bluuebunny/crossref_metadata_2025 huggingface dataset:
An Analytical Examination of the Combustion of a Turbulent Jet in an Environment of Air Containing a Premixed Fuel or a Diluent
Authors: Wierzba P. , Karim G. A. , Wierzba I.
Published: February 2008

A simple analytical model for the mixing and combustion of an axisymmetric turbulent gaseous fuel jet discharging into a co-flowing streaming gaseous environment of an auxiliary fuel and/or a diluent homogeneously mixed with air is presented. A number of gaseous fuels and diluents are considered. It is shown that the combustion characteristics of a fuel jet can be modified significantly by the presence of a relatively small amount of a fuel in the surrounding air at concentrations well below the corresponding local flammability limits. Correlative procedures are presented for estimating changes in the flame length, the size of the combustion zone, and the blowout limits with changes in the type and concentration of the fuel in the surroundings. Predicted values showed generally good agreement with the corresponding experimental values.
Leak Detection—Transient Flow Simulation Approaches
Authors: Liou J. C. P. , Tian J.
Published: February 2008

The basis for and field trials of two leak detection algorithms by transient flow simulations are presented. Data noise in pressure and flow measurements are considered. Noise is found to limit leak detectability. The ability of the two algorithms to reliably detect small to moderate size leaks under steady and transient flow conditions is demonstrated.
The San Andreas Fault Zone Drilling Project: Scientific Objectives and Technological Challenges
Authors: Hickman S. H. , Younker L. W. , Zoback M. D. , Cooper G. A.
Published: February 2008

We are leading a new international initiative to conduct scientific drilling within the San Andreas fault zone at depths of up to 10 km. This project is motivated by the need to understand the physical and chemical processes operating within the fault zone and to answer fundamental questions about earthquake generation along major plate-boundary faults. Through a comprehensive program of coring, fluid sampling, downhole measurements, laboratory experimentation, and long-term monitoring, we hope to obtain critical information on the structure, composition, mechanical behavior and physical state of the San Andreas fault system at depths comparable to the nucleation zones of great earthquakes. The drilling, sampling and observational requirements needed to ensure the success of this project are stringent. These include: 1) drilling stable vertical holes to depths of about 9 km in fractured rock at temperatures of up to 300°C; 2) continuous coring and completion of inclined holes branched off these vertical boreholes to intersect the fault at depths of 3, 6, and 9 km; 3) conducting sophisticated borehole geophysical measurements and fluid/rock sampling at high temperatures and pressures; and 4) instrumenting some or all of these inclined core holes for continuous monitoring of earthquake activity, fluid pressure, deformation and other parameters for periods of up to several decades. For all of these tasks, because of the overpressured clay-rich formations anticipated within the fault zone at depth, we expect to encounter difficult drilling, coring and hole-completion conditions in the region of greatest scientific interest.
NOx Emissions From a Diesel Engine Fueled With Natural Gas
Authors: Tao Y. , Hodgins K. B. , Hill P. G.
Published: February 2008

The performance and emission characteristics of a single-cylinder two-stroke diesel engine fueled with direct injection of natural gas entrained with pilot diesel ignition enhancer have been measured. The thermal efficiency of the optimum gas-diesel operation was shown to exceed that of the conventional diesel at full load, but to be less at part load where the ignition delay was excessive. At high load, where the NOx emission problem is most serious, substantial reduction in NOx emission rate was obtained with delay of injection timing and also with use of exhaust gas recirculation. Measured cylinder pressures were used with a three-zone combustion model to determine ignition delay and the temperatures of the burned gas. The predicted NOx emissions based on equilibrium concentration of NO at the maximum burned gas temperature were found to correlate closely with exhaust pipe measurements of NOx.
Prediction of Solid Oxide Fuel Cell Power System Performance Through Multi-Level Modeling
Authors: Bessette N. F. , Wepfer W. J.
Published: February 2008

This paper presents an integrated multi-level model of a solid oxide fuel cell system, which accounts for the effects of concentration, activation, and ohmic polarizations on single-cell performance, as well as the cell-to-cell interactions in a cell stack module. Furthermore, this model extends the work of Lu and Mahoney (1988) and Harvey and Richter (1994) by including the performance of a cell stack operating with a fuel reformer, heat exchangers, and a steam generator over a range of design parameters. This paper also demonstrates the procedure by which a single-cell model is scaled to a system model.
Unsteady Forced Convection Heat Transfer From a Translating and
Spinning Body
Authors: O¨ztu¨rk A. , Ece M. C.
Published: February 2008

The initial laminar thermal boundary-layer flow past an impulsively started translating and spinning rotational symmetric body of uniform temperature is investigated. Velocity components and temperature are expanded in series in powers of time. Leading and first-order functions are obtained analytically, second and third-order functions are determined numerically. Application of the general results to a sphere shows that the surface heat flux is reduced in the neighborhood of the point of separation and enhanced by the reversed flow inside the separated region.
Optimal Operational Planning of Cogeneration Systems With Thermal Storage by the Decomposition Method
Authors: Yokoyama R. , Ito K.
Published: February 2008

