bluuebunny/crossref_metadata_2025 huggingface dataset:
A Finite Element Analysis of Mode III Quasi-Static Crack Growth at a Ductile-Brittle Interface
Authors: Omprakash S. , Narasimhan R.
Published: February 2008

Steady-state quasi-static crack growth along a bimaterial interface is analyzed under Mode III, small-scale yielding conditions using a finite element procedure. The interface is formed by an elastic-plastic material and an elastic substrate. The top elastic-plastic material is assumed to obey the J2 incremental theory of plasticity. It undergoes isotropic hardening with either a bilinear uniaxial response or a power-law response. The results obtained from the full-field numerical analysis compare very well with the analytical asymptotic results obtained by Castan˜eda and Mataga (1991), which forms one of the first studies on this subject. The validity of the separable form for the asymptotic solution assumed in their analysis is investigated. The range of dominance of the asymptotic fields is examined. Field variations are obtained for a power-law hardening elastic-plastic material. It is seen that the stresses are lower for a stiffer substrate. The potential of the bimaterial system to sustain slow stable crack growth along the interface is studied. It is found that the above potential is larger if the elastic substrate is more rigid with respect to the elastic-plastic material.
Analytical Study of the Duffing Oscillator Excited by Colored Noise Using a Systematic Adiabatic Expansion
Authors: Wu M. M. , Billah K. Y. R. , Shinozuka M.
Published: February 2008

Analytical studies of nonlinear systems driven by colored noise are quite involved. If the inertia of the system is included in analysis, the results are physically realistic although the problem becomes more complex. Research along this line is in progress and this paper is an effort to study a nonlinear oscillator excited by correlated noise. The work delves on the Duffing oscillator driven by exponentially correlated noise. The colored Fokker-Planck equation is derived and the method of systematic adiabatic expansion is used to obtain the reduced probability density function from which the second-order moments are evaluated for different values of system parameters. Numerical simulation is carried out by generating colored noise using the spectral method. In the region where perturbation is valid, the results of adiabatic expansion agree very well with that of Monte Carlo simulation.
Elastothermodynamic Damping in Particulate Composites: Hollow Spherical Inclusions
Authors: Kinra V. K. , Bishop J. E.
Published: February 2008

When a composite material is subjected to a time-harmonic stress field (homogeneous or inhomogeneous), different phases undergo different temperature fluctuations due to the well-known thermoelastic effect. As a result irreversible heat conduction occurs within each phase and between phases, and entropy is produced. This entropy production is the genesis of elastothermodynamic damping and, as a consequence of the second law of thermodynamics, manifests itself as a conversion of work into heat. This paper is concerned with the calculation of elastothermodynamic damping in a matrix reinforced with hollow spheres. Numerical results are presented for an alumina/aluminum composite sphere subjected to a uniform radial stress at the outer boundary. When the cavity occupies more than 75 percent volume fraction of the alumina inclusion, the total damping becomes vanishingly small.
A Nonclassical Vibration Analysis of a Multiple Rotating Disk and Spindle Assembly
Authors: Shen I. Y. , Ku C.-P. R.
Published: February 2008

This paper studies natural frequencies and mode shapes of a spinning disk/spindle assembly consisting of multiple elastic circular plates mounted on a rigid spindle that undergoes infinitesimal rigid-body translation and rotation. Through use of Lagrangian mechanics, linearized equations of motion are derived in terms of Euler angles, rigid-body translation, and elastic vibration modes of each disk. Compared with a single rotating disk whose spindle is fixed in space, the free vibration of multiple disks with rigid-body motion is significantly different in the following ways. First of all, lateral translation of the spindle, rigid-body rotation (or rocking) of the spindle, and one-nodal diameter modes of each disk are coupled together. When all the disks (say N disks) are identical, the coupled disk/spindle vibration splits into N − 1 groups of “balanced modes” and a group of “unbalanced modes.” For each group of the balanced modes, two adjacent disks vibrate entirely out of phase, while other disks undergo no deformation. Because the out-of-phase vibration does not change the angular momentum, the natural frequencies of the balanced modes are identical to those of the one-nodal-diameter modes of each disk. For the group of the unbalanced modes, all disks undergo the same out-of-plane vibration resulting in a change of angular momentum and a steady precession of the spindle. As a result, the frequencies of the unbalanced modes are significantly lower than those of one-nodal-diameter modes of each disk. Secondly, axial translation of the spindle and the axisymmetric modes of each disk are couple together. Similarly, the coupled motion split into N − 1 groups of “balanced modes” and one group of “unbalanced modes,” where the frequencies of the balanced and unbalanced modes are identical to and smaller than those of the axisymmetric modes of each disk, respectively. Thirdly, the rigid-body motion of the spindle does not affect disk vibration modes with two or more nodal diameters. Response of those modes can be determined through the classical vibration analysis of rotating disks. Moreover, vibration response of the disk/spindle assembly from a ground-based observer is derived. Finally, a calibrated experiment is conducted to validate the theoretical predictions.
Strain-Rate Effects in the Dynamic Buckling of a Simple Elastic-Plastic Model
Authors: Karagiozova D. , Jones N.
Published: February 2008

