bluuebunny/crossref_metadata_2025 huggingface dataset:
A Similarity Solution for Flow in a Narrow Channel of Varying Gap
Authors: Tichy J. A. , Bourgin P.
Published: July 2009

A similarity solution may be obtained for the case of a narrow channel where the gap h varies, according to (a + bx)m. The lower surface may slide in either direction and there may be suction or injection at either surface which must vary as h−1. Asymptotic solutions are found for large and small values of a modified Reynolds number which is based on the sliding velocity or the suction/injection rate. Boundary layer behavior may be exhibited at high Reynolds number. The present solution, being “exact” for all Reynolds numbers once the thin film assumptions have been invoked, may be of value to hydrodynamic lubrication workers to test approximations for the fluid inertia effect.
An Acoustoelastic Theory for Surface Waves in Anisotropic Media
Authors: Mase G. Thomas , Johnson G. C.
Published: July 2009

A theory for surface waves in an anisotropic material is developed in the framework of acoustoelasticity in which the material’s strain energy density is taken to be a cubic function in the strain. In order to relate the surface wave speeds to the applied stress, a configuration is introduced in which the effect of the local rotation is removed. The development shows that the surface wave speed can be determined from the eigenvalues of a particular real symmetric 2×2 matrix. Numerical results are given for uniaxial loading applied to aluminum and copper single crystals and to an ideal transversely isotropic aggregate of aluminum.
On the Initiation of Necking Modes in Layered Plastic Solids
Authors: Steif P. S.
Published: July 2009

The deformation of a solid consisting of alternating material layers with interface undulations is studied analytically. We assess the relative rate of growth or decay of these interface imperfections with straining. The analysis is based on a regular perturbation expansion of the finite strain, nonlinear field equations, the small parameter being the amplitude of the undulations relative to the layer thickness. Attention is focused on the influence of material and geometric parameters on imperfection growth-rates. It is found that significant connections exist between the growth of imperfections and the tendency for undulatory bifurcation modes to emerge from a perfect, layered solid.
Crushing of an Elastic-Perfectly Plastic Ring or Tube Between Two Planes
Authors: Wang C. Y.
Published: July 2009

A thin ring is crushed between two rigid planes. Due to plastic deformation the ring does not recover its original shape when the compression is removed. For an elastic-perfectly plastic flexural material, the ring undergoes two to five different stages. The mathematical problem is formulated and solved by exact numerical integration and accurate analytical approximations.
Initial Postbuckling Behavior of Imperfect, Antisymmetric Cross-Ply Cylindrical Shells Under Torsion
Authors: Hui David , Du I. H. Y.
Published: July 2009

This paper deals with the initial postbuckling of antisymmetric cross-ply closed cylindrical shells under torsion. Under the assumptions employed in Koiter’s theory of elastic stability, the structure is imperfection-sensitive in certain intermediate ranges of the reduced-Batdorf parameter (approx. 4 ≤ ZH ≤ 20.0). Due to different material bending-stretching coupling behavior, the (0 deg inside, 90 deg outside) two-layer clamped cylinder is less imperfection sensitive than the (90 deg inside, 0 deg outside) configuration. The increase in torsional buckling load due to a higher value of Young’s moduli ratio is not necessarily accompanied by a higher degree of imperfection-sensitivity. The paper is the first to consider imperfection shape to be identical to the torsional buckling mode and presents concise parameter variations involving the reduced-Batdorf paramter and Young’s moduli ratio.
Turbulent Boundary Layers With Mass Transfer by the Dorodnitsyn Finite Element Method
Authors: Fletcher C. A. J. , Fleet R. W.
Published: July 2009

The Dorodnitsyn finite element formulation is extended to cover incompressible, two-dimensional turbulent boundary layers with surface mass transfer in the normal direction. The method is shown to give accurate and economical answers with only eleven points spanning the boundary layer. Good agreement is obtained when the computational solutions are compared with the experimental results of McQuaid [13] for skin friction coefficient, displacement and momentum thickness and velocity profiles. Zero and adverse pressure gradient and discontinuous injection cases have been considered.
Frequency Response of a Nonlinear Pneumatic System
Authors: Wang Ying-Tsai , Singh Rajendra
Published: July 2009

This paper studies the dynamic behavior of a pneumatic chamber connected to a reservoir through an orifice and to a linear mechanical system. In this paper, we focus our attention mainly on the nonlinearity associated with mass flow rate through the orifice and its effect on the overall system behavior. Nonlinearities induced by the friction and gas compressibility are also considered. Using the method of harmonic balance, we reduce a difficult mathematical formulation of this nonlinear pneumatic system to a simple nonlinear governing equation and a set of algebraic equations which yield frequency response easily at the first, second, and third harmonics. An excellent agreement between the method of harmonic balance and numerical integration has been found. Results obtained using a quasi-linear model are also given.
Balance Laws and Constitutive Relations for Plane Flows of a Dense, Binary Mixture of Smooth, Nearly Elastic, Circular Disks
Authors: Jenkins J. T. , Mancini F.
Published: July 2009