An optimal operational planning method is proposed for cogeneration systems with thermal storage. The daily operational strategy of constituent equipment is determined so as to minimize the daily operational cost subject to the energy demand requirement. This optimization problem is formulated as a large-scale mixed-integer linear programming one, and it is solved by means of the decomposition method. Effects of thermal storage on the operation of cogeneration systems are examined through a numerical study on a gas engine-driven cogeneration system installed in a hotel. This method is a useful tool for evaluating the economic and energy-saving properties of cogeneration systems with thermal storage.
Controlling Propulsive Forces in Gait Initiation in Transfemoral Amputees
Authors: van Keeken Helco G. , Vrieling Aline H. , Hof At L. , Halbertsma Jan P. K. , Schoppen Tanneke , Postema Klaas , Otten Bert
Published: February 2008

During prosthetic gait initiation, transfemoral (TF) amputees control the spatial and temporal parameters that modulate the propulsive forces, the positions of the center of pressure (CoP), and the center of mass (CoM). Whether their sound leg or the prosthetic leg is leading, the TF amputees reach the same end velocity. We wondered how the CoM velocity build up is influenced by the differences in propulsive components in the legs and how the trajectory of the CoP differs from the CoP trajectory in able bodied (AB) subjects. Seven TF subjects and eight AB subjects were tested on a force plate and on an 8m long walkway. On the force plate, they initiated gait two times with their sound leg and two times with their prosthetic leg. Force measurement data were used to calculate the CoM velocity curves in horizontal and vertical directions. Gait initiated on the walkway was used to determine the leg preference. We hypothesized that because of the differences in propulsive components, the motions of the CoP and the CoM have to be different, as ankle muscles are used to help generate horizontal ground reaction force components. Also, due to the absence of an active ankle function in the prosthetic leg, the vertical CoM velocity during gait initiation may be different when leading with the prosthetic leg compared to when leading with the sound leg. The data showed that whether the TF subjects initiated a gait with their prosthetic leg or with their sound leg, their horizontal end velocity was equal. The subjects compensated the loss of propulsive force under the prosthesis with the sound leg, both when the prosthetic leg was leading and when the sound leg was leading. In the vertical CoM velocity, a tendency for differences between the two conditions was found. When initiating gait with the sound leg, the downward vertical CoM velocity at the end of the gait initiation was higher compared to when leading with the prosthetic leg. Our subjects used a gait initiation strategy that depended mainly on the active ankle function of the sound leg; therefore, they changed the relative durations of the gait initiation anticipatory postural adjustment phase and the step execution phase. Both legs were controlled in one single system of gait propulsion. The shape of the CoP trajectories, the applied forces, and the CoM velocity curves are described in this paper.
Predicting Knee Replacement Damage in a Simulator Machine Using a Computational Model With a Consistent Wear Factor
Authors: Zhao Dong , Sakoda Hideyuki , Sawyer W. Gregory , Banks Scott A. , Fregly Benjamin J.
Published: February 2008

Wear of ultrahigh molecular weight polyethylene remains a primary factor limiting the longevity of total knee replacements (TKRs). However, wear testing on a simulator machine is time consuming and expensive, making it impractical for iterative design purposes. The objectives of this paper were first, to evaluate whether a computational model using a wear factor consistent with the TKR material pair can predict accurate TKR damage measured in a simulator machine, and second, to investigate how choice of surface evolution method (fixed or variable step) and material model (linear or nonlinear) affect the prediction. An iterative computational damage model was constructed for a commercial knee implant in an AMTI simulator machine. The damage model combined a dynamic contact model with a surface evolution model to predict how wear plus creep progressively alter tibial insert geometry over multiple simulations. The computational framework was validated by predicting wear in a cylinder-on-plate system for which an analytical solution was derived. The implant damage model was evaluated for 5 million cycles of simulated gait using damage measurements made on the same implant in an AMTI machine. Using a pin-on-plate wear factor for the same material pair as the implant, the model predicted tibial insert wear volume to within 2% error and damage depths and areas to within 18% and 10% error, respectively. Choice of material model had little influence, while inclusion of surface evolution affected damage depth and area but not wear volume predictions. Surface evolution method was important only during the initial cycles, where variable step was needed to capture rapid geometry changes due to the creep. Overall, our results indicate that accurate TKR damage predictions can be made with a computational model using a constant wear factor obtained from pin-on-plate tests for the same material pair, and furthermore, that surface evolution method matters only during the initial “break in” period of the simulation.
The Effect of Strain Rate on the Mechanical Properties of Human Cortical Bone
Authors: Hansen Ulrich , Zioupos Peter , Simpson Rebecca , Currey John D. , Hynd David
Published: February 2008

