrained Kinetic Energy
Authors: Hubbard M. , Trinkle J. C.
Published: July 2009

This paper addresses the question: In order to clear a given height, defined as that which is passed over by all points in the moving body, what is the minimum initial kinetic energy required and what are the other conditions that specify the solution completely? An expression is derived for the height cleared above an original supporting ground plane. This transcendental expression is maximized numerically subject to certain equality and inequality constraints using nonlinear constrained optimization techniques. The optimal solution includes the height cleared and the required control variables. The parameter space of body descriptors in which the optimal solution is presented decomposes into two regions in which the solutions differ qualitatively.
The Constitutive Theory for Fluid-Filled Porous Materials
Authors: Katsube N.
Published: July 2009

The static constitutive theory for fluid-filled porous materials, well established by Biot, is reinvestigated by modifying the recent developments of the micromechanical approach by Carroll. Introducing a new kinematical quantity that allows an equal treatment of fluid and solid, we show that the constitutive theory by Carroll is identical to that developed by Biot. This comparison provides a further insight into Biot’s theory by clarifying the distinct deformation mechanisms that Biot did not express explicitly. Applying the same methods to the dynamic case, we investigate the fluid flow mechanism of a porous fluid material.
Directional Sensitivity of Cylindrical Hot-Film Velocity Sensors
Authors: Raman A. , Krishnan V. S. , Roy R. P.
Published: July 2009

Directional sensitivities of alumina and quartz-coated cylindrical hot-film velocity sensors with ls/ds ratios near 20 were investigated in air and liquid Refrigerant-113 flows. The well-known effective cooling velocity relation Ueff2(α) = U2(0)[cos2α+k2sin2α] represents the experimental data well. Values for the parameter k as well as heat transfer relations are presented.
Stress Field in and Around a Coated Short Fiber in an Infinite Matrix Subjected to Uniaxial and Biaxial Loadings
Authors: Mikata Y. , Taya M.
Published: July 2009

The stresses induced in and around a coated short-fiber composite are investigated by use of the Boussinesq-Sadowsky stress function. The coated fiber is assumed to consist of two confocal spheroids and it is embedded in an infinite body. The major parameters in this analysis are the fiber aspect ratio, the coating thickness-to-fiber radius ratio, the coating-to-matrix stiffness ratio and the fiber-to-matrix stiffness ratio. It is found in the analysis that the stiffness and thickness of the coating and the fiber aspect ratio have some effect on the stress field in and around the coating in a coated short-fiber composite.
Boundary Layer Flow Over Long Cylinders With Suction
Authors: Bar-Haim B. , Weihs D.
Published: July 2009

The full, axisymmetric boundary layer equations over a long circular cylinder have been repeatedly solved in the past by a variety of approximate Pohlhausen-type and series expansion methods. These methods are not suitable however, for axisymmetric solutions with wall suction boundary condition. In the present paper, the basic equations are solved by a simple approximate method, based on successive derivatives of the wall compatibility condition. A family of velocity profiles, which coincides with the asymptotic suction profile at infinity, is assumed, and the wall shear force is found by integrating an ordinary differential equation. The computed boundary layer properties for the impermeable (zero-suction) cylinder case are shown to be in good agreement with solutions of other, more sophisticated techniques. The case of an infinite cylinder with constant suction asymptotically approaches the well-known constant thickness boundary layer solution, in analogy with the case of constant suction on a flat plate. The present method is further explored to exhibit the drag reduction properties of wall suction. An optimal suction profile is found, as a function of free stream conditions and the cylinder fineness ratio. For example, in the case of a cylinder fineness ratio 5, and Re = 25 × 106, the flow can be laminarized with only 80 percent of the mass sucked off, relative to uniform suction.
Wind-Generated Surface Waves on a Viscous Fluid
Authors: Katsis C. , Akylas T. R.
Published: July 2009

The excitation of surface waves on a viscous fluid by shear flows is studied. Turbulent and laminar air flows over oil of low and high viscosity are considered. It is found that the dominant wave-generation mechanism depends crucially on the shear-flow profile: for a turbulent flow, long surface waves are generated at low wind speeds due to the work done by the stress components in phase with the surface slope, while Kelvin-Helmholtz instability is responsible for the excitation of short waves at higher wind speeds. On the other hand, for a laminar shear flow, direct resonance between surface waves and Tollmien-Schlichting waves in the shear flow is the dominant wave-generation mechanism.
Thermoelastic Stress Due To Surface Parallelepiped Inclusions
Authors: Lee S. , Hsu C. C.
Published: July 2009