The phenomenon of dynamic buckling is examined when the influence of material strain-rate sensitivity is retained in the basic equations for a simple elastic-plastic model with linear strain hardening when subjected to an impact by a mass. Two approaches are proposed for taking into account the material strain-rate effects and both use the Cowper-Symonds constitutive equation. The critical impact velocities depend on the impact mass and are determined for a wholly elastic material, a strain-rate insensitive elastic-plastic material and an elastic-plastic material with a dynamic yield force together with linear or nonlinear hardening due to the strain-rate effects. The results obtained show that both strain-rate sensitive models predict impact velocities which are higher than those predicted by the strain-rate insensitive idealization and that the influence of any initial imperfections is important for the three material models considered.
Effect of Mass Transfer on a Similar Flow in the Magnetohydrodynamic Squeeze Film
Authors: Usha R. , Sridharan R.
Published: February 2008

An exact similarity solution has been obtained for the magneto-hydrodynamic squeeze flow between two parallel disks with suction or injection at the porous disk. The disks, at time t*, are spaced a distance H(1−αt*)1/2 apart and a magnetic field proportional to B0(1−αt*)−1/2 is applied perpendicular to the disks. Approximate analytic solutions are given and a numerical solution to the resulting nonlinear ordinary differential equation is obtained. The effects of magnetic forces on the velocity profiles and on the normal forces which the fluid exerts on the disks with suction or injection on the stationary porous disk are studied. It has been found that the effect of injection is to increase the load carrying capacity and it is the reverse in the case of suction.
Minimum Weight Design of Symmetric Angle-Ply Laminates With Incomplete Information on Initial Imperfections
Authors: Adali S. , Richter A. , Verijenko V. E.
Published: February 2008

An angle-ply laminated plate is optimized with the objective of minimizing its weight subject to maximum deflection and buckling constraints. The plate has an initial deflection the shape of which is not known a priori, i.e., the initial deflection is not specified in a “deterministic” manner and as such it is “uncertain.” The weight is proportional to the laminate thickness which is minimized taking the ply angles as design variables and under the least favorable conditions of initial imperfections. The convex modeling approach is employed to analyze the uncertain initial deflection with the uncertain quantities allowed to vary arbitrarily around their average values subject to the requirement that these variations are bounded in L2 norm. The results are given for both single load and multiple load cases and the effect of uncertainty on the optimal design is investigated. It is shown that the minimum weight increases with increasing level of uncertainty and the optimal ply angles also depend on the level of uncertainty.
Singularities at Grain Triple Junctions in Two-Dimensional Polycrystals With Cubic and Orthotropic Grains
Authors: Picu R. C. , Gupta V.
Published: February 2008

Stress singularities at grain triple junctions are evaluated for various asymmetric grain boundary configurations and random orientations of cubic and orthotropic grains. The analysis is limited to elastic plane-strain deformation and carried out using the Eshelby-Stroh formalism for anisotropic elasticity. For both the cubic and orthotropic grains, the most singular configuration corresponds to the fully symmetric case with grain boundaries 120 deg apart, and with symmetric orientations of the material axes. The magnitude of the singularities are obtained for several engineering polycrystals.
Dynamics and Control of Electrostatic Structures
Authors: Silverberg L. , Weaver L.
Published: February 2008

This paper formulates the equations governing the dynamics and control of electrostatic structures. Using a Lagrangian mechanics approach, a potential energy function composed of a strain component, an electric component, and a gravitational component is defined. The resulting system of nonlinear ordinary differential equations are linearized about the electrostatic equilibrium leading to a linear system of ordinary differential equations characterized by mass, stiffness, damping, gyroscopic, and circulatory effects. In the absence of feedback control, the damping, gyroscopic, and circulatory effects vanish resulting in a symmetric system that admits normal mode vibration. Voltages applied over the charged subsurfaces (control points) of the electrostatic structure can control its shape. In the presence of feedback controls, control gains can be tailored to produce desirable levels of stiffness and damping. Two different control approaches are studied, one using control points that are attached to the electrostatic structure and one where the control points are fixed in space. Example problems illustrate the dynamics and control; specifically, circumstances that lead to instabilities, shape control using attached control surfaces, shape control using fixed control surfaces, and electrostatic damping.
Modeling of Interfacial Shear for Gas Liquid Flows in Annular Film Condensation
Authors: Narain A.
Published: February 2008