Bone mechanical properties are typically evaluated at relatively low strain rates. However, the strain rate related to traumatic failure is likely to be orders of magnitude higher and this higher strain rate is likely to affect the mechanical properties. Previous work reporting on the effect of strain rate on the mechanical properties of bone predominantly used nonhuman bone. In the work reported here, the effect of strain rate on the tensile and compressive properties of human bone was investigated. Human femoral cortical bone was tested longitudinally at strain rates ranging between 0.14–29.1s−1 in compression and 0.08–17 s−1 in tension. Young’s modulus generally increased, across this strain rate range, for both tension and compression. Strength and strain (at maximum load) increased slightly in compression and decreased (for strain rates beyond 1 s−1) in tension. Stress and strain at yield decreased (for strain rates beyond 1 s−1) for both tension and compression. In general, there seemed to be a relatively simple linear relationship between yield properties and strain rate, but the relationships between postyield properties and strain rate were more complicated and indicated that strain rate has a stronger effect on postyield deformation than on initiation of yielding. The behavior seen in compression is broadly in agreement with past literature, while the behavior observed in tension may be explained by a ductile to brittle transition of bone at moderate to high strain rates.
A Method for Measuring Linearly Viscoelastic Properties of Human Tympanic Membrane Using Nanoindentation
Authors: Huang Gang , Daphalapurkar Nitin P. , Gan Rong Z. , Lu Hongbing
Published: February 2008

A viscoelastic nanoindentation technique was developed to measure both in-plane and through-thickness viscoelastic properties of human tympanic membrane (TM). For measurement of in-plane Young’s relaxation modulus, the TM sample was clamped on a circular hole and a nanoindenter tip was used to apply a concentrated force at the center of the TM sample. In this setup, the resistance to nanoindentation displacement can be considered due primarily to the in-plane stiffness. The load-displacement curve obtained was used along with finite element analysis to determine the in-plane viscoelastic properties of TM. For measurements of Young’s relaxation modulus in the through-thickness (out-of-plane) direction, the TM sample was placed on a relatively rigid solid substrate and nanoindentation was made on the sample surface. In this latter setup, the resistance to nanoindentation displacement arises primarily due to out-of-plane stiffness. The load-displacement curve obtained in this manner was used to determine the out-of-plane relaxation modulus using the method appropriate for viscoelastic materials. From our sample tests, we obtained the steady-state values for in-plane moduli as ∼17.4 MPa and ∼19.0 MPa for posterior and anterior portions of TM samples, respectively, and the value for through-thickness modulus as ∼6.0 MPa for both posterior and anterior TM samples. Using this technique, the local out-of-plane viscoelastic modulus can be determined for different locations over the entire TM, and the in-plane properties can be determined for different quadrants of the TM.
Tracking the Motion of Hidden Segments Using Kinematic Constraints and Kalman Filtering
Authors: Halvorsen Kjartan , Johnston Christopher , Back Willem , Stokes Virgil , Lanshammar Håkan
Published: February 2008

Motion capture for biomechanical applications involves in almost all cases sensors or markers that are applied to the skin of the body segments of interest. This paper deals with the problem of estimating the movement of connected skeletal segments from 3D position data of markers attached to the skin. The use of kinematic constraints has been shown previously to reduce the error in estimated segment movement that are due to skin and muscles moving with respect to the underlying segment. A kinematic constraint reduces the number of degrees of freedom between two articulating segments. Moreover, kinematic constraints can help reveal the movement of some segments when the 3D marker data otherwise are insufficient. Important cases include the human ankle complex and the phalangeal segments of the horse, where the movement of small segments is almost completely hidden from external observation by joint capsules and ligaments. This paper discusses the use of an extended Kalman filter for tracking a system of connected segments. The system is modeled using rigid segments connected by simplified joint models. The position and orientation of the mechanism are specified by a set of generalized coordinates corresponding to the mechanism’s degrees of motion. The generalized coordinates together with their first time derivatives can be used as the state vector of a state space model governing the kinematics of the mechanism. The data collected are marker trajectories from skin-mounted markers, and the state vector is related to the position of the markers through a nonlinear function. The Jacobian of this function is derived. The practical use of the method is demonstrated on a model of the distal part of the limb of the horse. Monte Carlo simulations of marker data for a two-segment system connected by a joint with three degrees of freedom indicate that the proposed method gives significant improvement over a method, which does not make use of the joint constraint, but the method requires that the model is a good approximation of the true mechanism. Applying the method to data on the movement of the four distal-most segments of the horse’s limb shows good between trial consistency and small differences between measured marker positions and marker positions predicted by the model.
Age-Related Effect of Static and Cyclic Loadings on the Strain-Force Curve of the Vastus Lateralis Tendon and Aponeurosis
Authors: Mademli Lida , Arampatzis Adamantios , Walsh Mark
Published: February 2008

