bluuebunny/crossref_metadata_2025 huggingface dataset:
Linear Elastic Behavior of a Low-Density Kelvin Foam With Open Cells
Authors: Warren W. E. , Kraynik A. M.
Published: February 2008

A micromechanical analysis for the linear elastic behavior of a low-density foam with open cells is presented. The foam structure is based on the geometry of a Kelvin soap froth with flat faces: 14-sided polyhedral cells contain six squares and eight hexagons. Four struts meet at every joint in the perfectly ordered, spatially periodic, open-cell structure. All of the struts and joints have identical shape. Strut-level force-displacement relations are expressed by compliances for stretching, bending, and twisting. We consider arbitrary homogeneous deformations of the foam and present analytic results for the force, moment, and displacement at each strut midpoint and the rotation at each joint. The effective stress-strain relations for the foam, which has cubic symmetry, are represented by three elastic constants, a bulk modulus, and two shear moduli, that depend on the strut compliances. When these compliances are evaluated for specific strut geometries, the shear moduli are nearly equal and therefore the elastic response is nearly isotropic. The variational results of Hashin and Shtrikman are used to calculate the effective isotropic shear modulus of a polycrystal that contain grains of Kelvin foam.
Theoretical Transient Analysis of the Interaction Between a Dynamically Propagating In-Plane Crack and Traction-Free Boundaries
Authors: Tsai Chwan-Huei , Ma Chien-Ching
Published: February 2008

In this study, the transient response of a propagating in-plane crack interacting with half-plane boundaries is investigated in detail. The reflected waves which are generated from traction-free boundaries will interact with the propagating crack and make the problem extremely difficult to analyze. The complete transient solutions are constructed by superimposing fundamental solutions in the Laplace transform domain. The fundamental solutions represent the responses of applying exponentially distributed loadings in the Laplace transform domain on the surface of a half-plane or the propagating crack faces. We focus our attention on the determination of the dynamic stress intensity factor. The dynamic stress intensity factors of a propagating crack in a configuration with boundaries and subjected to dynamic loadings are obtained in an explicit closed form. The transient solutions obtained in this study are in agreement with the experimental results from the literature. Some interesting phenomena observed in the published experimental works are also identified and discussed. It is concluded that the reflected waves generated from the boundary parallel to the crack have much stronger influence on the propagating crack than those generated from the boundary perpendicular to the crack. When the reflected waves generated from the boundary parallel to the crack return to the moving crack tip, the stress intensity factor will increase rapidly.
Flexural Wave Scattering at a Through Crack in a Conducting Plate Under a Uniform Magnetic Field
Authors: Shindo Y. , Ohnishi I. , Tohyama S.
Published: February 2008

Following a classical plate bending theory of magneto-elasticity, we consider the scattering of time-harmonic flexural waves by a through crack in a conducting plate under a uniform magnetic field normal to the crack surface. An incident wave giving rise to moments symmetric about the crack plane is applied. It is assumed that the plate has the electric and magnetic permeabilities of the free space. By the use of Fourier transforms we reduce the problem to solving a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic moment intensity factor versus frequency is computed and the influence of the magnetic field on the normalized values is displayed graphically. It is found that the existence of the magnetic field produces higher singular moments near the crack tip.
Post-buckling Analysis of Multiply Delaminated Composite Plates
Authors: Huang Haiying , Kardomateas G. A.
Published: February 2008

This paper presents an elastic post-buckling analysis of an axially loaded beam-plate with two central across-the-width delaminations located at arbitrary depths. The analysis is based on the nonlinear beam equations, combined with the appropriate kinematic continuity and equilibrium conditions. A perturbation technique is employed, which transforms the nonlinear equations into a sequence of linear equations. An asymptotic solution of the post-buckling behavior of the plate is thus obtained. It is shown that with two delaminations, both the maximum deflection and the internal load of the first buckled (top) subplate increase as the external load increases. Of particular interest is the redistribution of load among subplates, which keeps the increase rate of internal load of the top buckled subplate much less than that of the external load. In other words, the load of the buckled subplate is close to the critical value even though the externally applied load is much larger than the critical load. In addition to the two-delamination configuration, a single delamination case is studied based on the present approach in order to verify the accuracy of the method. Also, a comparison with available finite element results is performed.
Stability Analysis of Piezoelectric Circular Cylindrical Shells
Authors: Chang-qing Cheng , Ya-peng Shen
Published: February 2008

A study on the problem of linear buckling of piezoelectric circular cylindrical shells subjected to external pressure as well as on an electric field is presented. In this paper, the structure is treated as a three-dimensional one. The results reveal that the piezoelectric effect has significant effect on the critical load, while the stress due to the uniformly applied electric field alone is not likely to cause elastic buckling. In addition, they can also be used to assess the limitation of shell theories in predicting buckling of piezoelectric smart shell structures.
Derivation of Plate Theory Accounting Asymptotically Correct Shear Deformation
Authors: Sutyrin V. G.
Published: February 2008

