bluuebunny/crossref_metadata_2025 huggingface dataset:
Blast Loading of a Spherical Container Surrounded by an Infinite Elastic Medium
Authors: Glenn L. A. , Kidder R. E.
Published: July 2009

Closed-form solutions are derived for the response of a spherical elastic shell, surrounded by a different elastic medium of infinite extent, and subjected to Heaviside or impulsive loading. The results are compared with earlier solutions in which the surrounding medium was a fluid. The importance of interfacial separation is also investigated by comparing the impulsive loading results with finite difference calculations in which it was possible for the shell to decouple from the surroundings when radial tensile stresses occurred at the shared boundary.
Vibrations of a Thick-Walled Pipe or a Ring of Arbitrary Shape in Its Plane
Authors: Nagaya K.
Published: July 2009

This paper is concerned with a method for solving in-plane vibration problems of thick-walled pipes and rings of arbitrary shape. The solution to the equation of motion based on the theory of elasticity under the plane-strain assumption is obtained exactly by using polar coordinates. The boundary conditions along both the outer and the inner surfaces of the ring of arbitrary shape are satisfied directly by means of the Fourier expansion collocation method which has been developed in the author’s previous reports concerning vibration, dynamic response, and wave propagation problems of plates and rods with various shapes. Numerical calculations have been carried out for a thick elliptical ring, a rectangular ring with rounded corners, and a rectangular ring with a circular inner boundary. To discuss the accuracy of the present analysis, the results of a thick circular ring have also been calculated, and the present results are compared with the previously published ones.
Effective Properties of Fiber-Reinforced Materials
Authors: Tzadka U. , Schulgasser K.
Published: July 2009

A material consisting of a matrix in which aligned fibers of uniform circular cross section are embedded is considered. A method is developed for computing the effective axial shear modulus and transverse thermal conductivity (which are mathematically analogous) for such materials. The method, an approximate technique based on pairwise interactions, introduces a new consistency concept uniquely appropriate for this problem, and is universal in the sense that it is readily and quickly applicable to any fiber arrangement. It overcomes an apparent in consistency in other interaction methods.
A Hybrid Finite Element Approach to Composite Laminate Elasticity Problems With Singularities
Authors: Wang S. S. , Yuan F. G.
Published: July 2009

A hybrid finite element method is presented for studying composite laminate elasticity problems with singularities. The basic equations of laminate anisotropic elasticity and stress singularities in composite laminates are discussed briefly. Formulation of a singular, hybrid composite-wedge element for this class of problems is given in detail. Two numerical examples are shown to illustrate the accuracy and efficiency of the present method of approach. The first example is the well-known laminate free-edge problem, which has a rather weak stress singularity; the second one is the important composite problem, which is shown to have a strong stress singularity. Results are compared with existing analytical elasticity solutions for these problems. Excellent solution accuracy, convergence, and computational efficiency are demonstrated.
Stress Concentrations in a Hybrid Composite Sheet
Authors: Fukuda H. , Chou T. W.
Published: July 2009

This paper examines the load redistribution in a hybrid composite sheet due to fiber breakage. The hybrid composite contains both high modulus and low modulus fibers arranged in alternating positions. Stress concentration factors for both types of fibers immediately adjacent to a group of fractured fibers have been evaluated. The method of influence function and Fourier series representation are adopted. Results of stress concentration factors are presented in terms of the number of fractured fibers and their geometric arrangements. Reduction of the stress concentration factor of the high modulus fibers when dispersed among the low modulus fibers provides a theoretical explanation of the observed “hybrid effect.” The present analysis can be readily incorporated into a failure model taking into account the statistical nature of fiber strength.
An Alternative Analysis of the Plane Stick-Slip Problem
Authors: Dutta A.
Published: July 2009

The plane stick-slip problem has been solved analytically using the separation of variable technique. The essence of the mathematical procedure is to solve the problem separately for the “stick” and the “slip” regions and then to match the two solutions at the exit plane. The present solution, which is relatively easy to evaluate, yields results that compare favorably with those obtained by the Wiener-Hopf technique. Furthermore, the stick-slip solution has been used to estimate the expansion of a two-dimensional plane Newtonian jet at very low Reynolds numbers. For capillary numbers less than 0.1, the approximate method predicts swell ratios that are in fairly good agreement with those obtained from a more elaborate numerical solution of the jet swell problem.
The Role of Cavitation in Whirl Instability in a Rotor Bearing, 1: The π-Film Model
Authors: Brindley J. , Elliott L. , McKay J. T.
Published: July 2009

Dynamically loaded rotor bearings are frequently observed to perform whirling motions, in which the center of the rotor describes some sort of closed orbit. In this paper we demonstrate, by using numerical computations of whirl orbits in a simple π-film model, the role of cavitation of the lubricant in enabling fluid forces alone to drive such stable orbits for certain ranges of parameter values. For other parameter values cavitation may actually enhance the instability always associated with the effects of fluid forces in a full-film bearing.
The Role of Cavitation in Whirl Instability in a Rotor Bearing, 2: Effect of Oil Inlet Position and Supply Pressure
Authors: Brindley J. , Elliott L. , McKay J. T.
Published: July 2009

