bluuebunny/crossref_metadata_2025 huggingface dataset:
Inclined Flat Punch of Arbitrary Shape on an Elastic Half-Space
Authors: Fabrikant V. I.
Published: July 2009

A new method is proposed for the analysis of elastic contact problems for a flat inclined punch of arbitrary planform under the action of a normal noncentrally applied force. The method is based on an integral representation for the reciprocal distance between two points obtained by the author earlier. Some simple yet accurate relationships are established between the tilting moments and the angles of inclination of an arbitrary flat punch. Specific formulae are derived for a punch whose planform has a shape of a polygon, a triangle, a rectangle, a rhombus, a circular sector and a circular segment. All the formulae are checked against the solutions known in the literature, and their accuracy is confirmed.
Torsional Wave Sensor—A Theory
Authors: Bau H. H.
Published: July 2009

Experimental observations suggest that the speed of propagation of torsional waves in a solid, elastic wave guide with a noncircular cross section is inversely proportional to the density of the fluid adjacent to the waveguide. Thus, by measuring the speed of propagation of the torsional wave, one can infer the density of the fluid. Additionally, the above procedure may be utilized to measure, among other things, liquid level and the composition of binary solutions. A simple theory is derived to correlate the torsional wave speed and the fluid density; the theoretical results are also compared with experiments.
Numerical Solution to an Inextensible Plate Theory With Experimental Results
Authors: Darmon P. , Benson R. C.
Published: July 2009

A numerical and experimental study of the Simmonds-Libai (1979) plate theory is presented in this paper. This concerns the large, inextensional, noncylindrical bending of cantilevered plates.
Beams on Variable Winkler Elastic Foundation
Authors: Clastornik J. , Eisenberger M. , Yankelevsky D. Z. , Adin M. A.
Published: July 2009

A stiffness approach is presented for computing the solution of beams on variable Winkler foundation. The solution may be achieved using only a small number of elements along the beam. Accuracy is dependent only on a preset user criterion. A numerical example demonstrates the efficiency and accuracy of the procedure.
Post-Buckling Behavior of a Circular Rod Constrained Within a Circular Cylinder
Authors: Sorenson K. G. , Cheatham J. B.
Published: July 2009

An axially loaded weightless circular rod buckles helically when constrained within a circular cylinder. The effects of pinned and fixed-end conditions are investigated. Both end conditions locate the rod end on the cylinder axis, and are found to perturb the helix in an exponentially decaying manner for a distance of less than one helix pitch length. Far from the end, the rod behaves as an undisturbed constant-pitch helix. The distance from the rod end to the point of initial contact with the cylinder wall is calculated. Closed-form analytical solutions are obtained for the deflected shapes and internal reactions of the end sections. The solution procedure applies to rods of either finite or infinite length.
Asymmetric Wave Propagation in an Elastic Half-Space by a Method of Potentials
Authors: Pak R. Y. S.
Published: July 2009

A method of potentials is presented for the derivation of the dynamic response of an elastic half-space to an arbitrary, time-harmonic, finite, buried source. The development includes a set of transformed stress-potential and displacement-potential relations which are apt to be useful in a variety of wave propagation problems. Specific results for an embedded source of uniform distributions are also included.
Ray Solutions on Surfaces of Revolution
Authors: Chien L. S. , Steele C. R.
Published: July 2009

Our concern is the development of techniques for the analysis of wave propagation and general transient response of thin shells to local loading. In general, ray methods are useful for such problems. In the present work, the ray solutions are obtained for a shell of revolution with high prestress, for which the bending stiffness of the shell wall can be neglected. The equation is that for an inhomogeneous, anisotropic medium with a non-Euclidean metric. Of special interest in the present shell problem is the global connectivity of ray paths. For an example the conical shell is considered. The rays for uniform pressure are shown to deviate substantially from geodesics. A ray emitted from a point on the cone may make several spirals around the small end of the cone before moving toward the large end in an almost straight line. The implication is that high focusing of energy can occur from a mild impact on the side of a conical shell.
Asymptotic Solutions for Warping and Distortion of Thin-Walled Box Beams
Authors: Balch C. D. , Steele C. R.
Published: July 2009

The equations of conventional thin plate theory are used to formulate an eigenvalue problem for effects of self-equilibrating end loads in thin-walled rectangular cross section tubes, or box beams. The problem is analyzed by a perturbation procedure, which is based on a small parameter proportional to the square root of the ratio of wall thickness to cross section width. Solution of the unperturbed problem yields a family of membrane and inextensional end-effect eigenfunctions which are found to have decay distances on the order of the beam width or shorter. The perturbation procedure is carried out to obtain closed form asymptotically valid solutions for warping and distortional effects which decay much more slowly. These asymptotic solutions compare favorably with previous analytical and experimental results.
Transfer Function of a Class of Nonlinear Multidegree of Freedom Oscillators
Authors: Galhoud L. E. , Masri S. F. , Anderson J. C.
Published: July 2009