We derive balance laws and constitutive relations for plane flows of a dense, binary mixture of smooth, nearly elastic, circular disks. The disks may differ in size and mass and in the coefficients of restitution characterizing the energy lost in collisions between like and unlike pairs. We focus attention on those parts of the fluxes and sources of momentum and energy that are due to collisions. To calculate them, we suppose that the complete pair distribution function for two colliding disks is the product of Maxwellian velocity distributions for each disk and a factor that incorporates the effects of excluded area and collisional shielding. In an Appendix we provide constitutive relations calculated in a similar way for a dense, binary mixture of smooth, nearly elastic, spheres.
The Modified Mixture Theory for Fluid-Filled Porous Materials: Theory
Authors: Katsube N. , Carroll M. M.
Published: July 2009

The mixture theory by Green and Naghdi is modified and applied to the problems of flow-through porous materials. By introducing porosity, we make clear that two constituents occupying the same point in the original mixture theory are an equivalent homogeneous solid and an equivalent homogeneous fluid which, respectively, represent a porous solid and a porous fluid in the actual sample. The micro-mechanical response studied by Carroll and Katsube is introduced and detailed deformation and flow mechanisms are provided at each point of the mixture. The resulting theory is compared with Biot’s theory and in fact reduces to Biot’s theory when the fluid velocity gradient terms are ignored.
Asymptotic Analysis of a Mode I Crack Propagating Steadily in a Deformation Theory Material
Authors: Ponte Castan˜eda P.
Published: July 2009

The near-tip asymptotic stress and deformation fields of a crack propagating steadily and quasi-statically into an elastic-plastic material are presented. The material is characterised by J2-deformation theory, suitably modified to account for unloading and reloading, together with linear strain-hardening. The cases of plane strain and plane stress Mode I are considered. The governing equations are integrated analytically with the assistance of Muskhelishvili’s complex variable formulation. The boundary and continuity conditions then lead to a set of nonlinear algebraic equations in the coefficients of the stress functions to be solved numerically. Explicit results are given for the strength of the singularity, and for the distribution of stress in the plastic loading, elastic unloading, and plastic reloading regions, as functions of the strain-hardening parameter.
A Semi-Infinite Crack Partially Penetrating a Circular Inclusion
Authors: Steif P. S.
Published: July 2009

When a crack is lodged in an inclusion, differences between the moduli of the inclusion and the bulk material can cause the near-tip stress intensity factor to be greater or less than that prevailing in a homogeneous body. To study the influence of such moduli differences, we solve the problem of a semi-infinite crack half-way penetrating a circular inclusion. The field equations are automatically satisfied by choosing appropriate series expansions for the complex stress potentials; a doubly-infinite system of linear algebraic equations for the series coefficients then enforces continuity of traction and displacement at the inclusion boundary. Results for the reduction (or enhancement) of the stress intensity factor are given for the entire range of material parameters.
An Evaluation of Recent Developments in Hardening and Flow Rules for Rate-Independent, Nonproportional Cyclic Plasticity
Authors: McDowell D. L.
Published: July 2009

The Mroz kinematic hardening rule has previously demonstrated superior capability to correlate cyclically stable nonproportional stress-strain response. In this paper, recently proposed kinematic hardening rules for single and multiple surface cyclic plasticity models are evaluated. Significant improvement over the Mroz rule, without loss of generality, is achieved with a deviatoric stress rate-dominated rule proposed by Tseng and Lee for two surface theory. Recent approaches for correlation of the modulus function and isotropic hardening are discussed. The norm of the Mroz distance vector is found to uniquely correlate the variation of plastic hardening modulus through a cycle; it is necessary to include a measure of instantaneous nonproportionality, however, to properly normalize the modulus function. A new evolution equation is offered to correlate the additional isotropic hardening observed during nonproportional loading, and several contemporary approaches are also considered.
A Boundary Element Analysis of Metal Extrusion Processes
Authors: Chandra A. , Mukherjee S.
Published: July 2009

The subject of this paper is an analysis of metal extrusion processes by the boundary element method (BEM). It is demonstrated here that the BEM can be used to analyze, efficiently and accurately, this complicated class of problems including both material and geometrical nonlinearities. Numerical results for sample problems of plane extrusion of aluminum bars, obtained by the BEM, are presented and discussed in this paper. The BEM results are compared against FEM results for the same sample problems. The FEM results were reported by the authors in a previous publication.
The Normal Impact of an Elastic Rod-Mass System on a Viscoelastic Half Space
Authors: Downey H. A. , Bogy D. B.
Published: July 2009

