bluuebunny/crossref_metadata_2025 huggingface dataset:
On Measuring the Near-Tip Plastic Strain Singularity
Authors: Kamath Sundar M. , Kim Kyung S.
Published: April 2008

A recently developed experimental method, stress intensity factor tracer, is extended to measure the strength, J, of the HRR singularity for near-tip plastic deformation. Focal-plane mapping of the HRR field shows that the light intensity, I, collected on a finite area of the focal plane has a simple relationship with J as I = βJ2n/(2n+1). The constant, β, is a product of several experimental parameters and “n” is the hardening parameter of a power-law hardening material. The focal-plane mapping technique is also capable of estimating the shape and size of the HRR-field dominant region for a relatively thin (<10mm) metallic specimen. In addition, a continuous trace of the J variation can be monitored using a single, stationary photodetector. Because the measurement value of this method is independent of crack-tip motion, the transition of HRR singularity from stationary to moving can also be studied. In this paper, the theoretical analysis of the method is presented.
Thermal Stresses in an Anisotropic Plate Disturbed by an Insulated Elliptic Hole or Crack
Authors: Hwu Chyanbin
Published: April 2008

The solutions presented in the literature for the thermal stresses under uniform heat flow disturbed by an insulated elliptic hole are for an isotropic or orthotropic medium. However, the solution for the latter cannot be specialized to the former due to the repeated eigenvalue of the elastic constants of isotropic materials, which also restricts the application to other degenerate materials. Based upon the Stroh formalism, a simple and compact version of general solutions for plane anisotropic thermoelasticity is given in this paper. Some new identities concerning the eigenvalues and eigenvectors are developed, which are the keys for the present solutions to be valid in any kind of anisotropic materials including degenerate materials. The hoop stress around the elliptic hole is given in an explicit form. The effect of geometry, heat flow, elastic and thermal anisotropy, and heat conductivity can then be studied. The solutions for the crack problem are obtained by setting the minor axis of the ellipse approach to zero. The stress intensity factors, crack opening displacement, and strain energy release rate are expressed in terms of the fundamental elasticity matrix L and thermal vector γ˜2* introduced in this paper. The validity of the fully open crack assumption is also discussed.
Plane Contact of an Elastic Layer Supported by a Winkler Foundation
Authors: Dempsey J. P. , Zhao Z. G. , Minnetyan L. , Li H.
Published: April 2008

Plane contact problems of an elastic, homogeneous, and isotropic layer supported by a Winkler foundation are studied in this paper. The elastic layer has a finite depth and infinite in-plane dimensions. The upper surface of the layer is in plane contact with a rigid indenter. The particular applications studied in this paper are formulated by first providing the solution for a line load. For the case of a rigid cylinder, the upper portion of the load deflection response is modeled using beam theory with wrapping. The contact pressure distributions for the relatively flexible foundation cases can be accurately determined from the wrapping theory.
Buckling and Post-buckling Behavior of Elliptical Plates: Part II—Results
Authors: Chai Herzl
Published: April 2008

The large-deflection plate solution developed in Part I is used here to study the buckling and post-buckling deformation and stress characteristics of an elliptically-shaped surface layer that has been delaminated from a large material body. The economical, yet accurate nature of this solution, together with available graphic routines, has made it possible to present, figuratively, a comprehensive description of the plate behavior. The conditions for a layer-substrate overlap and the variations of membrane and bending stresses along the plate boundary are emphasized. Deformations were induced either by a normal pressure or a biaxial displacement field applied to the plate boundary. The problem variables are plate size and shape, details of load biaxiality, and load level.
Generalized Variational Principle of Plates on Elastic Foundation
Authors: Yuan R. L. , Wang L. S.
Published: April 2008

The theory of variational principle is enhanced by using the Lagrange multiplier to establish a generalized variational principle for plates on an elastic foundation. In the first part of this paper, the principle of minimum potential energy is introduced in which the integral equation is employed as the variational constrained condition. In the second part, it is shown that the generalized variational principle with two variational functions can be established. This represents, to the authors’ knowledge, the first treatment of the variational principle with these types of equations.
Stability Analysis for the Head-Disk Interface in a Flexible Disk Drive
Authors: Ono Kyosuke , Chen Jen-San , Bogy D. B.
Published: April 2008

This paper describes the modeling, theoretical formulation, and eigenvalue analysis for a combined system of a spinning flexible disk and a pair of head and suspension systems that contact the disk at opposing points on its two sides. In the analytical model a constant friction force between the sliders and disk and the slider pitch motion, as well as its transverse motion, are taken into account. From the eigenvalue analysis it is found that pitch stiffness and moment of inertia of the heads induce instability above the critical rotation speed similarly to the transverse stiffness and mass. This instability can be effectively stabilized by increasing the external damping which is spinning with the disk. It is also found that the friction force makes all forward modes unstable over the entire rotational speed range. The friction induced instability can be effectively suppressed by increasing the transverse stiffness and mass and it can be stabilized by the pitch damping and the external damping. The characteristics of instability due to the friction force qualitatively agree well with experimental results reported previously.
Dynamic Stability of Elastic Rotor-Bearing Systems via Liapunov’s Direct Method
Authors: El-Marhomy Abd Alla , Schlack A. L.
Published: April 2008

