bluuebunny/crossref_metadata_2025 huggingface dataset:
Multi-Flexible Body Dynamics Capturing Motion-Induced Stiffness
Authors: Banerjee A. K. , Lemak M. E.
Published: April 2008

This paper presents a multi-flexible-body dynamics formulation incorporating a recently developed theory for capturing motion-induced stiffness for an arbitrary structure undergoing large rotation and translation accompanied by small vibrations. In essence, the method consists of correcting dynamical equations for an arbitrary flexible body, unavoidably linearized prematurely in modal coordinates, with generalized active forces due to geometric stiffness corresponding to a system of 12 inertia forces and 9 inertia couples distributed over the body. Computation of geometric stiffness in this way does not require any iterative update. Equations of motion are derived by means of Kane’s method. A treatment is given for handling prescribed motions and calculating interaction forces. Results of simulations of motions of three flexible spacecraft, involving stiffening during spinup motion, dynamic buckling, and a slewing maneuver, demonstrate the validity and generality of the theory.
A Geometrical Approach Assessing Instability Trends for Galloping
Authors: Yu P. , Popplewell N. , Shah A. H.
Published: April 2008

Although the galloping of an iced electrical conductor has been considered by many researchers, no special attention has been given to the galloping’s sensitivity to alternations in the system’s parameters. A geometrical method is presented in this paper to describe these instability trends and to provide compromises for controlling an instability. The conventional but uncontrollable parameter of the wind speed is chosen as the basis for obtaining the critical conditions under which bifurcations occur for a representative two degrees-of-freedom model. Variations in these critical conditions are found in a two-dimensional parameter space in order to determine the trends for the initiation of galloping as well as to evaluate the stability of the ensuring periodic vibrations.
Bending of a Thin Reissner Plate With a Through Crack
Authors: Joseph P. F. , Erdogan F.
Published: April 2008

The title problem was first considered by Knowles and Wang (1960) and was shown to be related to the solution given by the classical plate theory. This solution is actually the outer solution of a singular perturbation problem, and therefore is valid only away from the crack-tip region. Within a boundary layer of order h/a, where h is the plate thickness and a is the half-crack length, the two theories differ considerably. In this study the leading order solution is obtained for h/a - 0 and it is shown that the limiting stress intensity factor given by the Reissner plate theory is more than 50 percent higher than the asymptotic result (1 + v)/(3 + v) which is obtained from the displacement field as given by the classical plate theory.
Analysis and Application of a Coupled Thermoviscoplasticity Theory
Authors: Ghoneim H.
Published: April 2008

Coupled thermoviscoplasticity equations are developed based on the rational theory of thermodynamics. A power-form internal state variable constitutive equation is proposed. Limitation of the proposed constitutive equation is discussed and simulation results of cyclic loading of 1070 steel at different temperatures and strain rates are presented. The developed coupled equations and the proposed constitutive equation are implemented into a finite element program which is used to investigate the thermomechanical problem of cyclic loading of a constrained-ended cylinder.
A General Theory on Media with Randomly Distributed Inclusions: Part I—The Average Field Behaviors
Authors: Wang B.
Published: April 2008

In this paper, a theory is developed to calculate the average strain field in the materials with randomly distributed inclusions. Many previous researches investigating the average field behaviors were based upon Mori and Tanaka’s idea. Since they were restricted to studying those materials with uniform distributions of inclusions they did not need detailed statistical information of random microstructures, and could use the volume average to replace the ensemble average. To study more general materials with randomly distributed inclusions, the number density function is introduced in formulating the average field equation in this research. Both uniform and nonuniform distributions of inclusions are taken into account in detail.
Correspondence Relations for the Interface Crack in Monoclinic Composites Under Mixed Loading
Authors: Wu Kuang-Chong , Hwang Shyh-Jye
Published: April 2008

A correspondence is established between the problem of an interface crack in mon-oclinic composites and that of an interface crack in isotropic composites. The interface crack considered is subjected to a combined tension-compression, in-plane shear and antiplane shear loading at the crack faces. Under the applied loading, the interface crack is assumed to be partially opened. Through the correspondence, quantities of interest such as stress intensity factors, sizes of the contact zones, for monoclinic composites can be obtained from the results of the isotropic interface crack problem.
On the Wave Propagation in Elastic Multilayer Periodic Media With Nonlocal Interactions
Authors: Nowinski J. L.
Published: April 2008

After a brief review of the main concepts of the nonlocal theory of elasticity, the equations of the nonlocal elastic moduli are derived, and the constitutive equations of the nonlocal medium established. Propagation of a longitudinal time-periodic wave normal to the laminae of the layered medium is then analyzed, and the equation of the wave dispersion determined. The dispersion originates from two sources: the configuration (discreteness) of the structure, and the nonlocal constitution of the material of the laminae. A numerical example accompanied by a graph illustrates the dependence of the effective wave velocity on the wave number in the entire Brillouin zone. It is found that for very short waves the wave velocity decreases to about 64 percent of its conventional value established for waves of long wavelength.
Thermal Stresses in a Multilayered Anisotropic Medium
Authors: Thangjitham Surot , Choi Hyung Jip
Published: April 2008

