bluuebunny/crossref_metadata_2025 huggingface dataset:
Elastic Field of a Partially Debonded Elliptic Inhomogeneity in an Elastic Matrix (Plane-Strain)
Authors: Karihaloo B. L. , Viswanathan K.
Published: July 2009

The problem of the stress-field of an elliptic inhomogeneity that has debonded over an arc of its common boundary with a different elastic material is studied under plane-strain conditions. Eshelby’s method of equivalent inclusion is employed. The “equivalence relation” is solved by a method that is applicable to any general plane-strain situation. Further, the relative displacements of the debonded faces are derived from the discontinuous behavior of individual terms associated with the derivatives of Green’s function. Numerical results are presented for the stress-intensity factors at the tips of the debonded arc and the relative displacements across the debond.
A New Approach to Large Deflection Analyses of Spherical and Cylindrical Shells
Authors: Sinharay G. C. , Banerjee B.
Published: July 2009

In this paper large deflections of thin elastic shallow spherical shell and cylindrical shells are investigated by a new approach. Numerical results for moveable as well as immoveable edge conditions are presented graphically and compared with other known results.
Nonlinear Asymptotic Solution of the Reissner Plate Equations
Authors: Taber L. A.
Published: July 2009

Based on the Reissner plate equations for large displacements and rotations within the limits of small strain, asymptotic solutions are developed for circular plates under uniform pressure. With the boundary layer solution assumed in exponential form, the boundary conditions are applied directly at the plate edge without the need for matched asymptotic expansions. Results are presented for plates with clamped edges. When compared to the solution for the special case of von Ka´rma´n plate theory, stresses generally deviate by less than 10 percent for rotation angles up to about 30 deg.
Load-Supporting Fluid-Filled Cylindrical Membranes
Authors: Namias V.
Published: July 2009

When long cylindrical flexible membranes are filled with a fluid and used to support external weights, the shape they assume and the relevant geometrical and dynamical quantities are governed by a nonlinear differential equation subject to particular boundary conditions. First, a complete and exact analytical solution is obtained for an unloaded membrane. Very accurate approximate expressions are derived directly from the exact solution for the entire range of applied pressures and fluid densities. Next, the nonlinear differential equation is solved exactly under boundary conditions corresponding to the loading of the membrane. Simple asymptotic expressions are also obtained in the limit of large loads.
Beams in Receding/Advancing Contact: Dundurs Problems
Authors: Pawlak T. P. , Salamon N. J. , Mahmoud F. F.
Published: July 2009

The response of beams constrained unilaterally by a foundation and upper barriers while under monotonic loading is treated. Several scenarios featuring gaps and clearances are solved and shown to agree with Dundurs’ predictions. The solutions are generated by a numerical simulation featuring a direct incremental algorithm in conjunction with the finite element method.
Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method
Authors: Pierre C. , Ferri A. A. , Dowell E. H.
Published: July 2009

A multi-harmonic, frequency domain analysis of dry friction damped systems is presented which uses an incremental harmonic balance method. When compared with time domain solution methods, it is found that the incremental harmonic balance method can yield very accurate results with some advantages over the time domain methods. Both one and two degree-of-freedom systems are studied.
Optimal Forms of Shallow Cylindrical Panels With Respect to Vibration and Stability
Authors: Plaut R. H. , Johnson L. W.
Published: July 2009

Thin, shallow, elastic, cylindrical panels with rectangular planform are considered. We seek the midsurface form which maximizes the fundamental frequency of vibration, and the form which maximizes the buckling value of a uniform axial load. The material, surface area, and uniform thickness of the panel are specified. The curved edges are simply supported, while the straight edges are either simply supported or clamped. For the clamped case, the optimal panels have zero slope at the edges. In the examples, the maximum fundamental frequency is up to 12 percent higher than that of the corresponding circular cylindrical panel, while the buckling load is increased by as much as 95 percent. Most of the solutions are bimodal, while the rest are either unimodal or trimodal.
Plates in Unilateral Contact With Simple Supports: Pressure Loading
Authors: Salamon N. J. , Pawlak T. P. , Mahmoud F. F.
Published: July 2009

The response of a square plate, simply and unilaterally supported, to pressure loading is numerically treated. The support system consists of discrete elastic springs whose stiffnesses range from near-rigid to compliant character. It is found that, except for rather low support stiffnesses, the plate will lift off the foundation. After demonstrating good agreement with a recent analytical work, the deflections and shear fields are provided. The response mode changes dramatically as the supports approach rigidity.
Differential Kinematics of Spherical and Spatial Motions Using Kinematic Mapping
Authors: McCarthy J. M. , Ravani B.
Published: July 2009