Whirl orbits have been calculated for a cavitated rotor bearing in which the cavity is assumed to form at an oil inlet groove and occupy the region in which subambient pressure is predicted from the equations of motion. Variations in position of the inlet groove and in the oil supply pressure have a profound influence on the behavior of the journal, largely through the variations in cavity size and position that are produced.
Strange Attractors and Chaos in Nonlinear Mechanics
Authors: Holmes P. J. , Moon F. C.
Published: July 2009

We review several examples of nonlinear mechanical and electrical systems and related mathematical models that display chaotic dynamics or strange attractors. Some simple mathematical models — iterated piecewise linear mappings — are introduced to explain and illustrate the concepts of sensitive dependence on initial conditions and chaos. In particular, we describe the role of homoclinic orbits and the horseshoe map in the generation of chaos, and indicate how the existence of such features can be detected in specific nonlinear differential equations.
A Pre´cis of Developments in Computational Methods for Transient Analysis
Authors: Hughes T. J. R. , Belytschko T.
Published: July 2009

Recent developments in computational transient analysis methodology are described. Emphasis is placed on fundamental properties of some of the most widely used algorithms, the techniques used to analyze their behavior, and newer procedures that attain greater computational efficiency.
Boundary-Layer Interaction Theory
Authors: Messiter A. F.
Published: July 2009

Boundary-layer theory for flows at high Reynolds number fails locally in small regions with large gradients, where special solutions are required, with the pressure initially unknown. Examples include the flow near a discontinuity in surface geometry or near a separation point. During the past 15 years, local-interaction problems have been studied extensively for laminar flows, with particular attention to the description and prediction of separation, and a few examples have been worked out for turbulent flows. The basic ideas of asymptotic local-interaction theory are described, and applications are summarized for a variety of flows.
On Finite Plastic Flow of Crystalline Solids and Geomaterials
Authors: Nemat-Nasser S.
Published: July 2009

Certain fundamentals of finite-deformation elastoplastic flow of crystalline solids and geomaterials are discussed from microscopic and macroscopic phenomenological points of view. In the first case, physically based constitutive relations for microelements are formulated on the basis of slip-induced plastic deformation with due account of possible frictional or pressure dependencies and inelastic volumetric changes. The close relation between the double-slip theory of single crystals and that of granular materials is discussed. The calculation of overall instantaneous moduli in terms of the local quantities for arbitrary strains and rotations is examined, and some recent results for polycrystals and granular materials are reviewed. Then, attention is focused on phenomenological constitutive relations which apply to both metals and geomaterials. Specific results are given for an isotropic-kinematic hardening model, including frictional and plastic dilatancy effects. Finally, certain fundamental thermodynamic aspects of finite-deformation inelasticity are reviewed, emphasizing conditions under which flow potentials exist.
Quantitative Ultrasonic Nondestructive Evaluation Methods
Authors: Thompson R. B.
Published: July 2009

Quantitative ultrasonic techniques for determining the serviceability of structural components are reviewed. Particular emphasis is placed on the use of forward and inverse elastic wave scattering theory as a fundamental foundation for predicting such engineering parameters as the probability of flaw detection and for developing improved techniques for flaw sizing. Ultrasonic measurement techniques for the determination of distributed failure-related properties such as residual stresses are discussed, and the status of the prediction of failure by the detection of acoustic emission precursors is reviewed.
The Overall Elastic Response of Composite Materials
Authors: Willis J. R.
Published: July 2009

If a composite is modeled as a randomly inhomogeneous medium, an “overall modulus operator” relates the ensemble average of the stress to that of the strain. This paper reviews methods for estimating the overall modulus operator when only a limited amount of statistical information on the composite is available. The most securely based estimates come from bounds on the energy. Such bounds induce bounds on the components of the overall modulus operator and have a precise status, independent of the pointwise quality of the approximating fields from which they are derived. Other approximations are also outlined, however; these include perturbation series, estimates obtained from making ad hoc closure assumptions, and self-consistent estimates. The paper concludes with a discussion of possible future developments.
Dynamic Plasticity
Authors: Clifton R. J.
Published: July 2009