A steady-state thermoelasticity problem of a multilayered anisotropic medium under the state of generalized plane deformation is considered in this paper. By utilizing the Fourier transform technique, the general solutions of thermoelasticity for layers with transversely isotropic, orthotropic, and monoclinic properties are derived. The complete solution of the entire layered medium is then obtained through introducing the thermal and mechanical boundary and layer interface conditions. This is accomplished via the flexibility/stiffness matrix method. As a numerical illustration, the distributions of temperature and thermal stresses in a laminated anisotropic slab subjected to a uniform surface temperature rise are presented for various stacking sequences of fiber-reinforced layers.
An Invariant-Based Flow Rule for Anisotropic Plasticity Applied to Composite Materials
Authors: Hansen Andrew C. , Blackketter Donald M. , Walrath David E.
Published: April 2008

In this paper we discuss some fundamental problems associated with incremental anisotropic plasticity theories when applied to unidirectional composite materials. In particular, we question the validity of an effective stress-strain relation for highly anisotropic materials of this nature. An effective stress-strain relation is conventionally used to determine a flow rule for plastic strain increments. It is our view that such a relation generally does not exist for many high-performance unidirectional composites. To alleviate the problem associated with defining an effective stress-strain curve we develop an anisotropic plasticity theory in which the flow rule does not requires such a relation. The proposed theory relies on developing an accurate expression for a scalar hardening parameter g(σ). The general form of g(σ) is substantially reduced by invoking invariance requirements based on material symmetry. The general invariant-based theory developed herein is specialized to case of transverse isotropy and applied to the analysis of a nonlinear elastic-plastic unidirectional composite material. The invariant-based theory is shown to produce superior results over the traditional approach for a series of uniaxial and biaxial load cases predicted using finite element micromechanics.
Elastic-Plastic Deformation in Surface-Cracked Plates: Experiment and Numerical Analysis
Authors: Wang Y.-Y. , Parks D. M. , Lloyd W. R. , Reuter W. G. , Epstein J.
Published: April 2008

Detailed three-dimensional nonlinear finite element (FE) analyses and experimental moire studies are performed on a plate containing a moderately deep part-through surface crack to establish limits of HRR-dominance. The plate is subjected to predominantly far-field tensile loading. The material under investigation is ASTM A710 steel, which was constitutively modeled by large deformation J2 flow theory of plasticity. The FE mesh was carefully constructed to resolve both crack front fields (such as J-integral and CTOD) and global fields (such as surface displacements, strains). By comparing the J-integral and CTOD results with an earlier HRR-dominance study using (small strain) deformation theory of plasticity, we found little effect of the different formulations on the crack front fields. The global deformation fields from the numerical simulation are in good agreement with our experimental results. The eventual loss of HRR-dominance is intimately related to the interaction of the global plastic flow fields with those of the crack front.
Measurement of Monotonic Biaxial Elastoplastic Stresses at Notch Roots
Authors: Sharpe W. N.
Published: April 2008

Biaxial principal strains were measured at the roots of notches in aluminum specimens with a laser-based interferometric technique. Interference patterns from three tiny indentations spaced 150 or 200 micrometers apart in an orthogonal pattern were monitored with a microcomputer-controlled system. Elastoplastic strains up to one percent were measured in real time with a resolution of 25 microstrain. Procedures were developed for computing the two principal stresses from the incremental strain data using J2-flow theory. The validity of the computations was checked by computing the stresses in smooth tensile specimens. Anisotropy in the thin sheet material leads to errors in the computed lateral stresses (which should be zero), but the maximum deviation of the computed effective stress from the uniaxial stress is only five percent. Three kinds of double-notched specimens were prepared to vary the amount of constraint at the notch root. These were tested under monotonic tensile loading and the biaxial notch-root strains recorded. There is considerable variation among the strains once the elastic limit is passed. This is due primarily to the local inhomogeneity of plastic strain, since the gage length of the measurement is only a few times larger than the grain size of the material. Local biaxial stresses were computed from the measured strains for the three cases. The nature of the material’s stress-strain curve tends to smooth out the variations among tests, particularly when the effective stress is computed. It is discovered that the local stress predicted by the Neuber relation agrees very closely with the measured local effective stress.
A Crack Terminating at a Slipping Interface Between Two Materials
Authors: Gharpuray V. M. , Dundurs J. , Keer L. M.
Published: April 2008

The paper investigates an edge crack that terminates at a slipping interface with a different material. The formulation is reduced to a singular integral equation. The integral equation is solved and the stress intensity factor extracted using a numerical method. Moreover, the asymptotic nature of the stresses at the open tip of the crack is studied.
On the Behavior of Pretwisted Beams With Irregular Cross-Sections
Authors: Kosmatka J. B.
Published: April 2008