Analytical and experimental studies were made of the dynamic response of a multidegree-of-freedom system with a geometric nonlinearity, which is encountered in many practical engineering applications. An exact solution was derived for the steady-state motion of a viscously damped two-degree-of-freedom oscillator with an unsymmetric geomtric nonlinearity, under the action of harmonic excitation. Experimental measurements of a distributed-parameter mechanical model under harmonic excitation verified the analytical findings. The effect of various dimensionless parameters on the system response was determined.
Remaining at Yield During Unloading and Other Unconventional Elastic-Plastic Response
Authors: Drucker D. C. , Seereeram Devo
Published: July 2009

A rather special time-independent or elastic-plastic response is proposed in which, although there is elastic response to unloading, the material remains at yield for all or a significant portion of the unloading path following plastic deformation. In the most elementary form, the material exhibits no memory of prior plastic deformation; the current state of the material is given solely by the current state of stress. A simple but unconventional field of plastic moduli then can be chosen to produce a limit surface that cuts through a nested set of yield surfaces and to model critical aspects of the behavior of sand.
A Simple Kinetic Theory for Granular Flow of Rough, Inelastic, Spherical Particles
Authors: Lun C. K. K. , Savage S. B.
Published: July 2009

Using statistical methods analogous to those used in the kinetic theory of dense gases, conservation equations and constitutive equations are derived for the flow of an idealized granular material consisting of uniform, rough, inelastic spherical particles. Simple forms for the singlet and pair velocity distribution functions are employed to study the effects of particle rotary inertia in the specific case of Couette flow of such materials. A constant coefficient of restitution e is used to characterize the inelasticity of the particles and a roughness coefficient β is adopted to characterize the effects of surface friction in collisions between particles. During collisions, surface friction causes particle rotational velocity fluctuations. As a result of particle rotary inertia, the stress tensor is found to be asymmetric during general deformations. However, for the special case of steady Couette flow which is studied in detail, the stress tensor remains symmetric. The partition of fluctuation kinetic energy between the translational and rotational modes is examined; equipartition is achieved only for the case of perfectly rough particles. In agreement with previous investigations, the stresses are found to decrease with decreasing e. Except for the case of almost perfectly rough particles, the effects of rotary inertia generally reduce the stresses. However, the normal stresses are reduced more than the shear stresses, and the predicted ratio of shear to normal stress (the dynamic friction angle) is higher for rough particles than for smooth ones. The inclusion of roughness in the analysis yields shear to normal stress ratios that agree more closely with experimental measurements.
A Continuum Theory of Crack Shielding in Ceramics
Authors: Ortiz M.
Published: July 2009

A phenomenological constitutive model is proposed which aims at describing the overall effect of microfracture in ceramics. Based on this model, the asymptotic stress, strain, and displacement fields at the tip of a stationary macroscopic crack are determined in closed form. The near-tip stress-intensity factor is computed and observed to be significantly smaller than the applied stress-intensity factor even for moderate amounts of damage.
Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor
Authors: Danielson D. A. , Hodges D. H.
Published: July 2009

A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion, extension, shear deformation, and warping of an initially curved and twisted beam.
On Boundary Layers in a Pressurized Mooney Cylinder
Authors: Taber L. A.
Published: July 2009

Asymptotic expansions are developed for the equations governing large axisymmetric deformation of a circular cylindrical shell composed of a Mooney material. The shell equations allow large normal strains and thickness changes but ignore transverse shear deformation. For a pressurized cylinder with rigid end plugs, results are presented to illustrate the development of a primary and a secondary boundary layer as generalizations of those that occur in small-strain shell theory. The form of the WKB-type expansion divides the secondary layer into bending and stretching components, which lie within the wider primary boundary layer. While the bending component of the secondary layer can become significant when strains are still small, the stretching component emerges as a consequence of large geometry changes in the edge zone, becoming significant as strains grow large and material nonlinearity becomes important.
Large-Strain Axisymmetric Deformation of Cylindrical Shells
Authors: Brodland G. W. , Cohen H.
Published: July 2009

Nonlinear equations are derived for the axisymmetric deformation of thin, cylindrical shells made of Mooney-Rivlin materials and subject to arbitrarily large strains and rotations. These equations are then implemented numerically using an energy minimization technique. Finally, an extensive parametric analysis is done of cylindrical shells which are clamped at one end and loaded with either a radial force or an edge moment uniformly distributed along the circumference of the other end.
Bending Vibrations of a Class of Rotating Beams with Hypergeometric Solutions
Authors: Storti D. , Aboelnaga Y.
Published: July 2009

