bluuebunny/crossref_metadata_2025 huggingface dataset:
The Compressible Elastica on an Elastic Foundation
Authors: Nicolau A. M. , Huddleston J. V.
Published: July 2009

The nonlinear two-point boundary-value problem describing the compressible elastica on an elastic foundation is formulated exactly within the context of the technical theory of bending as a set of eight first-order differential equations plus appropriate initial-point conditions and terminal-point conditions. The problem is then solved by a shooting method that determines two missing quantities. Graphs of load versus displacements and load versus the missing quantities are presented for various combinations of the system parameters. These results show that the presence of the elastic foundation enables the member to sustain unsymmetric (as opposed to antisymmetric) shapes in its postbuckled state, and that bifurcations from the straight configuration to symmetric buckled modes and bifurcations from symmetric buckled modes to unsymmetric ones depend on two system parameters—a compressibility measure and the foundation modulus. For a given compressibility and foundation stiffness, equilibrium paths are plotted globally, enabling unsymmetric paths to be extended from one bifurcation point to another, with the result that the complete postbuckling process can be traced. Finally, a discussion of path shapes as a function of foundation stiffness is given.
Cable Kink Analysis: Cable Loop Stability Under Tension
Authors: Yabuta T. , Yoshizawa N. , Kojima N.
Published: July 2009

Submarine cable kinking is a continuing design problem. Cable kink occurs when a cable loop forms due to torsion and tension action, and then tightens under subsequent tension increase. This paper describes cable loop stability under the subsequent tension and clarifies the kinking mechanism. Results show that kinking occurrence mainly depends on residual twist in the cable loop.
The Dynamics of a Gyroscope Supported by a Flexible Circular Plate
Authors: Burdess J. S.
Published: July 2009

The dynamics of a rigid rotor supported on a flexible circular plate is investigated and it is shown that the arrangement is capable of operating as a tuned free rotor gyroscope. The performance characteristics of the gyroscope are evaluated and the analysis shows that the steady displacment of the rotor may be used to measure either the angular velocity or angular displacement of the supporting casing. For both modes of operation the free motion and the response to a constant rate and a vibratory input is determined.
Nonparametric Identification of Nearly Arbitrary Nonlinear Systems
Authors: Masri S. F. , Sassi H. , Caughey T. K.
Published: July 2009

A nonparametric identification technique is presented for use with discrete multidegree-of-freedom nonlinear dynamic systems. The method requires information regarding the system response and estimates of its pertinent “mode shapes” to determine, by means of regression techniques involving the use of two-dimensional orthogonal functions, an approximate expression for the system generalized restoring forces in terms of the corresponding generalized system state variables. The technique is applied to several example systems. The method can be used with deterministic or random excitation to identify dynamic systems with arbitrary nonlinearities, incuding those with hysteretic characteristics. It is also shown that the method is easy to implement and needs much less computer time and storage requirements compared to the Wiener-kernel approach.
Natural Frequencies of Thick Annular Plates
Authors: Irie T. , Yamada G. , Takagi K.
Published: July 2009

The natural frequencies of vibration based on the Mindlin plate theory are tabulated for uniform annular plates under nine combinations of boundary conditions.
A Constitutive Model of Cyclic Plasticity With a Nonhardening Strain Region
Authors: Ohno N.
Published: July 2009

By introducing the concept of a nonhardening region in the plastic strain space, a constitutive model is proposed for cyclic plastic loadings between variable, as well as fixed, strain limits. It is assumed that the isotropic hardening of materials does not occur when the plastic strain point moves inside this region after a load reversal. The region expands and translates as cyclic straining proceeds, and when strain limits are fixed, it eventually occupies the cyclic range of plastic strain so as to describe the saturation of cyclic hardening. The phenomena of cyclic relaxation and cyclic creep are also taken into account in the formulation. In the simple case of a linear hardening material, the present theory is verified by comparing predictions with experimental results on type 304 stainless steel under torsional cyclings between variable, as well as fixed, strain limits at room temperature.
Optimal Cooling of Cross-Ply Composite Laminates and Adhesive Joints
Authors: Weitsman Y. , Harper B. D.
Published: July 2009

This paper concerns the optimal cooling of symmetric, balanced, cross-ply composite laminates and adhesive joints so as to minimize the residual thermal stresses upon termination of the cool-down process. The computations are based on a recently developed analytical scheme and employ up-to-date data on graphite/epoxy laminas. The calculations consider the thermoviscoelastic response of the polymeric resins and incorporate the temperature dependence of the coefficients of thermal expansion. It is shown that the viscoelastic behavior may contribute to a significant reduction of the residual stresses.
Plane-Strain Surface Waves in a Laminated Composite
Authors: Herrmann G. , Hemami M.
Published: July 2009