An analytical model is developed to study the extension-bending-torsion coupling behavior of an initially twisted elastic beam with an irregular cross-section. The determination of the complete displacement field requires solving a coupled two dimensional boundary value problem in a curvilinear coordinate system for the local deformations in the section plane and warping out of the section plane. The principle of minimum potential energy is applied to a discretized representation of the cross-section (Ritz method) to calculate solutions to this problem. Numerical results illustrate the pronounced effects pretwist, initial twist axis location, and in-plane deformation have on the behavior of solid and single and multi-celled sections, including airfoil sections.
Low-Dimensional Chaos in a Flexible Tube Conveying Fluid
Authors: Pai¨doussis M. P. , Cusumano J. P. , Copeland G. S.
Published: April 2008

This paper describes the observed dynamical behavior of a cantilevered pipe conveying fluid, an autonomous nonconservative (circulatory) dynamical system, limit-cycle motions of which, upon loss of stability via a Hopf bifurcation, interact with nonlinear motion-limiting constraints. This system was found to become chaotic at sufficiently high flow rates. Motions of the system, sensed by an optical tracking system, were analyzed by Fast Fourier Transform, autocorrelation, Poincare´ map, and delay embedding techniques, and the fractal dimension of the system, dc, was calculated. Values of dc = 1.03, 1.53, and 3.20 were obtained in the period-1, “fuzzy” period-2 and chaotic regimes of oscillation of the system. Based on these calculations, a four-dimensional analytical model was constructed, which was found to capture the essential dynamical features of observed behavior quite well.
Improved Bounds on the Effective Elastic Moduli of Random Arrays of Cylinders
Authors: Torquato S. , Lado F.
Published: April 2008

Improved rigorous bounds on the effective elastic moduli of a transversely isotropic fiber-reinforced material composed of aligned, infinitely long, equisized, circular cylinders distributed throughout a matrix are evaluated for cylinder volume fractions up to 70 percent. The bounds are generally shown to provide significant improvement over the Hill-Hashin bounds which incorporate only volume-fraction information. For cases in which the cylinders are stiffer than the matrix, the improved lower bounds provide relatively accurate estimates of the elastic moduli, even when the upper bound diverges from it (i.e., when the cylinders are substantially stiffer than the matrix). This last statement is supported by accurate, recently obtained Monte Carlo computer-simulation data of the true effective axial shear modulus.
Strain-Hardening Creep Relaxation
Authors: Huneault P. A.
Published: April 2008

Relaxation testing is an important alternative for investigating the creep properties of a material. A solution for the strain-hardening form of the power law is derived and compared to its time-hardening counterpart.
Modeling of Creep of Misaligned Short-Fiber Reinforced Ceramic Composites
Authors: Pachalis John R. , Chou Tsu-Wei
Published: April 2008

A model is developed to predict the steady-state creep behavior of misaligned short-fiber-reinforced ceramic matrix composites. The approach is based on an advanced shear-lag model and uses the multiaxial creep law for the fibers and matrix. The analysis incorporates some unique characteristics of ceramic matrix composites, such as the fiber/matrix interface sliding effect, shear and axial loads carried by the matrix, and the fact that both the fibers and matrix creep at elevated temperatures. Several parameters are varied to determine their effect on the creep behavior.
Static Axisymmetric End Problems in Semi-infinite and Finite Solid Cylinders
Authors: Kim Yoon Young , Steele Charles R.
Published: April 2008

Our earlier technique for a semi-infinite strip (Kim and Steele, 1990) is extended to study general end problems and corner singularities for semi-infinite and finite solid cylinders with free walls. For handling general end conditions, we expand the displacement and stress in term of the Dini series which are the solutions of the cylinders with mixed wall conditions. The relation between the harmonic coefficients of the end displacement and stress is then formed, which we call the end stiffness matrix. One advantage of the end stiffness matrix approach is that the procedure for finite cylinders can be easily built up from that of semi-infinite cylinders. For some end conditions which may yield singular stresses, the nature of the singularity is investigated by the asymptotic analysis of the Dini series coefficients of the stresses. The problems studied by Benthem and Minderhoud (1972) and Robert and Keer (1987) are solved with the present approach.
Grain Size Reduction in Granular Flows of Spheres: The Effects of Critical Impact Energy
Authors: Richman M. W. , Oyediran A. A.
Published: April 2008

