bluuebunny/crossref_metadata_2025 huggingface dataset:
Linear Stability of Jet Flows
Authors: Bajaj A. K. , Garg V. K.
Published: November 2010

A theoretical investigation into the linear, spatial stability of plane laminar jets is presented. The three cases studied are: 1. Inviscid stability of Sato’s velocity profile. 2. Viscous stability of the Bickley’s jet using parallel-flow stability theory. 3. Viscous stability of the Bickley’s jet using a theory modified to account for the inflow terms. The integration of stability equations is started from the outer region of the jet toward the jet axis using the solution of the asymptotic forms of the governing equations. An eigenvalue search technique is employed to find the number of eigenvalues and their approximate location in a closed region of the complex eigenvalue plane. The accurate eigenvalues are obtained using secant method. The inviscid spatial stability theory is found to give results that are in better agreement with Sato’s experimental results than those obtained by him after transformation of the temporal theory results. For the viscous case the critical Reynolds number found by using the theory accounting for inflow is in better agreement with the experimental value than that given by the parallel-flow theory, implying thereby that the parallel-flow approximation for a jet is erroneous for the stability analysis.
Quasi-Bifurcation in Dynamics of Elastic-Plastic Continua
Authors: Lee L. H. N.
Published: November 2010

In this study, a stability concept in terms of the properties of an effective force field is introduced. A criterion for determining certain infinitesimal disturbances which may amplify with time in an elastic-plastic body subject to prescribed initial, kinematic, and time-dependent traction boundary conditions is introduced and developed. The body may be made of a general work-hardening continuum having a piecewise continuous motion and finite deformation. The transition from the dynamic criterion to Hill’s quasi-static bifurcation criterion is indicated.
Stress Analysis and Stress-Intensity Factors for Finite Geometry Solids Containing Rectangular Surface Cracks
Authors: Gyekenyesi J. P. , Mendelson A.
Published: November 2010

The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement field in a finite geometry bar containing a variable depth rectangular surface crack under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Using the obtained displacement field, normal stresses, and the stress-intensity factor variation along the crack periphery are calculated for different crack depth to bar thickness ratios. Crack opening displacements and stress-intensity factors are also obtained for a through-thickness, center-cracked bar with variable thickness. The reported results show a considerable potential for using this method in calculating stress-intensity factors for commonly encountered surface crack geometries in finite solids.
Gas Flow in a Permeable Earth Formation Containing a Crack
Authors: Pitts J. H. , Brandt H.
Published: November 2010

Gas flow in a permeable earth formation following an experimental underground nuclear explosion is analyzed to predict conditions that might lead to venting of radioactive gases to the atmosphere. A three-dimensional analysis considers flow of the explosion gas through the permeable earth formation as well as flow of the gas through a propagating crack. Effects of variations in permeability, k, from 10−6 to 1.0 (μm)2 and ratio of the maximum resistive overburden pressure to the initial gas-driving pressure of explosions, Prmax/P1 from 0.1–0.9 are delineated. Initial dimensions of the crack range from 30–110 m in the vertical direction, 30–170 m in the horizontal direction and 10–50 mm in thickness. Propagation of a crack to the earth’s surface following a typical experimental underground nuclear explosion buried at a depth of 500 m would require unusual conditions such as when k < 10−4 (μm)2 and Prmax/P1 < 0.75.
The Elastic Energy of Interacting Edge Dislocations in an Infinite Array
Authors: Masumura R. A. , Glicksman M. E.
Published: November 2010

The interaction among edge dislocations in an infinite array is introduced via a traction-free core boundary condition. The problem is reduced to a two-dimensional elastostatic one in which the formulation results in an integral equation. The solution of the integral equation yields the information required to calculate the elastic energy. The present method is compared to approximate theories where interaction between dislocation cores is neglected.
The Plane Symmetric Contact Problem for Dissimilar Elastic Semi-Infinite Strips of Different Widths
Authors: Adams G. G. , Bogy D. B.
Published: November 2010

The solution is obtained for both smooth and bonded contact between strips of different elastic materials and widths. First, the problems are reduced to singular integral equations which are unusual because of the mixed boundary condition on the end of the wider strip. With minor extensions of the usual methods the order of the stress singularity at the corners is extracted from the integral equations and numerical solutions are then obtained for various material combinations and width ratios. The results are compared to previous solutions in which the width ratio is either one or infinity.
On the Changing Order of Singularity at a Crack Tip
Authors: Nuismer R. J. , Sendeckyj G. P.
Published: November 2010