The normal impact of a one-dimensional elastic rod, with a lumped mass on the trailing end, onto a viscoelastic half space is considered and the problem is solved for the time dependent interface stress and displacement. The problem is reduced to an integral equation, whose two-part kernel consists of solutions of two simpler problems. One part pertains to the half space only and the other is for the rod-mass system. The half-space portion of the kernel is obtained through a numerical inversion of the Laplace transformed solution. Given the half-space kernel contribution, which depends only on the two viscoelastic parameters and Poisson’s ratio, the integral equation is solved numerically for two families of half space materials. The viscoelastic effects on the half space are quite pronounced. Certain combinations of the parameters cause a large hysteresis in the impact, and softer half spaces require longer contact times before the rod leaves the surface.
Impact on Ceramic Targets
Authors: Mayseless M. , Goldsmith W. , Virostek S. P. , Finnegan S. A.
Published: July 2009

A series of approximately 150 tests were conducted on ceramic targets struck by cylindro-conical hard-steel projectiles at normal incidence up to velocities of about 1000 m/s. The primary objective was the determination of the effect of layering and the delineation of the ballistic limit of various combinations. In addition, a study of the erosive effect of the ceramic was executed. It was found that, on the basis of areal density, metal plates prefaced by ceramic materials are ballistically more inefficient than purely metallic targets in the low velocity range, while the reverse was found at speeds above 250 m/s. The eroded length was found to be related to the velocity of the projectile and the thickness of the ceramic layer. The projectile displacement data were found to be in very good accord with the results obtained from a previously utilized analytic force history taking into account the erosion process. The energy required to erode the projectile was found to be several orders of magnitude greater than that consumed in the fracture process of the frontal ceramic plate.
Plastic Stress Intensity Factors in Steady Crack Growth
Authors: Ponte Castan˜eda P.
Published: July 2009

The asymptotic stress and deformation fields of a crack propagating steadily and quasi-statically into an elastic-plastic material, characterized by J2-flow theory with linear strain-hardening, were first determined by Amazigo and Hutchinson (1977) for the cases of mode III and mode I (plane strain and plane stress). Their solutions were approximate in that they neglected the possibility of plastic reloading on the crack faces. This effect was taken into account by Ponte Castan˜eda (1987b), who also introduced a new formulation for the (eigenvalue) problem in terms of a system of first order O.D.E.’s in the angular variations of the stress and velocity components. The strength of the power-type singularity, serving as the eigenvalue, and the angular variations of the field were determined as functions of the hardening parameter. The above analysis, however, does not determine the amplitude factor of these near-tip asymptotic fields, or plastic stress intensity factor. In this work, a simple, approximate technique based on direct application of a variational statement of compatibility is developed under the assumption of small scale yielding. A trial function for the stress function of the problem, that makes use of the asymptotic information in the near-tip and far-field limits, is postulated. Such a trial function depends on arbitrary parameters that measure the intensity of the near-tip fields and other global properties of the solution. Application of the variational statement then yields optimal values for these parameters, and in particular determines the plastic stress intensity factor, thus completing the knowledge of the near-tip asymptotic fields. The results obtained by this novel method are compared to available finite element results.
Response Bounds for Linear Underdamped Systems
Authors: Yae K. H. , Inman D. J.
Published: July 2009

This paper examines simple bounds on the displacement response of linear oscillatory multiple degree of freeodm systems. Both the free and steady state forced responses are considered. The effect of mode coupling due to viscous damping is examined. The bounds are derived and stated in terms of the physical parameters of the structure and its inputs. Simple examples are given to illustrate the bounds and to compare the bounds developed here with previously published results.
Nonstationary Response Analysis of a Duffing Oscillator by the Wiener-Hermite Expansion Method
Authors: Orabi I. I. , Ahmadi G.
Published: July 2009

The Wiener-Hermite functional series expansion method is used to analyze the nonstationary response of a Duffing oscillator under random excitations. The formal procedure for the derivation of the deterministic equations governing the Wiener-Hermite kernel functions is described. The first three terms in the series are retained. The nonstationary response of a damped Duffing oscillator subjected to a modulated white noise is studied. For several values of nonlinearity strength and different damping coefficients the nonstationary mean-square responses are obtained. The results are compared with those found by a single-term expansion and other methods. It is shown that mean-square responses obtained by the three-term expansion agree with the exact stationary variances and the simulation results.
Rayleigh-Lamb Waves in an Elastic Plate With Voids
Authors: Chandrasekharaiah D. S.
Published: July 2009

Rayleigh-Lamb waves in a homogeneous and isotropic linear elastic plate containing a distribution of vacuous pores (voids) are studied. Assuming that the plate is of uniform thickness and that its faces are stress-free, it is found that the waves move, in general, in two uncoupled families, of which one is symmetrical with respect to the midplane of the plate and the other antisymmetrical; each of these families is affected by the presence of voids. If the plate is thin and the frequency is small, the voids influence only the symmetric waves and, because of this influence, the waves propagate slower than their classical counterparts. If the plate thickness and the frequency are large, each of the two families degenerates into two uncoupled waves; one of these is a classical Rayleigh wave and the other is a new wave not encountered in the classical theory.
An Elastic-Viscoplastic Model for Metals Subjected to High Compression
Authors: Rubin M. B.
Published: July 2009