The thermoelastic stress generated by surface parallelepiped inclusions has been solved by the Mindlin method. The stress components near the free surface and inside the solid have been discussed. Numerical results using this method are compared with Chiu’s results obtained by using the Fourier transform.
Progressing and Oscillatory Waves for Hybrid Synthesis of Source-Excited Propagation and Diffraction
Authors: Felsen L. B.
Published: July 2009

Time-harmonic and transient propagation and diffraction phenomena can be described alternatively by progressing and oscillatory waves that express the wave motion in terms of direct and multiple wavefronts or rays, and in terms of resonances or modes, respectively. Each description is convenient and physically appealing when it requires few contributing elements. It is inconvenient and physically less transparent when it requires many elements, and it would then be desirable to combine many inconvenient elements into fewer convenient ones. For a variety of propagation environments, including layered or other guiding regions, this can be done by expressing a group of rays collectively in terms of modes, or a group of modes collectively in terms of rays. When this ray-mode equivalence is invoked selectively, there emerges a hybrid representation that combines ray fields and modal fields in uniquely defined proportions. The theory is based on Poisson summation and on alternative treatments of wave spectra. It has been applied to electromagnetics, underwater acoustics, and SH elastic motion, and is now being extended to general propagation in elastic media.
The Rapid Tearing of a Half Plane
Authors: Dempsey J. P. , Smith E. B.
Published: July 2009

The surface of an elastic half space is subjected to sudden antiplane mechanical disturbances. Crack initiation and subsequent crack instability are examined via two idealized problems; the first is concerned with instantaneous crack bifurcation and the second with instantaneous skew crack propagation. In either problem, crack propagation occurs at a constant subsonic velocity under an angle κπ with the normal to the surface. For the externally applied disturbances that are considered here, and for contstant crack-tip velocities, the particle velocity and τθz are functions of r/t and θ only, which allows Chaplygin’s transformation and conformal mapping to be used. The problems can then be solved using analytic function theory. For various values of the angle of crack propagation, the dependence of the elastodynamic stress intensity factors on the crack propagation velocity is investigated. For certain specific geometries, fully analytical solutions are derived to provide check cases.
Analysis of the Reflection of Point Force-Induced Crack Surface Waves by a Crack Edge
Authors: Brock L. M. , Rossmanith H. P.
Published: July 2009

Dynamic stress fields near cracks follow in part from the reflection of crack surface waves by the crack edges. To gain insight into the reflection process, the problem of stationary normal and tangential point forces applied to one surface of a stationary semi-infinite crack is considered, and analytical expressions for the crack surface reflection-generated particle velocity waves presented. Study of these expressions shows that the dominant reflected wave is singular at its wave front, travels at the Rayleigh speed, and is generated by the reflection of a singular Rayleigh wave. However, the reflection process “moves” the singularity from the velocity component parallel to the particular force to the component normal to it.
An Elastic Stress-Strain Relation for Sphere Arrays Undergoing Initial Stage Sintering
Authors: George T. L. , Kennedy T. C. , Peddicord K. L.
Published: July 2009

An analytical model for predicting the elastic constants for isotropic random sphere arrays is described. The model is based on the Hertz contact theory and accounts for the restructuring (neck growth) associated with initial stage sintering. The stress-strain relation is incremental since the stiffness depends on the loads at sphere contacts. As part of the model development, relationships are given for the elastic constants of an isotropic aggregate consisting of orthotropic parts. Predicted elastic constants are presented as functions of the neck size and hydrostatic compression, and comparisons are made with experimental data for cohesionless sphere arrays and fully restructured arrays approaching a porous body.
Dynamic Impact Over a Subsurface Crack: Applications to the Dynamic Tear Test
Authors: Brock L. M. , Jolles M. , Schroedl M.
Published: July 2009

Dynamic fracture is often studied by means of the dynamic tear (DT) test, which involves transverse impact by a mass on a beam. This process generates a complicated elastic wave pattern in the beam which, however, consists of two wave types: impact waves and reflected waves. The former are the compression wave radiating from the impact line and its diffractions at the notch end, while the latter are all waves originated by reflections from the beam surfaces. To gain insight into the role of specific waveforms in generating the fracture at the notch end in this process, the effects of the impact waves on the dynamic notch end stress field is studied. For both an idealized and an experimentally determined impact force, these waves are shown to initially place the notch end in compression. Moreover, even when a tensile stress state is eventually achieved, the stress intensity factor levels lie well below experimentally determined fracture toughness values. These results suggest that reflected waves generate the fracture, which agrees with experimental evidence.
Three-Dimensional Fully Plastic Solutions for Plates and Cylinders With Through-Wall Cracks
Authors: Yagawa G. , Takahashi Y. , Ueda H.
Published: July 2009