Elastic wave propagation in plane strain in a periodically layered half space is considered, with the layering parallel to the bounding traction-free plane. Attention is focused on surface waves of the Rayleigh-type propagating parallel to the bounding plane. It is found that such waves are highly dispersive and that higher branches may be discontinuous.
Effect of Shear and Rotary Inertia on Dynamic Fracture of a Beam or Plate in Pure Bending
Authors: Levy C. , Herrmann G.
Published: July 2009

The dynamic fracture response of a long beam of brittle material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased quasi-statically to a critical value, a crack will propagate from the tensile side of the beam. As an extension of previous work, the effect of shear and of rotary inertia on the moment and induced axial load at the fracturing section is included in the present analysis. Thus an improved formulation is presented by means of which the crack length, crack-tip velocity, bending moment, and axial force at the fracture section are determined as functions of time after crack initiation. It is found that the rotary effect diminishes the axial force effect and retards total fracture time whereas the shear has an opposite effect. Thus by combining the two effects (to simulate to first order the Timoshenko beam) overall fracture is retarded and better agreement with experimental data is achieved. The results also apply for plane-strain fracture of a plate in pure bending provided the value of the elastic modulus is appropriately modified.
Extension and Torsion of Elastic Bars With Initial Twist
Authors: Shield R. T.
Published: July 2009

In contrast to straight bars, elastic bars with initial twist exhibit coupling between tension and torsion. The coupling is examined for pretwisted bars composed of homogeneous isotropic material under the assumption that each section undergoes the same deformation. The expressions for the axial force and torsional moment are transformed by use of the governing equations and boundary conditions to forms that are particularly useful for rods with small amounts of pretwist. The elliptical section with center on the axis of pretwist and the off-centered circular section are treated in order to illustrate the coupling between extension and torsion caused by the initial twist.
A Global Local Finite Element Analysis of Axisymmetric Scattering of Elastic Waves
Authors: Goetschel D. B. , Dong S. B. , Muki R.
Published: July 2009

A global local finite element method is developed for axisymmetric scattering of a steady, compressive, incident elastic wave in a homogeneous, isotropic host medium by an axisymmetric inclusion. The inclusion may be arbitrary with respect to its geometry and can have inhomogeneous, anisotropic elastic material properties. Examples on spheroidal and finite circular cylindrical inclusions are given. Comparison of current data with available results show good agreement.
Axisymmetric Elastic Waves Excited by a Point Source in a Plate
Authors: Weaver R. L. , Pao Yih-Hsing
Published: July 2009

The response of an infinite elastic plate to dynamic loading is presented by the method of superposition of normal modes, a method particularly appropriate in the intermediate and far field. The method is compared with the method of integral transforms. Explicit expressions are given for the case of loading by a concentrated vertical step force. These expressions are evaluated numerically over a range of distances from 4 to 40 plate thicknesses. The numerical results are compared with qualitative stationary phase analyses and with the exact results of generalized ray theory.
Implicit Numerical Integration for Periodic Solutions of Autonomous Nonlinear Systems
Authors: Thurston G. A.
Published: July 2009

A change of variables that stabilizes numerical computations for periodic solutions of autonomous systems is derived. Computation of the period is decoupled from the rest of the problem for conservative systems of any order and for any second-order system. Numerical results are included for a second-order conservative system under a suddenly applied constant load. Near the critical load for the system, a small increment in load amplitude results in a large increase in amplitude of the response.
The Nature of the Temporal Solutions of Damped Distributed Systems With Classical Normal Modes
Authors: Inman D. J. , Andry A. N.
Published: July 2009

Conditions under which the time response of certain distributed parameter systems, which are assumed to possess “classical normal” modes, is critically damped, overdamped, or underdamped are presented. The conditions are derived from the definiteness of certain combinations of the coefficient operators of the describing equations. These conditions are compared to previous results and their usefulness is illustrated by examples.
An Analysis of Adhesive-Bonded Single-Lap Joints
Authors: Chen Du , Cheng Shun
Published: July 2009

Because of the technical importance and difficulty of the analysis, the present problem has been treated, as seen in the literature, by a number of authors. In the current paper a unified method is presented that has advantages in several respects for the analysis of this difficult problem and may also be employed for solving other similar problems. The method is based on two-dimensional elasticity theory in conjunction with the variational principal of complementary energy. Minimizing the energy functional leads to two coupled, fourth-order ordinary differential equations with constant coefficients for the determination of the stresses. By means of the present approach, a closed-form solution, which is adaptable for any possible adhesive layer flexibility and capable of satisfying all the boundary stress conditions of the joint, is obtained. To illustrate the application of the present unified theory, three typical examples for flexible, medium, and inflexible adhesive layers are provided and comparisons are made among these examples and with other known solutions. Special attention is given to the stress distribution in the end zones where high stress intensities of the joints occur.
The Interface Crack Between Dissimilar Anisotropic Composite Materials
Authors: Wang S. S. , Choi I.
Published: July 2009