Internal flow of pure vapor experiencing film condensation on the walls of a straight horizontal duct is studied. The commonly occurring annular case of turbulent (or laminar) vapor flow in the core and laminar flow of the liquid condensate—with or without waves on the interface—is emphasized. We present a new methodology which models interfacial shear with the help of theory, computations, and reliable experimental data on heat transfer rates. The theory—at the point of onset of condensation—deals with issues of asymptotic form of interfacial shear, nonuniqueness of solutions, and selection of the physically admissible solution by a stability type criteria. Other details of the flow are predicted with the help of the proposed modeling approach. These predictions are shown to be in agreement with relevant experimental data. The trends for film thickness, heat transfer rates, and pressure drops are also made available in the form of power-law correlations.
Study of Texture Effect on Sheet Failure in a Limit Dome Height Test by Using Elastic/Crystalline Viscoplastic Finite Element Analysis
Authors: Nakamachi E. , Dong X.
Published: February 2008

By combining the crystalline orientation distribution with a hardening evolution equation, a new elastic/crystalline viscoplastic material model is established. We focus our discussion on looking primarily at the texture effects on the strain localization of limit dome height (LDH) tests which are simulated using our Dynamic-Explicit finite element code. Three crystalline models in addition to the classical plastic potential and associated flow law model (J2F) are employed. The results demonstrate that, according to our failure criterion, the random orientation model shows the earliest indication of failure. The better formability is obtained for aluminum alloy 6111-T4 and cube texture models than the random crystalline orientation model. The J2F model shows no signs of strain localization. A comparison between numerical results also confirms that the strain localization region and crystalline rotation are different, due to the crystalline orientation distribution, which is initially set.
Stress Singularity of Edge Delamination in Angle-Ply and Cross-Ply Laminates
Authors: Chen Wen-Hwa , Huang Tain-Fu
Published: February 2008

By utilizing the general solutions derived for the plies with arbitrary fiber orientations under uniform axial strain (Huang and Chen, 1994), the explicit solutions of the edge-delamination stress singularities for the angle-ply and cross-ply laminates are obtained. The dominant edge-delamination stress singularities for the angle-ply laminates are found to be a real constant, −1/2, and a pair of complex conjugates, −1/2±i/2πln{(b+b2−a2)/a}. For the cross-ply laminates, the significant effect of transverse shear stresses of the laminate is considered and the dominant edge-delamination stress singularities are shown as −1/2 and −1/2±i/2πln{(c2+c22−4c1c3)/2c1}. a, b, cl, c2, and c3 are the corresponding combined complex constants. In addition, two elementary forms of edge-delamination stress singularity, say, r−1/2 and rδr(lnr)n(δr=n−3/2,n=1,2...) exist for both the angle-ply and cross-ply laminates. Excellent correlations between the present results and available solutions show the validity of the approach. The deficiencies of the solutions available in the literature are compensated. New results for other angle-ply and cross-ply laminates are also provided.
Determination of Noncontributing Forces and Noncontributing Impulses in Three-Phase Motions
Authors: Djerassi S.
Published: February 2008

Numerous dynamical systems undergo, while in motion, imposition and/or removal of constraints. Three phases of motion are involved: a phase during which the motion is defined as unconstrained, a phase during which the motion is defined as constrained, and an intermediate, transition phase, when constraints are imposed or removed. Noncontributing forces (sometimes called nonworking, reaction forces), and noncontributing impulses, namely, impulses associated with noncontributing forces in the transition phase, play a central role in the mechanics of systems undergoing such motions, and are the subject matter of the present paper. Specifically, a six-step procedure is introduced for the determination of noncontributing forces and of noncontributing impulses throughout three phase motions.
Modeling the Dynamic Response and Establishing Post-buckling/ Post Snap-thru Equilibrium of Discrete Structures via a Transient Analysis
Authors: Hilburger M. W. , Waas A. M. , Starnes J. H.
Published: February 2008

Results of a transient analysis developed to model the dynamic response and establish post-buckling/post snap-thru equilibrium of discrete structures are presented. Three systems that exhibit unstable buckling characteristics are analyzed. The analysis consisted of first statically loading the structures up to there respective static limit loads. The structure is then perturbed from their critical state and a transient analysis is used to model the ensuing dynamic response. The transient formulation is first applied to two simple one-degree-of-freedom systems consisting of rigid links, springs, dampers, and lumped masses. The first of these systems was an arch with a point load applied at its vertex. This structure admits dynamic snap-thru response when loaded beyond its limit load. The second system was a model of a curved panel under an applied axial end-shortening. This system exhibited dynamic buckling behavior consisting of a large decrease in the resultant axial load when loaded beyond its limit load. The transient analysis was then applied to a finite element model of a cylindrical shell with a cutout under an applied axial compression load to model the dynamics of the global buckling response upon reaching its limit load. The results from this study illustrate the usefulness of the transient analysis in modeling the dynamics of an unstable structural response and establishing equilibrium beyond any points of instability.
Stress Concentrations in an Intermingled Hybrid Composite
Authors: Luo H. A. , Wang Q.
Published: February 2008