This paper develops the basic framework for studying differential kinematics of spherical and spatial motions using a mapping of spatial kinematics. Relationships are derived relating the intrinsic properties of the image curves corresponding to a mapping of spherical and spatial kinematics and the instantaneous invariants of the corresponding spherical and spatial motions. In addition, in the case of spherical motions, the equations for the inflection cone and cubic cone of stationary geodesic curvature, important in spherical mechanism synthesis, are derived in terms of the curvature and torsion of corresponding image curves. Similar relationships defining the polhodes of spherical motions and their curvature at the reference instant are recast as well. A simple example involving a special spherical four-bar motion is also presented.
Flow-Induced Vibrations Caused by Roughness in Pipes Conveying Fluid
Authors: Shulemovich A.
Published: July 2009

This paper presents a theoretical investigation of self-excited vibrations of pipes conveying fluid due to roughness. A model of a laminar friction, considered as the excitation mechanism, is based on Prandtl’s universal velocity distribution for the turbulent boundary layer and on Nikuradse’s experiments. The analysis has shown that the friction characteristic has a negative slope in a certain range of fluid velocities. This range is a function of pipe roughness and is shifted to lower flow velocities due to roughness growth during pipe operation. It was found that the differential operator of a piping loop motion based on the nonlinear restoring characteristic coincides with the differential operator of Duffing’s equation for the hardening system. The energy method was used to obtain the approximate closed-form solution for the amplitude of steady self-excited vibrations. The unstable response with jump phenomena can appear due to interaction of small turbulent disturbances in conveying fluid with a given nonlinear system.
On the Variational Foundations of Assumed Strain Methods
Authors: Simo J. C. , Hughes T. J. R.
Published: July 2009

So-called assumed strain methods are based on the a-priori assumption of an interpolation for the discrete gradient operator, not necessarily derivable from the displacement interpolation. It is shown that this class of methods falls within the class of variational methods based on the Hu-Washizu principle. The essential point of this equivalence lies in the statement of the appropriate stress recovery procedure compatible with this variational structure. It is noted that most currently existing assumed strain methods fail to perform the stress recovery in a manner consistent with the variational structure discussed herein. Application is made to recently proposed methods such as mode decomposition techniques.
On the Understanding of Chaos in Duffings Equation Including a Comparison With Experiment
Authors: Dowell E. H. , Pezeshki C.
Published: July 2009

The dynamics of a buckled beam are studied for both the initial value problem and forced external excitation. The principal focus is on chaotic oscillations due to forced excitation. In particular, a discussion of their relationship to the initial value problem and a comparison of results from a theoretical model with those from a physical experiment are presented.
A New Boundary Element Method Formulation for Linear Elasticity
Authors: Ghosh N. , Rajiyah H. , Ghosh S. , Mukherjee S.
Published: July 2009

A new boundary element formulation for linear elasticity problems is presented in this paper. The standard formulation for planar problems uses two kernels — one of which is logarithmic singular and the other is 1/r singular, where r is the distance between a source and a field point. The new formulation avoids the use of the strongly singular kernel so that both kernels are now only logarithmic singular. The new formulation has several potential advantages over the standard one, the most significant of which is that it delivers stresses accurately at internal points which are extremely close to the boundary of a body. Numerical results for sample problems, from each of the formulations, are presented and compared here.
A General Theory of Optimal Elastic Design for Structures With Segmentation
Authors: Rozvany G. I. N. , Ong T. G. , Karihaloo B. L.
Published: July 2009

Optimal plastic design of segmented structures is reviewed and then general static-kinematic optimality criteria are introduced for segmented elastic structures. The proposed theory is illustrated with beam and plate examples and the results are checked by independent calculations.
Influence of the Bending Stiffness on the Shape of a Belt in Steady Motion
Authors: Fosdick R. , Villaggio P.
Published: July 2009

The equilibrium and steady forms of a pulley belt are determined. We consider large displacements of the central line of the belt for a special class of nonlinear stress-strain relations which includes the usual linear elastic case. If the centrifugal force on the belt is neglected, it is possible to obtain an explicit solution; if the centrifugal force is taken into account, but it is not very large, an approximate, but still explicit, solution can be derived.
Combined Loading of a Fully Plastic Ligament Ahead of an Edge-Crack
Authors: Shih C. F. , Hutchinson J. W.
Published: July 2009

Complete, accurate numerical results are given for the solution to the problem of a semi-infinite crack aligned perpendicularly to the free-edge of a semi-infinite half space in which the ligament is subject to arbitrary combinations of bending and tension or compression. The material is an incompressible, pure power-law deformation theory solid. Conditions of plane strain are assumed. Approximate solutions are proposed for predominantly bending loadings and also for predominantly stretching loadings.
The Stress Field Induced by a Twisting Sphere
Authors: Hills D. A. , Sackfield A.
Published: July 2009

Analytical solutions are presented for the stress field induced in an elastic half space by a sphere pressed normally into its surface, and twisted. It is found that the stresses decay rapidly with depth, and that the severest stress state occurs in the surface. Cases of both partial slip, i.e., where there is a central disk where no relative rotation occurs, surrounded by a slip annulus, and full slip where the disk degenerates to a point, are considered. The largest tensile stress, associated with brittle fracture and cracking, occurs on the edge of the contact circle, while the greatest tendency to yield, by von Mises criterion, occurs somewhere within the slip annulus, depending on the coefficient of friction. Twisting has a first order effect on the strength of contact as measured by each of these criteria.
Surface Waves Guided by the Exterior of a Rectangular Elastic Solid
Authors: Gautesen A. K.
Published: July 2009