The fundamental nature of an interface crack between dissimilar, strongly anisotropic composite materials under general loading is studied. Based on Lekhnitskii’s stress potentials and anisotropic elasticity theory, the formulation leads to a pair of coupled governing partial differential equations. The case of an interlaminar crack with fully opened surfaces is considered first. The problem is reduced to a Hilbert problem which can be solved in a closed form. Oscillatory stress singularities are observed in the asymptotic solution. To correct this unsatisfactory feature, a partially closed crack model is introduced. Formulation of the problem results in a singular integral equation which is solved numerically. The refined model exhibits an inverse square-root stress singularity for commonly used advanced fiber-reinforced composites such as a graphite-epoxy system. Extremely small contact regions are found for the partially closed interlaminar crack in a tensile field and, therefore, a simplified model is proposed for this situation. Physically meaningful fracture mechanics parameters such as stress intensity factors and energy release rates are defined. Numerical examples for a crack between θ and −θ graphite-epoxy composites are examined and detailed results are given.
On the Stability of Large Discrete Buckling Structures
Authors: Maher A.
Published: July 2009

An approximate applicable method is presented for the computation of the critical buckling load of a moderately large complicated assembly in terms of traces of successive powers of the stability matrix. The method is based on the use of the bound approach of reference [1, 2]. An illustrative example and comparison with known results are given.
Dynamic Singular Stresses for a Griffith Crack in a Soft Ferromagnetic Elastic Solid Subjected to a Uniform Magnetic Field
Authors: Shindo Y.
Published: July 2009

The problem of the diffraction of normally incident longitudinal waves on a Griffith crack located in an infinite soft ferromagnetic elastic solid is considered. It is assumed that the solid is a homogeneous and isotropic one and is permeated by a uniform magnetostatic field normal to the crack surfaces. Fourier transforms are used to reduce the problem to two simultaneous dual integral equations. The solution to the integral equations is expressed in terms of a Fredholm integral equation of the second kind having the kernel that is a finite integral. The dynamic singular stress field near the crack tip is obtained and the influence of the magnetic field on the dynamic stress intensity factor is shown graphically in detail. Approximate analytical expressions valid at low frequencies are also obtained and the range of validity of these expressions is examined.
Dynamic Stress Concentration Around a Circular Hole in an Infinite Elastic Strip
Authors: Itou S.
Published: July 2009

Transient response of an infinite elastic strip with a circular hole is investigated in this study. A normal stress is suddenly applied and maintained at the hole. The boundary condition equations are satisfied in the Laplace transformed domain. A numerical Laplace inversion technique is then used to recover the time dependence of the solution.
Stress Couple Concentrations for Cylindrically Bent Plates With Circular Holes or Rigid Inclusions
Authors: Reissner E.
Published: July 2009

We obtain explicit solutions for the two problems considered, in terms of Poisson’s ratio ν and in terms of a parameter μ which is of the order of the ratio of hole radius a to plate thickness h, through application of a sixth-order theory of shear deformable plates, with this solution involving distinct edge zone and interior solution contributions when 1 < < μ. It is shown that in this range some relevant asymptotic Bessel function formulas furnish explicit examples concerning the distinction between first-order shear corrections and second-order (Timoshenko-type) shear corrections which have been established in a recent general analysis.
Plastic Buckling of Initially Imperfect Stiffened Cylinders in Axial Compression
Authors: Duffett G. A. , Reddy B. D.
Published: July 2009

The behavior in the plastic range of axially compressed stringer-stiffened cylinders is investigated. The shell under consideration is assumed to have an initial imperfection in the form of sinusoidal deviation both axially and circumferentially. The constitutive relation employed here is J2 deformation theory of plasticity. This relation, as well as kinematic assumptions regarding the behavior of the panels and stiffeners that constitute the stiffened shell, is used in the principle of virtual work to obtain a set of nonlinear algebraic equations whose solution provides complete information about the prebuckling equilibrium path. Bifurcation from the primary path is examined by making use of a functional whose first variation is zero when two solutions to the problem are possible. This leads to an eigenvalue problem, the eigenvalue being the critical compressive load and the eigenfunction being the corresponding buckling mode. Results are presented for shells of different geometries and material properties, and a comparison of results is made with results obtained by others. The imperfect shells analyzed all exhibit stable behavior, with sufficiently large imperfections having a beneficial effect. Results for bifurcation from these paths are also discussed.
A Numerical Investigation for Curved Pipe Flow at High Reynolds Number
Authors: Holt M. , Yeung W.-S.
Published: July 2009

A numerical scheme for solving the curved pipe flow at high Reynolds number is presented in considerable detail. This paper complements an earlier paper presenting mainly numerical results. An efficient scheme based on the conventional Telenin method is developed to solve the general three-dimensional Laplace equation subject to Dirichlet, Neumann, or mixed boundary conditions.
Boundary Layers on Characteristic Surfaces for Time-Dependent Rotating Flows
Authors: Gans R. F.
Published: July 2009