The objective of the present study was to investigate the age-related effects of submaximal static and cyclic loading on the mechanical properties of the vastus lateralis (VL) tendon and aponeurosis in vivo. Fourteen old and 12 young male subjects performed maximal voluntary isometric knee extensions (MVC) on a dynamometer before and after (a) a sustained isometric contraction at 25% MVC and (b) isokinetic contractions at 50% isokinetic MVC, both until task failure. The elongation of the VL tendon and aponeurosis was examined using ultrasonography. To calculate the resultant knee joint moment, the kinematics of the leg were recorded with eight cameras (120Hz). The old adults displayed significantly lower maximal moments but higher strain values at any given tendon force from 400N and up in all tested conditions. Neither of the loading protocols influenced the strain-force relationship of the VL tendon and aponeurosis in either the old or young adults. Consequently, the capacity of the tendon and aponeurosis to resist force remained unaffected in both groups. It can be concluded that in vivo tendons are capable of resisting long-lasting static (∼4.6min) or cyclic (∼18.5min) mechanical loading at the attained strain levels (4–5%) without significantly altering their mechanical properties regardless of age. This implies that as the muscle becomes unable to generate the required force due to fatigue, the loading of the tendon is terminated prior to provoking any significant changes in tendon mechanical properties.
Comparison of Axisymmetric and Three-Dimensional Models for Gas Uptake in a Single Bifurcation During Steady Expiration
Authors: Madasu Srinath , Ultman James S. , Borhan Ali
Published: February 2008

Reactive gas uptake is predicted and compared in a single bifurcation at steady expiratory flow in terms of Sherwood number using an axisymmetric single-path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM). ASPM is validated in a two-generation geometry by comparing the average gas-phase mass transfer coefficients with the experimental values. ASPM predicted mass transfer coefficients within 20% of the experimental values. The flow and concentration variables in the ASPM were solved using Galerkin finite element method and in the CFDM using commercial finite element software FIDAP. The simulations were performed for reactive gas flowing at Reynolds numbers ranging from 60 to 350 in both symmetric bifurcation for three bifurcation angles, 30deg, 70deg, and 90deg, and in an asymmetric bifurcation. The numerical models compared with each other qualitatively but quantitatively they were within 0.4–8% due to nonfully developed flow in the parent branch predicted by the CFDM. The radially averaged concentration variation along the axial location matched qualitatively between the CFDM and ASPM but quantitatively they were within 32% due to differences in the flow field. ASPM predictions compared well with the CFDM predictions for an asymmetric bifurcation. These results validate the simplified ASPM and the complex CFDM. ASPM predicts higher Sherwood number with a flat velocity inlet profile compared to a parabolic inlet velocity profile. Sherwood number increases with the inlet average velocity, wall mass transfer coefficient, and bifurcation angle since the boundary layer grows slower in the parent and daughter branches.
Convective Dispersion During Steady Flow in the Conducting Airways of the Human Lung
Authors: Fresconi Frank E. , Prasad Ajay K.
Published: February 2008

The adverse health effects of inhaled particulate matter from the environment depend on its dispersion, transport, and deposition in the human airways. Similarly, precise targeting of deposition sites by pulmonary drug delivery systems also relies on characterizing the dispersion and transport of therapeutic aerosols in the respiratory tract. A variety of mechanisms may contribute to convective dispersion in the lung; simple axial streaming, augmented dispersion, and steady streaming are investigated in this effort. Flow visualization of a bolus during inhalation and exhalation, and dispersion measurements were conducted during steady flow in a three-generational, anatomically accurate in vitro model of the conducting airways to support this goal. Control variables included Reynolds number, flow direction, generation, and branch. Experiments illustrate transport patterns in the lumen cross section and map their relation to dispersion metrics. These results indicate that simple axial streaming, rather than augmented dispersion, is the dominant steady convective dispersion mechanism in symmetric Weibel generations 7–13 during normal respiration. Experimental evidence supports the branching nature of the airways as a possible contributor to steady streaming in the lung.
Tensile Properties of the Mandibular Condylar Cartilage
Authors: Singh M. , Detamore M. S.
Published: February 2008

Mandibular condylar cartilage plays a crucial role in temporomandibular joint (TMJ) function, which includes facilitating articulation with the temporomandibular joint disc and reducing loads on the underlying bone. The cartilage experiences considerable tensile forces due to direct compression and shear. However, only scarce information is available about its tensile properties. The present study aims to quantify the biomechanical characteristics of the mandibular condylar cartilage to aid future three-dimensional finite element modeling and tissue engineering studies. Porcine condylar cartilage was tested under uniaxial tension in two directions, anteroposterior and mediolateral, with three regions per direction. Stress relaxation behavior was modeled using the Kelvin model and a second-order generalized Kelvin model, and collagen fiber orientation was determined by polarized light microscopy. The stress relaxation behavior of the tissue was biexponential in nature. The tissue exhibited greater stiffness in the anteroposterior direction than in the mediolateral direction as reflected by higher Young’s (2.4 times), instantaneous (1.9 times), and relaxed (1.9 times) moduli. No significant differences were observed among the regional properties in either direction. The predominantly anteroposterior macroscopic fiber orientation in the fibrous zone of condylar cartilage correlated well with the biomechanical findings. The condylar cartilage appears to be less stiff and less anisotropic under tension than the anatomically and functionally related TMJ disc. The anisotropy of the condylar cartilage, as evidenced by tensile behavior and collagen fiber orientation, suggests that the shear environment of the TMJ exposes the condylar cartilage to predominantly but not exclusively anteroposterior loading.
Dynamic Buckling of Laminated Anisotropic Spherical Caps
Authors: Ganapathi M. , Varadan T. K.
Published: February 2008