This paper studies the stress redistribution in a tensile hybrid composite sheet due to the breakage of a high modulus fiber. Employing a continuous distribution of dislocations, a set of singular integral equations is established to analyze the fiber crack impinging upon weakly bonded fiber-matrix interfaces. After solving the integral equations numerically, the stress concentration factors of both high modulus and low modulus fibers are evaluated as a function of loading stress and interfacial parameters. The results are compared with those obtained from shear-lag model solution.
Scale Effects in Media With Periodic and Nearly Periodic Microstructures, Part I: Macroscopic Properties
Authors: Schraad M. W. , Triantafyllidis N.
Published: February 2008

Traditional averaging and homogenization techniques, developed to predict the macroscopic properties of heterogeneous media, typically ignore microstructure related scale effects—that is, the influence of the size of the representative volume, relative to the size of the unit cell. This issue is presently investigated by exploring the behavior of a nonlinearly elastic, planar, lattice model, which is subjected to general macroscopic deformations. For these materials, scale effects may be due to nonuniformities in the macroscopic strain field throughout the specimen, or alternatively, to the presence of microstructural imperfections that may be either geometric or constitutive in nature. For the case of macroscopic strain nonuniformities, it is shown that the microstructure related scale effects can be accounted for by the presence of higher order gradient terms in the macroscopic strain energy density of the model. For the case of microstructural imperfections, the difference between the respective macroscopic properties of the perfect and imperfect models are shown to depend on the relative size of the specimen, and on the imperfection amplitude and wavelength, while being nearly insensitive to the imposed macroscopic strain. For all of the cases considered, several analytical approximations are proposed to predict the influence of scale on the macroscopic properties, and the accuracy of each method is examined.
Scale Effects in Media With Periodic and Nearly Periodic Microstructures, Part II: Failure Mechanisms
Authors: Schraad M. W. , Triantafyllidis N.
Published: February 2008

Using the nonlinearly elastic planar lattice model presented in Part I, the influence of scale (i.e., the size of the representative volume, relative to the size of the unit cell) on the onset of failure in periodic and nearly periodic media is investigated. For this study, the concept of a microfailure surface is introduced—this surface being defined as the locus of first instability points found along radial load paths through macroscopic strain space. The influence of specimen size and microstructural imperfections (both geometric and constitutive) on these failure surfaces is investigated. The microfailure surface determined for the infinite model with perfectly periodic microstructure, is found to be a lower bound for the failure surfaces of perfectly periodic, finite models, and an upper bound for the failure surfaces of finite models with microstructural imperfections. The concept of a macrofailure surface is also introduced—this surface being defined as the locus of points corresponding to the loss of ellipticity in the macroscopic (homogenized) moduli of the model. The macrofailure surface is easier to construct than the microfailure surface, because it only requires calculation of the macroscopic properties for the unit cell, at each loading state along the principal equilibrium path. The relation between these two failure surfaces is explored in detail, with attention focused on their regions of coincidence, which are of particular interest due to the possible development of macroscopically localized failure modes.
Fracture Mechanics of Composites With Residual Thermal Stresses
Authors: Nairn J. A.
Published: February 2008

The problem of calculating the energy release rate for crack growth in an arbitrary composite in the presence of residual stresses is considered. First, a general expression is given for arbitrary, mixed traction, and displacement boundary conditions. This general result is then applied to a series of specific problems including statistically homogeneous composites under traction or displacement boundary conditions, delamination of double cantilever beam specimens, and microcracking in the transverse plies of laminates. In many examples, the energy release rate in the presence of residual stresses can be reduced to finding the effect of damage on the effective mechanical properties of the composite. Because these effective properties can be evaluated by isothermal stress analysis, the effect of residual stresses on the energy release rate can be evaluated without recourse to any thermal elasticity stress analyses.
Boundary Element Solution for Free Edge Stresses in Composite Laminates
Authors: Davi` G. , Milazzo A.
Published: February 2008

The edge-stress problem in multilayered composite laminates under uniform axial extension is analyzed through an alternative method based on a boundary integral formulation. The basic equations of the formulation are discussed and solved by the multiregion boundary element method. Generalized orthotropic elasticity analytic fundamental solutions are employed to establish the integral equations governing the problem. The formulation is absolutely general with regard to the laminate stacking sequence and the section geometry and it does not require any aprioristic assumption on the elastic response nature. This makes the formulation suitable for an investigation of the singular behavior of the stress field at the free edge in composite laminates. The interlaminar normal and shear stress distributions are examined in detail with the aim of calculating the stress singularity at the interlaminar free edge. The singularity parameters, i.e., power and strength, are determined for two family of laminates in order to ascertain the effectiveness of the method for the free edge-stress problem.
Contact Stresses in Cables due to Tension and Torsion
Authors: Kumar K. , Cochran J. E. , Cutchins J. A.
Published: February 2008