Time-dependent motion of a fluid in a container rotating at Ω is characterized by boundary layers on the container surfaces if ν/Ω, where ν denotes kinematic viscosity, is small compared to the square of a typical length of the container. Let the frequency of the motion, measured in a corotating coordinate system, be ωΩ. If ω ~ 1, then the length scale of the boundary layer is (ν/Ω)1/2, unless |ω| is equal to twice the normal component of the unit rotation vector. If |ω| does equal twice the normal component of the unit rotation vector, scales of (ν/ΩL2)1/3 L and (ν/ΩL2)1/4 L are possible. If the normal vector and rotation vectors are parallel, the former scale vanishes.
The Effect of a Normal Shock on the Aeroelastic Stability of a Panel
Authors: Williams M. H.
Published: July 2009

The effect of a standing shock wave on the static and dynamic aeroelastic stability of a flexible panel is investigated using a linear structural and aerodynamic theoretical model. It is found that the shock is generally stabilizing. The lowest critical dynamic pressures are associated with shock positions downstream from the panel, where the panel is uninfluenced by the shock.
Magnetoelastic Plane Waves in Infinite Rotating Media
Authors: Roy Choudhuri S. K. , Debnath L.
Published: July 2009

A study is made of the propagation of magnetoelastic plane waves in an electrically conducting, infinite elastic solid permeated by a primary uniform magnetic field when the entire medium rotates with a constant angular velocity. A more general dispersion relation is obtained to investigate the effects of rotation and the external magnetic field on the phase velocity of the waves. This analysis reveals that when the applied magnetic field has both longitudinal and transverse components, the coupled magnetoelastic waves are dispersive and damped in an infinitely conducting medium in contrast to the nonrotating medium where the coupled waves are dispersive, but undamped. In the case of finite conductivity, the waves are dispersive and undamped in the absence of the applied magnetic field. At low frequency ω, the phase velocity of the waves varies as ω1/2 for finite conductivity, and is independent of the external magnetic field and rotation; while in the nonrotating case with low frequency (when the applied magnetic field has either longitudinal or transverse components) the phase speed is less than that in the rotating medium and is found to depend on the applied magnetic field. Also in both rotating and nonrotating cases, the phase velocity becomes very small for finitely conducting material with a very high magnetic permeability.
Use of Coefficients of Influence to Solve Some Inverse Problems in Plane Elasticity
Authors: Durelli A. J. , Wu D.
Published: July 2009

The principle of superposition of the order of isochromatic fringes and the concept of the coefficient of influence of the order of those fringes are introduced. The method is proposed to solve some inverse problems in elasticity and is applied to the determination of the forces that act at the points of contact between disks loaded in their plane. For this purpose Michell equations are used to determine the stresses at selected points of a disk and the coefficients of influence are computed numerically. The method can be generalized to other plane bodies loaded in the plane and if no theoretical solution is available the problem could be solved completely experimentally. The application presented in the paper is related to a study of discrete, or granular, media.
Sanders’ Energy-Release Rate Integral for a Circumferentially Cracked Cylindrical Shell
Authors: Nicholson J. W. , Weidman S. T. , Simmonds J. G.
Published: July 2009

Analytical and numerical values for Sanders’ path-independent energy-release rate integral I and the combined stress-intensity factor are obtained for a circumferentially through-cracked cylindrical shell. Two types of loadings are considered. First, the shell is subject to axial tension and, second, the shell is subject to edge moments. New procedures for evaluating I from the governing integral equations are presented. In particular, for a very thin shell subject to edge moments, a method of evaluating I by circumventing the solution of the integral equations is shown.
Acoustoelastic Determination of Forces on a Crack in Mixed-Mode Loading
Authors: King R. B. , Herrmann G.
Published: July 2009

A technique previously presented [1] for the nondestructive evaluation of the J integral in cracked samples from ultrasonic measurements of stress, and successfully tested on specimens under mode I loading, is extended here to mixed-mode loading. Experimental results are presented for both the J and L integrals in a specimen with a slanted central crack loaded in tension, which agree well with theoretical values.
The Determination of the Elastodynamic Fields of an Ellipsoidal Inhomogeneity
Authors: Fu L. S. , Mura T.
Published: July 2009

Elastic fields of a single ellipsoidal inhomogeneity embedded in an infinite elastic matrix subjected to plane time-harmonic waves are studied by employing the concept of eigenstrain and the extended version of Eshelby’s method of equivalent inclusion. Using the dynamic version of the Betti-Rayleigh reciprocal theorem, an integral representation of the displacement field, due to the presence of inhomogeneity, is given in terms of the eigenstrains. Two types of eigenstrains arise in the elastodynamic case. Expanding the eigenstrains and applied strains in the polynomial form in the position vector r and satisfying the equivalence conditions at every point, the governing simultaneous algebraic equations for the unknown coefficients in the eigenstrain expansion are derived. Elastodynamic field outside an ellipsoidal inhomogeneity in a linear elastic isotropic medium is given as an example. The angular and frequency dependence of the induced displacement field, which is in fact the scattered displacement field, the differential and the total cross sections are formally given in series expansion form for the case of uniformly distributed eigenstrains.
Reflection Coefficient for Plane Waves in a Fluid Incident on a Layered Elastic Half-Space
Authors: Bogy D. B. , Gracewski S. M.
Published: July 2009