A general method of analysis based on Liapunov’s direct method is presented for studying the dynamic stability of elastic rotor-bearing systems. A model comprised of a continuous elastic shaft mounted on two 8-coefficient bearings is used to develop closed-form (series) stability criteria involving system stiffness and damping parameters. It is quantitatively shown by means of graphs how the instability regions are reduced by (a) increasing the shaft dimensionless stiffness parameters, (b) increasing the bearing direct stiffness and damping parameters, and (c) decreasing the bearing cross-coupling stiffness and damping parameters.
Vertical Autorotation of a Single-Winged Samara
Authors: Rosen A. , Seter D.
Published: April 2008

A derivation of a theoretical model for the vertical autorotation of a samara wing is presented. The dynamic effects are treated in an accurate manner. The aerodynamic effects are calculated by using the blade element/momentum theory. Because of basic differences between the mode of operation of a samara wing and other rotary wings, the model differs from existing rotary wing models. An experimental setup, aimed at verifying the theoretical model, is also described. Comparison between theoretical and experimental results are presented.
Vibration Localization by Disorder in Assemblies of Monocoupled, Multimode Component Systems
Authors: Cha Philip D. , Pierre Christophe
Published: April 2008

Disorder in nominally periodic engineering structures results in the localization of the mode shapes to small geometric regions and in the attenuation of waves, even in the passbands of the corresponding perfectly periodic system. This paper investigates, via probabilistic methods, the transmission of steady-state harmonic vibration from a local source of excitation in nearly periodic assemblies of monocoupled, multicomponent mode substructures. A transfer matrix formulation is used to derive analytical expressions for the localization factor (the rate of exponential decay of the vibration amplitude) in the limiting cases of strong and weak modal coupling. The degree of localization is shown to increase with the ratio of disorder strength to modal coupling. The increase is nearly parabolic for small values of this ratio, and logarithmic for large values. Furthermore, the localization factor increases very rapidly with the passband number. Typically, the transition from weak to strong localization occurs from one passband to the next, and severe vibration confinement is unavoidable at high frequencies, even for very small disorder.
On the Calculation of Deformations and Stresses During Axially Symmetric Solidification
Authors: Zabaras Nicholas , Ruan Yimin , Richmond Owen
Published: April 2008

In this paper finite element modeling of the deformation and stress development in solidifying bodies is presented. Emphasis is given to axially symmetric problems and especially to the accurate implementation of thermal and mechanical phenomena occurring at the freezing front. More specifically, the interface velocity and location are treated as primary variables of the heat transfer analysis, and the isostatic stress condition at the front is utilized as an initial condition in the stress analysis. A hypoelastic-viscoplastic constitutive model and a rate form of the principle of virtual work are involved to model the stresses and deformation. The mechanical and thermal properties are allowed to vary with temperature and strain rate in a realistic manner. Several examples of calculated residual stresses are shown for pure aluminum under axially symmetric geometries and realistic boundary conditions. The effects on the evolving deformations and stresses of the melt pressure, geometry, and cooling conditions are examined and reported.
Steady Penetration of a Rigid Cone With a Rough Wall Into a Power-Law Viscous Solid
Authors: Fleck N. A. , Durban D.
Published: April 2008

Singular strain rate and stress fields are examined at the tip of a rigid conical indentor penetrating an incompressible viscous solid. Attention is focused on friction effects induced by wall roughness. The problem is formulated within the usual framework of eigenvalue analysis of locally singular fields. Some special cases are investigated further with emphasis on a boundary layer expansion for the rigid/perfectly plastic solid sliding along the perfectly rough wall. It has been found that the level of singularity increases as the cone becomes sharper and the wall friction decreases. Numerical results, presented for a variety of cases, suggest a boundary layer build up for sharp cones with rough walls.
Acoustic Emission From Single-Plate Martensitic Transformation
Authors: Liu Xiangying , Kannatey-Asibu Elijah
Published: April 2008

Martensitic transformation occurs in a diffusionless manner at high velocity, with acoustic emission (AE) being generated during the process. The AE signal contains information about the dynamic process of martensitic transformation. In this analysis, a model is developed for the AE signal, or dynamic displacement, from the transformation strains and the growth process of martensitic transformation in an elastic half-space using Green’s functions. The AE signal amplitude is found to be inversely proportional to the distance between the martensite source and the sensor, and to the duration of transformation. It also depends on the orientation of the martensite plate. The spectral bandwidth increases as the duration of plate formation decreases. In addition, raising the carbon content increases the fraction of plate martensite, and consequently the signal amplitude.
Weight Function Analysis of Interface Cracks: Mismatch Versus Oscillation
Authors: Gao Huajian
Published: April 2008