The fundamental theory of wire ropes developed by Costello and Phillips is utilized to obtain closed-form expressions for maximum contact stresses in single strand cables with fibrous cores. These should be useful for gaining an insight into the influence of various parameters of the cable as well as the material properties on its strength and hence design.
Localized Modes in Periodic Systems With Nonlinear Disorders
Authors: Cai C. W. , Chan H. C. , Cheung Y. K.
Published: February 2008

The localized modes of periodic systems with infinite degrees-of-freedom and having one or two nonlinear disorders are examined by using the Lindstedt-Poincare (L-P) method. The set of nonlinear algebraic equations with infinite number of variables is derived and solved exactly by the U-transformation technique. It is shown that the localized modes exist for any amount of the ratio between the linear coupling stiffness kc and the coefficient γ of the nonlinear disordered term, and the nonsymmetric localized mode in the periodic system with two nonlinear disorders occurs as the ratio kc/γ, decreasing to a critical value depending on the maximum amplitude.
On the Computation of Relative Rotations and Geometric Phases in the Motions of Rigid Bodies
Authors: O’Reilly O. M.
Published: February 2008

In this paper, expressions are established for certain relative rotations which arise in motions of rigid bodies. A comparison of these results with existing relations for geometric phases in the motions of rigid bodies provides alternative expressions of, and computational methods for, the relative rotation. The computational aspects are illustrated using several examples from rigid-body dynamics: namely, the moment-free motion of a rigid body, rolling disks, and sliding disks.
Large Deflections of Clamped Circular Plates Under Initial Tension and Transitions to Membrane Behavior
Authors: Sheploak M. , Dugundji J.
Published: February 2008

The large deflections of a clamped circular plate are investigated over a wide range of transverse loadings and initial in-plane tension loads. The continuous transition from plate behavior to membrane behavior is described in detail, along with the development of the accompanying edge zone region where properties change rapidly. We give a simple approximation of this edge zone and its properties, provide limits for the validity of small deflection, linear theory, and note the similar effects of large in-plane tension and large transverse loading. The values and trends are presented in general nondimensional form, and should prove useful for the design of thin circular disks for microsensing applications.
A Parametric Study on the Free Vibration of Noncylindrical Helical Springs
Authors: Yıldırım V.
Published: February 2008

In the work based on the stiffness method reported in this paper, considering the rotary inertia, the axial and shear deformation terms, the natural frequencies of conical, barrel and hyperboloidal-type helical springs fixed at both ends are calculated. The results are presented in dimensionless graphical forms for the six lowest natural frequencies of all types of noncylindrical helices for a wide range of vibrational parameters which influence the natural frequencies. A discussion about the effects of vibrational parameters on the natural frequencies is also presented.
A Thermoviscoelastic Dynamic Vibration Absorber
Authors: Fosdick R. , Ketema Y.
Published: February 2008

A dynamic vibration absorber with a viscoelastic element is studied. The viscoelastic element is modeled as a material with memory in which the internal dissipative force depends on current, as well as previous deformations. The viscoelastic behavior is governed by two parameters: the relaxation modulus Go, and the relaxation time γ. We apply the principle of time-temperature superposition to affect a dependence of the relaxation time γ on temperature. This temperature dependence can be used to tune a vibration absorber so as to be effective at more than one excitation frequency.
Viscoelastic Effects in Modeling Web Handling Systems: Unsteady-State Analysis
Authors: Guan Xiaofeng , High M. S. , Tree D. A.
Published: February 2008

A model to predict the tension in open spans of web handling systems during transient operations has been developed. Governing equations were developed by using the White-Metzner equation to describe the material response in conjunction with mass and force balances. The governing equations were nondimensionalized and solved via the MacCormack predictor/corrector technique. Two dimensionless parameters emerged from the analysis, the Deborah number, De, and the ratio of the viscous stress to the steady state stress, N. The resulting model is the companion to a previously reported model for steady-state operations (Guan et al, 1995). The model was used to predict the behavior of a web handling system during start-up, transition between steady states, and a periodic disturbance. During start-up and transition, systems responded more rapidly at low De. The system response during a periodic disturbance was correlated to De, the frequency, and the magnitude of the disturbance.
Inflation of a Thick-Walled Shell Which Exhibits Stress Softening
Authors: Haddow J. B. , Wegner J. L.
Published: February 2008