The focus of this paper is the development of linear, asymptotically correct theories for inhomogeneous orthotropic plates, for example, laminated plates with orthotropic laminae. It is noted that the method used can be easily extended to develop nonlinear theories for plates with generally anisotropic inhomogeneity. The development, based on variational-asymptotic method, begins with three-dimensional elasticity and mathematically splits the analysis into two separate problems: a one-dimensional through-the-thickness analysis and a two-dimensional “plate” analysis. The through-the-thickness analysis provides elastic constants for use in the plate theory and approximate closed-form recovering relations for all truly three-dimensional displacements, stresses, and strains expressed in terms of plate variables. In general, the specific type of plate theory that results from variational-asymptotic method is determined by the method itself. However, the procedure does not determine the plate theory uniquely, and one may use the freedom appeared to simplify the plate theory as much as possible. The simplest and the most suitable for engineering purposes plate theory would be a “Reissner-like” plate theory, also called first-order shear deformation theory. However, it is shown that construction of an asymptotically correct Reissner-like theory for laminated plates is not possible in general. A new point of view on the variational-asymptotic method is presented, leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible while it is a Reissner-like. This uniquely determines the plate theory. Numerical results from such an optimum Reissner-like theory are presented. These results include comparisons of plate displacement as well as of three-dimensional field variables and are the best of all extant Reissner-like theories. Indeed, they even surpass results from theories that carry many more generalized displacement variables. Although the derivation presented herein is inspired by, and completely equivalent to, the well-known variational-asymptotic method, the new procedure looks different. In fact, one does not have to be familiar with the variational-asymptotic method in order to follow the present derivation.
Different Features of a Stability Problem of Underconstrained Structures
Authors: Volokh K. Y. , Vilnay O.
Published: February 2008

Stability problem of bearing pin-jointed assemblies, in which the number of equilibrium equations is greater than the equilibrium matrix rank (underconstrained structures), is investigated. Local and overall stability of initial and loaded states are discussed. Theoretical considerations are accompanied by numerical examples.
Approximate and Analytic Solutions for Deformation of Finite Porous Filters
Authors: Barry S. I. , Mercer G. N. , Zoppou C.
Published: February 2008

The deformation, using linear poroelasticity, of a two-dimensional box of porous material due to fluid flow from a line source is considered as a model of certain filtration processes. Analytical solutions for the steady-state displacement, pressure, and fluid velocity are derived when the side walls of the filter have zero solid stress. A numerical solution for the case where the porous material adheres to the side walls is also found. It will be shown, however, that simpler approximate solutions can be derived which predict the majority of the deformation behavior of the filter.
Three-Dimensional Vibrations of a Beam on an Elastic Half-Space: Resonance Interaction of Vertical-Longitudinal and Lateral Beam Waves
Authors: Metrikine A. V. , Dieterman H. A.
Published: February 2008

Three-dimensional vibrations of a Euler-Bernoulli beam on an elastic half-space are investigated. In the model the beam has a finite width and the half-space and beam deflections are equal along the centre line of the beam. It is shown that the vertical and longitudinal beam vibrations are uncoupled from the lateral ones. The dispersion relations for the lateral and vertical-longitudinal waves in the beam are derived and the respective dispersion curves are plotted. These curves can cross each other due to the different equivalent stiffnesses of the half-space in vertical and lateral directions and different vertical and lateral bending stiffnesses of the beam. The existence of a crossing point implies that if the vertical-longitudinal and lateral beam vibrations are coupled for some reason (half-space inhomogeneity, beam asymmetry, etc.), the energy of the vertical vibrations of the beam can be resonantly transferred into the energy of lateral vibrations. This transfer will take place if the frequency of vibrations is close to the frequency determined by the crossing point. The dependency of the frequency of the crossing point on axial compressional stresses in the beam is studied. It is shown that this frequency decreases as the stresses increase.
Explicit Vibration Solutions of a Cable Under Complicated Loads
Authors: Yu P.
Published: February 2008

This paper is concerned with the dynamical analysis of a sagged cable having small equilibrium curvature and horizontal supports under both distributed and concentrated loads. The loads are applied in vertical as well as horizontal directions. Based on a free vibration analysis, a transfer matrix method is generalized for solving coupled, nonhomogeneous differential equations to obtain closed-form solutions for the natural frequencies and the associated vibration mode shapes in vertical, horizontal, and longitudinal directions. It is shown that two sets of independent mode shapes associated with two sets of independent frequencies always exist and can be obtained via an equation of one variable only. This method demonstrates its advantages in dealing with interactions of modes in different directions, complex arrangement of concentrated loads, and high-order modes oscillations.
A Lyapunov Function for Systems Whose Linear Part is Almost Classically Damped
Authors: Cox S. J. , Moro J.
Published: February 2008