This paper has two goals. First, it is aimed at providing a fundamental understanding of the oscillatory behavior of an interface crack between two dissimilar materials from the viewpoint of the interface mismatch that results from the cracking. Second, we extend the Bueckner-Rice weight function method to facilitate the interface crack analysis. Using properties of the surface Green’s functions of a homogeneous solid and solutions obtained from weight function formulae, a mismatch analysis is carried out which indicates that the local mismatch near the crack tip results in the oscillatory near-tip field while the mismatch on the global scale leads to the corresponding stress intensity factors. For an oscillatory interface crack field, it is shown that, other than a few extra material constants, the interface weight function analysis is completely parallel to the well-developed homogeneous theory so that knowledge of one crack solution for a given bimaterial geometry is sufficient for determination of solutions under any other loading conditions.
Green’s Functions for a Point Load and Dislocation in an Annular Region
Authors: Worden R. E. , Keer L. M.
Published: April 2008

This paper contains an analysis of a two-dimensional annular region whose inner boundary is that of either a hole or a perfectly bonded, rigid inclusion. Fast-converging Green’s functions for a point load or a dislocation on the annulus are determined using analytic continuation across the boundaries of the annulus.
Conditionally Averaged Response Formulations for Two-Phase Random Mixtures
Authors: McCoy John J.
Published: April 2008

A technique known as a projection or a smoothing, which has been used successfully to derive formulations on the mean (or unconditionally averaged) field response of specimens with a random substructure, is extended to obtain formulations on conditionally averaged response measures for two-phase mixtures. The condition in the averaging refers to the location of the field point, in one or the other of the phases. The obtained formulation has the structure of a theory for interacting mixtures of nonlocal continua. The formulations are then investigated in a two-scale microscale/macroscale limit; specifically we determine the conditions necessary for the obtained formulations to reduce to local formulations which can be interpreted to provide bases for physical theories. It is argued that for weakly coupled, two-phase mixtures for which both phases are connected over distances that are measured on the macroscale, the mixture theory-type formulation is local in the limit whereas the mean-field formulation is not. In the presence of strong coupling, or for mixtures in which one of the phases is connected only for distances measured on the microscale, both type formulations are local in the two-scale limit.
Elastodynamic Local Fields for a Crack Running in an Orthotopic Medium
Authors: Piva A. , Radi E.
Published: April 2008

The dynamic stress and displacement fields in the neighborhood of the tip of a crack propagating in an orthotropic medium are obtained. The approach deals with the methods of linear algebra to transform the equations of motion into a first-order elliptic system whose solution is sought under the assumption that the local displacement field may be represented under a scheme of separated variables. The analytical approach has enabled the distinction between two kinds of orthotropic materials for which explicit espressions of the near-tip stress fields are obtained. Some results are presented graphically also in order to compare them with the numerical solution given in a quoted reference.
Frequency-Dependent Element Mass Matrices
Authors: Fergusson N. J. , Pilkey W. D.
Published: April 2008

This paper considers some of the theoretical aspects of the formulation of frequency-dependent structural matrices. Two types of mass matrices are examined, the consistent mass matrix found by integrating frequency-dependent shape functions, and the mixed mass matrix found by integrating a frequency-dependent shape function against a static shape function. The coefficients in the power series expansion for the consistent mass matrix are found to be determinable from those in the expansion for the mixed mass matrix by multiplication by the appropriate constant. Both of the mass matrices are related in a similar manner to the coefficients in the frequency-dependent stiffness matrix expansion. A formulation is derived which allows one to calculate, using a shape function truncated at a given order, the mass matrix expansion truncated at twice that order. That is the terms for either of the two mass matrix expansions of order 2n are shown to be expressible using shape functions terms of order n. Finally, the terms in the matrix expansions are given by formulas which depend only on the values of the shape function terms at the boundary.
Chaotic Dynamics of a Quasi-Periodically Forced Beam
Authors: Yagasaki K.
Published: April 2008

A straight beam with fixed ends, forced with two frequencies is considered. By using Galerkin’s method, the equation of motion of the beam is reduced to a finite degree-of-freedom system. The resulting equation is transformed into a multi-frequency system and the averaging method is applied. It is shown, by using Melnikov’s method, that there exist transverse homoclinic orbits in the averaged system associated with the first-mode equation. This implies that chaotic motions may occur in the single-mode equation. Furthermore, the effect of higher modes and the implications of this result for the full beam motions are described.
A Boundary Element Method Formulation for Design Sensitivities in Steady-State Conduction-Convection Problems
Authors: Chandra Abhijit , Chan Cho Lik
Published: April 2008