The Mullins effect (Mullins, 1947), also known as stress softening, is exhibited by certain rubberlike materials and refers to changes of the mechanical properties, due to prior deformation. Johnson and Beatty (1995) have investigated the Mullins effect in equibiaxial tension by performing cycles of static inflation and deflation experiments on latex balloons. These experiments show that stress softening results in a decrease in the pressure necessary to inflate a balloon, and in addition, indicate inelastic effects of hysteresis and permanent set. The objective of this paper is to investigate the finite deformation static inflation from the virgin state, followed by quasi-static removal of the internal pressure, of a thick-walled homogeneous spherical shell composed of an incompressible isotropic rubberlike material which exhibits stress softening and permanent set. Since the initial inflation of the shell, due to application of an internal pressure, does not result in a homogeneous deformation, a state of residual stress is present after complete removal of the internal pressure. A procedure is presented for the determination of the response of the shell for the first cycle of inflation and deflation from the virgin state, and the analysis includes strain softening and the inelastic effects of hysteresis and permanent set. It is assumed that, for the initial static inflation of the shell from the virgin state, the internal pressure and stress distribution for a monotonically increasing internal or external radius are the same as for a hyperelastic shell, and also that the magnitude of the permanent set of an element of the material is related monotonically to the deformation at the end of the inflation.
Thermal Stresses in a Generally Anisotropic Body With an Elliptic Inclusion Subject to Uniform Heat Flow
Authors: Chao C. K. , Shen M. H.
Published: February 2008

A general analytical solution for the elliptical anisotropic inclusion embedded in an infinite anisotropic matrix subjected to uniform heat flow is provided in this paper. Based upon the method of Lekhnitskii formulation, the technique of conformal mapping, the method of analytical continuation, and the concept of superposition, both the solutions of the temperature and stress, functions either in the matrix or in the inclusion are expressed in complex matrix notation. Numerical results are carried out and provided in graphic form to elucidate the effect of material and geometric parameters on the interfacial stresses. Since the general solutions have not been found in the literature, comparison is made with some special cases of which the analytical solutions exist, which shows that our solutions presented here are exact and general.
Rigid Stamp Indentation on a Curvilinear Hole Boundary of an Anisotropic Elastic Body
Authors: Fan C. W. , Hwu Chyanbin
Published: February 2008

A general solution for the problems of rigid stamp indentation on a curvilinear hole boundary of an anisotropic elastic body is obtained by employing the Stroh formalism, the method of analytical continuation, and the technique of mapping a closed curve to a unit circle. With this general solution, two typical curvilinear holes are studied. One is an ellipse, the other is a polygon. Since the transformation functions used in our solutions are not always one to one, some of the solutions are not exact but only approximate. For example, the solutions to the problems of anisotropic plates containing an elliptic hole and isotropic plates containing a polygonal hole are exact, but the solutions to the problems of anisotropic plates containing a polygonal hole are only approximate. Because the solutions presented in this paper are new and no other analytical solution has been found in the literature, the correctness of the present results can only be checked analytically by their reduced forms such as those for isotropic media or those for the stress boundary value problems. To show the generality of our solutions and to see clearly the physical behavior of the indentation problems two numerical examples are given, and their related hoop stress and stress contour are also plotted.
Probabilistic Representation and Transmission of Nonstationary Processes in Multi-Degree-of-Freedom Systems
Authors: Masri S. F. , Smyth A. W. , Traina M.-I.
Published: February 2008

A relatively simple and straightforward procedure is presented for representing non-stationary random process data in a compact probabilistic format which can be used as excitation input in multi-degree-of-freedom analytical random vibration studies. The method involves two main stages of compaction. The first stage is based on the spectral decomposition of the covariance matrix by the orthogonal Karhunen-Loeve expansion. The dominant eigenvectors are subsequently least-squares fitted with orthogonal polynomials to yield an analytical approximation. This compact analytical representation of the random process is then used to derive an exact closed-form solution for the nonstationary response of general linear multi-degree-of-freedom dynamic systems. The approach is illustrated by the use of an ensemble of free-field acceleration records from the 1994 Northridge earthquake to analytically determine the covariance kernels of the response of a two-degree-of-freedom system resembling a commonly encountered problem in the structural control field. Spectral plots of the extreme values of the rms response of representative multi-degree-of-freedom systems under the action of the subject earthquake are also presented. It is shown that the proposed random data-processing method is not only a useful data-archiving and earthquake feature-extraction tool, but also provides a probabilistic measure of the average statistical characteristics of earthquake ground motion corresponding to a spatially distributed region. Such a representation could be a valuable tool in risk management studies to quantify the average seismic risk over a spatially extended area.
The Problem on Dynamical Loading of Plane Elastic Regions With Irregular Boundaries
Authors: Morozov N. , Sourovtsova I.
Published: February 2008

The study of the problem of wave propagation in elastic wedge meets considerable difficulties, which are intensified by the presence of waves of two types that interact with each other through boundary conditions. However, some special surface loading permits separation of the potentials in the boundary conditions, but even in this case the problem cannot be simply reduced to two acoustic ones. The reason for this is that the edge condition cannot be satisfied if the disturbances are limited to a single type (longitudinal or shear). In spite of this the problem, such a special boundary loading nevertheless turns out to be very similar to the acoustic one, which makes it possible to find a closed analytical solution by means of the modified Kostrov method (Kostrov, 1966) and the idea of extension of operators. A similar approach is used for the study of the general problem of loading of the body with several angles.
Modeling and Identification of Inelastic Systems Using the Endochronic Model
Authors: Chiang Dar-Yun
Published: February 2008