We show that one may construct a Lyapunov function for any classically damped linear system. The explicit nature of the construction permits us to show that it remains a Lyapunov function under both perturbation of the linear part and introduction of a nonlinear term. We apply our findings to a stability analysis of the discrete, as well as continuous, damped mechanical transmission line.
Critical Speed for Floppy Disks
Authors: Renshaw A. A.
Published: February 2008

This paper uses Lyapunov’s method to determine the critical speed of a flexible spinning disk enclosed in a housing that hydrodynamically couples the transverse motion of the disk to the motion of the thin films of air surrounding the disk. Depending on the clamping ratio, this critical speed is three to ten times higher than the critical speed in the absence of hydrodynamic coupling and does not depend on the strength of the hydrodynamic coupling. Despite the nonlinearity of the underlying model, the critical speed problem is linear and tractable. The linearized free-vibration problem is also computed to verify the stability prediction and to examine linearized damping and stiffness as possible design criteria. The results are relevant to the design of both conventional computer floppy disks and the emerging generation of 100+ MB floppies.
Property Distribution Determination for Nonuniform Composite Beams From Vibration Response Measurements and Galerkin’s Method
Authors: Chen Wei-Hung , Gibson R. F.
Published: February 2008

This paper presents initial results from a program to develop a “rapid screening test” for determining the in-plane fiber distributions in unidirectionally reinforced composite structures by the use of the vibration response measurements and Galerkin’s method. Theoretical models and experimental data are generated on the basis of two methods: (1) the “shifting method,” in which the effective length of the beam is changed, and (2) the “added mass method”, in which the mass distribution of the beam is changed. The elastic constants and the density are all assumed to be functions of fiber volume fraction, while the spatial distribution of the fiber volume fraction is assumed to be given by a polynomial function. The concept of an effective density is employed to obtain the appropriate solution to the coefficients of the polynomial function. Results show that the fundamental mode gives rise to better predictions of physical properties than the higher modes do. An error analysis includes discussion of the errors due to the influences of the mode number, the assumed order of the polynomial in the fiber volume fraction distribution, and the bending-extension coupling effect caused by the unsymmetrical distribution of properties about the beam middle surface.
Nonlinear Waves in Strings: The Barrage Balloon Problem
Authors: Hall J. F.
Published: February 2008

This paper develops a theory for geometrically nonlinear waves in strings and presents analytical solutions for a traveling kink, generation of a geometric wave with its accompanying P wave, reflection of a kink at a fixed support and at a smooth sliding support, and interaction of a P wave and a kink. Conditions that must be satisfied for linear wave theory to hold are derived. The nonlinear theory is demonstrated by extending an historically important solution of the barrage balloon problem that was obtained during World War II.
Numerical Study of Unsteady Flow Around Airfoil With Spoiler
Authors: Xu Cheng , Yeung W. W. H.
Published: February 2008

A discrete vortex model based on the panel method has been developed to simulate the two-dimensional unsteady separated flow generated by the rapid deployment of a spoiler on the upper surface of an airfoil. This method represents the boundary surfaces by distributing piecewise linear-vortex and constant source singularities on discrete panels. The wake of the spoiler and airfoil is represented by discrete vortices. At each sharp edge, a vortex sheet is used to feed discrete vortices at every time-step to form the downstream wake. The length and strength of each shed vortex sheet are determined by the continuity equation and a condition such that the flow, the net force, and the pressure difference across the vortex sheet are zero. The flow patterns behind the spoiler at different time-steps are presented. The pressure distributions on the airfoil based on the unsteady Bernoulli’s equation are compared, where possible, with the experimental results and other computational results. The adverse lift effects have been obtained, and similar effects have been measured in experiments.
Elastodynamic Solution for the Thermal Shock Stresses in an Orthotropic Thick Cylindrical Shell
Authors: Cho H. , Kardomateas G. A. , Valle C. S.
Published: February 2008

An elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell is presented. The solution is achieved by the proper usage of integral transforms such as the finite Hankel transform and the Laplace transform. No restrictive assumptions on the shell thickness are placed. Results are presented for the well-formed wave propagation phenomenon of elastic stresses through the thickness of an orthotropic thick cylindrical shell. Thermal shock stresses become of significant magnitude due to stress wave propagation which is initiated at the boundaries by sudden thermal loading.
On-Line Identification of Hysteretic Systems
Authors: Chassiakos A. G. , Masri S. F. , Smyth A. W. , Caughey T. K.
Published: February 2008