A Boundary Element Method (BEM) formulation for the determination of design sensitivities of temperature distributions to various shape and process parameters in steady-state convection-diffusion problems is presented in this paper. The present formulation is valid for constant or piecewise-constant convective velocities. This approach is based on direct differentiation (DDA) of the relevant BEM formulation of the problem. It retains the advantages of the BEM regarding accuracy and efficiency while avoiding strongly singular kernels. The BEM formulation is also observed to avoid any false diffusion. This approach provides a new avenue toward efficient optimization of steady-state convection-diffusion problems and may be easily adapted to investigate the thermal aspects of various machining processes.
Interaction Between an Edge Dislocation and a Lamellar Inhomogeneity With a Slipping Interface
Authors: Stagni L. , Lizzio R.
Published: April 2008

The plane elasticity problem of an internal stress source located near a lamellar inhomogeneity is considered. It is assumed that the lamella-matrix interface does not transmit tangential displacements or shear tractions (slipping interface). The elastic field is given in terms of the source bulk field and one parameter formed from the elastic constants. The image force on an edge dislocation near the lamella is calculated and discussed. A dislocation stable-equilibrium position exists in a domain of elastic constants and Burgers vector directions. This result is characteristic of the interaction with a slipping lamellar inhomogeneity having finite thickness.
Three-Dimensional Effective Moduli of Orthotropic and Symmetric Laminates
Authors: Roy Ajit K. , Tsai Stephen W.
Published: April 2008

A simple and accurate method for estimating the three-dimensional effective moduli of symmetric and orthotropic laminated composites is presented. The method is based on obtaining the exact displacement field of three boundary value problems of laminated composites using the Airy stress function solution technique. The effective moduli are estimated by matching the boundary displacements of the equivalent homogeneous system with those of the laminated system. Among the estimated effective moduli, those associated with the interlaminar direction are of special interest. It is found that the effective interlaminar normal stiffness in extensional deformation is independent of laminae stacking sequence which is consistent with the finding of Pagano (1974). However, the laminate interlaminar shear stiffness is dependent on stacking sequence, and it is shown that the rule of mixtures can not predict the interlaminar shear stiffness accurately.
Corner Singularities of Three-Dimensional Planar Interface Cracks
Authors: Ghahremani F. , Shih C. F.
Published: April 2008

Very high stresses develop near the intersection of a planar interfacial crack with the free surface of joined materials with large mismatch of elastic moduli. The socalled corner singularity is more singular than the 1/distance singularity of the interior fields. The eigenvalues corresponding to the most singular state, and for which the strain energy of a finite cone is bounded, are in general complex. For a wide selection of material pairs, our calculations show that the eigenvalue of the dominant singularity, 0(r−s), is real and s increases from 0.5 to about 0.75 as the moduli mismatch increases. Values of s are reported for a broad range of material combinations. A class of anisotropic materials and bicrystals is also investigated.
A Torque-Free Flexible Model Gyro
Authors: Rimrott F. P. J. , Janabi-Sharifi F.
Published: April 2008

The present investigation is concerned with the behavior of an elastic, oblate, torquefree gyro model. The model has been devised such that it represents accurately arbitrarily large attitudes and arbitrarily large deformations. All simplifying assumptions are incorporated into the model before the theory is applied. The subsequent theoretical development is consequently exact; i.e., the expressions for inertia moments, angular moments, kinetic and elastic energies are all exact. Also, the mass center of the model gyro does not shift within the gyro. Equations remain tractable and the practicing engineer can readily get a feel for the phenomena uncovered. The model is composed of a rigid massless rod connected elastically to a rigid massive disk. At the tip of each rod there is a point mass. The nonlinear equations of quasistatic motion are derived using Euler’s law, and a floating coordinate frame. Following the analysis, various numerical examples are investigated and the results are plotted. The total mechanical energy of the system is determined, and the condition for existence of an energy trap state (minimum energy state at an attitude other than zero) is obtained. When trapped, the gyro is in effect rigid, has a stable attitude, and rotates around the principal axis of maximum inertia, which in turn is collinear with the space-fixed angular momentum vector.
Crack-Tip Stress and Deformation Fields in Strain-Softening Nonlinearly Viscoelastic Materials
Authors: Moran B. , Knauss W. G.
Published: April 2008

In some polymers, stress-induced changes in molecular mobility give rise to a strain-softening effect. The influence of this effect on the stress and deformation fields near a crack tip are examined using the finite element method. A phenomenological nonlinearly viscoelastic constitutive model (based on the concept of free volume) is used in the calculations. When a load is suddenly applied to a cracked specimen, the instantaneous response of the material is linearly elastic. However, strain-induced softening in the crack-tip region leads to a relaxation in the stress and time variation of the region over which the singular field prevails. For realistic material parameters, this region may become extremely small. In addition, a zone of strain-softened material emanantes from the crack tip and extends along the crack line. This process zone can promote conditions which are favorable for the nucleation and growth of microvoids and the formation of crazes.
The Stress Fields Caused by a Circular Cylindrical Inclusion
Authors: Hasegawa Hisao , Lee Ven-Gen , Mura Toshio
Published: April 2008