The nature of the transition in the crack tip stress singularity from an inverse square root to an inverse fractional power as a crack tip reaches a phase boundary or a geometrical discontinuity for interface cracks is examined. This is done by analyzing the simple closed-form solution to the problem of a rigid line inclusion with one side partially debonded for the case of antiplane deformation. For this example, the crack tip stress singularity changes from an inverse square root to an inverse three-quarters power as the crack tips approach the inclusion tips (i.e., when one face of the rigid line inclusion is completely debonded). A detailed analysis, based on series expansions of the closed-form solution, is used to show how the singularity transition occurs. Moreover, the expansions indicate difficulties that may be encountered when solving such problems by approximate methods.
Dynamic Fracture of 6061-T6 Aluminum Cylinders
Authors: Wesenberg D. L. , Sagartz M. J.
Published: November 2010

Radial expansion and subsequent fracture into segments of thin-walled cylindrical shells at large initial strain rates are studied analytically and experimentally. The theory of probability along with a description of relief wave propagation away from each fracture is used to formulate a theory which predicts the number of fractures and the distribution of fragment lengths. Eleven 6061-T6 Aluminum cylinders were expanded at strain rates of ∼104 s−1 by magnetic pressure pulses from a capacitor bank discharge, and these results are compared with predictions. Good agreement is shown between experimental results and predictions. In addition, the physical and material parameters to which the problem is sensitive are discussed.
Effect of Axial Force on Dynamic Fracture of a Beam or Plate in Pure Bending
Authors: Adeli H. , Herrmann G. , Freund L. B.
Published: November 2010

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam. As an extension of previous work, a dynamically induced axial force which is generated during the fracture process is included in the analysis. Thus an improved formulation is presented by means of which the crack length, crack tip velocity, bending moment, and axial force at the fracturing section are determined as functions of time after crack initiation. It is found that the effect of the axial force becomes significant after the crack travels about one third of the beam thickness, and better agreement with experimental data is achieved. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.
A Self-Consistent Approach to Multiple Scattering by Elastic Ellipsoidal Inclusions
Authors: Datta S. K.
Published: November 2010

This paper deals with the scattering of plane longitudinal and shear waves by a distribution of elastic ellipsoidal inclusions. The scattered field is determined correct to O(ε3) where ε is a nondimensional wave number, assumed small. Assuming then that the distribution of scatterer centers is random homogeneous function of position and using a self-consistent (“quasi-crystalline”) approximation effective wave speeds are determined for the case of preferred orientation. Various limiting cases, viz., spherical inclusions and voids, elliptic and penny-shaped cracks, and fluid-filled cavities, are derived.
Buckling of Cylindrical Shells Subjected to Nonuniform Axial Loads
Authors: Libai A. , Durban D.
Published: November 2010

The linear buckling problem of a cylindrical shell subjected to circumferentially varying axial edge loads or thermal loads is considered. The case of an oscillatory loading having a cosinusidal form with a single arbitrary harmonic index is treated first. Closed-form expressions for the critical eigenvalues are obtained, spanning the entire range of the harmonic index. Buckling modes are also presented. An interaction law among harmonic loadings based on existing numerical evidence is then postulated. This leads to the capability of calculating the buckling load for any given distribution. The method is compared, and good agreement is obtained, with published results on the heating of an axial strip. It is then used to calculate the buckling of a cylindrical shell subjected to a concentrated axial force.
Dynamic Plastic Instabilities in Stretching Plates and Shells
Authors: Taylor J. W. , Harlow F. H. , Amsden A. A.
Published: November 2010

An approximate formulation of the problem of dynamic plastic instability in a thin sheet of material subjected primarily to enertial forces is presented. It is shown that the classic static plastic instability condition reappears with a new and more detailed interpretation. When perturbations are introduced at strain values less than the critical strain, they tend to smooth out in a calculable and rapid rate. When similar perturbations are introduced or remain after the critical strain level is passed, they develop in a calculable way at a progressively accelerated rate. The details depend strongly on whether or not perturbations are themselves work hardened. The size of a “critical flaw” is related to the strain rate, with the consequence that the definition of “quasi-static” conditions in the context of the present theory becomes self-evident. The net distortion of the perturbation depends strongly on the rate of expansion of the plate and the size of the perturbation in ways that are shown by analytical and numerical solutions of the equations.
Numerical Computation of the Stability of Plane Poiseuille Flow
Authors: Wolf L. , Lavan Z. , Nielsen H. J.
Published: November 2010