We show that surface waves can be guided on the exterior of an isotropic elastic bar with a rectangular cross section. We assume that the dimensionless wavenumber is sufficiently large that elastodynamic ray theory is valid. Dispersion relations are obtained and representative curves for various cross sections are shown.
A Reduction Method for Nonhomogeneous Boundary Conditions
Authors: Sloss J. M. , Sadek I. , Bruch J. C.
Published: July 2009

A procedure is described for reducing dynamical equations in two-space variables defined in a rectangle with nonhomogeneous time dependent boundary data to equations with homogeneous boundary data. The procedure applies not only to a single equation but to systems of equations with systems of boundary conditions. One-space dimensional problems are treated separately and a condition for applicability is developed in this case. Examples are presented in which dynamical equations in one and two-space variables with nonhomogeneous time dependent boundary data are reduced to equations with homogeneous boundary data. Specific applications to problems in one-space variable include a simple beam, a laminated composite plate, and a Timoshenko beam. For two-space variable problems defined in a rectangle, the application of the procedure is made to an antisymmetric angle-ply circular cylindrical panel.
The Effect of Viscoelasticity on the Vibration of a Rotor
Authors: Hendricks S. L.
Published: July 2009

This paper analyzes the dynamics of a simple rotor mounted on a shaft constructed from a viscoelastic material. The equations are solved using a perturbation technique that is valid whenever viscoelastic time constants are much larger than elastic time constants. Regions of stable and unstable motion are discovered analytically. Several time histories for the rotor motion are presented.
Dynamic Stability of the Rotating Shaft Made of Boltzmann Viscoelastic Solid
Authors: Zhang W. , Ling F. H.
Published: July 2009

A general theory is developed in this paper for studying the dynamic stability of high-speed nonuniform rotating shafts made of a Boltzmann viscoelastic solid. The equation of motion of the shaft is deduced. The stability criteria are derived by using this equation. The unstable regions for a nonhomogeneous viscoelastic shaft are worked out numerically. Analytical formulas are also given in this paper for determining the planar deflection of the shaft and its inclined angle due to a planar static load. The conclusions for special cases given in the literature known to the authors are all covered by the results in this paper.
Analytic Solution of a Finite-Width Rough Surface Hydrodynamic Bearing
Authors: White J. W.
Published: July 2009

An analytic solution of the full incompressible unaveraged Reynolds equation is obtained by regular perturbation expansion for the case of a finite width bearing with transverse roughness. Results show that the unaveraged pressure is first influenced by the roughness statistics at the 0 (ε2) level and is negligibly affected by the details of the roughness distribution. Through second order effects, it is shown that the closure assumption utilized by Christensen and To̸ender in developing their theory for striated roughness effects on incompressible lubrication is correct. That is, for transverse roughness [h = h(x)], h3 and ∂P/∂y are statistically independent. Due to the linearity of the incompressible Reynolds equation, it is likely that a similar approach can be used for the study of fully three-dimensional roughness effects on lubrication in order to reveal the detailed relationship between clearance and pressure.
Stress Distribution in and Around Spheroidal Inclusions and Voids at Finite Concentration
Authors: Tandon G. P. , Weng G. J.
Published: July 2009

A simple, albeit approximate, close-form solution is developed to study the elastic stress and energy distribution in and around spheroidal inclusions and voids at finite concentration. This theory combines Eshelby’s solution of an ellipsoidal inclusion and Mori- Tanaka’s concept of average stress in the matrix. The inclusions are taken to be homogeneously dispersed and undirectionally aligned. The analytical results are obtained for the general three-dimensional loading, and further simplified for uniaxial tension applied parallel to the axis of inclusions. The ensuing stress and energy fields under tensile loading are illustrated for both hard inclusions and voids, ranging from prolate to oblate shapes, at several concentrations.
Simultaneous and Mixed Stress Relaxation in Tension and Creep in Torsion of 2618 Aluminum
Authors: Ding J. L. , Findley W. N.
Published: July 2009

The time dependent behavior of 2618-T61 aluminum under mixed loads and constraints (tension relaxation and torsion creep) is investigated. Experiments include tensile relaxation; simultaneous tension relaxation with step changes in torsion creep and reversed torsion; and alternate creep and relaxation. Results were compared with theoretical models developed previously using as input creep and creep recovery data under constant stress states only. Experimental observations were generally well described by strain hardening flow rules. Some failures in describing the material behavior by the state variable approaches (kinematic hardening) are also discussed.
Fully Plastic Plane Stress Solutions for Biaxially Loaded Center-Cracked Plates
Authors: Jansson S.
Published: July 2009