Specific constitutive equations are proposed for a material exhibiting isotropic-elastic response in its reference configuration, strain-rate, temperature and density dependent plastic flow with isotropic and directional hardening, and thermal recovery of hardening. The shear modulus is temperature and density dependent and it vanishes when the temperature reaches the density dependent melting temperature. These equations include modifications, relative to those proposed by Rubin (1986), which are appropriate to describe metals subjected to high compression. The constitutive functions characterizing pressure are determined by comparison with a Mie-Gru¨neisen equation of state which includes functions that are obtained from common shock-wave experiments. To examine some of the features of these equations at high compression we consider an example of homogeneous uniaxial strain and show that the deviatoric stress may be quite large at ultra high compression rates and high compression.
The Effect of Shear Deformation on Post-Buckling Behavior of Laminated Beams
Authors: Sheinman I. , Adan M.
Published: July 2009

A geometrical nonlinear theory of composite laminated beams is derived with the effect of transverse shear deformation taken into account. The theory is based on a high-order kinematic model, with the nonlinear differential equations solved by Newton’s method and a special finite-difference scheme. A parametric study of the shear effect involving several kinematic approaches was carried out for isotropic and anisotropic beams.
Calculation of Damping Matrices for Linearly Viscoelastic Structures
Authors: Segalman D. J.
Published: July 2009

A technique is presented for the systematic calculation of “damping” and “stiffness” matrices to represent the linearly viscoelastic properties of structures. The technique generates explicit expressions for these matrices in terms of the measurable viscoelastic properties of the components of the structure.
Analysis of Pipe Bends With Symmetrical Noncircular Cross Sections
Authors: Whatham J. F.
Published: July 2009

A thin shell analysis is presented for pipe bends with symmetric noncircular cross sections under in-plane bending or internal pressure, using the static-geometric analogy and neglecting end effects. Any symmetric shape is possible but the analysis mainly concerns cross sections with double symmetry; an investigation of two-lobe (oval) and four-lobe cross sections demonstrates that pipe bend flexibility is almost inversely proportional to flank radius if the pipe wall is thin. Pressurizing a pipe bend of oval cross section produces a similar hoop stress distribution to that of a bending moment straightening the pipe.
Nearly Circular Connections of Elastic Half Spaces
Authors: Gao Huajian , Rice James R.
Published: July 2009

In this paper we solve the elasticity problem of two elastic half spaces that are joined together over a region that does not differ much from a circle, i.e., the problem of an external planar crack leaving a nearly circular uncracked connection. The method we use is based on the perturbation technique developed by Rice (1985) for solving the elastic field of a crack whose front deviates slightly from some reference geometry. Quantities such as crack opening displacement and stress intensity factor are derived in detail to the first order of accuracy in the deviation of the shape of the connection from a circle. In addition, some results such as the crack face weight functions and Green’s functions for a perfectly circular connection are also discussed under various boundary conditions at infinity. The formulae derived are used to study the configurational stability problem for quasistatic growth of an external circular crack. The results, derived when the crack front is perturbed from circular in a harmonic wave form and is subjected to axisymmetric loading, suggest that a perturbation of wavenumber higher than one is configurationally stable under all boundary conditions at infinity. The perturbation with wavenumber equal to one, which corresponds to a translational shift of the geometric center of the circular connection, turns out to be configurationally stable if any rotation in the remote field is suppressed and configurationally unstable if there is no such restraint.
The Dynamic Energy Release Rate for a Steadily Propagating Antiplane Shear Crack in a Linearly Viscoelastic Body
Authors: Walton J. R.
Published: July 2009

The steady-state propagation of a semi-infinite, antiplane shear crack is reconsidered for a general, infinite, homogeneous and isotropic linearly viscoelastic body. As with an earlier study, the inertial term in the equation of motion is retained and the shear modulus is only assumed to be positive, continuous, decreasing, and convex. A Barenblatt type failure zone is introduced in order to cancel the singular stress, and a numerically convenient expression for the dynamic Energy Release Rate (ERR) is derived for a rather general class of crack face loadings. The ERR is shown to have a complicated dependence on crack speed and material properties with significant qualitative differences between viscoelastic and elastic material. The results are illustrated with numerical calculations for both power-law material and a standard linear solid.
Eigenproperties of Nonclassically Damped Primary Structure and Oscillator Systems
Authors: Suarez L. E. , Singh M. P.
Published: July 2009

The calculation of the combined eigenproperties of a nonclassically damped structure and a supported equipment is of practical interest. Herein an approach is developed whereby these properties can be obtained, in terms of the eigenproperties of the structure and equipment, without a conventional eigenvalue analysis of the combined system. The eigenvalues are obtained as the solutions of a nonlinear characteristic equation, easily solvable by a simple Newton-Raphson scheme. Once the eigenvalues are known, the corresponding eigenvectors can be obtained from closed-form expressions. The approach can also be used effectively to obtain exact eigenproperties for very light as well as very heavy equipment supported on structures.
Recursive Simulation of Stationary Multivariate Random Processes—Part I
Authors: Mignolet M. P. , Spanos P. D.
Published: July 2009