The hydrodynamic stability of plane Poiseuille flow to infinitesimal and finite amplitude disturbances is investigated using a direct numerical technique. The governing equations are cast in terms of vorticity and stream function using second-order central differences in space. The vorticity equation is used to advance the vorticity values in time and successive over-relaxation is used to solve the stream function equation. Two programs were prepared, one for the linearized and the other for the complete disturbance equations. Results obtained by solving the linearized equations agree well with existing solutions for small disturbances. The nonlinear calculations reveal that the behavior of a disturbance depends on the amplitude and on the wave number. The behavior at wave numbers below and above the linear critical wave number is drastically different.
Deterministic Stability Analysis of a Wind Loaded Structure
Authors: Holmes P. J. , Lin Y. K.
Published: November 2010

We discuss the qualitative behavior of a pair of nonlinear differential equations arising in the study of a wind loading problem when turbulence terms are ignored. We obtain quantitative estimates of stability boundaries and are able to identify the most dangerous excitation conditions. This deterministic study provides the basis for further work on the full stochastic differential equations resulting when turbulence terms are included.
Response Envelope Statistics for Nonlinear Oscillators With Random Excitation
Authors: Iwan W. D. , Spanos P.-T.
Published: November 2010

An approximate analytical method is presented for determining both the stationary and nonstationary amplitude or envelope response statistics of a lightly damped and weakly nonlinear oscillator subject to Gaussian white noise. The method is based on the solution of an equivalent linear system whose parameters are functions of the response itself. The solution derived by the approximate method is compared with that obtained by computer simulation for a Duffing oscillator.
Dynamics of Developing Laminar Non-Newtonian Falling Liquid Films With Free Surface
Authors: Narayanamurthy V. , Sarma P. K.
Published: November 2010

The dynamics of accelerating, laminar non-Newtonian falling liquid film is analytically solved taking into account the interfacial shear offered by the quiescent gas adjacent to the liquid film under adiabatic conditions of both the phases. The results indicate that the thickness of the liquid film for the assumed power law model of the shear deformation versus the shear stress is influenced by the index n, the modified form of (Fr/Re). The mathematical formulation of the present analysis enables to treat the problem as a general type from which the special case for Newtonian liquid films can be derived by equating the index in the power law to unity.
Peristaltic Pumping of a Newtonian Fluid With Particles Suspended in It at Low Reynolds Number Under Long Wavelength Approximations
Authors: Kaimal M. R.
Published: November 2010

The peristaltic motion of a fluid in which are distributed uniform rigid particles through an axisymmetric tube of arbitrary wave shape is considered for low Reynolds numbers. Solutions for the stream functions and vorticity functions are obtained in the form of asymptotic expansions regarding the ratio (ε) of the tube radius to the wavelength of the peristaltic wave to be small. We have assumed the velocity equilibration length of particulate phase to be equal to the wavelength of the peristalsis. Expressions for mean pressure gradient and shear stress are obtained. Also we have discussed phenomena like “reflux” and “trapping”. The study is particularly helpful in engineering applications such as pumping of solid-fluid mixtures by peristalsis.
Indentation of a Membrane on an Elastic Half Space
Authors: Hajji M. A.
Published: November 2010

An analysis is presented of the deformation of a homogeneous isotropic elastic half space whose surface behavior departs from the classical due to the presence of a pretensed membrane or a material surface which exhibits surface tension. Two related problems are considered: the axisymmetric displacements caused by a uniform circular load and by a concentrated normal force. In contrast to the classical solution, the uniform load problem with surface tension is found to have a finite slope and zero shear stress over the entire boundary. The analysis is used to interpret data from indentation tests on inflated dog lobes and the mechanical properties of both the lung parenchyma and the surface membrane are obtained. The observed shape of the indented surface agrees well with the prediction of the analysis.
Harmonic Wave Propagation in a Periodically Layered, Infinite Elastic Body: Antiplane Strain
Authors: Delph T. J. , Herrmann G. , Kaul R. K.
Published: November 2010

The propagation of horizontally polarized shear waves through a periodically layered elastic medium is analyzed. The dispersion equation is obtained by using Floquet’s theory and is shown to define a surface in frequency-wave number space. The important features of the surface are the passing and stopping bands, where harmonic waves are propagated or attenuated, respectively. Other features of the spectrum, such as uncoupling at the ends of the Brillouin zones, conical points, and asymptotic values at short wavelengths, are also examined.
Implicit-Explicit Finite Elements in Transient Analysis: Implementation and Numerical Examples
Authors: Hughes T. J. R. , Liu W. K.
Published: November 2010