Numerical values for the J integral of fracture mechanics, crack opening and load-point displacements are given for stationary cracks in thin quadratic plates where the material is assumed to obey a power-law relation. The plates are loaded biaxially in their own plane under plane stress conditions and the solutions are given under the restriction of small strain and deformation theory. The remote boundaries of the plates are kept straight but free to slide in the tangential direction. This approximates the loading conditions for cruciform specimens with thinner center-sections as used in biaxial testing. It also represents a unit cell in a periodically cracked material. The cracks are loaded in Mode I. The present analysis clarifies the influence of load parallel to the crack and the sensitivity of remote boundary conditions on fracture mechanics parameters.
Flat-Crush Failure Mechanism of Corrugated Fiberboard
Authors: Liu Jen Y.
Published: July 2009

This paper analyzes the behavior of corrugated fiberboard under flatcrush loading using the elastica theory. The analysis is useful for evluating the quality of the board as well as for studying its damping characteristics. We considered the linerboard facings as rigid plates, compressing the fluted corrugating medium between them. The flute is composed of linear and circular elements. We used a procedure of reduced geometry to account for the flattening of the flute in conformation with the liner-boards during compression. Analytical results for A-flute fiberboard reveal that in the load-displacement curve reported in the literature the first hump occurs when the curvature of the flute tip disappears and the second hump occurs when the ultimate compressive and tensile stresses are reached at the intersection of the curved and flattened portions of the flute.
Vibrations of Free Hollow Circular Cylinders
Authors: Hutchinson J. R. , El-Azhari S. A.
Published: July 2009

A series solution of the general three-dimensional equations of linear elasticity is developed and used to find accurate natural frequencies for the vibration of hollow elastic circular cylinders with traction free surfaces. The series solution is found to converge to accurate frequencies with the use of very few terms. Comparison of the results with previous finite element results, shows good agreement. The highly accurate series solution is used as a basis of comparison for the Timoshenko beam theory. The comparison of results clearly shows the accuracy and range of applicability of the Timoshenko beam theory as well as suggesting a reasonable choice of shear coefficient.
Vibrations of Completely Free Shallow Shells of Curvilinear Planform
Authors: Narita Y. , Leissa A.
Published: July 2009

A method is presented for the free vibration analysis of shallow shells having free edges of arbitrary curvilinear shape. The method of Ritz which was developed for free rectangular plates is extended to the present problem. Components of displacement are expressed as algebraic polynomials. Shells of arbitrary curvature may be treated. Results are obtained for the previously unsolved vibration problems of cylindrical, spherical and hyperbolic paraboloidal shells having free edges of circular and elliptical planform. Convergence of the method is demonstrated. Comparisons with previous solutions are made in the case of zero curvature (i.e., a flat plate). Effects of increasing curvature and ellipticity upon vibration frequencies are examined.
Projection Moire Using Digital Video Processing: A Technique for Improving the Accuracy and Sensitivity
Authors: Gasvik K. J. , Fourney M. E.
Published: July 2009

This paper investigates the possibilities for improving the accuracy and the sensitivity of the projected fringe moire technique in combination with digital image processing. Several techniques for improving the accuracy of various moire methods are reviewed. The method of translation of the grating between exposures is investigated, both theoretically and experimentally. It is found that the sensitivity and accuracy can be increased by at least one order of magnitude using this method. Also the “hills and valleys” problem is easily solved by this method.
Stresses and Deformations in Composite Tubes Due to a Circumferential Temperature Gradient
Authors: Hyer M. W. , Cooper D. E.
Published: July 2009

This paper presents a linear elasticity solution for determining the response of composite tubes subjected to a circumferential temperature gradient of the form ΔTo+ ΔT1 cos(θ). The temperature does not vary with distance along the tube nor through the wall. Temperature-independent material properties are assumed and a displacement approach is used. The results are limited to tubes with the fibers in each layer oriented axially or circumferentially, so-called cross-ply tubes. It is shown that for both single layer and multiple layer tubes, one constant characterizes overall bending of the tube and one constant characterizes overall axial deformation. Numerical results show that fiber orientation strongly influences the stresses in a single layer tube. When the fibers are aligned axially, all components of stress in the tube are small. When the fibers are aligned circumferentially, the hoop stress becomes large. This is due to the large difference between the radial and circumferential coefficients of thermal expansion when the fibers are oriented circumferentially. Also, for a single layer tube constructed of a material with no thermal expansion in the axial direction, the overall change of length of the tube due to the temperature gradient will be zero only if the material is transversely isotropic. However, even if the material is transversely isotropic, the tube will still experience overall bending.
Asymptotic Fields of a Perfectly-Plastic, Plane-Stress Mode II Growing Crack
Authors: Ponte Castan˜eda P.
Published: July 2009