Using adaptive estimation approaches, a method is presented for the on-line identification of hysteretic systems under arbitrary dynamic environments. The availability of such an identification approach is crucial for the on-line control and monitoring of nonlinear structural systems to be actively controlled. In spite of the challenges encountered in the identification of the hereditary nature of the restoring force of such nonlinear systems, it is shown through the use of simulation studies and experimental measurements that the proposed approach can yield reliable estimates of the hysteretic restoring force under a very wide range of excitation levels and response ranges.
Constructing Exact Dynamic Elasticity Solutions for Axisymmetrically Deformed Plates From Classical Plate Theory Solutions
Authors: Qian Z. , Simmonds J. G.
Published: February 2008

This paper addresses the question of how to assess the errors made when the exact three-dimensional linear elasticity solution for the axisymmetric dynamic deformation of an elastic plate is approximated by a solution inferred from the classical plate theory of Kirchhoff. Following the strategy used by Ladeve`ze and Simmonds for beams, the exact solution of a “nearby” three-dimensional problem, which differs from the original problem by the addition of incremental, computable body forces, face shears, and initial conditions—error increments, for short—is expressed in terms of the solution of a wave equation in which distance normal to the plate’s midplane plays the role of a time-like variable while the physical time itself enters only as a parameter. The error increments which, ultimately, can be computed in terms of the solution delivered by plate theory, can be regarded as an “engineering norm” because with them an engineer can decide if such a shift in the external data lies within acceptable bounds.
The Transient Response of Structures Using Asymptotic Modal Analysis
Authors: Reynolds R. R. , Dowell E. H.
Published: February 2008

The transient response of a structure is predicted using an asymptotic modal approximation of the classical modal solution. The method is aimed at estimating the impulse response problem for high frequency regimes where typical numerical methods (e.g., finite elements) are impractical. As an example, the response of a thin elastic panel is modeled in a frequency range that includes a sufficient number of modes. Both impulsive and arbitrary forms of excitation are considered. It is shown that the asymptotic modal analysis yields an excellent estimate of both the local displacement near the excitation location and of the spatially averaged transient response of the panel for moderate time spans after the excitation is applied. Furthermore, as this approach does not require that the mode shapes or natural frequencies of the structure to be calculated, it is an extremely efficient technique.
A Circular Inclusion With Circumferentially Inhomogeneous Sliding Interface in Plane Elastostatics
Authors: Ru C. Q.
Published: February 2008

A general method is presented to obtain the rigorous solution for a circular inclusion embedded within an infinite matrix with a circumferentially inhomogeneous sliding interface in plane elastostatics. By virtue of analytic continuation, the basic boundary value problem for four analytic functions is reduced to a first-order differential equation for a single analytic function inside the circular inclusion. The finite form solution is obtained that includes a finite number of unknown constants determined by the analyticity of the solution and certain other auxiliary conditions. With this method, the exact values of the average stresses within the circular inclusion can be calculated without solving the full problem. Several specific examples are used to illustrate the method. The effects of the circumferential variation of the interface parameter on the mean stress at the interface and the average stresses within the inclusion are discussed.
Toroidal Vibrations of Anisotropic Spheres With Spherical Isotropy
Authors: Chau K. T.
Published: February 2008

This paper derives the exact frequency equation for the toroidal mode of vibrations for a spherically isotropic elastic sphere. The vibrations of spherically isotropic solids are solved by introducing two wave potentials (Φ and Ψ) such that the general solutions for free vibrations can be classified into two independent modes of vibrations, namely the “toroidal” and “spheroidal” modes. Both of these vibration modes can be written in terms of spherical harmonics of degree n. The frequency equation for the toroidal modes is obtained analytically, and it depends on both n and β[=(C11-C12)/(2C44)], where C11C12, and C44 have the usual meaning of moduli and are defined in Eqs. (2)–(3); and, as expected, Lamb’s (1882) classical frequency equation is recovered as the isotropic limit. Numerical results show that the normalized frequency ωa/Cs increases with both n and β, where ω is the circular frequency of vibration, a the radius of the sphere, and Cs is the shear wave speed on the spherical surfaces. The natural frequencies for spheres of transversely isotropic minerals and crystals, with β ranging from 0.3719 to 1.8897, are also tabulated. However, two coupled differential equations are obtained for the spheroidal modes, which remain to be solved.
The Hypersingular Boundary Contour Method for Three-Dimensional Linear Elasticity
Authors: Mukherjee S. , Mukherjee Y. X.
Published: February 2008

A variant of the usual boundary element method, called the boundary contour method, has been presented in the literature in recent years. In the boundary contour method in three-dimensions, the surface integrals on boundary elements of the usual boundary element method are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. The boundary contour method employs global shape functions with the weights, in the linear combinations of these shape functions, being defined piecewise on boundary elements. A very useful consequence of this approach is that stresses at points on the boundary of a body, where they are continuous, can be easily obtained from the boundary contour method. The hypersingular boundary element method has many important applications in diverse areas such as wave scattering, fracture mechanics, symmetric Galerkin formulations, and adaptive analysis. This paper first presents the derivation of a regularized hypersingular boundary contour method for three-dimensional linear elasticity. This is followed by a discussion of special cases of the general formulation, as well as some numerical results.
Singular Integral Equation Method for Interaction Between Elliptical Inclusions
Authors: Noda Nao-Aki , Matsuo Tadatoshi
Published: February 2008