Computer implementation aspects and numerical evaluation of a new family of implicit-explicit finite element, transient algorithms are presented. It is shown that the new methods are easily coded, and may be introduced into many existing implicit, finite-element codes with only slight modification. Numerical tests confirm the theoretical stability and accuracy characteristics of the methods presented in a companion paper.
On the Exact Solution for the Two-Sphere Problem in Axisymmetrical Potential Flow
Authors: Bentwich M. , Miloh T.
Published: November 2010

The authors obtain an exact solution for the stream function representing the title flow problem when the gaps, the radii, and the velocities of the two spheres are arbitrary. For spheres spaced apart it is in the form of infinite series. For touching spheres that solution reduces by a suitable limit process to an integral form. A general expression is then obtained for the kinetic energy of the system, and using Lagranges equation, the forces experienced by the spheres are calculated. It is thus found that the interactive force between them does not vanish when one is stationary and the other is accelerating at an infinite distance away. Another interesting result concerns the logarithmically singular dependence of the interactive force on the gap when the latter is very small.
Computational Aspects of Time Integration Procedures in Structural Dynamics—Part 2: Error Propagation
Authors: Park K. C. , Felippa C. A.
Published: November 2010

The propagation of computational error in the direct time integration of the equations of structural dynamics is investigated. Asymptotic error propagation equations corresponding to the computational paths presented in Part 1 are derived and verified by means of numerical experiments. It is shown that there exists an implementation form that achieves optimum error control when used in conjunction with one-derivative methods. No such form is found for two-derivative methods. A numerical beating phenomenon is observed for certain implementations of the average acceleration method and the trapezoidal rule, which from an error propagation standpoint, is highly undesirable.
Dynamics of Viscoelastic Plate With Curved Boundaries of Arbitrary Shape
Authors: Nagaya K.
Published: November 2010

This paper is concerned with vibration and transient response problems of viscoelastic plates with curved boundaries of arbitrary shape subjected to general dynamic loads. The results for free and forced vibration problems are given in generalized forms for arbitrary-shaped viscoelastic plates. As examples of this problem, the free vibration of a circular clamped viscoelastic plate with an eccentric hole and the dynamic response of a circular solid viscoelastic plate subjected to an eccentric annular impact load are discussed. Numerical calculations are carried out for both the problem, and experimental results are also obtained as an additional check of this study.
Free Convection Effects on Stokes’ Problem for a Vertical Plate in Rarefied Gas-Medium
Authors: Soundalgekar V. M. , Pohanerkar S. G. , Patil M. R.
Published: November 2010

An exact analysis of Stokes’ problem for the flow past an impulsively started infinite vertical plate in a rarefied gas-medium has been presented under first-order velocity slip and temperature jump boundary conditions. The effects of an externally heating or cooling of the plate by the free convection currents are studied. It is observed that there may exist a reverse type of flow when the plate is being cooled by the free convection currents. The rate of heat transfer has been found to decrease with increasing the temperature jump coefficient h2.
On the Hardening Response in Small Deformation of Metals
Authors: Caulk D. A. , Naghdi P. M.
Published: November 2010

This paper is concerned with a special class of hardening response functions for small deformation of elastic-plastic materials, its application to isotropic metals, and comparison of the theoretical results with experimental cyclic stress-strain curves for two different metals. The theoretical development is carried out within the scope of the existing purely mechanical theory for the “rate-independent” response of elastic-plastic materials, which admits the existence of a single loading function, as well as certain accepted idealizations. After summarizing the basic equations for small deformation, detailed attention is given to the development of a special form of the hardening response function, motivated mainly by the observation that the stress-strain curves for uniaxial cyclic loading of a fairly large class of metals attain—after several cycles—the so-called saturation hardening. We exploit this property; and, in the case of isotropic metals, systematically derive some restrictions on the constitutive coefficients in the loading function and the hardening response. Comparison of the results with two sets of experimental data, obtained from uniaxial cyclic loading of a 304 stainless steel and a 2024 aluminum alloy, shows good agreement within the understood idealizations of the basic theory.
Construction of Nonlinear Monotonic Functions With Selectable Intervals of Almost Constant or Linear Behavior
Authors: Cernocky E. P. , Krempl E.
Published: November 2010