We study the transverse deflections of a straight tapered symmetric beam attached to a rotating hub as a model for the bending vibration of blades in turbomachinery. A broad class of blade shapes is obtained for which the equation of motion can be solved analytically in terms of hypergeometric functions. Based on this analytic solution, an algorithm for computing the natural bending frequencies and mode shapes as a function of setting angle and rotation rate is presented and applied to an example.
A Complementary Work Bounding Principle for Forward Integration Along the Path of Loading for Elasto-Plastic Bodies
Authors: Martin J. B.
Published: July 2009

The paper presents an extension of the complementary work bounding principle of Hodge (1966) for integration along the path of loading for a statically loaded elastic-plastic body. Using an internal variable framework, the concept of a piecewise holonomic constitutive equation, updated at discrete intervals along the loading path, is introduced. It is shown that the complementary work over the entire path decreases (or does not increase) each time the last interval is subdivided. The result has some interesting implications with regard to the formulation of a mechanical principle for time discretisation along the loading path, and these are explored.
Static Loads in Layered Halfspaces
Authors: Kausel E. , Seale S. H.
Published: July 2009

A solution is presented for Mindlin’s problem of point loads applied in the interior of a layered elastic halfspace. The algorithm described differes from available numerical solutions for this problem in that the displacement functions found are expressed explicitly in the spatial domain. Thus, no numerical transformations are necessary. Furthermore, since the resulting equations can readily be subjected to mathematical manipulations (such as derivations or integrals), they could be used without difficulty as Green’s functions in procedures in Elastomechanics such as the Boundary Integral Method.
An Approach to Calculating Random Vibration Integrals
Authors: Spanos P-T. D.
Published: July 2009

Integrals required for the determination of the response statistics of an arbitrary order linear and time-invariant dynamic system under stationary excitation are examined. These integrals are found as the solution of a set of linear algebraic equations. The application of the derived general formula is exemplified by considering as excitation models white noise, band-limited white noise, and other important stationary random processes. Besides random vibration applications, the derived formula has purely mathematical merit and can be used for the calculation of complicated integrals encountered in a variety of other technical fields.
Kane’s Equations With Undetermined Multipliers—Application to Constrained Multibody Systems
Authors: Wang J. T. , Huston R. L.
Published: July 2009

A procedure for automated analysis of constrained multibody systems is presented. The procedure is based upon Kane’s equations and the concept of undetermined multipliers. It is applicable with both free and controlled systems. As with Lagrange’s equations, the multipliers are identified as scalar components of constraining forces and moments. The advantage of using Kane’s equations is that they are ideally suited for development of algorithms for numerical analyses. Also, generalized speeds and quasi-coordinates are readily accommodated. A simple example illustrating the concepts is presented.
Response Bounds for Nonclassically Damped Mechanical Systems Under Transient Loads
Authors: Nicholson D. W.
Published: July 2009

Time-decaying upper bounds are derived for the response of damped linear mechanical systems under impulsive loads and under step loads. The bounds are expressed in terms of the extreme eigenvalues of the symmetric, positive definite constituent system matrices. The system is assumed to exhibit nonclassical damping by which we mean that classical normal modes do not occur: i.e., the modes are coupled (complex). The governing system equation is first reduced to a particular version of “state form” suited for application of the one-sided Lipschitz constant. A formal bound for general transient loads is then presented. This is specialized to the case of impulsive loads. For step loading, an overshoot measure is introduced which generalizes the corresponding notion for single degree-of-freedom systems. A bound is derived for the overshoot and for the settling time of the system. A simple example is given.
Large Elastic Deformation of Shear Deformable Shells of Revolution: Theory and Analysis
Authors: Taber L. A.
Published: July 2009

Large axisymmetric deformation of pressurized shells of revolution is studied. The governing equations include the effects of transverse normal strain and transverse shear deformation for shells composed of an incompressible, hyperelastic material. Asymptotic solutions to the equations are developed which are valid for moderately large strains. Application to Mooney-Rivlin clamped spherical caps reveals that, for large enough bending and stretching, the consequences of shear deformation include: (1) bending moments can decrease at the edge after the load passes a critical point; (2) even thick shells can behave as membranes; (3) transition points can occur in the shell which divide regions of shell-like behavior from regions of membrane-like behavior.
An Improved Shear-Deformation Theory for Moderately Thick Multilayered Anisotropic Shells and Plates
Authors: Di Sciuva M.
Published: July 2009