A unified approach is presented in determining autoregressive moving average (ARMA) algorithms for simulating realizations of multivariate random processes with a specified (target) spectral matrix. The ARMA algorithms are derived by relying on a prior autoregressive (AR) approximation of the target matrix. Several AR to ARMA procedures are formulated by minimizing a frequency domain error. Equations which can lead to a convenient computation of the ARMA matrix coefficients for a particular problem are given. Finally, the features of the various procedures are critically assessed.
Recursive Simulation of Stationary Multivariate Random Processes—Part II
Authors: Spanos P. D. , Mignolet M. P.
Published: July 2009

Stability and invertibility aspects of the AR to ARMA procedures developed in Part I in connection with simulation of multivariate random processes are addressed. A general criterion is proved for this purpose. Furthermore, several properties regarding the matching of the correlations at various time lags of the target and the simulated processes are shown. Finally, the reliability and efficiency of the discussed procedures are demonstrated by application to spectra encountered in earthquake engineering, offshore engineering, and wind engineering.
Characteristics of Numerical Simulations of Chaotic Systems
Authors: Tongue B. H.
Published: July 2009

A generalized form of Duffing’s Equation is examined in order to gain insight into the characteristics and properties of chaotic motion. It is shown that variations in the forcing function parameters as well as variations in the system’s initial conditions can lead to a chaotic response. The incidence of chaos is presented in the form of chaos maps and the structure of these maps is discussed. The influence of linear spring force on these maps is also examined. Finally, it is shown that an improper choice of time step can cause spurious results with regard to the existence of chaotic motion.
Sufficient Symmetry Conditions for Isotropy of the Elastic Moduli Tensor
Authors: Christensen R. M.
Published: July 2009

Symmetry conditions are found that assure isotropy of the fourth rank tensor of elastic moduli. Crystallography provides the answer to this problem in the two-dimensional context, namely one axis of three-fold symmetry assures the isotropy of properties in the plane normal to the axis. The present work provides the answer in the three-dimensional problem: 6 axes of five-fold symmetry are sufficient to give isotropy of the elastic moduli. An important restriction must accompany the present result. The derivation is given in the special form appropriate to low density materials which have a microstructure that transmits load according to the axial deformation of a space network of material distributed into micro-struts. The corresponding fiber composite idealization is that of a fiber dominated system, it therefore follows that if the fibers take the 6 specific orientations in three-space then isotropy is obtained.
Poroelastic Solution of a Plane Strain Point Displacement Discontinuity
Authors: Detournay E. , Cheng A. H-D.
Published: July 2009

The plane strain fundamental solution of an instantaneous and a continuous point displacement discontinuity is presented in this paper. These solutions, together with the one of a fluid source, are obtained on the basis of a decomposition technique proposed by Biot, which separates the displacement field into a time independent part satisfying an elasticity equation, and an irrotational part governed by a diffusion equation. We begin the derivation by presenting a continuous edge dislocation. The continuous point displacement discontinuity is obtained by differentiating, along the direction of the cut, the corresponding edge dislocation solution. The instantaneous influence functions are determined by further differentiating with respect to time. The displacement discontinuity and source singularities can be distributed on a crack surface to create displacement and flux jumps required for the numerical modeling of a fracture in a poroelastic medium.
Wave Propagation Through Fluid Saturated Porous Rocks
Authors: Walton K. , Digby P. J.
Published: July 2009

A sedimentary rock is modeled by a random packing of identical spherical particles. The connected pore space is filled with an inviscid, compressible fluid. A low-frequency expansion technique is used to calculate the effective wave speeds explicitly in terms of the microstructural properties of the rock considered. The effect of both the pore fluid and the initial confining pressure to which the rock is subjected can be included in the calculations.
Thermal Conditions for Inhibition of Stress Induced Slip in Zinc-Blende Crystals in Czochralski Growth Configuration
Authors: Motakef S.
Published: July 2009

The methodology for calculation of thermal conditions required for control of thermal stresses at below the plasticity limit during Czochralski growth of crystals with the zinc-blende structure is developed, and quantitative results are obtained for GaAs as the model crystal.
A Finite Element Study of Stable Crack Growth Under Plane Stress Conditions: Part II—Influence of Hardening
Authors: Narasimhan R. , Rosakis A. J. , Hall J. F.
Published: July 2009

A detailed finite element analysis is performed to model quasi-static crack growth under plane stress, small-scale yielding conditions in elastic-plastic materials characterized by isotropic power law hardening and the Huber-Von Mises yield surface. A nodal release procedure is used to simulate crack extension. Results pertaining to the influence of hardening on the extent of active yielding and the near-tip stress and deformation fields are presented. Clear evidence of an elastic unloading wake following the active plastic zone is found, but no secondary (plastic) reloading along the crack flank is numerically observed for any level of hardening. A ductile crack growth criterion based on the attainment of a critical crack opening displacement at a small microstructural distance behind the tip, is employed to investigate the nature of the J resistance curves under plane stress. In addition, the same criterion is employed to investigate the influence of hardening on the potential for stable crack growth under plane stress. It is found that predictions based on a perfectly plastic model may be unconservative in this respect, which is qualitatively similar to the conclusions reached in antiplane shear and Mode I plane strain.
Treatment of Body Forces in 2D Elastostatic BEM Using Particular Integrals
Authors: Pape D. A. , Banerjee P. K.
Published: July 2009