Recent advances in the understanding of the dynamic plastic response of crystalline solids are discussed. At the level of individual dislocations progress is being made on measurements of dislocation mobility at high stress levels and on elastodynamics solutions for transient dislocation motions. More progress is required on the understanding of changes in mobile dislocation density during dynamic plastic deformation. Widespread use of the Kolsky (or split-Hopkinson) bar has resulted in a reasonably clear picture of the dependence of flow stress on plastic strain rate for polycrystalline metals deformed at strain rates up to 103s−1. Influences of strain-rate history, temperature, and pressure require further investigation. At strain rates of approximately 103s−1’ to 105s−1 there is increasing evidence of a marked increase in flow stress with increasing strain rate. Pressure-shear plate impact experiments appear to be attractive for studying plastic response in this high strain-rate regime. Differences, if any, between stress-path effects at quasi-static strain rates and at strain rates of 103s−1 and higher remain poorly understood. Larger-than-predicted precursor decay observed in plate impact experiments on single crystals remains unresolved and of continuing fundamental interest; however, the importance of precursor decay measurements in determining dynamic plastic response appears to be diminishing because surface effects and limitations on the resolution of wave-front profiles represent serious constraints on the inferences that can be drawn from precursor decay measurements. Modeling of dynamic plastic response of polycrystals in terms of the response of slip systems is in an early stage of development. Kinematics of finite deformation by crystalline slip and consistent averaging techniques for modeling polycrystalline response are understood reasonably well. Increased emphasis on the understanding of the dynamic plastic response of single crystals and on the influence of microstructure appear desirable for sustained progress. Physically based models of wide applicability are required.
Random Vibration: A Survey of Recent Developments
Authors: Crandall S. H. , Zhu W. Q.
Published: July 2009

A general overview of the problems, methods, and results achieved in random vibration since its inception as a technical discipline nearly 30 years ago is given with particular emphasis on developments during the past 15 years. Research areas of current interest include development of improved probabilistic models for sources of random excitation, development of more effective random response prediction procedures for nonlinear systems and systems with parametric excitation, development of improved procedures for estimating reliability of systems undergoing random vibration, and development of improved techniques for identification of system parameters from measurements made during random vibration.
Contact-Line Problems in Fluid Mechanics
Authors: Davis S. H.
Published: July 2009

The types of contact-line problems that arise in fluid-dynamical applications are described and classified. Examples of each type are discussed in terms of the boundary conditions that are used and the singular nature of the solutions that emerge.
Hydrodynamic Stability
Authors: DiPrima R. C. , Stuart J. T.
Published: July 2009

Theoretical and experimental developments for the stability and transition of plane Poiseuille flow and for Couette flow between rotating concentric cylinders are reviewed. The paper concludes with brief comments on the stability of Hagen-Poiseuille flow in a pipe and brief comments on the stability of slowly varying flows.
Parametric Instability of a Periodically Supported Pipe Without and With Vibration Absorbers
Authors: Mallik A. K. , Kulkarni S. B. , Ram K. S.
Published: July 2009

Parametric instability of a periodically supported pipe without and with dynamic absorbers is investigated. A method based on the notion of propagation constant is used. This method requires no prior knowledge of the mode shapes and renders the amount of computation independent of the number of spans. Numerical results are presented for single and two-span pipes. Effective control of the instability regions by means of dynamic absorbers is also demonstrated.
Effects of Boundary Conditions on the Stability of Slender Viscous Fibers
Authors: Schultz W. W. , Davis S. H.
Published: July 2009

The one-dimensional isothermal flow of viscous-liquid fibers displays draw resonance instability when a constant-velocity winder condition is applied. This instability is removed when a constant-force condition occurs at the winder. The instability mechanism is examined and used to explain the stability trends when the effects of gravity, surface tension, inertia, and wind stress are included.
A Theoretical Analysis of Transient Sound Radiation From a Clamped Circular Plate
Authors: Akay A. , Tokunaga M. , Latcha M.
Published: July 2009

A theoretical analysis of transient sound radiation from a clamped circular plate is given using a pressure impulse response method. The vibration response of the plate to a transient point force is obtained. The modal pressure impulse response functions for the plate are derived from the Rayleigh surface integral and numerically convoluted with the modal acceleration response of the plate. The impulse response functions are closely related to the mode shapes and the geometry of the problem. They relate the spatial domain to the temporal domain of the pressure waves. The pressure impulse response waveforms are given for a number of plate modes and the changes in the waveforms with distance from the plate are shown. Sound radiation due to forced and free vibrations of the plate are discussed.
Fully Plastic Crack Problems, Part 2: Application of Consistency Checks
Authors: Shih C. F. , Needleman A.
Published: July 2009

Consistency checks, including short and deep crack limiting relations, are applied to the solutions obtained in Part 1. An error measure is introduced to quantify the consistency check. The accuracy of the solutions of Part 1 is discussed in light of these consistency checks and comparison is made with previous solutions. Consistency checks appear useful in ascertaining the accuracy of existing fully plastic crack solutions and of proposed new solutions.
On the Appearance of the Fractional Derivative in the Behavior of Real Materials
Authors: Torvik P. J. , Bagley R. L.
Published: July 2009