The dynamic axisymmetric behavior of clamped laminated composite spherical caps subjected to suddenly applied loads is investigated using an eight-noded quadrilateral doubly curved shear flexible shell element based on the field-consistency approach. Geometric nonlinearity is considered using von Karman’s strain-displacement relations. The solution is obtained using the Wilson-θ numerical integration scheme. The pressure corresponding to a sudden jump in the maximum average deflection in the time history of the shell structure is taken as dynamic buckling pressure. A detailed parametric study is carried out to bring out the effects of shell geometries and material properties, number of layers, lamination schemes, and type of loading on a dynamic buckling load.
Finite Element Analysis of Repeated Indentation of an Elastic-Plastic Layered Medium by a Rigid Sphere, Part I: Surface Results
Authors: Kral E. R. , Komvopoulos K. , Bogy D. B.
Published: February 2008

A comprehensive elastic-plastic finite element analysis is presented for the axisym-metric problem of a frictionless rigid sphere indenting a half-space with a harder and stiffer layer. The indenter is modeled by contact elements, thereby avoiding a priori assumptions for the pressure profile. Two layer thicknesses are examined, with layer elastic modulus and yield stress both two and four times greater than those of the substrate. Perfectly plastic and isotropic strain-hardening behavior of the layer and substrate media are investigated. At least three complete load-unload cycles are applied to a peak load of 300 times the load necessary to initiate yielding in a half-space of the substrate material. The effect of hardening properties on the loaded and residual stresses is presented and the consequences for crack initiation at the surface are discussed. Results for the contact pressure and surface stresses and deformations are presented, and the influence of residual displacements and load cycles on the contact pressure and the loaded and residual surface stresses is investigated.
Bifurcation of Equilibrium in Thick Orthotropic Cylindrical Shells Under Axial Compression
Authors: Kardomateas G. A.
Published: February 2008

The bifurcation of equilibrium of an orthotropic thick cylindrical shell under axial compression is studied by an appropriate formulation based on the three-dimensional theory of elasticity. The results from this elasticity solution are compared with the critical loads predicted by the orthotropic Donnell and Timoshenko nonshallow shell formulations. As an example, the cases of an orthotropic material with stiffness constants typical of glass/epoxy and the reinforcing direction along the periphery or along the cylinder axis are considered. The bifurcation points from the Timoshenko formulation are always found to be closer to the elasticity predictions than the ones from the Donnell formulation. For both the orthotropic material cases and the isotropic one, the Timoshenko bifurcation point is lower than the elasticity one, which means that the Timoshenko formulation is conservative. The opposite is true for the Donnell shell theory, i.e., it predicts a critical load higher than the elasticity solution and therefore it is nonconservative. The degree of conservatism of the Timoshenko theory generally increases for thicker shells. Likewise, the Donnell theory becomes in general more nonconservative with thicker construction.
Natural Frequencies of a Penny-Shaped Crack With Spring Boundary Condition
Authors: Eriksson A. S.
Published: February 2008

Natural frequencies of a penny-shaped crack are calculated for the three-dimensional elastic problem. The crack is imbedded in a homogeneous medium and on the crack surface the spring boundary conditions are assumed. Only the symmetric problem is considered and the complex frequencies are given as the SEM (singularity expansion method) poles of the symmetric part of the transition (T) matrix. The T matrix is calculated with a direct integral equation method leading to integral equations relating normal stress and displacement on the crack surface. The location of the poles in the complex frequency plane are compared with the scattering cross-section versus frequency and with Rayleigh surface waves.
Mechanics of the Segmentation of an Embedded Fiber, Part I: Experimental Investigations
Authors: ten Busschen A. , Selvadurai A. P. S.
Published: February 2008