This paper deals with numerical solutions of singular integral equations in interaction problems of elliptical inclusions under general loading conditions. The stress and displacement fields due to a point force in infinite plates are used as fundamental solutions. Then, the problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the unknowns are the body force densities distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. To determine the unknown body force densities to satisfy the boundary conditions, four auxiliary unknown functions are derived from each body force density. It is found that determining these four auxiliary functions in the range 0≦φk≦π/2 is equivalent to determining an original unknown density in the range 0≦φk≦2π. Then, these auxiliary unknowns are approximated by using fundamental densities and polynomials. Initially, the convergence of the results such as unknown densities and interface stresses are confirmed with increasing collocation points. Also, the accuracy is verified by examining the boundary conditions and relations between interface stresses and displacements. Randomly or regularly distributed elliptical inclusions can be treated by combining both solutions for remote tension and shear shown in this study.
Thermal Stresses in a Freezing Sphere and its Application to Cryobiology
Authors: Rabin Y. , Steif P. S.
Published: February 2008

Thermal stresses in an inwardly solidifying sphere are studied analytically. A closed-form solution is given which accounts for thermal expansion associated with temperature gradients and volume changes associated with phase transition. Consistent with the target application of cryopreservation of biological solutions and tissues, the material is modeled as elastic-perfectly plastic. Parametric studies using appropriate material properties and typical cryopreservation protocols suggest that strains associated with phase transition lead to far higher stresses than those associated with thermal expansion, with important implications for cryopreservation procedures.
Free-Vibration Analysis of Clamped Antisymmetrically Laminated Elliptical Plates
Authors: Hosokawa K. , Yamada Y. , Sakata T.
Published: February 2008

In a previous paper, a numerical approach for analyzing the free vibration problem of an unsymmetrically laminated fiber-reinforced plastic composite plate was proposed by the authors. In the present paper, this approach is applied to the clamped antisymmetrically laminated elliptical plate. As numerical examples, the natural frequencies and the mode shapes of the circular and elliptical plates are estimated. The effects of the fiber orientation angle on natural frequency and mode shape are studied. Furthermore, the vibration tests of the clamped antisymmetrically laminated circular and elliptical plates made of carbon fiber-reinforced plastic are carried out, and the experimental natural frequency and mode shape are compared with the numerical results.
Transient Residual Stresses in Thermal Barrier Coatings: Analytical and Numerical Results
Authors: Nusier S. Q. , Newaz G. M.
Published: February 2008

Thermal barrier coatings (TBCs) provide thermal insulation to high-temperature superalloys. Residual stresses develop in TBCs during cool-down from processing temperatures due to the thermal expansion mismatch between the different layers (substrate, bond coat, and the ceramic TBC). These residual stresses can initiate microcracks at the bond coat/TBC interface which can lead to debonding at the bond coat/TBC interface. Elasticity-based modeling was used to determine the transient stresses in the TBC, bond coat, and the superalloy substrate with specific attention to the interfaces. For the steady-state case, finite element modeling was undertaken as well. Closed-form elasticity solutions correlated well with the finite element results for the steady-state case. The highest residual stresses occurred at the interface between the bond coat and the TBC. An important result of this investigation was that the TBC/bond coat interface was under biaxial stress field. An important result was that the residual stresses developed in the substrate are higher for the case of partly cooled specimen compared to the fully cooled specimen which can be rationalized due to the presence of higher temperature gradients at earlier times during cool-down from processing temperature.
A Basic Problem in Thermoelasticodynamics and its Solution
Authors: Zhang Xiangzhou
Published: February 2008

Dynamic stresses in a solid sphere, brought about by a sudden temperature rise uniformly distributed over the whole volume of the sphere, is studied as a basic problem in thermoelasticodynamics. Using a simple reduction, the problem is first reduced to an isothermal dynamicresponse one. Exact solution to this dynamic response problem, for a hollow sphere with a fixed inner boundary, is developed with use of a solution in D’Alembertform and a technique of singularity extraction. This hollow sphere solution is further employed in a limit process, in which the inner radius of the sphere tends towards zero, with the objective of thereby creating a solution for the solid sphere. This limit process results in a solid sphere solution, which is exact and explicit, and takes various closed forms for each wave propagation and reflection. Numerical result and discussion regarding this solid sphere solution are given.
Decomposition of the Deformation Gradient in Thermoelasticity
Authors: Imam A. , Johnson G. C.
Published: February 2008