Exact solutions are presented in closed forms for the axisymmetric stress and displacement fields caused by a solid or hollow circular cylindrical inclusion (with uniform axial eigenstrain prescribed) in an infinite elastic solid. The same expressions are obtained for the elastic fields for interior and exterior points of the inclusion. Although Eshelby’s solutions for ellipsoidal inclusions are uniform in the interior points, the present solutions do not show the uniformity. When the length of inclusion becomes infinite, the present solutions agree with Eshelby ’s results. The strain energy is also shown. The method of Green’s function is used.
Transient Hygrothermal Stresses Induced in General Plane Problems by Theory of Coupled Heat and Moisture
Authors: Chen Tei-Chen , Weng Cheng-I , Chang Win-Jin
Published: April 2008

A general finite element model is proposed to deal with the transient, hygrothermal stress problems by the linear theory of coupled heat and moisture that is required in the analysis of some porous and composite materials. The method consists of formulating and solving the problem in the Laplace transform domain by the finite element method and then numerically inverting the transformed solution to obtain the time domain response. Therefore, the transient solutions at any time could be evaluated directly. A number of examples are presented which demonstrate the accuracy, efficiency, and versatility of the proposed method. It can be found from the numerical results that the coupling effect between thermal and moisture is significant for composite material T300/5208. The maximum discrepancy between coupled and uncoupled solutions might be as high as 50 percent.
Multiply Loaded Rigid Punch on a Stressed Orthotopic Half-Plane via a Thin Elastic Layer
Authors: Bjarnehed Hans L.
Published: April 2008

A uniaxially stressed orthotropic half-plane indented on the free edge by a multiply loaded rigid punch via a thin elastic layer is considered. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated for the unknown interface stresses between the cushion and the half-plane. Two kinds of friction conditions between the cushion and half-plane are treated, viz. completely adhesive and frictionless contact. An analytical solution for contact with a rigid cushion and a numerical solution with an elastic cushion are presented. Also, a comparison with a corresponding FEM model is performed. For frictionless contact, some analytical results concerning optimum design of the elastic cushion are given.
A General Treatment of the Elastic Field of an Elliptical Inhomogeneity Under Antiplane Shear
Authors: Gong S. X. , Meguid S. A.
Published: April 2008

A general solution to the antiplane problem of an elliptical inhomogeneity in an isotropic elastic medium is provided. The proposed analysis is based upon the use of conformal mapping and Laurent series expansion of the corresponding complex potentials. The general expressions of the complex potentials are derived explicitly in both the elliptical inhomogeneity and the surrounding matrix. Several specific solutions are provided in closed form which are verified by comparison with existing ones. The effect of material and geometrical parameters upon the change of the elastic energy, due to the presence of an elliptical inhomogeneity, has also been considered.
Flexural Wave Propagation in an Elastic Beam With Periodic Structure
Authors: Lee Sen Yung , Ke Huei Yaw
Published: April 2008

The theory of flexural waves in an elastic beam with periodic structure is developed in terms of Floquet waves. Special relationships have been determined among the fundamental solutions of the governing equation. Two lemmas about the properties of the fundamental solutions are proved. With the help of these relations and lemmas, the analysis and classification of the dynamic nature of the problem is greatly simplified. We show that the flexural wave propagation in a periodic beam can be interpreted as the superposition of two pairs of waves propagating in opposite directions, of which one pair behaves as an attenuated wave. The dispersion spectrum of the second pair of waves shows the band structure, consisting of stopping bands and passing bands. Exploiting the symmetry of the structure, the dispersion equation at the end points of Brillouin zones is uncoupled into two simpler equations. These uncoupled equations represent the dispersion spectrum of waves which are either symmetric, or antisymmetric.
Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions
Authors: Zu Jean Wu-Zheng , Han Ray P. S.
Published: April 2008

A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.
Response of a Flexible Printed Circuit Board to Periodic Shock Loads Applied to its Support Contour
Authors: Suhir E.
Published: April 2008