In the finite element method with the incremental procedure based on the flow theory of plasticity, which is now widely employed, a great amount of load increments and specially trained analysts are necessary to obtain sufficiently accurate results. Thus, the method is not suitable for the routine evaluation or parametric analysis of cracked structures in the plastic regime. With this consideration, an alternative evaluation method, called the engineering approach, has been developed, where the fully plastic solutions are utilized with the linear-elastic solutions to estimate the entire elastic-plastic behavior of cracked bodies. In this paper, a Selective Reduced Integration/Penalty Function (SRI/PF) method is developed for the analysis of three-dimensional fully plastic solutions. It is demonstrated through the calculation of center-cracked plates under plane strain condition that accurate solutions can be obtained with the present method. Then, using the method, fully plastic solutions for cylinders with a circumferential through-wall crack subjected to remote uniform tension are calculated and tabulated as functions of the crack angle and the hardening exponent.
Modeling Shrinkage Mechanisms in Porous Elastic Solids
Authors: Cowin S. C.
Published: July 2009

This paper concerns the applications of a method of modeling the mechanism of shrinkage in porous elastic materials. Examples of the effects of shrinkage in porous elastic materials include the cracks that appear in the sun-dried gumbo at the bottom of a former mud puddle or in concrete, and the warping and cracking of drying lumber. The model for shrinkage is applied here for drying wood, but with an emphasis on the method and the generality of the results with regard to shrinkage in other materials. The model is able to predict the stresses, strains, deformation, and warping associated with wood drying.
Optimal Boundary Tractions for Solids With Initial Strains
Authors: Meric R. A.
Published: July 2009

Optimal boundary loading of solids with initial strains has been analyzed as a steady-state optimal control problem. Discretization of the optimality conditions, obtained by calculus of variations, is achieved by the finite element method, while the minimization of a performance index is done via the conjugate gradient method. Numerical results are provided for two plane strain problems with initial thermal strains.
Theoretical Estimation of the Response of Helically Armored Cables to Tension, Torsion, and Bending
Authors: Lanteigne J.
Published: July 2009

This paper concerns the mechanical behavior of ACSR (aluminum conductor steel-reinforced) conductors under static-loading conditions, which may comprise any combination of tension, torsion, and bending. The model described is quite general and can be applied to other types of helically armored cables. A stiffness matrix is developed and relations are given for axial, torsional, and flexural rigidities and for coupling parameters. For small curvatures, the flexural rigidity is comparable to the upper limit accepted in current practice by ACSR users. As the curvature increases, however, frictional forces develop between the outer layers and sliding of wires may occur, with the result that the flexural rigidity decreases. The tension level also influences the flexural rigidity of the conductor. Actually the model does not consider the flexural rigidity of the system as a fixed entity but as directly influenced by local compressive forces and internal radial and tensile forces. The analysis can also apply to situations where a given number of initial constituent wires have failed and the load is transferred to neighboring wires, leaving the conductor unbalanced; it will be seen how internal arrangements manage to accommodate the local perturbation.
Period-Doubling Bifurcations and Modulated Motions in Forced Mechanical Systems
Authors: Tousi S. , Bajaj A. K.
Published: July 2009

Weakly nonlinear and harmonically forced two-degree-of-freedom mechanical systems with cubic nonlinearities and exhibiting internal resonance are studied for their steady-state solutions. Using the method of averaging, the system is transformed into a four-dimensional autonomous system in amplitude and phase variables. It is shown that for low damping the constant solutions of the averaged equations are unstable over some interval in detuning. The transition in stability is due to the Hopf bifurcation and the averaged system performs limit cycle motions near the critical value of detuning. The bifurcated periodic solutions are constructed via a numerical algorithm and their stability is analyzed using Floquet theory. It is seen that the periodic branch connects two Hopf points in the steady-state response curves. For sufficiently small damping, the averaged equations, therefore, have stable limit cycles where the constant solutions are unstable. Reduction in damping results in destabilization of these periodic solutions with one Floquet multiplier leaving the inside of the unit circle through −1. This leads to period-doubling bifurcations in the averaged equations. There is, thus, an interval in detuning parameter over which the constant and the periodic solutions are unstable and the period-doubled solutions are stable. For small enough damping there are cascades of period-doubling bifurcations that ultimately lead to chaotic motions. Some of these sequences seem to be compatible with the Feigenbaum Universality Constant.
The Effect of Curvature and Torsion on the Temperature Distribution in a Helix
Authors: Sayers D. D. , Potter M. C.
Published: July 2009