The asymptotic near-tip stress and velocity fields are presented for a plane-stress Mode II crack propagating quasi-statically in an elastic-perfectly plastic Mises solid. The solution is found to have fully continuous stress and velocity fields, and a configuration similar to that of the anti-plane strain problem: a singular centered fan plastic sector ahead of the crack, followed by an elastic unloading sector and a constant stress plastic sector extending to the crack flank. The impossibility of a plane-stress Mode I crack solution having these properties is also discussed.
On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part I
Authors: Simo J. C. , Vu-Quoc L.
Published: July 2009

The dynamic response of a flexible beam subject to large overall motions is traditionally formulated relative to a floating frame, sometimes referred to as the shadow beam. This type of formulation leads to equations of motion of the form g˜(y˙, y, t) = 0, that are implicit, nonlinear and highly coupled in the inertia terms. An alternative approach is proposed whereby all quantities are referred to the inertial frame. As a result, the inertia term enters linearly in the formulation simply as mass times acceleration. Crucial to this formulation is the use of finite strain rod theories capable of treating finite rotations. Numerical examples that involve finite vibrations coupled with large overall motions are presented in Part II of this paper.
Free Rotation of an Elastic Rod With an End Mass
Authors: Wang C. Y.
Published: July 2009

This paper models a rotating space satellite with a long flexible antenna. Large deformations of the elastic rod are caused by the centrifugal forces. Bifurcation analysis shows the effect of end mass on the critical rotation speeds above which sinuous equilibrium configurations occur. The nonlinear governing equations are then integrated numerically. We find a class of solutions with a looped configuration whose existence requires a certain minimum total energy and minimum angular momentum. Catastrophic changes are possible.
Kinetoelastostatics of Axisymmetric Nets
Authors: Kuznetsov E. N.
Published: July 2009

Intricately interrelated external loads, internal forces and equilibrium shapes of axisymmetric nets are studied. After developing the basic equations in a generic form, the most important particular types of nets are investigated—geodesic, Chebyshev, and orthogonal nets. Closed-form statical-geometric relations are obtained for each type of net and, as a by-product, for a wrinkling axisymmetric membrane. These allow a comprehensive investigation into the equilibrium configurations of the above systems and their evolution in the course of loading. Load combinations studied involved edge loads and normal surface loads such as net-solid contact pressure, pneumatic pressure or pressure induced by an axial gas flow.
Modal Parameter Analysis of Gyroelastic Continua
Authors: Hughes P. C. , D’Eleuterio G. M. T.
Published: July 2009

This paper builds on the theory of gyroelastic dynamics presented in a recent paper by the authors. An elastic continuum with a continuous distribution of stored angular momentum (called gyricity) is considered. We introduce the modal parameters (coefficients) thereof, including integrals of the mode shapes, and show they must satisfy a number of useful identities. In addition to the coefficients (pα and hα) associated with momentum and angular momentum which also arise in the dynamics of a purely elastic body, there is a third coefficient (gα) wholly attributable to the gyricity distribution. The modal parameter analysis presented here is an extension of that for purely elastic continua. The analysis concludes with a simple demonstration of the theoretical results using a spatially discretized model of a cantilevered rod.
On the Two-Dimensional Theory of Incompressible Flow Over Inlets
Authors: Sanz A.
Published: July 2009

The linearized solution for the two-dimensional flow over an inlet of general form has been derived, assuming incompressible potential flow. With this theory suction forces at sharp inlet lips can be estimated and ideal inlets can be designed.
Axisymmetric Motion of a Viscous Fluid Inside a Slender Surface of Revolution
Authors: Caulk D. A. , Naghdi P. M.
Published: July 2009

Starting with the exact three-dimensional equations for an incompressible linear viscous fluid, an approximate system of one-dimensional nonlinear equations is derived for axisymmetric motion inside a slender surface of revolution. These equations are obtained by introducing an approximate velocity field into weighted integrals of the momentum equation over the circular cross-section of the fluid. The general equations may be specialized to reflect specific conditions on the lateral surface of the fluid, such as the presence of surface tension, a confining elastic membrane, or a rigid tube. Two specific examples are considered which involve flow in a rigid tube: (1) unsteady starting flow in a nonuniform tube, and (2) axisymmetric swirl superimposed on Poiseuille flow. In each case comparison is made with earlier, more restricted results derived by perturbation methods.
Transient Stokes Flow in a Wedge
Authors: Xu Bohou , Hansen E. B.
Published: July 2009

The transient flow in the sector region bounded by two intersecting planes and a circular cylinder is determined in the Stokes approximation. The plane boundaries are assumed to be at rest while the cylinder is rotating with a constant velocity starting at t = 0. The problem is solved by means of three different methods, a finite element, a finite difference, and a boundary element method. The corresponding problem in which the constant velocity boundary condition on the cylinder is replaced by a condition of constant stress is also solved by means of the finite element method.
A Complex-Variable Method for Two-Dimensional Internal Stress Problems and Its Applications to Crack Growth in Nonelastic Materials: Part II—Applications
Authors: Wu K. C. , Hui C. Y.
Published: July 2009