We extend methods employed to derive recent kinetic theories for rapid noncomminuting granular flows, to homogeneous flows in which a fraction of the repeated collisions produce tiny fractures on the particles’ peripheries and gradually reduce their effective diameters. The theory consists of balance equations for mass, momentum, and energy, as well as constitutive relations for the pressure tensor and collisional rates of mass and energy lost. We improve upon the work of Richman and Chou (1989) by incorporating into the constitutive theory the critical impact energy below which no mass loss occurs in a binary collision. The theory is applied to granular shear flows and, for fixed shear rates, predicts the time variations of the solid fraction, granular temperature, and induced stresses, as well as their extreme sensitivities to small changes in the critical impact energy.
Compression of a Cord
Authors: Prakash Amit , Conway Ted A. , Costello George A.
Published: April 2008

Cord is a structural element that is generally used to resist relatively large axial loads in tension in comparison to bending and torsional loads. However, in certain cases, a cord may be called upon to resist a compressive load such as occurs when a cord is placed in a composite. When a cord is subjected to compression, the individual filaments lose contact with each other. This results in a considerable reduction in the axial stiffness of the cord. Generally, most cord composites are fabricated at elevated temperatures and cooled to room temperatures. Some remarks are made concerning the buckling of these cords since the coefficients of thermal expansion are different for the matrix and the cord.
Effect of Accuracy Loss in Classical Shell Theory
Authors: Berdichevsky V. , Misyura V.
Published: April 2008

It is shown that classical shell theory does not yield correct values of displacements in some shell problems. Underlying causes of this effect are discussed.
Frequency Window Method for Strongly Coupled and Multiply Connected Structural Systems: One-Mode Windows
Authors: Min Kyung-Won , Igusa Takeru , Achenbach Jan D.
Published: April 2008

A method is presented to analyze the dynamic behavior of a structural system consisting of a main structure and strongly coupled, multiply connected substructures. Lagrange’s equations are used to develop a characteristic equation for connected substructures in terms of substructure impedances and mobilities. Then, a frequency window method is used to reduce the complexity of the problem by a decomposition of the impedance and mobility functions into dominant and highorder rational expressions. From the reduced problem, simple expressions for the modal properties are developed using matrix algebraic methods, which provide insight into the resonance characteristics of the connected substructures. Higherorder terms, which become significant for strongly coupled substructures, are included in the eigenvalue analysis by using an iterative procedure. It is shown that the frequency window method developed in this paper, used as a numerical scheme, produces results which converge to exact results after only a few iterations.
Frequency Window Method for Strongly Coupled and Multiply Connected Structural Systems: Multiple-Mode Windows
Authors: Min K.-W. , Igusa T. , Achenbach J. D.
Published: April 2008

In a companion paper, a method is presented to analyze the dynamic behavior of a structural system consisting of a main structure and strongly coupled, multiply connected substructures. Lagrange’s equations are used to develop a characteristic equation for connected substructures in terms of substructure impedances and mobilities. A frequency window method is used to reduce the complexity of the problem by a decomposition of the impedance and mobility functions into dominant and higher-order rational expressions. From the reduced problem, simple expressions for the modal properties are developed using matrix algebraic methods, which provide insight into the resonance characteristics of the connected substructures. Onemode windows were discussed in detail and examples were presented. In the present paper the theory is extended to multiple-mode windows.
An Evaluation of the Neuber and Glinka Relations for Monotonic Loading
Authors: Sharpe W. N. , Yang C. H. , Tregoning R. L.
Published: April 2008

The Neuber relation is widely used to compute elastoplastic stresses and strains at stress concentrations, but a newer relation has been developed by Glinka. Prediction of local strain response is important because low cycle, fatigue life models are based on the strain range. The effects of notch root constraint on the response have been difficult to predict or measure. This paper evaluates the abilities of six models of notch root behavior by comparing them with experimental results over a range of constraints. The models are: the Neuber model, the Neuber model as modified by Walker, the Glinka models for plane stress and for plane strain, and two modifications of the Glinka models that are presented in this paper. Comparisons are made with strains measured at the roots of notches by resistance gages or by laser-based interferometry; data come from previous works as well as some new results of the authors. The constraints vary from plane stress to plane strain with several intermediate cases. Conclusions must take into account the fact that elastoplastic strain measurements have scatter arising from the gage length relative to the grain size. But, in general, one can say that the Neuber model is best for plane stress and the Glinka plane-strain model is best for very large constraint. Response for intermediate amounts of constraint are predicted better by one of the other models.
Reflection and Transmission of Obliquely Incident Surface Waves by an Edge of a Quarter Space: Theory and Experiment
Authors: Li Z. L. , Achenbach J. D. , Komsky I. , Lee Y. C.
Published: April 2008

The reflection and transmission of a plane time-harmonic surface wave which is obliquely incident on the edge of a quarter space is investigated theoretically, numerically, and experimentally. The theoretical formulation of the problem, which takes advantage of the translational invariance along the edge of the quarter space, is reduced to a system of singular integral equations along axes normal to the edge, for the defracted displacement components on the faces of the quarter space axes normal to the edge. The truncation of these equations leads to the definition of reflection and transmission coefficients, R and T. The equations are solved for R, T, and the diffracted displacements by the use of the boundary element method. A self-calibrated experimental technique is proposed which deploys four surface wave transducers, and which removes the effects of variable coupling between the transducers and the faces of the quarter space as the positions of the transducers are varied. The technique is particularly suited for the measurement of |R/T| as a function of the angle of incidence. Excellent agreement is observed between numerically and experimentally obtained values.
Flow Resistance and Mass Transfer in Slow Non-Newtonian Flow Through Multiparticle Systems
Authors: Satish M. G. , Zhu J.
Published: April 2008