The reflection coefficient is derived for an isotropic, homogeneous elastic layer of arbitrary thickness that is perfectly bonded to such an elastic half-space of a different material for the case when plane waves are incident from an inviscid fluid onto the layered solid. The derived function is studied analytically by considering several limiting cases of geometry and materials to recover previously known results. Approximate reflection coefficents are then derived using various plate models for the layer to obtain simpler expressions that are useful for small values of σd, where σ is the wave number and d is the layer thickness. Numerical results based on all the models for the propagation of interface waves localized near the fluid-solid boundary are obtained and compared. These results are also compared with some previously published experimental measurements.
The Radially Flexible Pendulum Subjected to a High-Frequency Excitation
Authors: Schmidt B. A.
Published: July 2009

A high-frequency harmonic excitation is applied to a pendulum that is flexible in the radial direction. Approximate equilibrium positions are found when the excitation is in a general and fixed direction. An approximate stable motion is found when the direction of the excitation changes constantly and slowly. It is found that the excitation causes a reduction of the radius.
A Note on Broken Pencil Points
Authors: Cowin S. C.
Published: July 2009

A stress analysis of a pencil writing tip at fracture is presented. It is an interesting illustration of combined axial and bending loading.
Analysis of Composite Materials—A Survey
Authors: Hashin Z.
Published: July 2009

The purpose of the present survey is to review the analysis of composite materials from the applied mechanics and engineering science point of view. The subjects under consideration will be analysis of the following properties of various kinds of composite materials: elasticity, thermal expansion, moisture swelling, viscoelasticity, conductivity (which includes, by mathematical analogy, dielectrics, magnetics, and diffusion) static strength, and fatigue failure.
Forced Oscillations in a Two-Layer Fluid of Finite Depth
Authors: Manna R. K.
Published: July 2009

An initial value investigation is made of the development of surface and internal wave motions generated by an oscillatory pressure distribution on the surface of a fluid that is composed of two layers of limited depths and of different densities. The displacement functions both on the free surface and on the interface are obtained with the help of generalized Fourier transformation. The method for the asymptotic evolution of the wave integrals is based on Bleistein’s method. The behavior of the solutions is examined for large values of time and distance. It is found that there are two classes of waves—the first corresponds to the usual surface waves with a changed amplitude and the second arises entirely due to stratification. Some interesting features of the wave system have also been studied.
Corotational Rates for Kinematic Hardening at Large Plastic Deformations
Authors: Dafalias Y. F.
Published: July 2009

To illustate the effect of the choice of corotational rates at large plastic deformations, expressions for the stresses developing in large simple shear are obtained in closed analytical form under the assumptions of a rigid-plastic material response and a Mises type isotropically and kinematically hardening constitutive model for two different corotational rates applied to the stress and the back-stress tensors. The observed difference in the simple shear response and the relative merits of the foregoing and other corotational rates are discussed, and a novel approach is proposed based on Mandel’ work and the representation theorem for isotropic second-order antisymmetric tensor valued functions.
Creep and Plastic Strains Under Side Steps of Tension and Torsion for 304 Stainless Steel at 593°C
Authors: Cho U. W. , Findley W. N.
Published: July 2009

Results of nonproportional stress changes on creep and plastic strains resulting from abrupt changes in proportion of tension and torsion are reported. Both step-up and step-down changes are included. Constitutive equations based on data for single step creep and recovery tests previously reported are used to describe the test results. A viscous-viscoelastic model with aging effects and modifications for step-down tests predicted the creep behavior reasonably well. The prediction of time-independent plastic strains is also described.
Statistical Theory of the Strength of Fiber Bundles
Authors: McCartney L. N. , Smith R. L.
Published: July 2009

Following a review of statistical models of the failure of single fibers and bundles of these fibers, algebraic recurrence formulas are derived that generate expressions for the failure probabilities of bundles of classical fibers. One of these recurrence relations is suitable for the accurate numerical calculation of failure probabilities of bundles consisting of up to 500 single fibers. It is shown how account can be taken of the effect of defect-free fibers having finite strength. Numerical results are compared to three asymptotic analytic approximations, two of which have been proposed in the statistical literature and are now applied to fiber problems for the first time.
The Crack Problem for a Nonhomogeneous Plane
Authors: Delale F. , Erdogan F.
Published: July 2009