The deformation gradient of a thermoelastic solid undergoing large deformations is decomposed into elastic and thermal components, corresponding to an intermediate configuration which is assumed to be stress-free. This decomposition is shown to be unique only to within a rigid-body motion of the intermediate configuration. An alternate decomposition is proposed in which this arbitrariness is removed. The thermoelastic theory developed on the basis of these decompositions is linearized, resulting in familiar expressions of linear thermoelasticity. The stress response function is further specialized for the particular case of isotropic linear solids.
An Inverse Problem for Determination of Transient Surface Temperature From Piezoelectric Sensor Measurement
Authors: Ashida Fumihiro , Tauchert T. R.
Published: February 2008

The time-varying ambient temperature on the face of a piezoelectric disk is inferred from a knowledge of the thermally induced electric potential difference across the disk thickness. The temperature-sensing disk has a circular planform, possesses hexagonal material symmetry properties, and is constrained by a rigid, thermally insulated, electrically charge-free ring. A potential function approach, together with Laplace transforms, is employed to solve the inverse problem for a particular form of electric potential difference. Also presented is a finite difference formulation which does not require specification of an analytical form for the potential difference. Numerical results are given for the predicted transient ambient temperatures corresponding to various combinations of disk thickness-to-radius ratios and surface heat transfer coefficients. Through-thickness distributions of temperature, stresses, and electric field intensities are shown, and a comparison of the exact and finite difference results is provided.
Mechanics of Polishing
Authors: Bulsara V. H. , Ahn Y. , Chandrasekar S. , Farris T. N.
Published: February 2008

A model has been developed to determine the number and sizes of abrasive particles involved in material removal in polishing, and the forces acting on these particles. The effect of particle size on these parameters has been simulated for a range of particle sizes. It is shown that when polishing with abrasive powders having relatively broad size distributions, only a very small percentage of the particles are involved in material removal. Further, these particles are comprised of the larger particles occurring in the tail end of the particle size distribution. The average force on a particle is found to be in the range of 5–200 mN under typical polishing conditions, which is of the order of loads used in micro-indentation hardness testing. These predictions of the model are consistent with observations pertaining to polished surfaces and the polishing process.
Guided Circumferential Waves in a Circular Annulus
Authors: Liu Guoli , Qu Jianmin
Published: February 2008

A two-dimensional circular annulus is considered in this paper as a waveguide. The guided steady-state time-harmonic waves propagating in the circumferential direction are studied. It is found that the guided circumferential waves are dispersive. The dispersion equation is derived analytically and numerical examples are presented for the frequency dispersion curves. The displacement profiles across the wall thickness of the annulus are also obtained for the first five propagating modes. In addition, the analogy between a flat plate and an annulus in the asymptotic limit of infinite radius of curvature is discussed to reveal some interesting wave phenomena intrinsic to curved waveguides.
Physical Restrictions on the Impulse Acting During Three-Dimensional Impact of Two “Rigid” Bodies
Authors: Rubin M. B.
Published: February 2008

It is well known that the impulse of the contact force acting during impact of two rigid bodies determines the abrupt change in the motions of the two bodies. Much recent work has been focused on determining a constitutive equation for this impulse which models the complicated phenomena occurring during the actual deformations of the two bodies. The objective of this paper is to discuss a set of physical conditions which impose nontrivial restrictions on general constitutive equations for the impulse. Due to the general nature of these restrictions they can be used to determine the range of validity of various proposals for the impulse. For the general case of three-dimensional impact, the impulse depends on an energetic coefficient of restitution and two angles defining its direction. However, when there are no directional properties of the roughness of the two impacting bodies, it is reasonable to propose a simpler form for the direction of the impulse which depends only on this coefficient of restitution and a single friction angle. An example of impact of two finite spheres is considered which shows that the condition that the two bodies have a tendency to separate after impact imposes nontrivial bounds on this friction angle.
Effects of Flexibility and Damping on Momentum Transfer During Locking of Two Moving Links, Part I: Numerical Simulation
Authors: Szyszkowski W. , Fielden K.
Published: February 2008

The system consisting of two links and two joints is examined. The joints are idealy frictionless when unlocked. Due to flexibility of the links, the locking generates some damped vibrations. It is demonstrated that the presence of these vibrations, even of very small and seemingly neglegible amplitudes, have dramatic effects on the after-locking motion of the links. Depending on the level of flexibility and damping involved, the locking triggers a large-scale “slow” motion that may have either oscillatory or circular (clockwise or counterclockwise) characters. The links will stop at some resting configuration only at certain “critical” values of damping. The set of “critical dampings” seems to be infinite, though only two degrees-of-freedom are used to model the system. Governing equations for these phenomena are derived and discussed in Part II of this paper.
Effects of Flexibility and Damping on Momentum Transfer During Locking of Two Moving Links, Part II: Analytical Approach
Authors: Szyszkowski W. , Fielden K.
Published: February 2008