Finite difference solutions for a power-law fluid flow through an assemblage of solid particles at low Reynolds numbers are obtained using both the free-surface cell model and the zero-vorticity cell model. It is shown that, unlike in the case of power-law fluid flow past a single solid sphere, the flow drag decreases with decrease of flow behavior index, and that the degree of this reduction is more significant at low voidage. The results from this study are found to be in good agreement with the approximate solutions at slight pseudoplastic anomaly and the available experimental data. The results are presented in closed form and compare favorably with the variational bounds and the modified Blake-Kozeny equations. Numerical results show that a decrease in the flow behavior index leads to a slight increase in the mass transfer rate for an assemblage of solid spheres, but this increase is found to be small compared with that for a single solid sphere.
Determination of the Angular Velocity Vector in Orthogonal Curvilinear Coordinate Systems
Authors: Richardson D. L.
Published: April 2008

An efficient, general procedure is developed for assembling the components of the angular velocity vector of orthogonal curvilinear coordinate frames
Chaotic Vibrations of Beams: Numerical Solution of Partial Differential Equations
Authors: Abhyankar N. S. , Hall E. K. , Hanagud S. V.
Published: April 2008

The objective of this paper is to examine the utility of direct, numerical solution procedures, such as finite difference or finite element methods, for partial differential equations in chaotic dynamics. In the past, procedures for solving such equations to detect chaos have utilized Galerkin approximations which reduce the partial differential equations to a set of truncated, nonlinear ordinary differential equations. This paper will demonstrate that a finite difference solution is equivalent to a Galerkin solution, and that the finite difference method is more powerful in that it may be applied to problems for which the Galerkin approximations would be difficult, if not impossible to use. In particular, a nonlinear partial differential equation which models a slender, Euler-Bernoulli beam in compression issolvedto investigate chaotic motions under periodic transverse forcing. The equation, cast as a system of firstorder partial differential equations is directly solved by an explicit finite difference scheme. The numerical solutions are shown to be the same as the solutions of an ordinary differential equation approximating the first mode vibration of the buckled beam. Then rigid stops of finite length are incorporated into the model to demonstrate a problem in which the Galerkin procedure is not applicable. The finite difference method, however, can be used to study the stop problem with prescribed restrictions over a selected subdomain of the beam. Results obtained are briefly discussed. The end result is a more general solution technique applicable to problems in chaotic dynamics.
A Bilinear Variational Principle Governing Longitudinal Vibration of Rods With Frequency-Dependent Material Damping
Authors: Lesieutre George A.
Published: April 2008

The equations governing the longitudinal vibration of rods with frequency-dependent material damping are developed as the Euler equations of a bilinear variational principle. Frequency-dependent material damping and modulus are accommodated through the introduction of an augmenting thermodynamic field that interacts with the mechanical displacement field. These two primary dependent fields are supplemented with two corresponding adjoint fields for the purpose of addressing nonconservative system behavior. The variational function is nearly symmetric in the primary and adjoint variables, a formulation which may be particularly useful in computational simulation of system behavior using finite elements. The augmenting thermodynamic field is found to be effectively internal—no boundary conditions involve it alone.
Boundary Layer Phenomena in Large Deflection, Small Strain Plate Theory
Authors: Berg L. J.
Published: April 2008

Boundary layers exist at the edges of thin plates undergoing large deformations because the interior of the plate must assume a developable shape. The developable shape is sometimes incompatible with the force and moment resultants prescribed at the plate’s boundary, in particular when the edge of the plate is stress free. A boundary layer solution is presented which describes the shape of a boundary layer in a plate undergoing large deflections. The boundary layer is a slight perturbation of the interior shape which allows the appropriate boundary conditions to be satisfied. Since developable shells are applicable to a plane, the boundary layer is also appropriate for arbitrary developable shells.
Hollow Circular Cylindrical Inclusion at the Surface of a Half-Space
Authors: Hasegawa Hisao , Lee Ven-Gen , Mura Toshio
Published: April 2008

Exact solutions are presented in closed form for the axisymmetric stresses and displacement fields caused by a solid or hollow circular cylindrical inclusion in the present of uniform eigenstrain in a half space. The elastic fields for interior and exterior points are expressed by one analytical form. The strain energy is also obtained in closed forms.
Comparison of Crystal Plasticity and Isotropic Hardening Predictions for Metal-Matrix Composites
Authors: Needleman A. , Tvergaard V.
Published: April 2008