In this paper the plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson’s ratio of the medium is constant and the Young’s modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy-type kernel. Hence, its solution and the stresses around the crack tips have the conventional square-root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson’s ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible. On the other hand, the results are highly affected by the parameter β describing the material nonhomogeneity in E (x) = E0exp(βx).
Impact Response of a Cracked Orthotropic Medium
Authors: Kassir M. K. , Bandyopadhyay K. K.
Published: July 2009

A solution is given for the problem of an infinite orthotropic solid containing a central crack deformed by the action of suddenly applied stresses to its surfaces. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of standard integral equations in the Laplace transform plane. A numerical Laplace inversion technique is used to compute the values of the dynamic stress-intensity factors, k1 (t) and k2 (t), for several orthotropic materials, and the results are compared to the corresponding elastostatic values to reveal the influence of material orthotropy on the magnitude and duration of the overshoot in the dynamic stress-intensity factor.
A Conservation Theorem for Simple Nonholonomic Systems
Authors: Kane T. R. , Banerjee A. K.
Published: July 2009

When the Hamiltonian of a holonomic system is free of explicit time dependence it remains constant throughout all motions of the system. In this paper, it is shown how, given a homogeneous simple nonholonomic system S, one can form a function E that remains constant throughout all motions of S, providing the forces acting on S fulfill certain requirements. An illustrative example is examined in detail.
Vibrations of Suspended Cables
Authors: Gale J. G. , Smith C. E.
Published: July 2009

An analytical investigation of the small, normal-mode motions of a homogeneous, inextensible, perfectly flexible cable suspended in a gravitational field was made. With cable arc length as the independent variable, the differential equations that govern the mode shapes have irrational coefficients. A transformation of the independent position variable yields equations that have polynominal coefficients, which then lend themselves to power series solutions. Natural frequencies of oscillation and corresponding mode shapes are determined from these solutions. Figures showing the natural frequency ratios for a variety of cable support geometries are presented for both in-plane and out-of-plane motion.
On the Crushing Mechanics of Thin-Walled Structures
Authors: Wierzbicki T. , Abramowicz W.
Published: July 2009

A self-consistent theory is presented which describes the crushing behavior of a class of thin-walled structures. Assuming a rigid-plastic material and using the condition of kinematic continuity on the boundaries between rigid and deformable zones, a basic folding mechanism is constructed. This mechanism closely reproduces all the main features of folds and wrinkles actually observed on typical crumpled sheet metal structures. Calculations based on the energy balance postulate show that two-thirds of the plastic energy is always dissipated through inextensional deformations at stationary and moving plastic hinge lines. The extensional deformations are confined to relatively small sections of the shell surface but they account for the remaining one-third of the dissipated energy. The theory is illustrated by application to the problem of progressive folding of thin-walled rectangular columns. A good correlation is obtained with existing experimental data as far as the mean crushing force and the geometry of the local collapse mode is concerned.
Small Deflections of Linear Elastic Circular Membranes Under Lateral Pressure
Authors: Stora˚kers B.
Published: July 2009

The classical Fo¨ppl equations, governing the deflection of plane elastic membranes, are cast in a form convenient for numerical analysis in the case of a circular contour. A solution based on a standard computer method is given for uniform pressure load. Quantitative results within determined accuracy are reported in considerable detail together with a discussion of the physical range of validity.
Analysis of the Optical Shadow Spot Method for a Tensile Crack in a Power-Law Hardening Material
Authors: Rosakis A. J. , Ma C. C. , Freund L. B.
Published: July 2009

If the crack tip deformation field in a cracked ductile solid can be characterized by means of a single plastic intensity factor, then the shadow spot method has potential as a means for direct measurement of this intensity factor. The value of the J-integral is adopted as a plasticity intensity factor, and the lateral contraction of a planar specimen of elastic-plastic power-law hardening material is calculated in terms of J from the HRR asymptotic field of elastic-plastic fracture mechanics. The theoretical caustic curve which would be generated by geometrical reflection of normally incident light from points of the deformed specimen surface lying well within the plastic zone is determined, and it is shown that the value of J is proportional to the maximum transverse diameter of the shadow spot to the power (3n + 2)/n, where n is the power hardening exponent. Synthetic shadow spot patterns obtained by numerical simulation of the optical reflection process are also shown.
Endochronic Analysis of Cyclic Elastoplastic Strain Fields in a Notched Plate
Authors: Valanis K. C. , Fan J.
Published: July 2009

In this paper we present an analytical cum-numerical scheme, based on endochronic plasticity and the finite element formalism. The scheme is used to calculate the stress and elastoplastic strain fields in a plate loaded cyclically in its own plane along its outer edges and bearing two symmetrically disposed edge notches. One most important result that stands out is that while the external loading conditions are symmetric and periodic, the histories of stress and strain at the notch tip are neither symmetric nor periodic in character. In cyclic tension ratcheting phenomena at the tip of the notches prevail and a progressive change of the residual stress field at the notch line is shown to occur.
Strain-Hardening Topography of Elastic-Plastic Materials
Authors: Casey J. , Lin H. H.
Published: July 2009