Micromechanical modeling is an important aspect in the study of fiber-reinforced composites. In such studies, an important class of structural parameters is formed by the interaction between the matrix and the embedded fibers. These interactive processes can be investigated by an appeal to a test which involves the segmentation of an embedded fiber. This test is referred to as a “fragmentation test.” During a fragmentation test, two distinct fracture phenomena are observed. These phenomena are directly related to the integrity of bond between the embedded fiber and the matrix. The first phenomenon involves situations where the interface bond is weaker than the matrix material. In this case the fiber fragment ends will slip and in this region shear stresses are transmitted by friction and/or interlocking mechanical actions. In contrast, when the interface bond has stronger properties than the matrix material, cracking will occur in the matrix region. Here, a crack initiated in the fiber will propagate into the matrix region typically forming conoidal cracks, or combinations of conoidal and flat cracks. This paper describes the background of the fragmentation test and the associated experimental research. Attention is focused on the experimental evaluation of matrix fracture topographies encountered in the fragmentation test.
Particle Orientation and Velocity Equations of Clay in a Plane-Strain Condition
Authors: Djavid M.
Published: February 2008

The directional property of soils, particularly clays, are directly related to the particle orientations. The platy clay particles do possess the tendency to reorient themselves in the most stable condition against applied stress. One may conceive of developing a soil model directly relating particle orientation and applied stress. In this study an angle θ, which is the preferred (therefore stable) orientation of clay particles, is introduced. Using this concept and slip-line theory, the velocity equations of clay in a plane-strain condition are developed. In this approach any change in clay particle orientation is essentially dependent on principal stresses magnitudes as well as their directions. Therefore, the effect of rotation of principal stresses can be included and quantified.
A Study of Embedded Piezoelectric Layers in Composite Cylinders
Authors: Mitchell J. A. , Reddy J. N.
Published: February 2008

A power series solution is presented for the static equilibrium equations of an axisymmetric composite cylinder under loadings due to surface mounted or embedded piezoelectric laminae. Both uniform and nonuniform distributions of the piezoelectric effect are studied and results are verified using a finite element model based on axisymmetric two-dimensional elasticity theory equations. A cylindrical truss element actuator is developed which may be used for damping vibrations of truss-type structures. Finally, the effects of a piezoelectric patch have been investigated. The axial forces generated at the fixed ends of a cylinder are found to be proportional to the length of the patch.
SH-Wave Interaction in a Harmonically Inhomogeneous Elastic Plate
Authors: Hawwa M. A.
Published: February 2008

The study focuses on the propagation of SH waves in an elastic plate whose material properties are sinusoidally varying in the direction of propagation. In light of the weak variation of the materials properties, the perturbation method of multiple scales is utilized to analyze the modal interaction which occurs upon the satisfaction of certain resonant conditions. The derived coupled-mode equations together with relevant boundary conditions at the ends of the inhomogeneous section form a two-point boundary value problem, which is solved numerically. The power reflection coefficient is then calculated to present the reflection characteristics of the plate.
Integral Equation Method via Domain Decomposition and Collocation for Scattering Problems
Authors: Zeng Xiaogang , Zhao Fang
Published: February 2008

In this paper an exterior domain decomposition (DD) method based on the boundary element (BE) formulation for the solutions of two or three-dimensional time-harmonic scattering problems in acoustic media is described. It is known that the requirement of large memory and intensive computation has been one of the major obstacles for solving large scale high-frequency acoustic systems using the traditional nonlocal BE formulations due to the fully populated resultant matrix generated from the BE discretization. The essence of this study is to decouple, through DD of the problem-defined exterior region, the original problem into arbitrary subproblems with data sharing only at the interfaces. By decomposing the exterior infinite domain into appropriate number of infinite subdomains, this method not only ensures the validity of the formulation for all frequencies but also leads to a diagonalized, blockwise-banded system of discretized equations, for which the solution requires only O(N) multiplications, where N is the number of unknowns on the scatterer surface. The size of an individual submatrix that is associated with a subdomain may be determined by the user, and may be selected such that the restriction due to the memory limitation of a given computer may be accommodated. In addition, the method may suit for parallel processing since the data associated with each subdomain (impedance matrices, load vectors, etc.) may be generated in parallel, and the communication needed will be only for the interface values. Most significantly, unlike the existing boundary integral-based formulations valid for all frequencies, our method avoids the use of both the hypersingular operators and the double integrals, therefore reducing the computational effort. Numerical experiments have been conducted for rigid cylindrical scatterers subjected to a plane incident wave. The results have demonstrated the accuracy of the method for wave numbers ranging from 0 to 30, both directly on the scatterer and in the far-field, and have confirmed that the procedure is valid for critical frequencies.
Topological Optimization Technique for Free Vibration Problems
Authors: Ma Zheng-Dong , Kikuchi Noboru , Cheng Hsien-Chie , Hagiwara Ichiro
Published: February 2008

A topological optimization technique using the conception of OMD (Optimal Material Distribution) is presented for free vibration problems of a structure. A new objective function corresponding to multieigenvalue optimization is suggested for improving the solution of the eigenvalue optimization problem. An improved optimization algorithm is then applied to solve these problems, which is derived by the authors using a new convex generalized-linearization approach via a shift parameter which corresponds to the Lagrange multiplier and the use of the dual method. Finally, three example applications are given to substantiate the feasibility of the approaches presented in this paper.
Study of Transient Coupled Thermoelastic Problems With Relaxation Times
Authors: Chen Han-Taw , Lin Hou-Jee
Published: February 2008