Traditional analysis treats the helix as a straight wire with the effects of nonuniform heating, torsion, and large curvature ignored. Using a helical coordinate system the governing partial differential equation including these effects is derived. The equation is then solved numerically using the finite element method. The results indicate a strong dependence of the temperature on the torsion parameter when the curvature parameter is significant. As the curvature parameter increases, the temperature distribution becomes skew-symmetric and the maximum temperature in the helix increases. Nonuniform heating influences the temperature distribution independent of the curvature and torsion.
A New Rate Principle Suitable for Analysis of Inelastic Deformation of Plates and Shells
Authors: Mukherjee S. , Kollmann F. G.
Published: July 2009

A variational principle for linear elasticity, using displacements and strains as independent functions, is presented in this paper. An extension of this principle in rate form is claimed to be extremely useful for the analysis of inelastic deformation of thin plates and shells.
Vibration and Stability of Circular Plates Under Partially Distributed or Concentrated Inplane Loads
Authors: Narita Y.
Published: July 2009

A method is presented for analyzing the free transverse vibration and elastic stability of circular plates under nonuniform distribution of the inplane stresses. A general solution procedure is developed, and a frequency equation is derived for the case when a pair of loads are locally distributed in the plane along the edge. Numerical results are presented for natural frequencies and buckling loads of the plates, and the effect of the partial inplane loading is discussed. A limiting case for a concentrated inplane load is also considered.
Transient Loads Analysis by Dynamic Condensation
Authors: Kubomura K.
Published: July 2009

This paper investigates an alternative finite-difference time-integration procedure in structural dynamics. The integral form of the equation of motion, instead of the differential form, is used to develop the finite-difference time-integration method. An expression called dynamic condensation is presented to relate the dynamic response and unknown force at a limited number of degrees of freedom. A stable and accurate method of analysis is derived to determine the transient loads of structural components in a structural system without constructing the system equation of motion.
Dynamic Fracture Under Normal Impact Loading of the Crack Faces
Authors: Kim K.-S.
Published: July 2009

Results of experiments on crack-face impact are presented. The transient stress-intensity factor variation of a crack has been traced by the Stress-Intensity Factor Tracer (SIFT) [1] under time-stepwise uniform pressure loading of the crack faces. To see the effects of various waves generated by the loading, part of the crack faces was left free of traction within the distance l0 from the crack tip. The crack-face impact loading was produced by an electromagnetic force induced by a square pulse of an electric current flowing through a copper strip inserted in the saw-cut crack of a Homalite 100 plate specimen. The current flowed in opposite directions in the two portions of the copper strip, between the crack faces, causing them to repel each other. The short-time and the long-time behavior of the transient stress-intensity factor variation under the impact loading have been carefully investigated. Brittle dynamic initiation of crack extension and the stress-intensity variation of a running crack have been also examined. The experimental results have been compared with theoretical predictions based on Freund’s crack-face concentrated load solution [2]. The agreement between the theory and the experiment is excellent. In this study, the various waves generated by the loading are shown to play different roles in transmitting the load to the crack tip. In addition, confirmation is given that the SIFT is excellent in tracing the stress-intensity factor regardless of the crack-tip motion.
A Continuum Model for Dynamic Tensile Microfracture and Fragmentation
Authors: Seaman L. , Curran D. R. , Murri W. J.
Published: July 2009

A continuum model for dynamic tensile cleavage fracture and fragmentation has been developed for detailed simulation of brittle fracture processes in elastoplastic materials. The model includes processes for nucleation of microcracks, stress-dependent growth, coalescence and fragmentation, and stress relaxation caused by the developing damage. Fracturing is characterized by a crack density with a distribution of sizes at each material point. The model extends previous work by treating more completely full material separation and stress-free volume growth, as well as multiple loadings, unloadings, and recompaction, and by describing the damage in greater microscopic detail.
Nonproportional Loading Steps in Multiaxial Creep of 2618 Aluminum
Authors: Ding J. L. , Findley W. N.
Published: July 2009