Generalized constitutive relationships for viscoelastic materials are suggested in which the customary time derivatives of integer order are replaced by derivatives of fractional order. To this point, the justification for such models has resided in the fact that they are effective in describing the behavior of real materials. In this work, the fractional derivative is shown to arise naturally in the description of certain motions of a Newtonian fluid. We claim this provides some justification for the use of ad hoc relationships which include the fractional derivative. An application of such a constitutive relationship to the prediction of the transient response of a frequency-dependent material is included.
Contact Between Plates and Unilateral Supports
Authors: Dempsey J. P. , Keer L. M. , Patel N. B. , Glasser M. L.
Published: July 2009

The tendency of a laterally loaded, unilaterally constrained, rectangular plate to separate from its simple supports motivates one to consider the actual extent of contact. In the case of a square plate, an appropriately chosen finite integral transform converts the dual series equations that result from the Levy-Nadai approach to one singular integral equation which can be solved by standard methods. Being a receding contact problem, the extent of contact depends on the geometry and elastic properties of the plate only. The support reactions are integrated to confirm that total equilibrium is obtained using classical plate theory.
Endochronic Theory of Cyclic Plasticity With Applications
Authors: Valanis K. C. , Lee C. F.
Published: July 2009

Integral constitutive equations of the endochronic type with only two easily determined material constants are shown to predict with computational ease the stress (plastic strain) response of normalized mild steel and Grade 60 steel to a variety of general strain (stress) histories, without a need for special unloading-reloading or memory rules. These equations are derived from the endochronic theory of plasticity of isotropic materials with an intrinsic time scale defined in the plastic strain space. Close agreement between theoretical predictions and experiments is obtained in the case of normalized mild steel in a variety of uniaxial, constant, strain-amplitude histories, variable strain-amplitude histories, and cyclic relaxation. Similar results are shown in the case of Grade 60 steel subjected to a random uniaxial strain history.
A Parametric Solution to the Elastic Pole-Vaulting Pole Problem
Authors: Griner G. M.
Published: July 2009

The fiberglass pole used in pole vaulting is approximated by an “elastica” having an applied concentrated force and moment at the upper end. Presented is a parametric solution expressed in terms of the tabulated elliptic integrals. The results suggest an advantageous pole-vaulting technique which is not generally recognized by coaches and athletes.
Calculations for Uniaxial Stress and Strain Cycling in Plasticity
Authors: Naghdi P. M. , Nikkel D. J.
Published: July 2009

Within the framework of an existing purely mechanical, rate-type theory of plasticity, detailed calculations are presented for certain types of material response during stress and strain cycling in a uniaxial homogeneous deformation. These features pertain specifically to material response in stress cycling between fixed values of stress in tension and compression (not necessarily equal in magnitude) resulting in ratcheting of strain, and a type of saturation hardening caused by strain cycling between any two fixed values of strain when the mean value of stress (in tension and compression) tends to zero.
Large Deflections of a Simply Supported Beam Subjected to Moment at One End
Authors: Seide P.
Published: July 2009

The large deflections of a simply supported beam, one end of which is free to move horizontally while the other is subjected to a moment, are investigated by means of inextensional elastica theory. The linear theory is found to be valid for relatively large angles of rotation of the loaded end. The beam becomes transitionally unstable, however, at a critical value of the bending moment parameter MIL/EI equal to 5.284. If the angle of rotation is controlled, the beam is found to become unstable when the rotation is 222.65 deg.
Torsional Shock Waves in a Viscoelastic Rod
Authors: Sugimoto N. , Yamane Y. , Kakutani T.
Published: July 2009

The propagation of torsional shock waves in a thin circular viscoelastic rod is investigated theoretically. An analysis is carried out based on the approximate equations previously derived. Two typical viscoelastic models are considered, which possess, respectively, the discrete and continuous relaxation spectrum. One is the usual Maxwell- Voigt model and the other is a new model whose relaxation function is given by a power law with weak singularity. The structures of steady shock profiles are presented and compared for both types. Finally a brief discussion is included on the simplified evolution equations for a far field transient behavior.
On Wave Modes With Zero Group Velocity in an Elastic Layer
Authors: Tassoulas J. L. , Akylas T. R.
Published: July 2009

A study is made of time-harmonic wave modes in an elastic layer in plane strain with traction-free surfaces. It is demonstrated that, at points of the Rayleigh-Lamb frequency spectrum where the group velocity vanishes, there exist nonseparable time-harmonic modes in which the amplitudes of the displacements vary linearly in the direction along the layer. These modes are used to explain the terrace-like structure of the free-vibration frequency spectrum of a circular disk.
Transient Stress Intensity Factors of an Interfacial Crack Between Two Dissimilar Anisotropic Half-Spaces, Part 2: Fully Anisotropic Materials
Authors: Kuo A.-Y.
Published: July 2009