A new hybrid numerical method based on the Laplace transform and control volume methods is proposed to analyze transient coupled thermoelastic problems with relaxation times involving a nonlinear radiation boundary condition. The dynamic thermoelastic model of Green and Lindsay is selected for the present study. The following computational procedure is followed for the solution of the present problem. The nonlinear term in the boundary condition is linearized by using the Taylor’s series approximation. Afterward, the time-dependent terms in the linearized equations are removed by the Laplace transform technique, and then the transformed field equations are discretized using the control volume method with suitable shape functions. The nodal dimensionless temperature and displacement in the transform domain are inverted to obtain the actual physical quantities, using the numerical inversion of the Laplace transform method. It is seen from various illustrative problems that the present method has good accuracy and efficiency in predicting the wave propagations of temperature, stress, and displacement. However, it should be noted that the distributions of temperature, stress, and displacement can experience steep jumps at their wavefronts. In the present study, the effects of the relaxation times on these thermoelastic waves are also investigated.
On First-Order Decoupling of Equations of Motion for Constrained Dynamical Systems
Authors: Loduha T. A. , Ravani B.
Published: February 2008

In this paper we present a method for obtaining first-order decoupled equations of motion for multirigid body systems. The inherent flexibility in choosing generalized velocity components as a function of generalized coordinates is used to influence the structure of the resulting dynamical equations. Initially, we describe how a congruency transformation can be formed that represents the transformation between generalized velocity components and generalized coordinate derivatives. It is shown that the proper choice for the congruency transformation will insure generation of first-order decoupled equations of motion for holonomic systems. In the case of nonholonomic systems, or holonomic systems with unreduced configuration coordinates, we incorporate an orthogonal complement in conjunction with the congruency transformation. A pair of examples illustrate the results. Finally, we discuss numerical implementation of congruency transformations to achieve first-order decoupled equations for simulation purposes.
Interaction Diagram of a Circular Bar in Torsion and Extension
Authors: Fuschi P. , Polizzotto C.
Published: February 2008

For a circular bar of perfectly plastic material and subjected to a cyclically variable torque and a constant axial force, the interaction (or generalized Bree) diagram is derived by a direct method in which Melan’s theorem is used to locate the nonratchetting load boundary.
An Alternative Derivation of Some New Perspectives on Constrained Motion
Authors: Barhorst A. A.
Published: February 2008

An alternative derivation of some recently reported results is presented. Specifically, some results regarding the fundamental view of Lagrangian mechanics and nonholonomic constraints.
Vibration of a Three-Dimensional, Finite Linear, Elastic Solid Containing Cracks
Authors: Shen I. Y.
Published: February 2008

This paper is to determine vibrational eigensolutions [λm2,vm(r)]m=1∞ of a three-dimensional, finite, linear, elastic solid C containing cracks in terms of crack configuration σc and eigensolutions [ωn2,un(r)n=1∞ of a perfect elastic solid P without the cracks. Use of Betti reciprocal theorem and the Green’s function of P expands vm(r) in terms of an infinite series of un(r). Substitution of the vm(r) series representation into the Kamke quotient of C and stationarity of the quotient result in a Fredholm integral equation whose nontrivial solutions predict λm2, and vm(r) of C. Finally, natural frequencies and mode shapes of a circular shaft of finite length containing a circumferential crack under torsional vibration are predicted through a two-term Ritz approximation of the Fredholm integral equation. The results differ significantly from those predicted by the method of flexibility matrices, when the ratio of the shaft length to the shaft radius is small.
An Analytical Crack-Tip Element for Layered Elastic Structures
Authors: Davidson B. D. , Hu Hurang , Schapery R. A.
Published: February 2008

A previously developed linear elastic crack-tip element analysis is reviewed briefly, and then extended and refined for practical applications. The element provides analytical expressions for total energy release rate and mode mix in terms of plate theory force and moment resultants near the crack tip. The element may be used for cracks within or between homogeneous isotropic or orthotropic layers, as well as for delamination of laminated composites. Classical plate theory is used to derive the equations for total energy release rate and mode mix; a “mode mix parameter,” Ω, as obtained from a separate continuum analysis is necessary to complete the mode mix decomposition. This parameter depends upon the elastic and geometrical properties of the materials above and below the crack plane, but not on the loading. A relatively simple finite element technique for determining the mode-mix parameter is presented and convergence in terms of mesh refinement is studied. Specific values of Ω are also presented for a large number of cases. For those interfaces where a linear elastic solution predicts an oscillatory singularity, an approach is described which allows a unique, physically meaningful value of fracture mode ratio to be defined. This approach is shown to provide predictions of crack growth between dissimilar homogeneous materials that are equivalent to those obtained from the oscillatory field solution. Application of the approach to delamination in fiber-reinforced laminated composites is also discussed.
A Statistical Approach for Fracture of Brittle Materials Based on the Chain-of-Bundles Model
Authors: Ruggieri C. , Minami F. , Toyoda M.
Published: February 2008