A rather general method is given to construct classes of functions with an arbitrary almost constant (linear) initial interval followed by a nonprescribed interval of monotonic nonlinear behavior. This region of nonlinear behavior is succeeded by an unbounded interval of almost constant (linear) behavior. The functions contain not more than four selectable parameters and are synthesized from analytic, monotonic, normalized, and bounded base functions through the introduction of two separate kernel sets, subsequent addition, and integration. As examples we give the special functions based on the error, the hyperbolic tangent, the inverse tangent, a rational, and the incomplete gamma function. Limiting function forms, such as the bilinear form, are derived for limiting values of the parameters. The functions developed herein are primarily used as coefficient functions in a differential constitutive equation for viscoplasticity developed elsewhere. They are indispensible tools for the numerical modeling of stress-strain diagrams, strain (stress)-rate effects, creep and relaxation curves for monotonic, and cyclic loading both in one and three dimensions.
Analysis of Branched Cracks
Authors: Lo K. K.
Published: November 2010

This paper presents a method for solving a class of two-dimensional elastic branched crack problems. In contrast to other approaches in the literature, the integral equation presented here enables different branched crack problems to be solved in a unified manner. Muskhelishvili’s potential formulation is used to derive, by means of a Green’s function technique, a singular integral equation in complex form. The problems of the asymmetrically, symmetrically, and doubly symmetrically branched cracks are considered. The ratio of the length of the branched crack to that of the main one may be varied arbitrarily and the limit in which this ratio goes to zero is obtained analytically. Stress-intensity factors at the branched crack tip are computed numerically and the results, where possible, are compared to those in the literature. Disagreements in the literature are discussed and clarified with the aid of the present results.
Three-Dimensional Wave Propagation in a Cracked Elastic Solid
Authors: Itou S.
Published: November 2010

The three-dimensional dynamic problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. On the surfaces of the crack, the self-equilibrated system of a load varies harmonically in time and is distributed arbitrarily on those surfaces. The Fourier transformations are utilized to reduce the problem to a solution of two simultaneous integral equations which can be solved by using the series expansion method. The dynamic stress-intensity factor is computed numerically for some applied loads.
Simulation of the Influence of Bonding Materials on the Dynamic Behavior of Laminated Composites
Authors: Nayfeh Adnan H. , Nassar Elsayed Abdel-Ati M.
Published: November 2010

Two model analyses are constructed in order to determine the influence of bonding materials on the dynamic behavior of otherwise bilaminated composites. The geometric arrangement of the composite with the bond is treated as a special type of a trilaminated composite in which each of its major constituents is sandwiched between two bonding layers. In the first model, the recently developed continuum mixture theories of wave propagation in bilaminated composites [2] are extended to treat the trilaminated composite. Here details of the propagation process in the major components and also in the bonding layers are derived. In the second model, the entire effect of the bonds is treated as a modifier to interfacial continuity conditions. In this model the details of the propagation process in the bonding material are ignored. It is found that the results of both models correlate well for relatively thin bonding layers.
Harmonic Waves in Layered Composites: New Bounds on Eigenfrequencies
Authors: Horgan C. O. , Lang K.-W. , Nemat-Nasser S.
Published: November 2010

The purpose of this paper is to present new approaches to the problem of wave frequency estimation for harmonic waves in layered elastic composites. Upper and lower bounds are obtained by adapting standard results for eigenvalue problems with smooth coefficients. The one-dimensional eigenvalue problem with discontinuous coefficients of concern here is first transformed by using an analog of the classical Liouville transformation. Upper bounds are obtained by application of a Rayleigh-Ritz technique to the transformed problem. Explicit lower bounds in terms of the coefficients are established. Results are illustrated by numerical examples.
The Coupled Response of a Dynamic Element Riding on a Continuously Supported Beam
Authors: Alexandridis A. A. , Dowell E. H. , Moon F. C.
Published: November 2010

The dynamic interaction between a Linear Induction Motor primary, modeled as a spring-mass-damper element, and its secondary-rail, modeled as a prestressed, continuously supported, infinitely long beam, is studied theoretically. The existence of two transition speeds is established. At the lower transition speed, the frequency and damping ratio of the coupled system response attain their minimum and maximum values, respectively. The system is unstable at speeds higher than the second transition speed. Using a rotating annular disk to simulate the secondary rail, measured values of the frequency and damping ratio confirm the validity of the mathematical model for speeds up to nearly the lower transition speed.
Experimental Study of Dispersive Waves in Beam and Rod Using FFT
Authors: Yew E. H. , Chen C. S.
Published: November 2010

A method of algorism of analyzing wave motions with the Fast Fourier Transform (FFT) is presented in this paper. The dispersive characteristics of wave motion in rod and beam were used here as illustrative examples.
Acoustic Emission From a Brief Crack Propagation Event
Authors: Achenbach J. D. , Harris J. G.
Published: November 2010