Dynamic stress intensity factors for an interfacial crack between two dissimilar elastic, fully anisotropic media are studied. The mathematical problem is reduced to three coupled singular integral equations. Using Jacobi polynomials, solutions to the singular integral equations are obtained numerically. The orders of stress singularity and stress intensity factors of an interfacial crack in a (θ(1)/θ(2)) composite solid agree well with the finite element solutions.
A Hybrid/Finite Element Approach for Stress Analysis of Notched Anisotropic Materials
Authors: Gerhardt T. D.
Published: July 2009

A hybrid/finite element is proposed to calculate stresses or stress intensity factors at notches, fillets, cutouts, or other geometric discontinuities in plane-loaded anisotropic materials. Stress and displacement fields assumed in the element satisfy all governing elasticity equations. Furthermore, the shape and stress-free conditions of the discontinuity are modeled exactly using conformal mapping and analytic continuation. Continuity of analytic and finite element displacement fields on the remaining element boundary are enforced in an approximate manner with a variational principle. Numerical results are presented for both elliptical void and circular fillet hybrid elements. Comparisons are made to analytic solutions. Results indicate that structural models using a hybrid element with a coarse conventional element mesh yield efficient and accurate calculations of critical stresses.
A Variational Approach to the Dynamics of Structures Having Mixed or Discontinuous Boundary Conditions
Authors: Torvik P. J.
Published: July 2009

A procedure is developed whereby the steady-state forced response and the modes of free vibration for elastic systems having mixed or discontinuous boundary conditions can be determined. Approximate solutions are obtained as a superposition of a set of functions, each of which satisfies the field equations but not the boundary conditions. The coefficients of this expansion are obtained through applying a variational principle developed from Hamilton’s principle which for simple harmonic motion, is equivalent to Reissner’s principle. The reduction from the general elastic solid to the elastic plate is given, as are some results obtained for the first several natural frequencies of an elastic circular plate, free on a portion of the boundary and clamped on the remainder.
On the Role of a Compliant Surface in Long Squeeze Film Bearings
Authors: Buckholz R. H.
Published: July 2009

The problem of compliant surface journal bearings with large slenderness ratio (length/diameter → ∞) is analyzed for the case of small journal eccentricities. In this model an elastic circular cylinder has an axial length that is large compared to its diameter. The elastic cylinder is rubber, the inner rubber surface is wetted with a Newtonian lubricant, and the outer rubber surface is bound to a rigid surface. Immersed within the lubricant is a rigid circular journal. The journal is held fixed, and a translatory motion is assigned to the rigidly backed elastomer bearing. The resulting squeeze film is analyzed for near concentricity between the undeformed rubber surface and the rigid journal. The development of the model proceeds from the basic Navier displacement equations for a solid and the Stokes equations for the fluid. The special case of Poisson’s ratio going to 1/2 is used for the solid. The field equations are linear; a nonlinearity is a consequence of the boundary conditions. Discrete distributions of singularities are used to represent the coupled fluid and elastic deformation. Surface stress traction vectors are matched at the liquid-solid interface. Explicit expressions for changes of the fluid film gap due to rubber deformation, together with the associated change in fluid film pressure, are presented.
A Discussion of Alternative Duncan Formulations of the Eigenproblem for the Solution of Nonclassically, Viscously Damped Linear Systems
Authors: Brandon J. A.
Published: July 2009

An equivalent alternative formulation of the usual Duncan Method of solution of a system of general viscous damping is discussed. For the solution of systems this alternative statement of the problem is no better and is in fact potentially inferior to the standard method. A potentially important application however removes a significant limitation in the implementation of the local modification procedures of Weissenburger and Pomazal.
Oscillator Response to Nonstationary Excitation
Authors: Solomos G. P. , Spanos P-T. D.
Published: July 2009

Analytical solutions are presented regarding probability density distributions of various response parameters of a lightly damped oscillator. The oscillator is subjected to a broad-band stochastic excitation which possesses a time-variant power spectrum. The analytical solutions are derived by utilizing appropriate Fokker-Planck equations which govern Markovian approximations of the response parameters considered. The reliability of the approximate analytical solution is tested by using pertinent data generated by a digital Monte Carlo study.
Arbitrarily Oriented Cracks in a Reinforced Sheet
Authors: Chu C.-C.
Published: July 2009

The elastic interaction between a crack and a fiber is studied for various loading conditions. Generalized from earlier work by Greif and Sanders, the present formulation is valid for arbitrary relative orientation between the crack and the fiber. Helpful design information, such as the critical loading condition and the critical fiber orientation to trigger a certain failure mode, is therefore attainable. The fundamental solutions, each associated with proper parameters and proper boundary conditions, can also be superposed to model more realistic problems.
A Pathological Situation in Micropolar Elasticity
Authors: Lakes R. S.
Published: July 2009

The case of zero coupling number N in micropolar elasticity is considered. This situation has been examined by several investigators to simplify the analysis of micropolar materials. We show that the case of N = 0 is pathological and present a physical example.
Elastic Wave Scattering From an Interface Crack in a Layered Half Space
Authors: Yang H. J. , Bogy D. B.
Published: July 2009