A new set of direct and indirect boundary element formulations for two-dimensional elastostatics have been developed. These new formulations differ from currently popular formulations in the treatment of body forces. The method of particular integrals is used resulting in a formulation which requires neither volume nor surface integration to solve the most general body force problem. This formulation is implemented in both direct and indirect boundary element methods using quadratic isoparametric elements. The efficiency and accuracy of this formulation for these two methods are compared for a range of problems. Finally, a multi-region problem with complicated geometry is run in order to show the complete generality of the particular integral method.
Closed-Form Analysis for Elastic Deformations of Multilayered Strands
Authors: Kumar K. , Cochran J. E.
Published: July 2009

Closed-form solutions are developed for elastic deformation characteristics of multilayered strands under tensile and torsional loads. These analytical results are successfully applied to obtain expressions for the effective extensional and torsional moduli of rigidity for the strands. Finally, a simple design criterion is established for “nonrotating” cables.
Identification of Nonlinear Vibrating Structures: Part I—Formulation
Authors: Masri S. F. , Miller R. K. , Saud A. F. , Caughey T. K.
Published: July 2009

A self-starting multistage, time-domain procedure is presented for the identification of nonlinear, multi-degree-of-freedom systems undergoing free oscillations or subjected to arbitrary direct force excitations and/or nonuniform support motions. Recursive least-squares parameter estimation methods combined with non-parametric identification techniques are used to represent, with sufficient accuracy, the identified system in a form that allows the convenient prediction of its transient response under excitations that differ from the test signals. The utility of this procedure is demonstrated in a companion paper.
Identification of Nonlinear Vibrating Structures: Part II—Applications
Authors: Masri S. F. , Miller R. K. , Saud A. F. , Caughey T. K.
Published: July 2009

A time-domain procedure for the identification of nonlinear vibrating structures, presented in a companion paper, is applied to a “calibration” problem which incorporates realistic test situations and nonlinear structural characteristics widely encountered in the applied mechanics field. The “data” set is analyzed to develop suitable, approximate nonlinear system representations. Subsequently, a “validation” test is conducted to demonstrate the range of validity of the method under discussion. It is shown that the procedure furnishes a convenient means for constructing reduced-order nonlinear nonparametric mathematical models of reasonably high fidelity in regard to reproducing the response of the test article under dynamic loads that differ from the identification test loads.
Mechanics of a Free-Surface Liquid Film Flow
Authors: Aidun Cyrus K.
Published: July 2009

The mechanics of a free surface viscous liquid curtain flowing steadily between two vertical guide wires under the influence of gravity is investigated. The Navier-Stokes equation is integrated over the film thickness and an integro-differential equation is derived for the average film velocity. An approximate nonlinear differential equation, attributed to G. I. Taylor, is obtained by neglecting the higher order terms. An analytical solution is obtained for a similar equation which neglects the surface tension effects and the results are compared with the experimental measurements of Brown (1961).
Scattering by Multiple Crack Configurations
Authors: Zhang Ch. , Achenbach J. D.
Published: July 2009

A system of boundary integral equations is presented which governs the crack-opening displacements for two-crack configurations. The integral equations are highly singular and they cannot be solved directly by numerical methods. By the approach of this paper the higher order singularities are, however, reduced to integrable singularities, and the integral equations are subsequently discretized and solved numerically. For several configurations numerical results have been obtained for scattered fields and for elastodynamic stress intensity factors. The scattered-field results are interpreted to apply for a partially closed crack as well as for two separate but neighboring cracks. The stress-intensity factors are intended to apply only to the case of separate cracks. The scattered-field results have relevance to the problem of detection and characterization of cracks in the field of quantitative nondestructive evaluation.
On the Validity of Saint Venant’s Principle in Finite Strain Plasticity
Authors: Durban D. , Stronge W. J.
Published: July 2009

Diffusion of effects from a local disturbance in a homogeneous stress field is analyzed within the framework of continuum plasticity. An axial rate of decay for the variability of the effects of a nonuniform disturbance imposed on one end of a long circular cylinder is determined as a function of the axial stress (or stretch). The analysis considers constitutive equations corresponding to incompressible, finite strain versions of J2 flow and deformation theories. Both theories result in effects that oscillate and decay exponentially with distance from the imposed disturbance; the rate of decay decreases as the uniaxial tension increases. Deformation theory predicts a larger rate of decay than flow theory except within a small range of stress near the ultimate (necking) load; at necking the rate of decay vanishes.
A Crack in an Anisotropic Layered Material Under the Action of Impact Loading
Authors: Ang W. T.
Published: July 2009