Treating a printed circuit board (PCB) as a thin flexible rectangular plate, we evaluate its dynamic response to periodic shock loads applied to the support contour. The effect of the load periodicity on the amplitudes, accelerations, and stresses is analyzed for transient and steady-state damped linear vibrations, as well as for steady-state undamped nonlinear vibrations. It is shown that the transient nonresonant linear response can exceed the steady-state response by up to two times, and that the linear approach can be misleading in the case of a nondeformable support contour and intense loading. The obtained results can be of help when evaluating the accelerations, experienced by surface mounted electronic components and devices, and the dynamic stresses in a PCB of the given type, dimensions, and support conditions.
Vibration of Harmonically Excited Oscillators With Asymmetric Constraints
Authors: Natsiavas S. , Gonzalez H.
Published: April 2008

investigation is carried out for a class of piecewise linear oscillators with asymmetric characteristics. The damping and restoring forces are general trilinear functions of the system velocity and displacement, respectively, while the excitation is harmonic in time. First, an analysis is presented which determines harmonic and subharmonic steady-state response. Then, a special formulation is employed in examining the stability of located periodic motions. Finally, numerical results are presented for several representative sets of the system parameters. Effects of asymmetries in the response due to unequal gaps as well as unequal stiffness and damping coefficients are analyzed in detail. Asymmetric response of a system with symmetric technical characteristics is also investigated. The behavior of the systems examined resembles response of similar nonlinear systems with continuous characteristics, like the response of the Duffing and van der Pol oscillators. Complicated nonperiodic response is also encountered and analyzed.
Viscoelastic Behavior of Elastomeric Membranes
Authors: Feng William W.
Published: April 2008

The formulation for large deformations of an axisymmetric nonlinear plane viscoelastic membrane is developed. The solutions from the formulation for both creep and relaxation of a circular membrane are presented. An experiment that demonstrates the relaxation phenomenon was performed, and the experimental data are used to determine the constitutive equation of an elastomer.
Stochastic Modeling of Crack Initiation and Short-Crack Growth Under Creep and Creep-Fatigue Conditions
Authors: Kitamura Takayuki , Ghosn Louis J. , Ohtani Ryuichi
Published: April 2008

A simplified stochastic model is proposed for crack initiation and short-crack growth under creep and creep-fatigue conditions. Material inhomogeneity provides the random nature of crack initiation and early growth. In the model, the influence of microstructure is introduced by the variability of (1) damage accumulation along grain boundaries, (2) critical damage required for crack initiation or growth, and (3) the grain-boundary length. The probabilities of crack initiation and growth are derived by using convolution integrals. The model is calibrated and used to predict the crack density and crack-growth rate of short cracks of 304 stainless steel under creep and creep-fatigue conditions. The mean crack initiation lives are predicted to be within an average deviation of about ten percent from the experimental results. The predicted cumulative distributions of crack-growth rate follow the experimental data closely. The applicability of the simplified stochastic model is discussed and the future research direction is outlined.
The Sliding Circular Inclusion in an Elastic Half-Plane
Authors: Lee Mikyoung , Jasiuk I. , Tsuchida E.
Published: April 2008

The elastic fields due to a circular inclusion embedded in an elastic half-plane, subjected either to a uniform uniaxial stress at infinity parallel to the edge boundary, or a uniform nonshear type eigenstrain loading, are investigated. The interface between the inclusion and the remaining material is perfectly bonded, or allows pure sliding (shear tractions are specified to vanish).
Crack Deflection at an Interface Between Two Orthotopic Media
Authors: Gupta V. , Argon A. S. , Suo Z.
Published: April 2008

To achieve toughness in many brittle composites, crack deflection at interfaces is essential. For this, it is necessary to establish crack deflection criteria by employing the principles of interfacial fracture mechanics applicable to anisotropic pair of materials. Such an analysis, with two aligned orthotropic media, is considered here. The stress and deformation fields derived for such cases are shown to depend on material parameters λ and p for the two media and on the two so-called Dundur constants α and β. For β = 0, the dependence on λ and λ2 collapses to Λ = (λ1,/λ2)1/4. The delamination criterion is insensitive to λ, p, Λ, and β over practical ranges of these material parameters. Thus, generalized delamination charts become possible as a function of the bi-material constant a alone, which characterizes the elastic dissimilarity between the two media. Using these charts, it is possible to determine the desired level of the interface strength required in composite manufacturing in order to enhance the overall toughness of a composite. Furthermore, such charts can be used for the interfaces between fiber/coating, fiber /matrix, or matrix/coating, depending on which interface is of critical interest for the crack deflection. It is shown how these charts can be used to identify composite systems where it is possible to maximize both the transverse strength and the longitudinal toughness.
Creep of Power-Law Material Containing Spherical Voids
Authors: Sofronis P. , McMeeking R. M.
Published: April 2008

Finite element calculations have been carried out for spherical unit cells containing a concentric spherical hole to characterize the power law creep of a material containing voids. Axisymmetric states of macroscopic stress were applied to the unit cells ranging from purely hydrostatic loading to purely deviatoric stressing. The results of the unit cell calculations are approximated well by a creep potential for the macroscopic behavior of a porous material. This potential agrees with the unit cell results for purely hydrostatic stress and purely deviatoric stress and involves a simple elliptical interpolation in between. The model predicts quite well the ratio of transverse to axial strain rate in uniaxial compression tests.
A Method to Evaluate Three-Dimensional Time-Harmonic Elastodynamic Green’s Functions in Transversely Isotropic Media
Authors: Zhu H.
Published: April 2008