In Part I of this work the internal stress due to a field of nonelastic strain in an infinite uncracked or cracked elastic body is derived for the case of antiplane shear, plane strain and plane stress. We will apply these results to solve a variety of self-stress problems in this paper. Exact solutions are obtained for a homogeneous distribution of nonelastic strain in a circular or polygonal region for an uncracked body. For a cracked body, closed form solutions are found for homogeneous nonelastic strain in two circular or polygonal regions symmetrically located with respect to the crack line. These results can also be applied to study internal stresses due to a homogeneous stress-free strain transformation or a uniform temperature distribution in the regions considered. Integral equations of stress are derived for stationary cracks and quasi-static growing cracks imbedded in nonelastic materials under small scale yielding condition. An integral equation for steady state dynamic Mode III crack growth is also given. It is shown that for steady-state crack growth problem, the presence of the trailing deformation wake introduces a residual stress that invalidates the dominance of the K field in the wake. Numerical implementation of the proposed method for inelasticity problems is discussed.
The Interface Crack in a Tension Field
Authors: Gautesen A. K. , Dundurs J.
Published: July 2009

The correct formulation of the interface crack must incorporate contact between the crack faces, because the tips of an interface crack are closed for all applied loads. A numerical solution of the resulting integral equation for an interface crack in a tension field was considered by Comninou several years ago. The present paper shows how to solve the integral equation exactly. The solution is found in the form of a slowly convergent series involving elliptic functions and it is demonstrated how to convert the results into a rapidly convergent series. Specifically, we give simple formulae valid over the entire range of the physical parameters for (1) the length of the contact zones, (2) the Mode II stress intensity factor, and (3) the finite but very large normal stress at the tip of the interface crack.
On the Numerical Boundary Integral Equation Method for Three-Dimensional Dynamic Shear Crack Problems
Authors: Das S. , Kostrov B. V.
Published: July 2009

The numerical boundary integral equation method for the solution of dynamic shear crack problems is discussed in detail, including the questions of the numerical approximation, stability, and efficiency. In particular, the necessary conditions for stability are developed. In addition to a discussion of the original algorithm proposed by Das (1980), a new version is proposed which is more efficient for some important particular cases, due to the fact that the domain of integration for the necessary convolutions is limited only to the slipping part of the crack plane instead of the entire disturbed area of the crack plane.
A Sixth-Order Plate Theory—Derivation and Error Estimates
Authors: Rychter Z.
Published: July 2009

Two consistent variants of a sixth-order theory for elastic plate bending are developed together with corresponding three-dimensional statically and kinematically admissible solutions. The relative mean square error of these solutions as compared with exact elasticity solutions is found to be proportional to the thickness squared in analogy with previous estimates for Reissner’s theory, but the contribution to the error governed by transverse shear deformability is reduced and shown to be of the order of the thickness cubed, this contribution being decisive in composite plates.
Imperfection-Sensitivity of Long Antisymmetric Cross-Ply Cylindrical Panels Under Shear Loads
Authors: Hui David , Du I. H. Y.
Published: July 2009

This paper examines the theoretical postbuckling behavior and imperfection-sensitivity of antisymmetrically laminated open, long, cylindrical panels under shear loads. The longitudinal edges may be simply-supported or clamped. It is found that the cylindrical panels may be sensitive to the presence of geometric imperfections depending primarily on the reduced-flatness parameter and Young’s modulus ratio. The shear buckling load and the postbuckling coefficients are plotted as a function of the shell geometry, number of layers, and material parameters. The paper is the first in the literature to examine the postbuckling behavior of open laminated cylindrical panels under shear loads.
Energy Release Rates and Related Balance Laws in Linear Elastic Defect Mechanics
Authors: Eischen J. W. , Herrmann G.
Published: July 2009

A simple and direct derivation of certain balance (or conservation) laws for linear dynamic elasticity is presented including nonhomogeneities, thermal effects, anisotropy, and body forces. Additionally, the connection between the balance laws and energy release rates for defect motions is established.
Exact Stationary-Response Solution for Second Order Nonlinear Systems Under Parametric and External White-Noise Excitations
Authors: Yong Y. , Lin Y. K.
Published: July 2009

Except for rare sporadic cases, exact stationary solutions for second order nonlinear systems under Gaussian white-noise excitations are known only for certain types of systems and only when the excitations are purely external (additive). Yet, in many engineering problems, random excitations may also be parametric (multiplicative). It is shown in this paper that the method of detailed balance developed by the physicists can be applied to obtain systematically the stationary solutions for a large class of nonlinear systems under either external random excitations or parametric random excitations, or both. Examples are given for those cases where solutions have been given previously in the literature as well as other cases where solutions are new. An unexpected result is revealed in one of the new solutions, namely, under suitable combination of the parametric and external excitations of Gaussian white noises, the response of a nonlinear system can be Gaussian.
Constituent Diffusion in a Deformable Thermoelastic Solid
Authors: Girrens S. P. , Smith F. W.
Published: July 2009