Many applications in industry utilize a layered elastic structure in which a relatively thin layer of one material is bonded to a much thicker substrate. Often the fabrication process is imperfect and cracks occur at the interface. This paper is concerned with the plane strain, time-harmonic problem of a single elastic layer of one material on a half space of a different material with a single crack at the interface. Green’s functions for the uncracked medium are used with the appropriate form of Green’s integral theorem to derive the scattered field potentials for arbitrary incident fields in the cracked layered half space. These potentials are used in turn to reduce the problem to a system of singular integral equations for determining the gradients of the crack opening displacements in the scattered field. The integral equations are analyzed to determine the crack tip singularity, which is found, in general, to be oscillatory, as it is in the corresponding static problem of an interface crack. For many material combinations of interest, however, the crack tip singularity in the stress field is one-half power, as in the case of homogeneous materials. In the numerical work presented here attention is restricted to this class of composites and the integral equations are solved numerically to determine the Mode I and Mode II stress intensity factors as a function of a dimensionless wave number for various ratios of crack length to layer depth. The results are presented in graphical form and are compared with previously published analyses for the special cases where such results are available.
Temperature Field Due to a Moving Heat Source: A Moving Mesh Finite Element Analysis
Authors: Kuang Z.-B. , Atluri S. N.
Published: July 2009

The transient temperature field (as seen by a moving observer) due to a moving heat source, such as the process zone near a dynamically propagating crack tip or an external agent as in the case of welding, is analyzed by a moving-mesh finite element procedure. The effects of the temperature-dependent material properties, and of the loss of heat to the surrounding medium through convection and radiation, are studied. Situations under which conditions in the process zone may be labeled as “isothermal” or “adiabatic” are explored. Estimates of temperature rise near the tip of a crack propagating at realistic speeds in structural steels are made.
Effect of Inertia on Finite Near-Tip Deformation for Fast Mode-III Crack Growth
Authors: Achenbach J. D. , Nishimura N.
Published: July 2009

The combined effects of finite deformation and material inertia have been analyzed for fast crack growth under antiplane loading conditions. A steady-state dynamic solution has been obtained for the finite strain on the crack line, from the moving crack tip to the moving transition boundary with the zone of small strains. The crack propagates in a material with a response curve in uniform shear that is linear at small strains, and which remains constant once a critical strain has been exceeded. The corresponding quasi-static solution is given in the full zone of large deformation. For the dynamic formulation, an explicit expression for the crack-line strain has been obtained by expanding the displacement in a power series in the distance to the crack line, with coefficients that depend on the distance to the moving crack tip. Substitution in the equation of motion yields a nonlinear ordinary differential equation for the relevant coefficient, which can be solved rigorously. The finite deformation crack-line fields have been matched to appropriate small-strain fields at the transition boundary. The principal result is that the dynamic strain remains bounded at the crack tip, apparently due to the effect of material inertia. The crack-line strain has been plotted for several crack-tip speeds. It decreases with higher crack-tip speed. An explicit expression has been given for the extent of the zone of finite deformation, as a function of the crack tip speed and the far-field loading.
A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part 1: Development of Appropriate Equations
Authors: McDowell D. L.
Published: July 2009

A two surface stress space model is introduced with internal state variable repositories for fading memory of maximum plastic strain range and non-proportionality of loading. Evolution equations for isotropic hardening variables are prescribed as a function of these internal variables and accumulated plastic strain, and reflect dislocation interactions that occur in real materials. The hardening modulus is made a function of prior plastic deformation and the distance of the current stress point from the limit surface. The kinematic hardening rules of Mroz and Prager are used for the yield and limit surfaces, respectively. The structure of the model is capable of representing essential aspects of complex nonproportional deformation behavior, including direction of the plastic strain rate vector, memory of plastic strain range, cross-hardening effects, variation of hardening modulus, cyclic hardening or softening, cyclic racheting, and mean stress relaxation.
A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part 2: Comparison of Theory With Experiments
Authors: McDowell D. L.
Published: July 2009

For the two surface cyclic plasticity model introduced in Part 1, methods for determination of model parameters are described. The model is specialized to axial-torsional loading of a thin-walled tubular specimen, and applied to non-proportional, room-temperature cycling of type 304 stainless steel. Computer simulations for two complex histories show good general agreement with experimental data obtained by the author.
Asymptotic Solutions of the Von Karman Equations for a Circular Plate Under a Concentrated Load
Authors: Frakes J. P. , Simmonds J. G.
Published: July 2009