Acoustic emissions produced by elementary processes of deformation and fracture at a crack edge are investigated on the basis of elastodynamic ray theory. To obtain a two-dimensional canonical solution we analyze wavefront motions generated by an arbitrary distribution of climbing edge dislocations emanating from the tip of a semi-infinite crack in an unbounded linearly elastic solid. These wavefront results are expressed in terms of emission coefficients which govern the variation with angle, and phase functions which govern the intensity of the wavefront signals. Explicit expressions for the emission coefficients are presented. The coefficients have been plotted versus the angle of observation, for various values of the crack propagation speed. The phase functions are in the form of integrals over the emanating dislocation distributions. Specific dislocation distributions correspond to brittle fracture and plastic yielding at the crack tip, respectively. Acoustic emission is most intense for brittle fracture, when the particle velocities experience wavefront jumps which are proportional to the stress-intensity factors prior to fracture. An appropriate adjustment of the canonical solution accounts for curvature of a crack edge. Such effects as focussing, finite duration of the propagation event, and finite dimensions of the crack are briefly discussed. As a specific example, the first signals generated by brittle Mode I propagation of an elliptical crack are calculated.
Harmonic Wave Propagation in a Periodically Layered, Infinite Elastic Body: Plane Strain, Analytical Results
Authors: Delph T. J. , Herrmann G. , Kaul R. K.
Published: November 2010

The problem of harmonic wave propagation in an unbounded, periodically layered elastic body in a state of plane strain is examined. The dispersion spectrum is shown to be governed by the roots of an 8 × 8 determinant, and represents a surface in frequency-wave number space. The spectrum exhibits the typical stopping band characteristic of wave propagation in a periodic medium. The dispersion equation is shown to uncouple along the ends of the Brillouin zones, and also in the case of wave propagation normal to the layering. The significance of this uncoupling is examined. Also, the asymptotic behavior of the spectrum for large values of the wave numbers is investigated.
Eigensolutions for Coupled Thermoelastic Vibrations of Timoshenko Beams
Authors: Shieh R. C.
Published: November 2010

A general solution procedure, together with two special case solutions, for the free-vibration boundary-value problem of a circular or rectangular cross-section Timoshenko beam under general mechanical boundary conditions and the thermal boundary conditions that follow the Newton surface heat transfer law is presented within the context of coupled linear thermoelasticity.
Dynamics of Slender Tapered Beams With Internal or External Axial Flow—Part 2: Experiments
Authors: Hannoyer M. J. , Paidoussis M. P.
Published: November 2010

This paper describes the experimental program which was conducted in parallel with the theoretical investigation presented in Part 1 of this study. Experiments were conducted in a special water tunnel with silicone rubber cantilevers which, in the case of external flow, were truncated cones, the free ends of which were streamlined; in the case of internal flow the beams were tubular, conical inside, and either conical or cylindrical outside, immersed either in still air or water. Experiments were also conducted with uniform tubular cylinders, and some with simultaneous internal and external axial flow. Qualitatively these experiments support theoretical predictions very well. The critical conditions for the various fluid-elastic instabilities which these systems can develop were measured and compared with theory. Quantitative agreement ranged from excellent to fair, the former for internal flow in conical tubes, and the latter for very slender cones in external flow.
On the Design of Thin Subsonic Airfoils
Authors: Chin W. C.
Published: November 2010

The inverse problem, which determines an airfoil geometry given some specified surface pressure, is considered in the subsonic, thin-airfoil limit. The full governing equations are expanded in powers of the thickness ratio and solved to second-order. The two sequential formulations contain free parameters, which are fixed by invoking “Kutta-type” conditions related to trailing edge closure. The correctness of the basic approach is demonstrated by using known classical examples for the simpler first-order problem.
Finite Elasticity Solutions Using Hybrid Finite Elements Based on a Complementary Energy Principle—Part 2: Incompressible Materials
Authors: Murakawa H. , Atluri S. N.
Published: November 2010

In a companion paper [1], the authors presented a total Lagrangean rate formulation for a hybrid stress finite-element method, based on a rate complementary energy principle which involves both the rates of Piola-Lagrange stress and rotation as variables, for finite strain analysis of nonlinear elastic compressible solids. In this paper the method is extended to the case of precisely incompressible rubber-like materials. Two plane stress problems, one corresponding to a biaxial strip test and, the other, a sheet with a circular hole, both involving strains in excess of 100 percent, are solved and the numerical results are discussed.
The Problem of an Inclined Crack in an Orthotropic Strip
Authors: Delale F. , Bakirtas I. , Erdogan F.
Published: November 2010