In a numerical micromechanical study of the tensile properties of a metal reinforced by short whiskers, the elastic-plastic deformations of the metal are described in terms of crystalline plasticity, using a planar crystal model that allows for either two or three slip systems. Plane strain analyses are carried out for a periodic array of aligned whiskers for whisker volume fractions of 10 percent to 30 percent, and comparison is made with predictions based on a corresponding flow theory of plasticity with isotropic hardening. The predicted trend for composite strengthening with whisker volume fraction is the same for the various matrix material constitutive characterizations. It is found that the crystal model can give rise to shear localization, initiating at the sharp whisker edges. As a consequence of this localization, the stress carrying capacity eventually drops.
Statistical Properties of Residual Stresses and Intergranular Fracture in Ceramic Materials
Authors: Ortiz M. , Suresh S.
Published: April 2008

The problem addressed in this paper concerns the statistical characterization of the state of residual stress generated in polycrystalline ceramics during cooling from the fabrication temperature. Detailed finite element simulations are carried out for an ensemble of large numbers of randomly oriented, planar hexagonal grains with elastic and thermal expansion anisotropy, and brittle grain interfaces. The calculations show that the distribution of normal and shear tractions induced by thermal contraction mismatch among grains is gaussian and that these tractions are statistically independent random variables. Although the gaussian nature of the distributions remains unaffected by the introduction of elastic anisotropy, the results indicate that elastic anisotropy has a significant effect on the residual stresses for finite departures from isotropy. When the hexagonal grains are randomly distorted, the magnitude and distribution of residual stresses are found to be insignificantly altered. Spontaneous microfracture due to the generation of internal stresses is also simulated in the analysis by allowing for the nucleation and growth of intergranular microcracks when the fracture energy along the grain facets exceeds a certain critical value. When such microcracking is incorporated into the computation, the levels of residual stress are markedly reduced as a consequence of stress dissipation. The dependence of intergranular microcracking on grain size and temperature variation is examined and the predicted trends on material degradation or the complete suppression of microfracture are discussed in the light of available experimental results.
Universal Relations in Piezoelectric Composites With Eigenstress and Polarization Fields, Part I: Binary Media—Local Fields and Effective Behavior
Authors: Benveniste Y.
Published: April 2008

Binary composite media of arbitrary phase geometry are considered. The constituent phases have general anisotropic piezoelectric behavior and contain constant eigenstress and spontaneous polarization fields. An electromechanical loading of the composite aggregate is found which results in uniform strain and electric field intensity throughout the solid. The existence of these uniform fields is used to derive exact universal relations between the local fields as well as between the effective constants of the composite aggregate.
Dynamics of Bipedal Gait: Part I—Objective Functions and the Contact Event of a Planar Five-Link Biped
Authors: Hurmuzlu Y.
Published: April 2008

Previous approaches to the problem of prescribing the motion of bipedal machines do not completely characterize the desired walking patterns in terms of coherent parameters. A well-structured parametric formulation that ties the objective functions to the resulting gait patterns has never been established. This article presents an approach that can be followed to formulate objective functions which can be used to prescribe the gait of a planar, five-element, bipedal automaton during single support phase. The motion of the biped is completely characterized in terms of progression speed, step length, maximum step height, and stance knee bias. Kinematic relations have been derived and the inverse problem has been solved to perform a parametric study that correlates the regions of the four-dimensional parameter space with the respective gait patterns. Major limitations include the assumptions of rigid elements and point contact between the lower limbs and the walking surface. Most importantly, the motion of the biped is assumed to perfectly conform with the objective functions at the instant of contact. The control and stability issues are presented in Part II of this paper.
On the Stability of the Damped Hill’s Equation With Arbitrary, Bounded Parametric Excitation
Authors: Rahn C. D. , Mote C. D.
Published: April 2008

The minimum damping for asymptotic stability is predicted for Hill’s equation with any bounded parametric excitation. It is shown that the response of Hill’s equation with bounded parametric excitation is exponentially bounded. The parametric excitation maximizing the bounding exponent is identified by time optimal control theory. This maximal bounding exponent is balanced by viscous damping to ensure asymptotic stability. The minimum damping ratio is calculated as a function of the excitation bound. A closed form, more conservative estimate of the minimum damping ratio is also predicted. Thus, if the general (e.g., unknown, aperiodic, or random) parametric excitation of Hill’s equation is bounded, a simple, conservative estimate of the damping required for asymptotic stability is given in this paper.
Multiply Loaded Timoshenko Beam on a Stressed Orthotropic Half-Plane via a Thin Elastic Layer
Authors: Bjarnehed H.
Published: April 2008