Reissner’s form of the axisymmetric von Karman equations for a centrally, point-loaded plate are written in dimensionless differential and integral form. To concentrate on essentials, we take Poisson’s ratio to be one-third (so that the limiting Fo¨ppl membrane equations have one-term solutions) and boundary conditions of simple support. A dimensionless parameter β measures the relative bending stiffness. A nine-term perturbation solution in powers of ε = β–6, the first term of which corresponds to linear plate theory, is constructured using MACSYMA. Although the resulting deflection-load power series appears to converge only if |ε| < 1/40, successive Aitken-Shanks’ transformations yield an expression valid up to ε ≈ 1. Solutions as β → 0 are constructed using singular perturbation methods and two terms of the deflection-load curve are computed numerically, the first term corresponding to the exact nonlinear membrane solution. A graph shows that there is a region of overlap of the large and small β-approximations to the deflection-load curve.
On the Theory of a Cosserat Point and Its Application to the Numerical Solution of Continuum Problems
Authors: Rubin M. B.
Published: July 2009

The theory of a Cosserat point is developed to describe motion of a body that is essentially a material point surrounded by some small volume. The development of this theory is motivated mainly by its applicability to the numerical solution of continuum problems. Attention is confined to the purely mechanical theory and nonlinear balance laws are proposed for Cosserat points with arbitrary constitutive properties. The linearized theory is developed and constitutive equations for an elastic material are discussed within the context of both the nonlinear and linear theories. Explicit constitutive equations for a linear-elastic isotropic Cosserat point are developed to model a parallelepiped composed of a linear-elastic homogeneous isotropic material.
Buckling of Truncated Conical Shells Under Combined Axial Load, Pressure, and Heating
Authors: Tani J.
Published: July 2009

On the basis of the Donnell-type shell equations with the effect of nonlinear prebuckling deformations taken into consideration, a theoretical analysis is performed on the buckling of clamped truncated conical shells under two loads combined out of uniform pressure, axial load, and uniform heating. The problem is solved by a finite difference method. It is found that the interaction curves of buckling loads are changed remarkably by the difference in the shape of conical shells. This is due to the large nonlinear prebuckling deformation and the difference in the buckling mode between two cases of single load.
Formulation of Equations of Motion for Systems Subject to Constraints
Authors: Wampler C. , Buffinton K. , Shu-hui J.
Published: July 2009

A method for constructing equations of motion governing constrained systems is presented. The method, which is particularly useful when equations of motion have already been formulated, and new equations of motion, reflecting the presence of additional constraints are needed, allow the new equations to be written as a recombination of terms comprising the original equations. An explicit form in which the new dynamical equations may be cast for the purpose of numerical integration is developed, along with special cases that demonstrate how the procedure may be simplified in two commonly occurring situations. An illustrative example from the field of robotics is presented, and several areas of application are identified.
An Experimental Study of the Reflection and Transmission of Flexural Waves at Discontinuities
Authors: Doyle J. F. , Kamle S.
Published: July 2009

The research reported is the study of the transmission and reflection characteristics of flexural waves at structural discontinuities. A Fast Fourier Transform (FFT) computer algorithm is used to characterize the dispersive flexural waves. The incident wave is propagated through two types of discontinuities namely, a stepped beam and the free end of a beam. At each stage, comparison with experimental results are made.
VLFEM Analysis of a Two-Dimensional Cochlear Model
Authors: Miller C. E.
Published: July 2009

A hybrid technique named here the Very Large Finite Element Method (VLFEM) is developed to analyze a two-dimensional model of the cochlea of the inner ear. In this method, the domain is divided into elements of constant material properties and the exact solution to the model equations obtained in each element. This involves two forms of eigenexpansion, allowing a one-dimensional instead of two-dimensional discretization. The discretization is related to the rate of change of the wavenumber of traveling waves on the elastic partition, producing an optimal mesh spacing. A full characterization of the multiple complex wavenumbers is obtained. The results of this analysis for partition (basilar membrane) amplitude and phase exactly correspond to those from previous finite difference and finite element analyses, but less computing effort is required for the same accuracy of results. Reflected waves, abrupt changes in material properties, and arbitrary boundary conditions pose no difficulties for VLFEM analysis, an advantage over the WKB (or LG) technique used previously on this problem.
The Effect of Inertia in Lubrication Flow Including Entrance and Initial Conditions
Authors: Tichy J. A. , Bourgin P.
Published: July 2009

This study is concerned with the influence of fluid inertia in thin film steady or transient laminar flows, emphasizing the role of initial conditions and inlet boundary conditions. Most existing studies implicitly omit these effects due to the method of formulation or the type of problem studied. In the present study, linearization for the convective inertia terms is used to transform the problem to a coordinate system which results in a simple diffusion equation. Closed-form solutions are obtained, considering initial or entrance conditions in the classical manner. Predictions are tested against cases for which solutions exist in the literature and against a numerical solution and excellent agreement is found. For simple squeeze films, large discrepancies from lubrication theory are found at short times following the start-up, or at moderate Reynolds numbers. In the steady flow case, fluid is assumed to enter the bearing with a slug flow profile. The inlet pressure is determined by coupling the bearing flow with the upstream inviscid flow. Large discrepancies from lubrication theory are found at Reynolds numbers where the lubrication theory was previously thought to be satisfactory. The load may increase or decrease, depending on the upstream conditions.
Cavitation Boundary Shapes for Submerged Short Journal Bearings Using Newtonian Lubricants
Authors: Buckholz R. H.
Published: July 2009