An effective modeling method is proposed for the endochronic model based on the concept of plastic equilibrium points, which reduces the number of parameters involved and greatly simplifies the modeling process for practical applications. A systematic, optimization-based parameter estimation procedure for the proposed class of endochronic models is also presented for identification studies. Validity of the proposed modeling technique in both modeling and identification of inelastic systems is demonstrated by biaxial tension-torsion applications using experimental results available in the literature.
On the Stability of Gyroscopic Systems
Authors: Lancaster P. , Zizler P.
Published: February 2008

Gyroscopic systems considered here have the form Ay¨ + Gy˙ + Ky = 0 where A, G, K are real n × n matrices with A > O, GT = −G, KT = K, and the stiffness matrix K has some negative eigenvalues; i.e., the equilibrium position is unstable (when G = 0). A new necessary condition for stability is established. It is also shown that gyroscopic systems with K < 0 and G singular are always unstable for G sufficiently large.
Solution of Impact-Induced Flexural Waves in a Circular Ring by the Method of Characteristics
Authors: Shim V. P. W. , Quah S. E.
Published: February 2008

A study of elastic wave propagation in a curved beam (circular ring) is presented. The governing equations of motion are formulated in two forms based on Timoshenko beam theory. Solutions are obtained using the method of characteristics, whereby a numerical scheme employing higher-order interpolation is proposed for the finite difference equations. Results obtained are verified by experiments; it is found that use of the higher-order numerical scheme improves correlation with experimental results. Comparison of the relative accuracy between the two mathematical formulations—one in terms of generalized forces and velocities and the other in terms of generalized displacements—shows the former to be mathematically simpler and to yield more accurate results.
Vibration of Thick Prismatic Structures With Three-Dimensional Flexibilities
Authors: Liew K. M. , Hung K. C. , Lim M. K.
Published: February 2008

This paper presents an investigation on free vibration of thick prismatic structures (thick-walled open sections of L, T, C, and I shapes). The derivation of a linear frequency equation based on an exact three-dimensional small-strain linearly elastic principle is presented. This formulation uses one and two-dimensional polynomial series to approximate the spatial displacements of the thick-walled open sections in three dimension. The proposed technique is applicable to vibration of thick-walled open sections of different cross-sectional geometries and end support conditions. In this study, however, we focus primarily on the cantilevered case which has high value in practical applications. The perturbation of frequency responses due to the variations of cross-sectional geometries and wall thicknesses is investigated. First-known frequency parameters and three-dimensional deformed mode shapes of these thick-walled open sections are presented in vivid graphical forms. The new results may serve as a benchmark reference to future research into the refined beam and plate theories and also for checking the accuracy of new numerical techniques.
A Physical Explanation of the Destabilizing Effect of Damping
Authors: Semler C. , Alighanbari H. , Pai¨doussis M. P.
Published: February 2008

In this paper, the destabilization due to small damping of the follower force system, known as Beck’s problem, and of the cantilevered pipe conveying fluid system, two nonconservative systems, is considered. Instead of looking for a mathematical explanation, e.g., the evolution of the eigenvalues with different parameters, a more “physical” explanation is provided. It is shown that it is of particular interest to focus on the different modes of vibration and to understand how they evolve when damping is varied. Also, based on energy considerations, the key factors influencing stability are highlighted, e.g., the phase angles between the different coordinates. In the case of the pipe conveying fluid, the methodology developed and insight gained help explain the presence of “jumps” p in the stability curves, that are known to play an important role in the linear and nonlinear dynamics of this system.
Bifurcation of Elastoplastic Pressure-Sensitive Hollow Cylinders
Authors: Papanastasiou P. , Durban D.
Published: February 2008

A linear bifurcation analysis is presented for pressure sensitive elastoplastic hollow cylinders under radial surface loads. Material response is modeled by flow and deformation theories of the Drucker-Prager solid accounting for arbitrary hardening. Sample calculations are given for cylinders that deform in axially symmetric patterns under uniform radial pressure applied at the boundaries. No bifurcation points were found with flow theory in the realistic range of stress though the primary equilibrium path is nearly identical for both theories. For thick-walled cylinders the dominant bifurcation mode predicted by deformation theory appears to be a circumferential surface instability. Deformation theory results for bifurcations are apparently not sensitive to deviations from associativity.
An Axisymmetric Membrane Element With Bending Stiffness for Static Implicit Sheet Metal Forming Simulation
Authors: Esche S. K. , Kinzel G. K. , Lee J. K.
Published: February 2008

This paper reviews techniques to include the bending behavior of sheet metals into finite element method formulations. A new, numerically efficient bending correction for the implementation into axisymmetric membrane elements is developed. This bending correction is based on a number of simplifying assumptions. The accuracy of the implementation is demonstrated by analyzing two round cup drawings for which experimental measurements were available from the literature. The range of applicability of the proposed approach is discussed.
The Stability of a Two-Layer Inviscid Flow Between an Elastic Layer and a Rigid Boundary
Authors: Schall P. J. , McHugh J. P.
Published: February 2008