The problem of bonded contact between a uniform finite Timoshenko beam and an orthotropic half-plane via a thin elastic layer is considered in this paper. The beam is loaded by distributions of normal and tangential forces, and a uniaxial stress load is applied to the half-plane. The Timoshenko beam theory is extended in such a way that the tangential load is included when the shear contribution to the beam central line deflection is calculated. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated and numerically solved for the unknown interface stresses. A comparison with a corresponding FE-model is also performed.
First-Order Perturbation Analysis of Transient Interlaminar Thermal Stress in Composites
Authors: Wang Y. R. , Chou T.-W.
Published: April 2008

The first-order perturbation analysis of the three-dimensional transient interlaminar thermal stresses of a symmetric composite laminate has been performed in this paper. Numerical results for a four-layer angle-ply laminate have shown that the first-order analysis was necessary for the solution of thick laminate (thickness-to-width ratio ε ≥ 0.02).
Dynamic Wrinkling of Viscoelastic Membranes
Authors: Jenkins C. H. , Leonard J. W.
Published: April 2008

Problems associated with viscoelastic membrane structures have been documented, e.g., dynamic wrinkling and its effects on fatigue analysis and on snap loading. In the proposed analysis method, the constitutive equation is approximated by a finite difference equation and embedded within a nonlinear finite element spatial discretization. Implicit temporal integration and a modified Newton-Raphson method are used within a time increment. The stress-strain hereditary relation is formally derived from thermodynamic considerations. Use of modified strain-energy and dissipation functions facilitates the description of wrinkling during the analysis. Applications are demonstrated on an inflated cylindrical cantilever and on a submerged cylindrical membrane excited by waves.
A General Method for Data Averaging of Anisotropic Elastic Constants
Authors: Gre´diac M. , Vautrin A. , Verchery G.
Published: April 2008

Redundant experimental data are usually required to determine the best value for the whole set of compliances of an anisotropic laminate. A method is presented here to optimize the compliance tensor values using the five invariants of fourth-rank compliance tensors. A vectorial representation of those invariants is given. It provides a compact presentation of the data and reveals the experimental scatter. Experimental data obtained with bending tests on plates are used as an example to optimize the flexural compliance tensor of a laminate and to show the relevance of the method in practice.
Finite Deformation Constitutive Relations for Elastic-Plastic Fibrous Metal Matrix Composites
Authors: Fares N. , Dvorak G. J.
Published: April 2008

This paper presents a finite strain formulation of a plasticity theory of fibrous composite materials. An additive decomposition is adopted to describe the kinematics of large deformations; a lattice is defined by the current fiber direction. Elastic and plastic constitutive relations are developed from the proposition that distortions take place relative to the fiber direction. A numerical method is proposed for integrating the constitutive equations. Finally, an illustrative example of the formulation indicates that when axial loads along the fiber direction are comparable to the instantaneous shear stiffness, the finite deformation formulation is needed even with small strains.
Frictionless Contact of Layered Half-Planes, Part I: Analysis
Authors: Pindera M.-J. , Lane M. S.
Published: April 2008

A method is presented for the solution of frictionless contact problems on multilayered half-planes consisting of an arbitrary number of isotropic, orthotropic, or monoclinic layers arranged in any sequence. A displacement formulation is employed and the resulting Navier equations that govern the distribution of displacements in the individual layers are solved using Fourier transforms. A local stiffness matrix in the transform domain is formulated for each layer which is then assembled into a global stiffness matrix for the entire multilayered half-plane by enforcing continuity conditions along the interfaces. Application of the mixed boundary condition on the top surface of the medium subjected to the force of the indenter results in an integral equation for the unknown pressure in the contact region. The integral possesses a divergent kernel which is decomposed into Cauchy type and regular parts using the asymptotic properties of the local stiffness matrix and the ensuing relation between Fourier and finite Hilbert transform of the contact pressure. For homogeneous half-planes, the kernel consists only of the Cauchy-type singularity which results in a closed-form solution for the contact stress. For multilayered half-planes, the solution of the resulting singular integral equation is obtained using a collocation technique based on the properties of orthogonal polynomials. Part I of this paper outlines the analytical development of the technique. In Part II a number of numerical examples is presented addressing the effect of off-axis plies on contact stress distribution and load versus contact length in layered composite half-planes.
The Effects of a Space-Fixed Friction Force on the In-Plane Stress and Stability of Transverse Vibrations of a Spinning Disk
Authors: Chen Jen-San , Bogy D. M.
Published: April 2008

The membrane stress field in a spinning disk induced by a stationary circumferential friction force is first derived in the form of an infinite series. It is then shown, both by analysis and numerical computation, that this membrane stress field has no effect on the stability of transverse vibration of the spinning disk.
Lyapunov Exponents and Stochastic Stability of Two-Dimensional Parametrically Excited Random Systems
Authors: Ariaratnam S. T. , Xie Wei-Chau
Published: April 2008