The general linear equations governing the motion of moderately thick multilayered anisotropic shells are derived by making use of the principle of virtual work in conjunction with an a priori assumed displacement field. The assumed displacement field is piecewise linear in the u and v components and fulfills the static and geometric continuity conditions between the contiguous layers; furthermore, it takes into account the distortion of the deformed normal. Shear and rotatory inertia terms have also been considered in the formulation. Particularization of the resulting equations to the flat multilayered anisotropic plates is straightforward; thus, only the final expressions are given. The proposed approach gives, as particular cases, the linear equations of motion of the classical shells theory based on the Kirchhoff-Love kinematic hypothesis and those of the shear deformation theory for which it is assumed that the deformed normal do not distort.
Elastic-Plastic Analysis of Pressurized Cylindrical Shells
Authors: Brooks G. N.
Published: July 2009

Plasticity in shells is often contained near the ends of a segment where the bending stresses are significant. Outside of this local neighborhood the behavior is elastic. Thus, an axisymmetric shell can be divided along its axis into a purely elastic region away from an end and the local region where plasticity is present. The moment-curvature relation in the elastic-plastic region is calculated using the Tresca yield condition. Use of the Tresca yield condition greatly simplifies this derivation because the principal directions are known. This moment-curvature relationship is “exact” in the sense that only the standard assumptions of thin shell theory are made. The solutions of the elastic and plastic regions are matched at their intersection for an efficient numerical solution. The technique is used here to study the semi-infinite clamped cylindrical shell with an internal pressure loading.
A Small Strain and Moderate Rotation Theory of Elastic Anisotropic Plates
Authors: Reddy J. N.
Published: July 2009

A general nonlinear theory for the dynamics of elastic anisotropic plates that accounts for transverse shear strains and moderate rotations is presented. The theory contains, as special cases, the von Ka´rma´n classical plate theory, the first-order shear deformation theory (i.e., the Reissner-Mindlin plate theory) and the third-order shear deformation plate theory. The theory is characterized, even for isotropic plates, by strong coupling between various equations of motion.
Cumulant-Neglect Closure Method for Nonlinear Systems Under Random Excitations
Authors: Sun Jian-Qiao , Hsu C. S.
Published: July 2009

The validity of the cumulant-neglect closure method is examined by applying it to a system for which an exact solution is available. A comparison of the results indicates that the Gaussian closure technique usually leads to a mean-square versus excitation strength curve which follows the same general shape as that of the exact solution but has substantial errors in some cases. The 4th order cumulant-neglect method is found to be inapplicable and to predict erroneous behavior for systems in certain parameter ranges, including a faulty prediction of a jump in response as the excitation varies through a certain critical value. On the other hand, for systems in other ranges the 4th order cumulant-neglect closure method predicts the mean square response quite well. These two parameter ranges are delineated in the paper. The 6th order cumulant-neglect closure method is also examined, leading to similar conclusions.
Shear Flows of Rapidly Flowing Granular Materials
Authors: Patton J. S. , Brennen C. E. , Sabersky R. H.
Published: July 2009

Shear flows of granular materials are studied in an open channel. The wall shear is calculated from an open channel momentum equation which includes the density variations in the flow. An experimental technique was developed that allowed the measurement of the average density of the flow at different longitudinal locations in the channel. Two sizes of glass beads are examined and results show the variations in the wall shear as a function of various dimensionless parameters.
Analytical Characterization of Shear Localization in Thermoviscoplastic Materials
Authors: Molinari A. , Clifton R. J.
Published: July 2009

Critical conditions for shear localization in thermoviscoplastic materials are obtained in closed form for idealized models of simple shearing deformations. The idealizations, which include the neglect of heat conduction, inertia, and elasticity, are viewed as quite acceptable for many applications in which shear bands occur. Explicit results obtained for the idealized, but fully nonlinear problem show the roles of strain-rate sensitivity, thermal softening, strain hardening, and initial imperfection on the localization behavior. Numerical solutions for two steels are shown to exhibit the principal features reported for torsional Kolsky bar experiments on these steels. Mathematically exact critical conditions obtained for the fully nonlinear problem are compared with critical conditions obtained by means of linear perturbation analysis. Use of relative changes instead of absolute changes in the linear perturbation analysis gives better agreement with predictions of the fully nonlinear analysis.
Crack Paralleling an Interface Between Dissimilar Materials
Authors: Hutchinson J. W. , Mear M. E. , Rice J. R.
Published: July 2009

A crack paralleling a bonded plane interface between two dissimilar isotropic elastic solids is considered. When the distance of the crack from the interface is small compared to the crack length itself and to other length scales characterizing the geometry, a simple universal relation exists between the Mode I and Mode II stress intensity factors and the complex stress intensity factor associated with the corresponding problem for the crack lying on the interface. In other words, if the influence of external loading and geometry on the interface crack is known, then this information can immediately be used to generate the stress intensity factors for the sub-interface crack. Conditions for cracks to propagate near and parallel to, but not along, an interface are derived.
On the Use of a Path-Independent Line Integral for Axisymmetric Cracks With Nonaxisymmetric Loading
Authors: Kuo An-Yu
Published: July 2009