Experimental data on the creep behavior of 2618-T61 aluminum alloy under nonproportional loadings are presented. Among the important findings are the anisotropy induced by creep strain, synergistic effects during creep recovery, and strongly nonlinear material behavior at high stress levels. Data were compared with two theoretical models, a viscous-viscoelastic (VV) model and a viscoplastic (VP) model. In the VV model the time-dependent strain was decomposed into recoverable (viscoelastic) and nonrecoverable components. The VP model differs from the VV model in that all the time-dependent strain is assumed nonrecoverable. In each model, three viscoplastic flow rules based on different hardening natures, namely, isotropic strain hardening, kinematic hardening, and independent strain hardening were derived to describe the time-dependent nonrecoverable strain component, and compared with experiments. The viscoelastic component in the VV model was represented by the third-order multiple integral representation combined with the modified superposition principle. Predictions for all theories used material constants obtained from creep and recovery data only. Possible causes for the discrepancies between theories and experimental data were discussed. Further experimental and theoretical work necessary for the study of the time-dependent material behavior at high temperature were also suggested.
Optimal Cooling Paths for a Class of Thermorheologically Complex Viscoelastic Materials
Authors: Harper B. D.
Published: July 2009

This paper concerns the optimal cooling of thin viscoelastic plates so as to minimize the residual thermal stresses upon completion of the cool-down process. The thermorheological behavior of the plate material is assumed complex in the sense that both horizontal and vertical shift factors are employed. The optimal path is shown to possess initial and final jump discontinuities and to depend on only one of the two components of the vertical shift factor. It is further demonstrated that significant reductions in the level of residual stress may be attained by following the optimal cooling path.
On the Uniqueness of Solution of the Initial Value Problem in Softening Materials
Authors: Valanis K. C.
Published: July 2009

The initial value problem in finite “softening” material domains is discussed. An inequality that is true of all materials irrespective of their constitution is first established. It is then shown that the solution to this problem is unique when the attending constitutive equation satisfies another inequality, which is characteristic of material models that we call “positive.” A number of constitutive equations that give rise to realistic softening behavior are shown to lead to a unique solution of the initial value problem.
Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA
Authors: Month L. A. , Rand R. H.
Published: July 2009

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.
Time-Dependent Stokes Flow Induced by Instantaneous Sources
Authors: Ajayi O. O. , Falade A.
Published: July 2009

Analytical solutions are provided for Stokes flow fields induced by an instantaneous thermal source located (i) in an infinite fluid and (ii) at the center of a solid spherical surface. In both cases it is assumed that the flow is driven by a body force that arises from buoyancy effects in the fluid due to the gradient of the source’s temperature field. In accordance with Stokes approximation, convective acceleration terms are left out of the momentum equations but the local acceleration term is retained. The retention of the local acceleration term is crucial if all the salient features of the flow, especially in its early stages, are to be included in the solution for low Prandtl number. The evolution of the flow field in each of the two cases is demonstrated by plotting streamline patterns at various times. The influence of Prandtl number on flow field development is also discussed. Problem (i) is the fundamental one for this class of problems. From its solution, solutions to problems where the heat-generating rate is a general but known function of position and time to bounded and unbounded domains may be synthesised using well-known techniques. These results may be fruitfully applied to such practical problems as the motion of vessels in which nuclear wastes are stored, the fluid dynamics of weak point explosions, and the cooling of electrical and electronic equipments.
Axisymmetric Postbuckling of Orthotropic Tapered Thick Annular Plates
Authors: Dumir P. C.
Published: July 2009

The postbuckling parameters of clamped and simply supported tapered thick annular plates with free hole are presented for several values of annular ratio, thickness-to-radius ratio, orthotropic parameter, and taper ratio.
Flow Driven by a Finite, Shrouded Spinning Disk With Suction
Authors: Hyun J. M.
Published: July 2009

Numerical solutions are presented for the flow driven by a spinning disk which forms an endwall of a finite, closed cylinder. The effects of imposing a uniform suction (or blowing) through the spinning disk in finite configuration are investigated. The Reynolds number is large and the cylinder aspect ratio is 0(1). Finite-difference techniques are employed to integrate the time-dependent Navier-Stokes equations. The initial state is taken to be a uniform axial motion. Integration is performed until an approximate steady state is attained. When there is no suction, the infinite disk model is shown to provide a qualitatively representative approximation to the flow in the central core region. As a suction (blowing) is imposed, the core rotation rate in the case of finite configuration becomes smaller (larger) than that for the case of no suction, which is in disagreement with the predictions of the infinite disk model. These significant discrepancies point to a fundamental difficulty of the infinite disk model to adequately describe the real flow infinite geometry when there is a mass flux across the system boundary. Plots showing the meridional stream function at various times are constructed. Details of the flow structure in the approximate steady state are analyzed. When there is a suction, a strong Ekman layer is present on the spinning disk but the Ekman layer on the stationary disk fades. When there is a blowing, a strong Ekman layer forms on the stationary disk. It is shown that the dynamic effects influencing the character of the flow are confined to these Ekman layers.