The elastostatic problem for an infinite orthotropic strip containing a crack is considered. It is assumed that the orthogonal axes of material orthotropy may have an arbitrary angular orientation with respect to the orthogonal axes of geometric symmetry of the uncracked strip. The crack is located along an axis of orthotropy, hence at an arbitrary angle with respect to the sides of the strip. The general problem is formulated in terms of a system of singular integral equations for arbitrary crack surface tractions. As examples Modes I and II stress-intensity factors are calculated for the strip having an internal or an edge crack with various lengths and angular orientations. In most calculations uniform tension or uniform bending away from the crack region is used as the external load. Limited results are also given for uniform normal or shear tractions on the crack surface.
The Influence of Rotatory Inertia and Transverse Shear on the Dynamic Plastic Behavior of Beams
Authors: Jones Norman , Gomes de Oliveira J.
Published: November 2010

The theoretical procedure presented herein examines the influence of retaining the transverse shear force in the yield criterion and rotatory inertia on the dynamic plastic response of beams. Exact theoretical rigid perfectly plastic solutions are presented for a long beam impacted by a mass and a simply supported beam loaded impulsively. It transpires that rotatory inertia might play a small, but not negligible, role on the response of these beams. The results in the various figures indicate that the greatest departure from an analysis which neglects rotatory inertia but retains the influence of the bending moment and transverse shear force in the yield condition is approximately 11 percent for the particular range of parameters considered.
A Theory of Viscoelastic Analogy for Wave Propagation Normal to the Layering of a Layered Medium
Authors: Ting T. C. T. , Mukunoki I.
Published: November 2010

Plane wave propagation in the direction normal to the layering of a periodically layered medium is studied. A period consists of two layers of homogeneous, linear elastic or viscoelastic materials. A theory is presented in which the layered medium is replaced by an “equivalent” linear homogeneous viscoelastic medium such that the stress response in the latter and in the layered medium are identical at points which are the centers of the odd layers. A means for determining the relaxation function of this equivalent homogeneous viscoelastic medium is presented and the transient waves in the layered medium are obtained by solving the transient waves in the equivalent homogeneous viscoelastic medium. Stieltjes convolutions with “auxiliary” functions are used to determine the solutions at points other than the centers of the odd layers and at points in the even layers. Numerical examples are presented for an elastic layered medium and comparisions are made with solutions obtained by the ray theory. The results show that the present theory can predict satisfactorily the transient response at any point in the layered medium regardless of whether the point is near or far from the impact end.
The Interface Crack in a Combined Tension-Compression and Shear Field
Authors: Comninou Maria , Schmueser D.
Published: November 2010

The interface crack was analyzed in two recent papers which considered applied tension and shear fields separately. The unrealistic oscillatory singularities and the ensuing material interpenetration were eliminated in these solutions by assuming small frictionless contact zones near the crack tips. The present paper presents a solution for the interface crack under combined normal and shear tractions. Both tensile and compressive normal tractions are considered and numerical results of the extents of the contact zones, shear stress-intensity factors, and interface crack opening profiles are presented.
Orthotropic Cylindrical Shells Under Line Load
Authors: Schwaighofer J. , Microys H. F.
Published: November 2010

Solutions for an orthotropic cylindrical shell which is subjected to a longitudinal line load along a generator are presented for Flu¨gge and Donnell type orthotropic shell equations. Experimental data of 2 orthotropic shells is presented and compared with the theoretical predictions. The results from the Flu¨gge-type equations agree well with the experimental data for all shells. The solutions based on Donnell-type equations agree well only in case of short shells.
Transient Response of Two Fluid-Coupled Cylindrical Elastic Shells to an Incident Pressure Pulse
Authors: Huang H.
Published: November 2010

The transient response of a system of two initially concentric circular cylindrical elastic shells coupled by an ideal fluid and impinged upon by an incident plane pressure pulse is studied. The classical techniques of separation of variable and Laplace transforms are employed for simultaneously solving the wave equations governing the fluid motions and the shell equations of motion. The transformed solutions are arranged in such a manner that their inverse transforms can be accurately calculated by solving a set of Volterra integral equations in the time domain. A sample calculation of shell responses was performed and results are compared to the case in which the outer shell is absent. It is found that the primary effects of a thin outer shell could be estimated by simple asymptotic formulas.
Residual Thermal Stresses Due to Cool-Down of Epoxy-Resin Composites
Authors: Weitsman Y.
Published: November 2010

This paper concerns the residual thermal stresses that develop within the resin of a fiber-reinforced composite-laminate as the material is cooled from cure temperature down to room temperature. The calculations presented herein consider the viscoelastic response of the resin and account for the temperature dependence and the stress sensivitity of the creep compliance. Comparisons with linear elasticity indicate that viscoelastic relaxation may reduce the residual stresses by about 20 percent.
Extrapolation of Strain and Stress From Holographically Measured Surface Displacement
Authors: Da¨ndliker R.
Published: November 2010