The numerical analysis presented in Part I of this paper revealed that small and seemingly negligible flexibility and damping effects influence significantly the post-locking motion of the assembly consisting of two joint-connected links. Here we concentrate on a more physical understanding and explanation of the phenomenon observed. It is shown that the main characteristic features of the post-locking motion can be recovered by decomposing it into the “fast” and “slow” modes. The governing equations of these two modes of motion are derived and discussed in detail.
Boundary Effects in Penetration or Perforation
Authors: Keer L. M. , Xu Yonglin , Luk V. K.
Published: February 2008

For the analysis of stress distributions around a projectile tip in penetration or perforation, a point force P associated with an expansion source Ez, which depends on the geometry of the projectile, is employed to simulate the projectile. Using the method of half-space analysis by Mindlin (1936), the boundary effects on the projectile are analyzed. The analytical solutions of an expansion source associated with a concentrated force are derived for the prediction of the damage zones in a target, as the projectile either approaches or leaves the boundary. As a projectile perforates a target, it forms a cratering area at the impact surface and leaves a cone-like spalling area at the exit surface. The presence of these two areas and the fact that the spalling area is larger than the cratering area in perforation, can be explained by the stress analysis of boundary effects. Solution of the cavity expansion source in a half-space is derived. This solution provides a theoretical evidence for the conclusion obtained from the empirical analysis by Forrestal et al. (1994). Their conclusion states that when the projectile is at about twice its shank diameters, it can be approximately treated as though it were in the infinite medium.
Dynamics of a Simple Model for a Wind-Loaded Nonlinear Structure: Bifurcations of Codimension One and Two
Authors: Yagasaki K.
Published: February 2008

The motion induced by vortex shedding of a structure with nonlinear restoring force is investigated. In particular, a conclusion about nonexistence of bounded motions obtained for a similar problem in the previous study is improved by taking into account the nonlinear restoring force characteristic. The vortex shedding frequency is assumed to be close to the natural frequency of the cross-wind oscillation and the along-wind oscillation is not excited, so that a single-degree-of-freedom model representing the cross-wind motions is obtained. The averaging method is applied to the single-degree-of-freedom system, and the normal form and center manifold theories are used to discuss bifurcations of codimension one, saddle-node and Hopf bifurcations. Moreover, it is shown that a multiple bifurcation of codimension two, called the Bogdanov-Takens bifurcation, occurs in the averaged system. The implications of the averaging results on the dynamics of the original single-degree-of-freedom system are described. Numerical examples are also given with numerical simulation results for both the averaged and original systems to demonstrate our theoretical predictions.
Interactively Induced Localized Buckling in Sandwich Structures With Core Orthotropy
Authors: Wadee M. Ahmer , Hunt G. W.
Published: February 2008

Recent work on the interactive buckling behavior of compressed sandwich structures (Hunt and Wadee, 1998) is extended to orthotropic core materials. The variation of the material properties can tend to maximize the interactive effect such that overall and secondary localized modes are triggered almost simultaneously, giving rise to highly unstable post-buckling behavior in systems of practical dimensions.
A Modified Element-by-Element Preconditioner for Elastostatics
Authors: Barboteu M. , Alart P. , Lebon F.
Published: February 2008

In this paper we present in detail a modified element-by-element strategy. This kind of method is well known to be effective for large-scale problems because of its implicit parallelism. Numerical experiments described in this paper confirm the efficiency of this solver.
Large Deflection of a Rigid-Plastic Circular Plate Pressed by a Sphere
Authors: Wang Ge , Ohtsubo Hideomi , Arita Kikuo
Published: February 2008

A rigid-plastic circular plate deflected by a rigid sphere is investigated. The behavior at large deflection is considered; the contribution from a bending moment is neglected. Approximate formulas for the load-deflection relationship are derived. Experiments are conducted and the test data compare well with the prediction results. It is revealed that the size of the rigid sphere has a strong effecton the resistance of the compressed plate.
Self-Similar Crack Expansion Method for Three-Dimensional Cracks Under Mixed-Mode Loading Conditions
Authors: Xu Yonglin , Moran B. , Belytschko T.
Published: February 2008

Three-dimensional planar cracks under mixed-mode loading conditions are investigated by using the selfsimilar crack expansion method with the boundary integral equation technique. For a planar crack under general loading (tensile and shear) conditions, the normal displacement and tangential displacements on the crack surface exhibit uncoupled characteristics. However, the tangential displacements in the two directions are generally coupled. In this paper, two coupled boundary integral equations for a crack subject to shear loading are solved using the analytically numerical method, where the integrals on elements’ are estimated by using the explicit expression of the close form of the integrals. Combination of the self-similar crack expansion method and the analytically numerical method results in good accuracy, with errors in stress intensity factors of penny-shaped cracks and elliptical cracks less than one percent. This numerical analysis is applicable to the analysis of cracks with arbitrary geometry.
The Elastodynamic Green’s Function for a Torsional Ring Source
Authors: Lu Yichi
Published: February 2008