The linear stability of two-layer flow over an infinite elastic substraw is considered. The problem is motivated by coating flow in a printing press. The flow is assumed to be inviscid and irrotational. Surface tension between the fluid layers is included, but gravity is neglected. The results show two unstable modes: one mode associated with the interface between the elastic layer and the fluid (mode 1), and the other concentrated on the interface between the two fluids (mode 2). The behavior of the unstable modes is examined while varying the elastic parameters, and it is found that mode 1 can be made stable, but mode 2 remains unstable at small wavenumber, similar to the classic Kelvin—Helmholtz mode.
The Influence of a Ductile Interphase on the Overall Elastoplastic Behavior of a Fiber-Reinforced Composite
Authors: Ding K. , Weng G. J.
Published: February 2008

While there exist various homogenization theories for the plasticity of a fiber-reinforced composite, no such theories have been explicitly developed to account for the influence of a ductile interphase. In this paper a simple scheme is developed for such a purpose. The theory evolved out of the work of Qiu and Weng (1992) and Hu (1996), and bears an identical structure to Ponte Castan˜eda’s (1991) variational procedure and Suquet’s (1995, 1996) modified secant moduli approach. An exact solution under the plane-strain biaxial loading is also developed to assess the accuracy of the theory. It is found that, with either a soft or a hard interphase and with or without work-hardening, the homogenization theory can produce sufficiently accurate results under this condition. The theory is then used to examine the influence of the interphase volume concentration on the anisotropic behavior of the composite under axial tension, transverse tension, axial shear, and transverse shear, with both a soft and a hard interphase. The results indicate that, while the axial tensile behavior is not sensitive to the interphase concentration, the behaviors under other types of loading are greatly affected by its presence, especially when the interphase is softer than the matrix.
The Modal Formulation and Adaptive-Passive Control of the Nonself-Adjoint One-Dimensional Acoustic System With a Mass-Spring Termination
Authors: Jayachandran V. , Sun J. Q.
Published: February 2008

This paper investigates the use of mass-spring type of impedances as absorbing elements for interior noise control. The general modal formulation for a one-dimensional acoustic system terminated by a spring-supported piston is presented. The boundary value problem has a nonself-adjoint operator which renders the mode functions unorthogonal. This is overcome by defining an associated self-adjoint operator in Hilbert space and using an operator-theoretic formulation of the problem. Orthogonal mode functions and an expansion theorem are presented which can be used to construct a series solution for the forced response. A numerical study is performed for the case of single frequency excitation in which the impedance parameters are optimized by minimizing the cost function. The results from the numerical simulations indicate the feasibility of interior noise control using tunable mechanical impedances, and provide guidelines and restrictions in designing such a system.
On the Elastic Constants of Transversely Isotropic, Quasi-Symmetric Composites
Authors: Chinh P. D.
Published: February 2008

Estimates for the elastic constants of transversely isotropic composites and the subclass of quasi-symmetric ones are given in unified simple forms from a common framework constructed also for the elastic moduli of three-dimensional isotropic composites and the transport properties.
Nature of Stress Singularities at the Reentrant Wedge Corner for a Branched Crack Problem
Authors: and A. S. Selvarathinam , Goree J. G.
Published: February 2008

The solution of the branched crack problem for an isotropic material, employing the dislocation method as developed by Lo (1978), results in a singular integral equation in which the slope of the crack-opening displacement is the unknown. In this brief note, using the function-theoretic method, the behavior of this unknown function is investigated at the corner where the branched and main crack meet and it is shown that the order of stress singularity obtained at the reentrant corner of the branched crack is given by the Williams’ (1952) characteristic equation for the isotropic wedge.
Buckling of Thick Orthotropic Cylindrical Shells Under Torsion
Authors: Kim Y. S. , Kardomateas G. A. , Zureick A.
Published: February 2008

A three-dimensional elasticity solution to the problem of buckling of orthotropic cylindrical shells under torsion is presented. A mixed form of the Galerkin method with a series of Legendre polynomials in the thickness coordinate has been applied to solve the governing differential equations. The accuracy of existing shell theory solutions has been assessed through a comparison study for both isotropic and orthotropic cylinders. For isotropic cylinders the solutions based on the Donnell shell theory were found to predict nonconservative values for the critical loads. As the circumferential wave numbers increase, shell theory solutions provide more accurate values. For orthotropic cylinders, the classical shell theory predicts much higher critical loads for a relatively short and thick cylinder, while the shear deformation theories provide results reasonably close to the elasticity solutions. Detailed data are also presented for the critical torsional loads over a wide range of length ratios and radius ratios for isotropic, glass/epoxy, and graphite/epoxy cylinders.