The problem of a plane crack in an anisotropic layered material under the action of impact loading is considered in this paper. The problem is reduced in the Laplace transform domain to a set of simultaneous Fredholm integral equations of the second kind. Once these integral equations are solved, the crack tip stress intensity factors in the Laplace transform domain may be readily calculated. The dynamic stress intensity factors can then be obtained through the use of a numerical technique for inverting Laplace transforms. Numerical results are given for specific examples involving particular transversely isotropic materials.
Optimal Design of Laminated-Composite Circular-Cylindrical Shells Subjected to Combined Loads
Authors: Sun G. , Hansen J. S.
Published: July 2009

Optimization of the buckling load of a laminated-composite, circular-cylindrical shell subjected to axial compression, external pressure, torsion, or a combination thereof is undertaken. In the optimization procedure it is assumed that the shell has a fixed weight (length, radius and thickness); the buckling load is taken as the objective function which is maximized by adopting the lamina fiber orientations as the optimizing parameters. For the shell analysis a perturbation approach is used and the boundary conditions and nonlinear prebuckling effects are included; the analysis yields both the buckling load and the post-buckling character of the shell. The procedure developed is demonstrated for eight loading configurations. In addition, selected laminates were chosen for an experimental programme involving a series of graphite/epoxy shells. The predicted analytical and the measured experimental buckling loads are in very good agreement.
An Approximate Analysis of Stresses in Multilayered Elastic Thin Films
Authors: Suhir E.
Published: July 2009

The analysis contains an engineering method for the approximate evaluation of thermally induced stresses in single and multilayered heteroepitaxial structures fabricated on thick substrates, with consideration of the finite size of the structure. The examined stresses include normal stresses, acting in the film layers themselves and responsible for their ultimate and fatigue strength, as well as interfacial stresses, responsible for film blistering and peeling. The developed formulas are simple, easy-to-use, and clearly indicate how material and structural characteristics affect the magnitude and the distribution of stresses and deflections. Some recommendations for smaller stresses in film structures are presented. The obtained results can be utilized as a guidance for physical design of multilayered heteroepitaxial structures in microelectronics.
Chaotic Motion of an Elastic-Plastic Beam
Authors: Poddar B. , Moon F. C. , Mukherjee S.
Published: July 2009

A numerical study is presented here which suggests that chaotic motion is possible from periodic excitation of an elastic-plastic beam. Poincare´ maps of the motion reveal a fractal-like structure of the attractor. The results suggest that geometric and material nonlinearities in solid mechanics problems may lead to extreme sensitivity to small changes in parameters and resulting unpredictability. These results may explain the total disagreement of nine finite element codes in the analysis of the transient response of an elastic-plastic beam, that has been reported recently by Symonds and his coworkers.
Approximate Nonstationary Random Vibration Analysis for MDOF Systems
Authors: Bucher C. G.
Published: July 2009

An approximate method for nonstationary random vibration analysis is presented. This method utilizes properties of the stationary solution for simplifying the analysis. This approach has previously been applied by the author to linear and nonlinearly damped SDOF systems. In the present paper the concept is extended to linear MDOF systems and applied to nonstationary earthquake-type loading. Comparisons with available exact solutions show very good agreement in numerical results with the additional benefit of reducing computer time by more than one order of magnitude.
On Three-Dimensional Nonlinear Subharmonic Resonant Surface Waves in a Fluid: Part I—Theory
Authors: Gu X. M. , Sethna P. R. , Narain A.
Published: July 2009

Three-dimensional surface waves in a rectangular container subjected to vertical excitation are studied. The analysis includes the effects of surface tension, energy dissipation, and critical depth. Both steady state and transient phenomena are discussed.
On Three-Dimensional Nonlinear Subharmonic Resonant Surface Waves in a Fluid: Part II—Experiment
Authors: Virnig J. C. , Berman A. S. , Sethna P. R.
Published: July 2009

A series of experiments have been performed to investigate wave motion in a rectangular container partially filled with water and shaken in a direction normal to the horizontal free water surface. For a (1-1) wave mode and for several water depths, the dependence of wave amplitude on both excitation frequency and excitation amplitude was found to be in good agreement with the predictions of the nonlinear theory in Part I. In general, at low wave amplitudes better agreement was observed when the surface tension was lowered by the addition of a surfactant. The experiments imply the existence of a critical water depth below which the frequency dependence of wave amplitude is qualitatively different than for depths greater than this critical.
A Microcrack Model of Dilatancy in Brittle Materials
Authors: Nemat-Nasser S. , Obata M.
Published: July 2009