In the context of a purely mechanical rate-type theory of plasticity, a special set of constitutive equations is discussed. A method [1,2] of characterizing strain-hardening behavior is utilized to examine the different types of response that may be exhibited. Loci of constant strain-hardening behavior in stress space and regions of hardening, softening, and perfectly plastic behavior are determined.
Finite Element Analysis of Dynamic Coupled Thermoelasticity Problems With Relaxation Times
Authors: Prevost J. H. , Tao D.
Published: July 2009

A general finite element model is proposed to analyze transient phenomena in thermoelastic solids. Green and Lindsay’s dynamic thermoelasticity model is selected for that purpose since it allows for “second sound” effects and reduces to the classical model by appropriate choice of the parameters. Time integration of the semidiscrete finite element equations is achieved by using an implicit-explicit scheme proposed by Hughes, et al. The procedure proves to be most effective and versatile in thermal and stress wave propagation analysis. A number of examples are presented which demonstrate the accuracy and versatility of the proposed model, and the importance of finite thermal propagation speed effects.
The Lumped Parameter Method for Elastic Impact Problems
Authors: Lee Y. , Hamilton J. F. , Sullivan J. W.
Published: July 2009

Transverse impact problems have recently been solved by several different methods including Timoshenko’s integral equation method, the energy method, and the finite element method. This paper presents a lumped parameter method (LMP) for impact analysis, which is attractive for the solutions of impact of complex bodies. The advantages are in its simplification of mathematical formulation, computational efficiency, and improved understanding of the coupling effect of excited modes on the occurrence of multiple impacts. Experimentally obtained information of the dynamic characteristics of these impacting bodies permit easy extension to nonsimple body shapes.
A Periodically Forced Impact Oscillator With Large Dissipation
Authors: Shaw S. W. , Holmes P. J.
Published: July 2009

We consider the simple harmonic oscillator with harmonic excitation and a constraint that restricts motions to one side of the equilibrium position. Thus, on the achievement of a specified displacement, the direction of motion is reversed using the simple impact rule. The coefficient of restitution for this impact, r, is taken to be small. For r = 0 the motions of the system can be studied using a one-dimensional mapping. Analysis of this map shows that stable periodic orbits exist at almost all forcing frequencies but that transient nonperiodic or chaotic motions can also occur. Moreover, over certain (narrow) frequency windows arbitrarily long stable periodic motions exist. These results are then extended to the case r ≠ 0, small.
A New Method of Stabilization for Holonomic Constraints
Authors: Baumgarte J. W.
Published: July 2009

A new method for the asymptotic stabilization of holonomic constraints is presented. The essential feature of this approach is the introduction of stabilizing momenta of constraint. The advantage of the method is the fact that to obtain the nonclassical Lagrangian multipliers in the equations of motion, the holonomic constraints need to be differentiated only once with respect to time.
Spectral Moments Calculation of Linear System Output
Authors: Spanos P-T. D.
Published: July 2009

The stationary output of a stable linear dynamic system to white noise input is considered. It is shown that the spectral moments of the output can be determined as the solution of a set of linear equations. The corresponding solutions are utilized for determining an improper integral which can be quite useful in random vibration analyses of linear dynamic systems.
Fundamentals of the Phenomenological Theory of Nonlinear Fracture Mechanics
Authors: Hutchinson J. W.
Published: July 2009

An introduction to the theoretical foundations of the phenomenological theory of nonlinear fracture mechanics is given. Following an outline of the full range of objectives of nonlinear fracture mechanics, the paper focuses on the phenomenological, or semiempirical, approach to the initiation of crack growth and the subsequent quasi-static crack growth and loss of stability under monotonic load histories.
Turbulence Modeling
Authors: Lumley J. L.
Published: July 2009

The historical development of and motivation for turbulence modeling is briefly surveyed. The models of various levels are described, and the performance of second-order models discussed. The various basic constraints to which second-order models are or are not subject are considered, including invariance, material frame indifference, realizability, and the preservation of moment inequalities. Finally, fundamental difficulties that arise in the case of multiple scales are discussed.
Elastic Waves in Solids
Authors: Pao Yih-Hsing
Published: July 2009

Research contributions over the past 50 years on the theory and analysis of elastodynamics are reviewed in this paper. Major topics reviewed are: general theories, steady-state waves in waveguides, transient waves in layered media, diffraction and scattering, and one and two-dimensional theories of elastic bodies. A brief discussion on the direct and inverse problems of elastic waves completes this review.
Analysis of Circular Cylindrical Shells
Authors: Sanders J. L.
Published: July 2009

The paper is an account of the present state of the linear theory of circular cylindrical shells, problems of current interest, and in a broad sense the analytical methods that can be brought to bear on these problems.
Impact Force of a Rigid-Plastic Missile
Authors: White M. P.
Published: July 2009