Cavitation boundary shapes for submerged short journal bearings are investigated in this study. In this analysis, the Reynolds lubrication equation is approximated by using the bearing slenderness ratio as a small parameter. The slenderness ratio appears explicitly in the Reynolds lubrication equation. The lubrication equation is solved subjected to the boundary condition of a subambient value for the cavitation pressure and the additional Reynolds’ free-surface boundary condition along the unknown cavitation boundary. The Ocvirk short bearing solution is shown to fail near the leading edge of the cavitation region, and a matched asymptotic theory is used to determine the shape and location of this cavitated region. Cavitation bubble location and size are shown to depend on bearing aspect ratio, journal eccentricity, and cavitation pressure. Finally the present journal bearing analysis is limited to those cases where the cavitation region has a large axial extent.
Asynchronous Instability of a Rotating Centrifuge Partially Filled With Fluid
Authors: Cheng C. A. , Berman A. S. , Lundgren T. S.
Published: July 2009

An experimental investigation of the asynchronous whirl motion of a partially filled rotating centrifuge on an elastic support system has been performed. Whirl runout amplitudes are measured and the data are used to deduce the stability boundaries of the asynchronous whirl. The effects of various parameters on the stability boundaries are studied systematically. These parameters are the fill ratio, mass ratio, Reynolds number, and the damping of the elastic support system. The experimental results are compared with theoretical predictions based on a linear analysis. Free surface shapes are compared with results of nonlinear analysis.
Short Subsurface Cracks Under Conditions of Slip and Stick Caused by a Moving Compressive Load
Authors: Sheppard S. , Barber J. R. , Comninou M.
Published: July 2009

The mechanism of spalling failure in rolling contact is modeled by an elastic half-plane with a subsurface crack parallel to the surface, loaded by a compressive normal force which moves over the surface. Coulomb friction at the crack faces reduces the Mode II Stress Intensity Factors and results in a number of history-dependent slip-stick configurations. The formulation used to study these involves a singular integral equation in two variables which must be solved numerically, and because of the history dependence, requires in an incremental solution. Only crack lengths and coefficients of friction that result in a maximum of two slip or stick zones for any load location are considered in this paper. It is found that the maximum range of stress intensity factors occurs at the trailing crack tip.
Continuous Damage Mechanics Revisited: Basic Concepts and Definitions
Authors: Krajcinovic D.
Published: July 2009

The paper proposes a geometrically consistent representation for the set of internal variables defining an arbitrary distribution of flat, planar microcracks. A special averaging procedure in conjunction with a characteristic length leads to an experimentally identifiable measure or damage. The model makes an essential distinction between the active and passive microcrack systems. The progressive deterioration of the material is modeled by a combination of nucleation (activation of new systems) and continued growth or cracks in already active systems.
A New Endochronic Approach to Computational Elastoplasticity: Example of a Cyclically Loaded Cracked Plate
Authors: Watanabe O. , Atluri S. N.
Published: July 2009

In this paper, a methodology for finite-element elastoplastic analyses of structures subjected to cyclic loading, based on a new form of endochronic (internal time) plasticity theory, is presented. In the present version of the endochronic theory, the rate forms of the stress/strain relations (stated here explicitly for plane stress, plane strain, and three-dimensional cases) are entirely analogous to those of the classical (isotropic or kinematic hardening) plasticity theory and, thus, are no more difficult or expensive to implement in computational algorithms. The problem of a double-edge-cracked panel, subjected to monotonic loading as well as to zero-to-tension or tension-compression cyclic external loading, is analyzed. The elastoplastic stress/strain fields at the root of the notch, for each of these loading conditions, are studied in detail. These results are compared and contrasted with those presented recently by Valanis and Fan, and the noted discrepancies are discussed. This paper is limited to considerations of small strains and small displacements only.
The Plastic Spin
Authors: Dafalias Y. F.
Published: July 2009

A macroscopic formulation of large deformations elastoplasticity with tensorial structure variables is presented. The novel features are the effect of constitutive relations for the plastic spin and, to a lesser degree of importance, of elastically embedding the structure variables. The plastic spin constitutive relations are obtained for different kinds of initial and induced anisotropies on the basis of the representation theorems for isotropic second-order antisymmetric tensor-valued functions, and their role is illustrated by the analysis of several examples at large homogeneous deformations. In particular the analysis of simple shear with nonlinear kinematic hardening of the evanescent memory type provides, on the basis of the second Liapunov method for stability, conditions on the material constants for the occurrence or not of stress oscillations with monotonically increasing shear strain.