For a solid containing preexisting flaws, overall nonlinear constitutive relations are developed on the basis of a model which endows a preexisting flaw with frictional and cohesive resistance, and which includes nucleation and growth of tension cracks at the preexisting flaw, as it deforms under the action of an overall compressive load. The preexisting flaws may be randomly distributed or may have an initial preferential distribution. They may be of varying sizes and orientations. Even when the flaws are randomly distributed, their preferential activation, and the nucleation and growth of tension cracks at preferential flaws, render the overall response of the solid highly anisotropic. As a first step toward a more complete constitutive micromechanical modeling, a dilute distribution of preexisting flaws is assumed, rate constitutive relations are developed for loading and unloading, which include hysteresis, dilatancy, and other characteristics observed experimentally in rocks, ceramics, concrete, and similar brittle materials. A number of illustrative examples are worked out, and the results are compared to relevant experimental observations.
Finite Axisymmetric Deformation of Rubber-Like Shells of Revolution
Authors: Keppel W. J. , DaDeppo D. A.
Published: July 2009

The finite axisymmetric deformation of a thin shell of revolution is treated in this analysis. The governing differential equations are given for a hyperelastic shell material with the Mooney-Rivlin strain-energy-density function. These equations are solved numerically using a 4th-order Runge-Kutta integration method. A generalized Newton-Raphson iteration procedure is used to systematically improve trial solutions of the differential equations. The governing differential equations are differentiated with respect to a set of generalized coordinates to derive associated rate equations. The rate equations are solved numerically to generate the tangent stiffness matrix which is used to determine the load deformation history of the shell with incremental loading. Numerical examples are presented to illustrate the major characteristics of nonlinear shell behavior.
Bounds on the Effective Transport and Elastic Properties of a Random Array of Cylindrical Fibers in a Matrix
Authors: Torquato S. , Lado F.
Published: July 2009

This paper studies the determination of rigorous upper and lower bounds on the effective transport and elastic moduli of a transversely isotropic fiber-reinforced composite derived by Silnutzer and by Milton. The third-order Silnutzer bounds on the transverse conductivity σe, the transverse bulk modulus ke, and the axial shear modulus μe, depend upon the microstructure through a three-point correlation function of the medium. The fourth-order Milton bounds on σe and μe depend not only upon three-point information but upon the next level of information, i.e., a four-point correlation function. The aforementioned microstructure-sensitive bounds are computed, using methods and results of statistical mechanics, for the model of aligned, infinitely long, equisized, circular cylinders which are randomly distributed throughout a matrix, for fiber volume fractions up to 65 percent. For a wide range of volume fractions and phase property values, the Silnutzer bounds significantly improve upon corresponding second-order bounds due to Hill and to Hashin; the Milton bounds, moreover, are narrower than the third-order Silnutzer bounds. When the cylinders are perfectly conducting or perfectly rigid, it is shown that Milton’s lower bound on σe or μe provides an excellent estimate of these effective parameters for the wide range of volume fractions studied here. This conclusion is supported by computer-simulation results for σe and by experimental data for a graphite-plastic composite.
Partial Release and Relocking of a Frictionally Locked Crack Due to Moving Tensile Loads
Authors: Mendelsohn D. A. , Whang K. H.
Published: July 2009

A finite length 2D crack is closed by remote compression followed by remote shear, and is sufficiently rough so that it remains locked with zero initial tangential crack-face shift. Then a pair of equal and opposite concentrated line loads acting in tension across the crack plane pass over the crack, causing partial opening and shift and then reclosure with residual (locked-in) shift and associated shear Stress Intensity Factors (SIF). Analytical and numerical solutions of the governing singular integral equations are used in studies of the mixed-mode transient and residual states for various coefficients of friction.
Bending of Sandwich Plates of Variable Thickness
Authors: Paydar N. , Libove C.
Published: July 2009

A small deflection theory, consisting of differential equations and a total potential energy expression, is presented for determining the stresses and deformations in variable thickness elastic sandwich plates symmetric about a middle surface. The theory takes into account the contribution of the face-sheet membrane forces (by virtue of their slopes) to the transverse shear. A finite-difference formulation of the stationary total potential energy principle is presented along with an illustrative application.
Buckling of Locally Loaded Isotropic, Orthotropic, and Composite Cylindrical Shells
Authors: Xiao Wei , Cheng Shun
Published: July 2009

This paper incorporates an analysis of the stability of orthotropic or isotropic cylindrical shells subjected to external pressure applied over all or part of their surfaces. An eighth-order governing equation for buckling of orthotropic, isotropic, and composite cylindrical shells is deduced. This governing differential equation can facilitate the analysis and enable us to resolve the buckling problem. The formulas and results, deduced for the first time in this paper, may be readily applied in determining critical loads for local loading of orthotropic, isotropic, and composite cylindrical shells.
Axisymmetric Free-Vibration Problems by Boundary Element Method
Authors: Wang Hui-Ching , Banerjee Prasanta K.
Published: July 2009

A new boundary-element formulation using particular integrals is developed for the free-vibration analysis of axisymmetric solids. The numerical results for a number of axisymmetric free-vibration problems are given and some of the results are compared with those obtained from Finite Element Method, Series Solution Method, or experimental method. Generally, agreement among all of these results is satisfactory.