Solid mixtures containing initially uniform dilute concentrations of impurity elements may, upon the application of mechanical and thermal loading, develop regions of high impurity concentration that could result in local degradation of material properties. To address these degradation processes, a fully coupled thermomechanical-diffusion theory has been developed to describe the mass transport of mobile constituents driven by gradients in concentration, strain dilatation and temperature in a solid deformable parent material. A finite element code has been assembled to solve plane transient thermomechanical-diffusion problems. The theory presented and the resulting code have been successfully used to model internal hydrogen redistribution in β-phase Ti alloys induced by elastic strain gradients during bending.
Discharge From a Vessel Through an Axisymmetric Control Valve
Authors: Chow W. L. , Ting Alice A. L. , Tsai P. H.
Published: July 2009

The problem of an incompressible flow discharge through an axisymmetric control valve has been examined through the method of hodograph transformation. The boundary value problem in the hodograph plane has an unusual feature in that part of the boundary is overlapped. Certain manipulations have been applied to produce the realistic free streamline configuration. The rate of discharge is obtained for various locations of the valve. This investigation provides the evidence that the method of hodograph transformation coupled with numerical computation is indeed effective in dealing with problems of this kind.
A Doubly Asymptotic, Nonreflecting Boundary for Ground-Shock Analysis
Authors: Mathews I. C. , Geers T. L.
Published: July 2009

This paper desribes the formulation and implementation of a nonreflecting boundary for use with existing finite-element codes to perform nonlinear ground-shock analyses of buried structures. The boundary is based on a first-order doubly asymptotic approximation (DAA1) for disturbances propagating outward from a selected portion of the soil medium surrounding the structure of interest. The resulting set of first-order ordinary differential equations is then combined with the second-order equations of motion for the finite-element model so as to facilitate solution by a staggered solution procedure. This procedure is shown to be computationally stable as long as the time increment is smaller than a limiting value based on the finite-element mass matrix and the DAA-boundary stiffness matrix. Computational results produced by the boundary are compared with exact results for linear canonical problems pertaining to infinite-cylindrical and spherical shells.
Transient Solutions for One-Dimensional Problems With Strain Softening
Authors: Belytschko T. , Wang Xiao-Jun , Bazant Z. P. , Hyun Y.
Published: July 2009

Closed-form solutions are presented for the transient response of rods in which strain softening occurs and the stress-strain laws exhibit nonvanishing stresses after the strain-softening regime. It is found that the appearance of any strain softening results in an infinite strain rate if the material is inviscid. For a stress-strain law with a monotonically decreasing stress the strains are infinite also. If the stress increases after the strain-softening portion, the strains remain finite and the strain-softening point moves through the rod.
Reexamination of Jumps Across Quasi-Statically Propagating Surfaces Under Generalized Plane Stress in Anisotropically Hardening Elastic-Plastic Solids
Authors: Narasimhan R. , Rosakis A. J.
Published: July 2009

Strong discontinuities across quasi-statically propagating surfaces in anisotropic elastic-plastic solids under generalized plane stress are reexamined allowing for some generality in constitutive response and taking into account the phenomenon of necking. Jumps in stresses are ruled out on the basis of material stability postulates and a previous approach (by Pan, 1982) is discussed. It is noted that for elastic-perfectly plastic solids, sliding velocity discontinuities occur under restrictive and exceptional conditions (when both the surface and its normal are stress characteristics) for generalized plane stress as compared to plane strain. Necks may form along (stress) characteristic directions with the relative velocity vector orthogonal to the other family of characteristics.
Incompressibility in Dynamic Relaxation
Authors: Silling S. A.
Published: July 2009

A method is described for enforcing the incompressibility constraint in large-deformation solid mechanics computations using dynamic relaxation. The method is well-suited to explicit time-integration schemes because it does not require the solution of a system of linear equations. It is based on an analogy with thermoelasticity involving manipulation of the natural state of a solid.
Plane Strain Dislocations in Linear Elastic Diffusive Solids
Authors: Rudnicki J. W.
Published: July 2009

Solutions are obtained for the stress and pore pressure due to sudden introduction of plane strain dislocations in a linear elastic, fluid-infiltrated, Biot, solid. Previous solutions have required that the pore fluid pressure and its gradient be continuous. Consequently, the antisymmetry (symmetry) of the pore pressure p about y = 0 requires that this plane be permeable (p = 0) for a shear dislocation and impermeable (∂p/∂y = 0) for an opening dislocation. Here Fourier and Laplace transforms are used to obtain the stress and pore pressure due to sudden introduction of a shear dislocation on an impermeable plane and an opening dislocation on a permeable plane. The pore pressure is discontinuous on y = 0 for the shear dislocation and its gradient is discontinuous on y = 0 for the opening dislocation. The time-dependence of the traction induced on y = 0 is identical for shear and opening dislocations on an impermeable plane, but differs significantly from that for dislocations on a permeable plane. More specifically, the traction on an impermeable plane does not decay monotonically from its short-time (undrained) value as it does on a permeable plane; instead, it first increases to a peak in excess of the short-time value by about 20 percent of the difference between the short and long time values. Differences also occur in the distribution of stresses and pore pressure depending on whether the dislocations are emplaced on permeable or impermeable planes.
The Stability of a Dislocation Threading a Strained Layer on a Substrate
Authors: Freund L. B.
Published: July 2009