A path-independent line integral JA is derived for axisymmetric cracks under nonaxisymmetric loading conditions. The nonaxisymmetric crack problem is solved by expressing its boundary conditions as the sum of a Fourier series. Contribution on JA from each of the Fourier terms in the nonaxisymmetric problem is shown to be decoupled from each other. Relationships between JA and stress intensity factors are also presented for linear elastic fracture problems. Application of JA to numerical fracture mechanics analysis is demonstrated by considering two example problems: an infinitely long circular bar with a penny-shaped internal crack at its center, and a circumferentially cracked pipe (both are under remote tension, bending, and torsion).
Transient Thermoelastic Fields in a Transversely Isotropic Infinite Solid With a Penny-Shaped Crack
Authors: Noda N. , Ashida F.
Published: July 2009

The present paper deals with a transient thermoelastic problem for an axisymmetric transversely isotropic infinite solid with a penny-shaped crack. A finite difference formulation based on the time variable alone is proposed to solve a three-dimensional transient heat conduction equation in an orthotropic medium. Using this formulation, the heat conduction equation reduces to a differential equation with respect to the spatial variables. This formulation is applied to attack the transient thermoelastic problem for an axisymmetric transversely isotropic infinite solid containing a penny-shaped crack subjected to heat absorption and heat exchange through the crack surface. Thus, the thermal stress field is analyzed by means of the transversely isotropic potential function method.
Bisynchronous Torsional Vibrations in Rotating Shafts
Authors: Bernasconi O.
Published: July 2009

In this study, the intrinsic behavior of rotating shafts with residual unbalance is considered. The longitudinal component of the angular momentum caused by synchronous precession (whirling) induces torsional vibrations with a frequency of twice the rotation frequency (bisynchronous). The nonlinear term which represents this coupling is characteristic of the asymmetrical aspect of rotating shaft kinematics. This result has been obtained analytically and confirmed experimentally.
Coupled Gas-Liquid-Structure Systems: Part 2—Applications
Authors: Joos F. M. , Huber P. W.
Published: July 2009

In the companion paper, Joos and Huber (1987) have developed an analysis that applies to certain types of systems in which a hydrodynamic transient creates pressure forces dependent on the flexibilities of the liquid boundary surfaces. To test the analysis we performed two pairs of experiments. Each pair involved identical experiments conducted in two geometrically identical cylindrical tanks. One tank was rigid, the other flexible. In the first set of experiments a gas bubble oscillated freely in a container partially filled with liquid. We compared experimentally measured natural frequencies with those predicted theoretically. In the second set of experiments a complex hydrodynamic transient was produced by injecting air into a tank partially filled with liquid. Using data from the rigid system experiments we predict the pressures and wall displacements in the flexible system and compare these predictions with measurements made in the flexible test tank. The inverse problem—predicting the pressures in the rigid tank from data obtained in the flexible tank—is also analyzed using the theoretical tools we have developed, and again predictions are compared with experiment.
Initiation, Propagation, and Kinking of an Antiplane Crack
Authors: Ma C. C. , Burgers P.
Published: July 2009

An infinite linear elastic body containing a semi-infinite crack is loaded by a planar antiplane stress pulse parallel to the crack. The stress wave strikes the crack at time t=0 and at some arbitrary later time tf, the crack begins to extend straight ahead with constant speed vo. After some later tb, the crack suddenly stops, then kinks and propagates with constant speed vc, making an angle δ with the original crack. A superposition scheme is used to construct the exact full-field solution of the propagating crack. The full-field solution for stresses for the constant speed propagating crack with a delay time tf is found to be the Mode III analog of Baker’s problem in Mode I plus the stress pulse, and the displacement on the crack faces behind the moving crack tip is just the solution of Baker’s problem when expressed in crack tip coordinates and is independent of the delay time tf. When the crack suddenly stops, the stress field, which is radiated out from the stopped crack tip, corresponds to the stationary crack stress field of a crack whose crack tip has been at the stopped crack position for all time. The dynamic stress intensity factor at the kinked crack tip is then obtained by using a perturbation method. The region of the stress intensity factor controlled field is investigated for both stationary and propagating cracks. It is found that this region depends on the loading conditions and which stress components are considered. The region also depends on the crack tip speed and will contract as the crack tip speed increases.
Optimal Design of a Rotating Disk for Kinetic Energy Storage
Authors: Berger M. , Porat I.
Published: July 2009