The three-dimensional time-harmonic elastodynamic Green’s functions in infinite transversely isotropic media have been derived explicitly. The Green’s functions consist of the corresponding static Green’s functions and double integral representations over a finite domain with the integrands being continuous. The Green’s functions will reduce to those for the isotropic case when the isotropic elastic constants are substituted. The singular parts of the Green’s functions have been shown to be the same as those of the static ones. The far-field approximations have been obtained by using the stationary phase method. In addition, a simpler method to construct wave front curves has been presented.
The Plastic Buckling of Axially Compressed Square Tubes
Authors: Li S. , Reid S. R.
Published: April 2008

A plastic buckling analysis for axially compressed square tubes is described in this paper. Deformation theory is used together with the realistic edge conditions for the panels of the tube introduced in our previous paper (Li and Reid, 1990), referred to hereafter as LR. The results obtained further our understanding of a number of problems related to the plastic buckling of axially compressed square tubes and simply supported rectangular plates, which have remained unsolved hitherto and seem rather puzzling. One of these is the discrepancy between experimental results and the results of plastic buckling analysis performed using the incremental theory of plasticity and the unexpected agreement between the results of calculations based on deformation theory for plates and experimental data obtained from tests conducted on tubes. The non-negligible difference between plates and tubes obtained in the present paper suggests that new experiments should be carried out to provide a more accurate assessment of the predictions of the two theories. Discussion of the results herein also advances our understanding of the compact crushing behavior of square tubes beyond that given in LR. An important conclusion reached is that strain hardening cannot be neglected for the plastic buckling analysis of square tubes even if the degree of hardening is small since doing so leads to an unrealistic buckling mode.
Elastodynamic Analysis of a Periodic Array of Mode III Cracks in Transversely Isotropic Solids
Authors: Zhang Ch.
Published: April 2008

Time-harmonic elastodynamic analysis is presented for a periodic array of collinear mode III cracks in an infinite transversely isotropic solid. The scattering problem by a single antiplane crack is first formulated, and the scattered displacement field is expressed as Fourier integrals containing the crack opening displacement. By using this representation formula and by considering the periodicity conditions in the crack spacing, a boundary integral equation is obtained for the crack opening displacement of a reference crack. The boundary integral equation is solved numerically by expanding the crack opening displacement into a series of Chebyshev polynomials. Numerical results are given to show the effects of the crack spacing, the wave frequency, the angle of incidence, and the anisotropy parameter on the elastodynamic stress intensity factors.
Shear Constitutive Relations for Laminated Anisotropic Shells and Plates: Part II—Vibrations of Composite Cylinders
Authors: Chun C. K. , Dong S. B.
Published: April 2008

In Part I of this paper, a system of shear constitutive relations was proposed for a first-order shear deformation theory of laminated anisotropic plates and shells. For laminated anisotropic structures, these shear constitutive equations involved the concept of generalized shear planes. Herein, an extensive parametric study is presented to assess the modeling capability of these shear constitutive relations in a class of laminated composite and sandwich cylinders. Classical theory results are also given in order to fully understand the influence of anisotropy on the accuracy and ranges of validity of both first-order shear deformation theory and classical theory. It is seen that the proposed system of shear constitutive relations provides highly accurate frequency results over the range of anisotropy considered.
A Theorem on the Exact Nonsimilar Steady-State Motions of a Nonlinear Oscillator
Authors: Vakakis A. F. , Caughey T. K.
Published: April 2008

In this work the steady-state motions of a nonlinear, discrete, undamped oscillator are examined. This is achieved by using the notion of exact steady state, i.e., a motion where all coordinates of the system oscillate equiperiodically, with a period equal to that of the excitation. Special forcing functions that are periodic but not necessarily harmonic are applied to the system, and its steady response is approximately computed by an asymptotic methodology. For a system with cubic nonlinearity, a general theorem is given on the necessary and sufficient conditions that a excitation should satisfy in order to lead to an exact steady motion. As a result of this theorem, a whole class of admissible periodic functions capable of producing steady motions is identified (in contrast to the linear case, where the only excitation leading to a steady-state motion is the harmonic one). An analytic expression for the modal curve describing the steady motion of the system in the configuration space is derived and numerical simulations of the steady-state motions of a strongly nonlinear oscillator excited by two different forcing functions are presented.
Vibrations of Sectorial Plates Having Corner Stress Singularities
Authors: Leissa A. W. , McGee O. G. , Huang C. S.
Published: April 2008