A cylindrical missile, assumed to be of a rigid-plastic material strikes a nonyielding target normally and end-on. Above a certain (critical) velocity the nose of the missile disintegrates or spatters, and below that velocity the nose flattens to a mushroom form. The contact force decreases with decreasing velocity during impact but experiences a jump as the critical velocity is passed during slowdown. This paper gives a method of calculating the critical velocity and the contact force as function of time, as well as the time variations of the other parameters of the impact process.
Multiaxial Creep of 2618 Aluminum Under Proportional Loading Steps
Authors: Ding J.-L. , Findley W. N.
Published: July 2009

Creep data of 2618-T61 aluminum alloy under multistep multiaxial proportional loadings at 200°C (392°F) are reported. Two viscoplastic flow rules were developed using constant stress creep and creep recovery data. One was based on the accumulated strain (isotropic strain hardening), and the other on a tensorial state varible (kinematic hardening). Data were represented by two models: a nonrecoverable viscoplastic model, and a viscous-viscoelastic model in which the time-dependent strain was resolved into recoverable (viscoelastic) and nonrecoverable components. The modified superposition principle was used to predict the viscoelastic strain component under variable stress states. The experiments showed that the viscous-viscoelastic model with either isotropic strain hardening or kinematic hardening gave very good predictions of the material responses. Isotropic strain hardening was best in some step-down stress states. The viscoelastic component accounted for not only the recovery strain but also the transient creep strain upon reloadings and step-up loadings.
Local Nonsimilarity Solutions for Boundary Layers at Lubricated Walls
Authors: Andersson H. I.
Published: July 2009

The effect of the lubricating film is accounted for by a slip flow boundary condition, and the nonsimilar boundary layer problem is solved by a local nonsimilarity solution method.
On the Torsion of the Slit Circular Cylindrical Shell
Authors: Mansfield E. H.
Published: July 2009

The complexity of shell analysis stems from the fact that loads are resisted, in general, by both membrane and flexural action. There is a need to develop a suitable shell finite element, but many of those proposed at the present time fail in the context of the “sensitive solutions” coupled with rigid body movements. These “sensitive solutions” refer to known solutions (within the framework of shell theory) of problem in which it is kinematically possible for the shell to deform with no straining of the midsurface. (Purely inextensional solutions were first considered by Lord Rayleigh [1].) In two cases, namely the torsion of a slit cylinder and the application of uniformly distributed moments Mθ and Mx = vMθ to a slit cylinder, the contribution of the membrane forces is identically zero. The second of these two cases is too trivial to be used for comparison with finite element solutions, but the first case exhibits many of the features that current finite elements have difficulty in reproducing. An exact solution within the context of shell theory is not necessarily, of course, an exact three-dimensional solution. However, the torsion of a slit cylinder has also been solved three-dimensionally (Love [2]) and the present Note focuses attention on the exact variation of shear stress through the wall of the shell and on how this compares with shell theory.
Effects of Geometric Imperfections on Large-Amplitude Vibrations of Rectangular Plates With Hysteresis Damping
Authors: Hui David
Published: July 2009

The present paper deals with the effects of initial geometric imperfections on large-amplitude vibrations of simply supported rectangular plates. The vibration mode, the geometric imperfection, and the forcing function are taken to be of the same spatial shape. It is found that geometric imperfections of the order of a fraction of the plate thickness may significantly raise the free linear vibration frequencies. Furthermore, contrary to the commonly accepted theory that large-amplitude vibrations of plates are of the hardening type, the presence of small geometric imperfections may cause the plate to exhibit a soft-spring behavior. The effects of hysteresis (structural) damping on the vibration amplitude are also examined.
Boundary Layer Control by Means of Strong Injection
Authors: Yang R.-J. , Holt M.
Published: July 2009

The gas mixture produced by coal gasifier contains components that have serious corrosive effects on the walls of the pipe flow system. To reduce these, a non-corrosive gas is injected into the stream of the coal gas products, in a direction parallel to the pipe wall. The interaction between the injected stream and the original pipe flow is investigated analytically and is an example of the so-called Wall Jet Problem.
Surface Motion Excited by Acoustic Emission From a Buried Crack
Authors: Harris J. G. , Pott J.
Published: July 2009

The surface motions excited by acoustic emissions produced by fracture processes at the edge of a buried, penny-shaped crack are investigated. Firstly, wave-front approximations to the emissions generated by the sudden growth of a tensile crack in an unbounded elastic solid are reviewed. Then these approximations are Fourier transformed to give the high-frequency portion of their spectra. Secondly, time and frequency-domain approximations to the surface motions excited by this growing crack, when it is buried in a half-space, are calculated. These results are then scrutinized to elucidate what parts of the signals measured at the surface carry information about the crack’s size, its orientation, and the fracture processes near the crack tip.