An analytical method for the assessment of failure probability of brittle materials exhibiting progressive cracking prior to cleavage fracture is presented. The underlying fracture mechanism is based on the assumption that instability of a critical flaw no longer leads to failure and causes redistribution of the local stresses. The fracture process progresses by consecutive unstable propagation of the surviving flaws up to total failure. A limiting distribution for the fracture stress, which is identical with the first asymptotic distribution of smallest values, is derived on the basis of a chain-of-bundles probability model. Numerical procedures for calculating the parameters of the limiting distribution are also described. Due to the nature of the resulting distribution, the method employs the maximum likelihood estimation of parameters combined with a finite element solution to the crack-tip fields. An application of the present model to analyze the effect of notch depth on fracture toughness values obtained from single-edge notch bend (SENB) specimens is also included.
Prediction of Kink Width in Compressed Fiber Composites
Authors: Fleck N. A. , Deng L. , Budiansky B.
Published: February 2008

Couple stress theory is used in the prediction of the size of the kink band width that occurs in the compressive failure of a fiber composite by microbuckling. The composite is assumed to be inextensible in the fiber direction, and to deform as a Ramberg-Osgood solid in shear and in transverse tension. Predictions are given for the kink width as a function of the fiber diameter, modulus and strength; the material nonlinearity of the composite; and the amplitude and wavelength of fiber waviness. The kink width scales with fiber diameter but is fairly insensitive to variations in other material properties and in the amplitude and wavelength of initial fiber waviness. For typical polymer matrix composites, the predicted kink width is of the order of 10–15 fiber diameters, in agreement with observed values. The couple stress theory is also used to assess the role of fiber bending resistance in the compressive strength of fiber composites that fail by microbuckling. It is found that although the compressive strength is sensitive to the amplitude of the initial waviness, it is not very sensitive to its wavelength.
Three-Dimensional Elasticity Solution for the Buckling of Transversely Isotropic Rods: The Euler Load Revisited
Authors: Kardomateas G. A.
Published: February 2008

The bifurcation of equilibrium of a compressed transversely isotropic bar is investigated by using a three-dimensional elasticity formulation. In this manner, an assessment of the thickness effects can be accurately performed. For isotropic rods of circular cross-section, the bifurcation value of the compressive force turns out to coincide with the Euler critical load for values of the length-over-radius ratio approximately greater than 15. The elasticity approach predicts always a lower (than the Euler value) critical load for isotropic bodies; the two examples of transversely isotropic bodies considered show also a lower critical load in comparison with the Euler value based on the axial modulus, and the reduction is larger than the one corresponding to isotropic rods with the same length over radius ratio. However, for the isotropic material, both Timoshenko’s formulas for transverse shear correction are conservative; i.e., they predict a lower critical load than the elasticity solution. For a generally transversely isotropic material only the first Timoshenko shear correction formula proved to be a conservative estimate in all cases considered. However, in all cases considered, the second estimate is always closer to the elasticity solution than the first one and therefore, a more precise estimate of the transverse shear effects. Furthermore, by performing a series expansion of the terms of the resulting characteristic equation from the elasticity formulation for the isotropic case, the Euler load is proven to be the solution in the first approximation; consideration of the second approximation gives a direct expression for the correction to the Euler load, therefore defining a new, revised, yet simple formula for column buckling. Finally, the examination of a rod with different end conditions, namely a pinned-pinned rod, shows that the thickness effects depend also on the end fixity.
Smooth Contact Between the Running Rayleigh Wave and a Rigid Strip
Authors: Zharii O. Y. , Ulitko A. F.
Published: February 2008

A problem of frictionless contact between the running Rayleigh wave and a rigid strip is investigated. The corresponding mixed boundary value problem of elastodynamics is reduced to a system of dual series equations involving trigonometric functions. On the base of the closed-form solution obtained, explicit analytic expressions for distributions of normal displacements and stresses and of tangential velocities on the surface have been derived.
The Theory of Torsion of Elastic Noncircular Cylinders Under Large Deformations
Authors: Zubov L. M. , Bogachkova L. U.
Published: February 2008

The Saint-Venant semi-inverse method generalization for the problem of torsion under large deformations is presented. The case where a prism cross-section possesses central symmetry is regarded. The torsion problem is reduced to a two-dimensional nonlinear boundary value problem. Differential balance equations and lateral conditions are satisfied by solving the boundary value problem. End conditions are implemented so that the stress system is equivalent to the torsion moment, and to the axial force passing through the cross-section center of inertia. The energy method, used to solve the torsion problem under small twist angles, is extended to the case of finite deformations. Approximate solutions of the torsion problem for elliptical, rectangular, and quadrantal cylinders made of Treloar and Blatz-Ko materials are obtained.