A procedure is presented for determining the free vibration frequencies and mode shapes of sectorial plates having re-entrant corners (i.e., vertex angles exceeding 180 degrees). No correct results for such problems have been found in the vast literature of plate vibrations. The procedure is applicable to sectorial plates having arbitrary (but continuous) boundary conditions (e.g., clamped, simply supported, or free) along the two radial edges and the circular edge. It is based upon the Ritz method, but utilizes two sets of admissible functions simultaneously. One set consists of algebraic-trigonometric polynomials. The other is the set of corner functions derived by Williams (1952) to deal with the bending stress singularities which may arise at the corner when the vertex angle becomes large. The method is demonstrated for sectorial plates having all edges simply supported, which yields the strongest singularity in a re-entrant corner. Frequencies are compared with those obtained from an analytical solution involving Bessel functions. It is shown that the latter solution is invalid for re-entrant corners. Analytical solutions are also obtained for annular sectorial plates having very small ratios of inner to outer boundary radii. These solutions are found to be consistent with those using polynomials and corner functions. Accurate fundamental frequency data is presented for simply supported sectorial plates having three values of Poisson’s ratio (0, 0.3, 0.5) and the full range of vertex angles (0 < α ≤ 360 deg).
Stochastic Dynamics of Nonlinear Systems Driven by Non-normal Delta-Correlated Processes
Authors: Di Paola Mario , Falsone Giovanni
Published: April 2008

In this paper, nonlinear systems subjected to external and parametric non-normal delta-correlated stochastic excitations are treated. A new interpretation of the stochastic differential calculus allows first a full explanation of the presence of the Wong-Zakai or Stratonovich correction terms in the Itoˆ’s differential rule. Then this rule is extended to take into account the non-normality of the input. The validity of this formulation is confirmed by experimental results obtained by Monte Carlo simulations.
General Crack-Tip Fields for Stationary and Steadily Growing Interface Cracks in Anisotropic Bimaterials
Authors: Deng X.
Published: April 2008

This study builds upon some recent results in the literature regarding the asymptotic behavior of bimaterial interface cracks, and gives the general form, both oscillatory and nonoscillatory, of the crack-tip stress and displacement fields for stationary and steadily growing interface cracks in anisotropic bimaterials, which are equivalent to complete Williams-type series expansions. Special cases, such as cracks in homogeneous anisotropic materials and interface cracks with decoupled antiplane shear and in-plane deformations, are discussed briefly. Explicit series expansions of the stress and displacement fields in crack-tip polar coordinates are derived for both stationary and steadily propagating interface cracks in isotropic bimaterials.
On the Conditions to Prevent Plastic Shakedown of Structures: Part II—The Plastic Shakedown Limit Load
Authors: Polizzotto Castrenze
Published: April 2008

Following the results of a companion paper, the concept of plastic shakedown limit load is introduced for an elastic-perfectly plastic material structure subjected to combined cyclic (mechanical and/or kinematical) loads and steady (mechanical) load. Static and kinematic approaches are available for the computation of this load, in perfect analogy with the classic (elastic) shakedown limit load. The plastic shakedown limit state of the structure being in an impending alternating plasticity collapse is studied and a number of interesting features of it are pointed out.
On the Interaction of Torsion and Bending in Rotating Shafts
Authors: Nataraj C.
Published: April 2008

The problem of torsional and transverse deformations of a shaft rotating at a constant speed is considered. The displacements are expressed in a perturbation series in terms of a small parameter. Energy expressions are derived to each order and Hamilton’s principle is applied to obtain the equations of motion and the boundary conditions governing the displacement functions of different orders. It is clearly shown that the interaction of torsion and transverse vibration occurs at second order. Previous work reporting results of torsional vibration caused at a frequency equal to twice the rotational speed due to this interaction is confirmed.
A Beam Theory for Laminated Composites and Application to Torsion Problems
Authors: Sankar Bhavani V.
Published: April 2008

A theory for laminated composite beams is derived from the shear deformable laminated plate theory. The displacement field in the beam is derived by retaining the first-order terms in the Taylor series expansion for the plate midplane deformations in the width coordinate. The displacements in the beam are expressed in terms of three deflections, three rotations, and one warping term. The equilibrium equations are assumed to be satisfied in an average sense over the width of the beam. This introduces a new set of force and moment resultants for the beam. The principle of minimum potential energy is applied to derive the equilibrium equations and boundary conditions. A closed-form solution is derived for the problem of torsion of a specially orthotropic laminated beam.
Exact Elasticity Solution for Laminated Anisotropic Cylindrical Shells
Authors: Bhaskar K. , Varadan T. K.
Published: April 2008

An exact three-dimensional elasticity solution is obtained for cylindrical bending of simply-supported laminated anisotropic cylindrical shell strips subjected to transverse loading. Displacements and stresses are presented for different angle-ply layups and radius-to-thickness ratios, so as to serve as useful benchmark results for the assessment of various two-dimensional shell theories. Finally, in the light of these results, the accuracy of the Love-type classical shell theory is examined.