The continuum theory of elastic dislocations is applied to estimate the critical thickness of a strained layer bonded to a substrate for a given mismatch strain. The formation of strained epitaxial layers is of interest due to their special electronic or optical properties, and critical thickness is understood to be the smallest thickness at which interface dislocations con form “spontaneously.” The criterion invoked here is based on the work done by the layer stress in driving a threading dislocation to lay down a misfit dislocation along the layer-substrate interface, and it is applied in a way that leads to a result that is independent of the deflected shape of the threading dislocation. The general form of the dependence of critical layer thickness on mismatch strain is similar to that based on equilibrium dislocation analysis.
Nonlinear Forced Response of Infinitely Long Circular Cylindrical Shells
Authors: Nayfeh A. H. , Raouf R. A.
Published: July 2009

A combination of the Galerkin procedure and the method of multiple scales is used to analyze the nonlinear forced response of infinitely long circular cylindrical shells (or circular rings) in the presence of internal (autoparametric) resonances. If ωf and af denote the frequency and amplitude of a flexural mode and ωb and ab denote the frequency and amplitude of the breathing mode, the steady-state response is found to exhibit a saturation phenomenon when ωb = 2ωf if the shell is excited by a harmonic load having a frequency Ω near ωb. As the amplitude f of the excitation increases from zero, ab increases linearly with f until a threshold value fc of f is reached. Beyond fc, ab remains constant and the extra energy spills over into the flexural resonant mode whose amplitude grows nonlinearly. Results of numerical investigations, guided by the perturbation analysis, show that the long-time response exhibits a Hopf bifurcation, yielding amplitude and phase-modulated motions. The amplitudes and phases experience a cascade of period-doubling bifurcations ending up with chaos. The bifurcation values are finely tuned.
Thick Composite Plates Subjected to Lateral Loading
Authors: Cairns D. S. , Lagace P. A.
Published: July 2009

An analytical solution for an orthotropic plate subjected to general lateral loading is presented. The solution uses a stress function approach to obtain the localized stresses and strains due to the loading by an axisymmetric rigid sphere. Plots of load versus local indentation are compared with experimental test data previously reported in the literature. The analysis agrees well with the experimental data and could be used in conjunction with failure criteria to predict damage initiation in such a localized region.
Integrals of Linearized Differential Equations of Motion of Mechanical Systems; Part I: Linearized Differential Equations
Authors: Kane T. R. , Djerassi S.
Published: July 2009

Part I of this paper deals with relationships between integrals of a set of nonlinear differential equations and integrals of equations obtained from such a set by a process of linearization. The terms “total linearization,” “reduction,” and “partial linearization” are introduced, a theorem is stated and proved in connection with each of these, and the use of each theorem is illustrated by means of an example. In Part II, the theorems are applied to differential equations of motion of mechanical systems.
On the Nonstationary Response of Stochastically Excited Secondary Systems
Authors: Iwan W. D. , Smith K. S.
Published: July 2009

The envelope response of a secondary system is derived for the case where the primary system is subjected to nonstationary stochastic excitation. An approximate closed form expression for the mean square envelope response is obtained for the case of transient response to stationary excitation when the primary and secondary systems are noninteracting. When the combined system is classically damped, the effect of the interaction is described by the introduction of an equivalent noninteracting system. The analytical results are compared with results of numerical simulations.
Entrainment of Self-Sustained Flow Oscillations: Phaselocking or Asynchronous Quenching?
Authors: Staubli T.
Published: July 2009

Asynchronous quenching and phaselocking are two different mechanisms leading to the onset of synchronization of flow instabilities with externally excited oscillations. Experimental evidence for asynchronous quenching as well as for phaselocking is given from response measurements of representative pressures, velocities, or of forces for the following types of flow - forcing interactions: an oscillating circular cylinder in crossflow; interaction of an unstable, planar jet with an oscillating leading edge; a forced mixing layer between parallel streams; and a thermally forced cavity shear-layer.
Elastic Wave Scattering by Surface-Breaking Planar and Nonplanar Cracks
Authors: Shah A. H. , Chin Y. F. , Datta S. K.
Published: July 2009

Scattering of elastic waves by surface-breaking planar and nonplanar (branched) cracks has been studied in this paper. Attention has been focused on the near-field surface displacements and the crack-tip(s) stress-intensity factors. For planar normal cracks the stress-intensity factors are shown to agree with earlier results. Numerical results showing normalized vertical surface displacements are presented for incident body and surface waves. It is shown that the results for planar and branched cracks can be significantly different in some instances.