The elastodynamic Green’s fimction for a torsional ring source in a homogeneous, linear elastic medium is derived using the Fourier-Hankel transform. The Green’s function is found to possess the same logarithmic singularity as the Legendre function of half-degree of the second kind.
The Cosserat Spectrum Theory in Thermoelasticity and Application to the Problem of Heat Flow Past a Rigid Spherical Inclusion
Authors: Liu Wensen , Markenscoff X. , Paukshto M.
Published: February 2008

We apply the Cosserat Spectrum theory to boundary value problems in thermoelasticity and show the advantages of this method. The thermoelastic displacement field caused by a general heat flow around a spherical rigid inclusion is calculatedand the results show that the discrete Cosserat eigenfunctions converge fast and thus provide a practical method for solving three-dimensional problems in thermoelasticity. In the case of uniform heat flow, the solution is obtained analytically in closed form and a variational principle within the frame of the Cosserat Spectrum theory shows that the solution maximizes the elastic energy.
A Hybrid Membrane/Shell Method for Rapid Estimation of Springback in Anisotropic Sheet Metals
Authors: Pourboghrat F. , Chung K. , Richmond O.
Published: February 2008

A semi-analytical method to predict springback in sheet metal forming processes has been developed for the case of plane strain. In the proposed hybrid method, for each deformation increment, bending, and unbending stretches are analytically superposed on membrane stretches which are numerically obtained in advance from a membrane finite element code. Springback is then obtained by the unloading of a force and a bending moment at the boundary of each element treated as a shell. Hill’s 1948 yield criterion with normal anisotropy is used in this theory along with kinematic and isotropic hardening laws during reverse loading. The method has been applied for the springback prediction of a 2008-T4 aluminum alloy in plane-strain draw-bending tests. The results indicate the necessity of including anisotropic hardening (especially Bauschinger effects) and elastoplastic unloading in order to achieve good agreement with experimental results.
Discrete Modeling of a String and Analysis of a Loop Soliton
Authors: Nishinari K.
Published: February 2008

A discrete model for an extensible string is proposed and analyzed by a discrete soliton theory and computer simulations. The relation between tension of the string and the size of a loop propagating on the string is obtained analytically by using the soliton theory. We use this relation to investigate dynamics and stability of loops, and it is found that one loop is stable against various kinds of perturbation. It is confirmed numerically that the loop can be formed by moving a boundary along a semicircle. If the moment of the string is introduced, behaviors of the formation are drastically changed and there is a critical value of stiffness of the string beyond which the loop cannot be formed. As for collision of two loops, we, found that two loops do not break after collision if the two are similar. This result of collision can be well explained by our former analysis of a continuous string theory (Nishinari, 1997).
Bernoulli Numbers and Rotational Kinematics
Authors: Pfister F.
Published: February 2008

The representation of rotation operators in the form of infinite tensor power series, R = exp(Ψˆ), has been found to be a valuable tool in multibody dynamics and nonlinear finite element analysis. This paper presents analogous formulations for the kinematic differential equations of the Euler-vector Ψ and elucidates their connection to Bernoulli-numbers. New power series such as the Bernoulli- and the Gibbs series are shown to provide compact expressions and a simple means for understanding and computing some of the fundamental formulae of rotational kinematics. The paper includes an extensive literature review, discussions of isogonal rotations, and a kinematic singularity measure.
Natural Frequencies and Normal Modes for Externally Damped Spinning Timoshenko Beams With General Boundary Conditions
Authors: Zu J. W. , Melanson J.
Published: February 2008

Vibration analysis of externally damped spinning Timoshenko beams with general boundary conditions is performed analytically. Exact solutions for natural frequencies and normal modes for the six classical boundary conditions are derived for the first time. In the numerical simulations, the trend between the complex frequencies and the damping coefficient is investigated, and complex mode shapes are presented in three-dimensional space.
Analysis of a Rotating Pendulum With a Mass Free to Move Radially
Authors: Schmidt B. A. , McDowell D. G.
Published: February 2008

Analysis of a pendulum pivoted on a rotating shaft. The mass of the pendulum is free to move radially. The shaft is nearly horizontal.
Measurement of Tensile Properties of Metallic Foils
Authors: Sharma V. , Isaacs J. B. , Nemat-Nasser S.
Published: February 2008

A fixture has been developed for testing thin specimens under uniaxial tension. The fixture consists of two cantilever beams with strain gauges attached to them close to their fixed ends. The displacement of one beam is used to measure the force and the difference in the displacements of the beams is used to measure the sample displacement. The tensile properties of 0.025 mm by 1.25 mm by 5 mm iron-nickel specimens were measured. The tensile plastic yield point of the specimens was observed to be 1.4 GPa and the total elongation to failure turned out to be five percent and eight percent, for the two tested specimens.