A thin homogeneous rotating disk of variable thickness is considered for the purpose of storing kinetic energy. The objective of the design is to find the optimal shape of the disk for which, in the presence of constraints on the geometry and strength of the disk, the Specific Kinetic Energy (SKE) is maximal. An upper bound for the SKE of a finite diameter disk is derived and a discrete formulation is presented by which an approximate optimal profile for arbitrary design parameters and rotational speeds can be obtained numerically. Applying a parametric study in which optimal designs for a sequence of rotational speeds are observed, a general configuration of the exact optimal profile is presented. The parametric study reveals the existence of three speed intervals, each characterized by a common type of optimal design. The optimal SKE corresponding to the ultimate rotational speed reaches a value very close to the theoretical upper bound, namely twice that of a thin ring. The model gives insight into the nature of optimal designs and serves as a simple and rapid computational tool for finding the optimal profile for arbitrary disk parameters and rotational speeds.
On the Dynamic Response of a Single-Degree-of-Freedom Structure Attached to the Interior of a Rotating Rigid Ring
Authors: Hernried A. G. , Gustafson G. B.
Published: July 2009

The dynamic response of a single-degree-of-freedom structure attached to the interior of a rigid ring that is rotating with constant angular velocity is investigated. It is assumed that the deformations of the structure from the undeformed configuration are small, and that the structure exhibits linear elastic material behavior. Both undamped and viscously damped structures are considered. Inclusion of all of the essential dynamic features of the problem (notably Coriolis effects) results in a nonlinear differential equation governing the response of the attached structure. Numerical and analytical studies are performed on the nonlinear governing equation to determine the response and stability of the structure.
Numerical Studies of Dynamic Compaction of Inert and Energetic Granular Materials
Authors: Baer M. R.
Published: July 2009

In this paper a numerical study of dynamic compaction of granular materials is presented. A multiphase mixture model treating two-phase nonequilibrium flow is applied to describe dynamic compaction experiments. Compaction is modeled using a description of grain distortion driven by pressure differences. Various energetic and inert granular materials including HMX, Fluid A (Nitrocellulose), Melamine, and Teflon are studied for various piston-impact conditions and compared to existing data. Numerical analysis of a ramp-wave piston-impact experiment is also examined. The multiphase mixture model predicts reasonably well the observed steady compaction wave characteristics. Dynamic compaction experiments with detailed resolution are needed to better address the transient behavior of compaction waves in granular materials.
A Nonlinear Analysis of an Equilibrium Craze: Part I—Problem Formulation and Solution
Authors: Ungsuwarungsri T. , Knauss W. G.
Published: July 2009

This study investigates the effect of nonlinear cohesive forces on crack growth with the special problem of craze mechanics in mind. The work is presented in two parts. In the first and present one, we develop a numerical method for determining the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement (P-V) behavior, including strain softening characteristics. The second part of this study deals with the numerical simulation of craze and crack growth (Ungsuwarungsri and Knauss, 1986).1 The problem formulation is based on the superposition of the relevant elasticity Green’s function and the solution for the resulting nonlinear problem is effected by using Picard’s successive approximation scheme. Both field equilibrium and the Barenblatt condition for vanishing stress and strain singularities are satisfied simultaneously, rendering the craze tip profile cusp-like. The formulation allows the stress distribution profile and the corresponding P-V relation to be computed from experimentally measured craze/crack displacement contours; it also allows the computation of the craze or crack/craze profile if the P-V relation, far-field load, and craze or crack size are specified. Numerical investigations indicate that only certain classes of the fibril P-V relations are consistent with measured craze profiles. In addition, it is found that for a given P-V relation, nontrivial solutions exist only for certain ranges of craze lengths.
Continuum Damage Mechanics: Part II—Damage Growth, Crack Initiation, and Crack Growth
Authors: Chaboche J. L.
Published: July 2009

Continuum Damage Mechanics (CDM) allows the description of the influence of damage on the stress-strain behavior of materials. In the present part, some practical damage growth equations are reviewed for creep, fatigue, creep-fatigue interaction, ductile damage, and brittle damage. The capabilities of CDM to improve both the crack initiation and crack propagation predictive tools are then discussed. Particular attention is given to the new developments of the “local approaches to fracture.”
Mechanical Modeling of Material Damage
Authors: Murakami S.
Published: July 2009