The variation of the largest Lyapunov exponent for two-dimensional parametrically excited stochastic systems is studied by a method of linear transformation. The sensitivity to random disturbance of systems undergoing bifurcation is investigated. Two commonly occurring examples in structural dynamics are considered, where the random fluctuation appears in the stiffness term or the damping term. The boundaries of almost-sure stochastic stability are determined by the vanishing of the largest Lyapunov exponent of the linearized system. The validity of the approximate results is checked by numerical simulation.
Representation of Strongly Stationary Stochastic Processes
Authors: Di Paola M.
Published: April 2008

A generalization of the orthogonality conditions for a stochastic process to represent strongly stationary processes up to a fixed order is presented. The particular case of non-normal delta correlated processes, and the probabilistic characterization of linear systems subjected to strongly stationary stochastic processes are also discussed.
A Similar Flow Between Two Rotating Disks in the Presence of a Magnetic Field
Authors: Usha R. , Vasudevan S.
Published: April 2008

A similarity solution is obtained for a flow between two rotating parallel disks which, 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 equations is presented. The effects of magnetic forces on the velocity profiles, the normal forces and the torques which the fluid exerts on the disks are studied. It is observed that by increasing the magnetic force a considerable increase in the load can be achieved. Also, the torques are more sensitive to changes in the squeeze Reynolds number than to changes in the rotation Reynolds number.
Contact With Friction Between Two Elastic Half-Planes
Authors: Johansson L.
Published: April 2008

In the present paper the problem of contact with friction between two elastic bodies is formulated in the form of variational inequalities using half-plane assumptions for the elastic behavior. The formulation fits directly into a computational method developed in a previous paper and some numerical examples investigating the effects of using dissimilar elastic constants in the bodies and of using different load paths in the application of the external forces are given.
Control of Underactuated-Ship Maneuvers Using Neural Gain Compensators
Authors: Saeed A. , Attia E. M. , Helmy A. A. , Awad T.
Published: April 2008

This paper addresses the trajectory-tracking problem of a 3-Degrees of Freedom (3 DOF) underactuated mariner class vessel. Feed-forward artificial neural networks were designed to enable the ship to track parabolic and S-shaped trajectories. A closed-feedback control system was developed using additional feed-forward neural gain compensators to minimize the path deviation and to obtain the required control input rudder angle. The results show that the path deviation is 6% when the main neural network is used without the gain compensator. The path deviation is limited to a maximum of 3% when the gain compensator is used alongside the main network.
Vibration Characteristics of the Respiratory Branched Network-Comparative Study
Authors: Au P. M. , Al-Jumaily A. M.
Published: April 2008

Determining the vibration characteristics of a realistic branched biological network, such as the respiratory system, faces many hurdles, which includes using the appropriate theory, specifying suitable boundary conditions and selecting accurate physical properties. Further, dichotomized or bifurcated structures beyond a simple circular cylindrical shell induce problems and difficulties in boundary matching between generations. This paper determines the natural frequencies using the Donnell-Mushtari formulation, membrane-shell approximation, a simplified limiting ring formula and the finite element method using COSMOS/Works™ for circular cylindrical shells with classical boundary conditions. Some experimental data are used for comparison and validation. Comparative study between the various methods sets the pros, cons, limitations of each method and the boundaries for the resonant frequencies of each individual generation of this system.
Validating the Vertical Dynamic Performance of a Multi-Wheeled Combat Vehicle Computer Simulation Model
Authors: Hillegass Matthew J. , Faller James G. , Bounds Mark S. , El-Gindy Moustafa , Chae Seokyong
Published: April 2008

Performance testing is an important step in the development of any vehicle model. Generally, full-scale field tests are conducted to collect the dynamic response characteristics for evaluating the vehicle performance. However, with increases in computational power and the accuracy of simulation models, virtual testing can be extensively used as an alternative to the time consuming and costly full-scale tests, especially for severe maneuvers. Validation of the simulation results is critical for the acceptance of such simulation models. In this paper, a methodology for validating the vertical dynamic performance of a virtual vehicle has been discussed. The dynamic performance of a multi-wheeled combat vehicle model specially developed using a multi-body dynamics code was validated against the measured data obtained on the U.S. Army Aberdeen Test Center’s (ATC) test courses. The multi-wheeled combat vehicle variant computer simulation model was developed in TruckSim, a vehicle dynamic simulation software developed by the Mechanical Simulation Corporation. Prior to validating the model, the vehicle weights, dimensions, tires and suspension characteristics were measured and referenced in the specially developed computer simulation model. The data for the tire and suspension characteristics were acquired from the respective leading manufacturers in the form of look-up tables. The predictions of the vehicle vertical dynamics on different road profiles at various vehicle speeds were compared with the field test results. The time domain data for the vertical acceleration at the vehicle center of gravity, pitching, vehicle speed and the suspension/damper displacement were compared to analyze the feasibility of using the computer simulation models to predict the vertical dynamic performance of the vehicle. Based on the results it was found that the particular combat vehicle computer simulation model is capable of predicting the vertical dynamic performance characteristics.