A systematic theory to describe the anisotropic damage states of materials and a consistent definition of effective stress tensors are developed within the framework of continuum damage mechanics. By introducing a fictitious undamaged configuration, mechanically equivalent to the real damaged configuration, the classical creep damage theory is extended to the general three-dimensional states of material damage; it is shown that the damage state can be described in terms of a symmetric second rank tensor. The physical implications, mathematical restrictions, and the limitations of this damage tensor, as well as the effects of finite deformation on the damage state, are discussed in some detail. The notion of the fictitious undamaged configuration is then applied also to the definition of effective stresses. Finally, the extension of the effective stresses incorporating the effects of crack closure is discussed. The resulting effective stress tensor is employed to analyze the stress-path dependence of the elastic behavior of a cracked elastic-brittle material.
The Linear Elastic Properties of Open-Cell Foams
Authors: Warren W. E. , Kraynik A. M.
Published: July 2009

A theoretical model for the linear elastic properties of three-dimensional open-cell foams is developed. We consider a tetrahedral unit cell, which contains four identical half-struts that join at equal angles, to represent the essential microstructural features of a foam. The effective continuum stress is obtained for an individual tetrahedral element arbitrarily oriented with respect to the principal directions of strain. The effective elastic constants for a foam are determined under the assumption that all possible orientations of the unit cell are equally probable in a representative volume element. The elastic constants are expressed as functions of compliances for bending and stretching of a strut, whose cross section is permitted to vary with distance from the joint, so the effect of strut morphology on effective elastic properties can be determined. Strut bending is the primary distortional mechanism for low-density foams with tetrahedral microstructure. For uniform strut cross section, the effective Young’s modulus is proportional to the volume fraction of solid material squared, and the coefficient of proportionality depends upon the specific strut shape. A similar analysis for cellular materials with cubic microstructure indicates that strut extension is the dominant distortional mechanism and that the effective Young’s modulus is linear in volume fraction. Our results emphasize the essential role of microstructure in determining the linear elastic properties of cellular materials and provide a theoretical framework for investigating nonlinear behavior.
The Wavefield Radiated Into an Elastic Half-Space by a Transducer of Large Aperture
Authors: Harris John G.
Published: July 2009

The wavefield radiated into an elastic half-space by an ultrasonic transducer, as well as the radiation admittance of the transducer coupled to the half-space, are studied. Two models for the transducer are used. In one an axisymmetric, Gaussian distribution of normal traction is imposed upon the surface, while in the other a uniform distribution of normal traction is imposed upon a circular region of the surface, leaving the remainder free of traction. To calculate the wavefield, each wave emitted by the transducer is expressed as a plane wave multiplied by an asymptotic power series in inverse powers of the aperture’s (scaled) radius. This reduces the wave equations satisfied by the compressional and shear potentials to their parabolic approximations. The approximations to the radiated waves are accurate at a depth where the wavefield remains well collimated.
The Optimal Version of Reissner’s Theory
Authors: Ladeve`ze P. , Pe´castaings F.
Published: July 2009

An improved version of Reissner’s theory, called Optimal version, is proposed in the case of homogeneous and isotropic plates with any edge boundary conditions. It differs from the classical theory by the value of the transverse shear deformability factor and by the boundary conditions. Three-dimensional displacement and stress distributions expressed in terms of the Optimal version are given for any point of the plate, whether within the plate itself or in the neighborhood of its edge. It is proved that these distributions are second-order approximations of the exact three-dimensional solution—relative error O(h2/L2). Consequently, Optimal version is a second-order theory; therefore it is better than Kirchhoff-Love’s theory.
Transient Dynamic Analysis of Rotors Using the Combined Methodologies of Finite Elements and Transfer Matrix
Authors: Subbiah R. , Kumar A. S. , Sankar T. S.
Published: July 2009

A new approach is proposed to predict the dynamic behavior of rotor-bearing systems in time domain using the combined methodologies of finite elements and transfer matrices. This approach makes use of the finite element method to model symmetric shafts and then transforms the system properties to transfer matrix mode. The formulation provides flexibility to include both linear and nonlinear system models, often encountered in rotor dynamic applications. Few example rotor cases had been studied and the results were compared with those obtained using finite element method. This establishes that considerable savings in computational effort can be achieved without losing any accuracy.
Experimental Investigation of Liquid Sloshing Under Parametric Random Excitation
Authors: Ibrahim R. A. , Heinrich R. T.
Published: July 2009

This paper presents an experimental investigation of the random parametric excitation of a dynamic system with nonlinear inertia. The experimental model is a rigid circular tank partially filled with an incompressible inviscid liquid. The random responses of the first antisymmetric and symmetric sloshing modes are considered for band-limited random excitations. These include the means, mean squares, and probability density functions of each sloshing mode. The response of the liquid-free surface is found to be a stationary process for test durations exceeding ten minutes. The time-history response records reveal four response characteristic regimes. Each regime takes place within a certain range of excitation spectral density level. An evidence of the jump phenomenon, which was predicted theoretically by using the non-Gaussian closure scheme, is also reported. Comparisons with analytical results, derived by three different approaches, are given for the first antisymmetric sloshing mode.
Elastic-Plastic Ring-Loaded Cylindrical Shells
Authors: Brooks Gregory N.
Published: July 2009

The elastic-plastic solution for an infinitely long cylindrical shell with an axisymmetric ring load is presented. Except for the material nonlinearity, the standard assumptions of small deflection shell theory were made. Because the principal directions are known for the axisymmetric problem, the Tresca yield condition wasused. This made it possible to obtain closed-form expressions for the elastic-plastic, moment-curvature relations, greatly simplfying the computational task. The actual stress distribution through the thickness was used, making these relations exact. Yielding was contained near the load. Thus, for the analysis the cylinder was divided along its axis into elastic-plastic and purely elastic regions. Solutions were obtained for each region which were then matched at their intersection to give the complete solution. All results are given in dimensionless form so that they may be applied to any shell.
Three-Dimensional Stress Field Near the Crack Front of a Thin Elastic Plate
Authors: Nakamura T. , Parks D. M.
Published: July 2009

Based on very detailed full-field finite element analysis of the near tip region of a thin isotropic elastic plate, the three-dimensional stress state in the vicinity of a through-crack front is characterized. The computed stress field reveals strong three-dimensional effects within a radial distance of about one-half thickness from the crack-tip. Further away from the tip, through-thickess variation of field quantities decreases and, at the radial distance of approximately 1.5 times the thickness, in-plane stresses merge with the dominant two-dimensional plane stress solutions. These “two-dimensional-three-dimensional” transition distances are essentially independent of the material Poisson’s ratio, yet the amplitude of variation is greatly affected by its value. The influence of Poisson’s ratio is clearly illustrated by local J along the crack front, which shows much higher variation through the thickness for nearly incompressible solids. At points very close to the crack front, relative magnitudes of out-of-plane strain components become very small, and asymptotic plane strain conditions prevail locally. On the mid-plane of the plate, the crack tip field converges to that given by the local plane strain stress intensity factor solution within a radial distance from the tip of less than 0.5 percent of thickness. In addition, it is found that the field near the intersection of crack front and free surface may be characterized by the corner singularity of a quarter infinite crack in a half space. The size of this domain is inferred from the gradient of local stress intensity factor with respect to distance from the free surface, and it appears that the corner singularity region extends up to a spherical radius of about 3 percent of plate thickness away from the intersection. Also the amplitude of the corner singularity field is described by a corner stress intensity factor, and its magnitude is determined for thin plates of various Poisson’s ratios.
The Differential Geometry of the General Helix as Applied to Mechanical Springs
Authors: Lin Yuyi , Pisano Albert P.
Published: July 2009

In order to improve the performance of helical springs, such as increasing the fatigue life and suppressing resonance, variable pitch angle and variable helix radius may be incorporated into the helical spring geometry. Employing the tool of differential geometry, new and complete formulae of curvature, torsion, and spring force are derived. It is shown that these formulae are more general and accurate than Kelvin’s curvature and torsion formulae, than commonly used force formulae (Wahl, 1963). Possible simplifications to the complete formulae and the corresponding errors introduced are both discussed and compared with experimental data.
The Elastica With End-Load Flip-Over
Authors: Wilson J. F. , Snyder J. M.
Published: July 2009

A high flexure manipulator arm is modeled as an elastic cantilever beam with a tip payload and an eccentric tip follower load that drives the arm. Shapes of the resulting elastic curves for finite deformations (the elastica) are calculated in terms of nondimensional system parameters. For critical combinations of these parameters, a small increment in the driving follower load causes an abrupt change in the shape of the elastica. The abrupt change in tip angle is typically of the order of π radians. These results are applicable to the design of high flexure robotic manipulators.
A Sufficient Condition for the Stability of Conservative Gyroscopic Systems
Authors: Inman D. J.
Published: July 2009

A sufficient condition for the stability of conservative gyroscopic systems with negative definite stiffness is presented. The conditions for stability are stated in terms of the definiteness of certain combinations of the coefficient matrices of the equations of motion. These conditions yield design constraints in terms of the physical parameters of the system. An example is given to illustrate the correctness of the result, as well as to provide a comparison with the results of other researchers.
Response of Linear Systems to Polynomials of Gaussian Processes
Authors: Grigoriu M. , Ariaratnam S. T.
Published: July 2009

Moments and mean crossing rates are determined for the response of linear systems subject to polynomial forms in Gauss-Markov processes. Differential equations describing the evolution in time of response moments are developed by the use of Itoˆ’s calculus. Estimators are obtained for mean crossing rates based on higher order moments and approximations of the distribution of the response. The method is applied to the analysis of a simple oscillator subject to the square of an Ornstein-Uhlenbeck process.