For isotropic elastic materials, following Hooke’s law, the strain and stress field below the surface is uniquely determined by the knowledge of the displacement of the surface itself. From the holographically measured surface displacement u and the boundary conditions for the surface-stresses one can determine all 9 components of the vector-gradient grad u, which describes the strains as well as the tilt and the rotation of a volume element adjacent to the surface. It is shown that strain and stress can be uniquely calculated in a cone-shaped zone below the observed part of the surface by stepwise linear extrapolation. The depth of this cone depends on the density of the sample points and on the accuracy of the displacement measurement on the surface, as well as on the required accuracy of the extrapolated strain and stress values. The suggested extrapolation method has been tested numerically for a thick-walled cylindrical tube under internal pressure using simulated input data. The limitations and the accuracy are discussed.
Plane-Strain Buckling of a Crack in a Harmonic Solid Subjected to Crack-Parallel Compression
Authors: Wu C. H.
Published: November 2010

The problem is studied by using a small-deformation-superposed-on-large-deformation analysis. It is found that a crack may buckle into infinitely many modes under one of a finite number of large crack-parallel compressive loads. Also, a crack-parallel tension has the effect of stiffening the crack when coupled with a small stress-intensity-producing load.
The Effect of Transverse Shear in a Cracked Plate Under Skew-Symmetric Loading
Authors: Delate F. , Erdogan F.
Published: November 2010

The problem of an elastic plate containing a through crack and subjected to twisting moments or transverse shear loads is considered. By using a bending theory which allows the satisfaction of the boundary conditions on the crack surface regarding the normal and the twisting moments and the transverse shear load separately, it is found that the resulting asymptotic stress field around the crack tip becomes identical to that given by the elasticity solutions of the plane strain and antiplane shear problems. The problem is solved for uniformly distributed or concentrated twisting moment or transverse shear load and the normalized Mode II and Mode III stress-intensity factors are tabulated. The results also include the effect of the Poisson’s ratio and material orthotropy for specially orthotropic materials on the stress-intensity factors.
Reflection, Refraction, and Absorption of Elastic Waves at a Frictional Interface: SH Motion
Authors: Miller R. K. , Tran H. T.
Published: November 2010

The reflection, refraction, and absorption of obliquely incident plane harmonic antiplane strain (SH) waves at a frictional interface between dissimilar semi-infinite elastic solids is investigated by an approximate analytical approach. The frictional stress at the interface is assumed to depend on the normal stress and the relative slip across the interface, but remains otherwise arbitrary throughout the analysis. General expressions are developed for the transmission and reflection coefficients, and the partitition of incident wave energy into reflection, transmission, and absorption. The special case of bonding by Coulomb friction is examined in detail as an example of application of the general procedure. An exact solution is also presented for the case of bonding by Coulomb friction, and a comparison between approximate and exact solutions provides an indication of the accuracy of the approximate method of analysis.
Finite Biaxial Extension of Completely Set Plain Woven Fabrics
Authors: Huang N. C.
Published: November 2010

This paper is concerned with the analysis of the finite biaxial extension of completely set plain woven fabrics with the yarns treated as curved rods. The undeformed configuration of the yarn is assumed to consist of segments of elastica resulting from deformed cantilevers under transverse end loads. In the undeformed state, there is no residual stress in the yarn. During deformation of the fabric, yarns are subjected to extension and bending. The mechanical behavior of the yarn is regarded as linearly elastic in extension. However, for the flexural deformation, due to loss in friction between fibers, the moment-curvature relation is bilinear. A nonlinear boundary-value problem can be formulated for the finite biaxial extension phenomenon of the fabric. Numerical solutions are sought by a trial and error procedure.
Effects of Shearing Loads and In-Plane Boundary Conditions on the Stability of Thin Tubes Conveying Fluid
Authors: Tani J. , Doki H.
Published: November 2010

The hydroelastic stability of short, simply supported, thin-walled tubes conveying fluid is examined with an emphasis on the effects of shearing loads and in-plane boundary conditions. The Donnell shell equation is used in conjunction with linearized, potential flow theory. The solution is obtained by using Fourier integral theory and Galerkin’s method. It is found that an increase of the shearing load reduces the critical divergence velocity and raises the corresponding number of circumferential waves. A change in the in-plane boundary conditions exerts the significant effect on the critical divergence velocity of short tubes.
Free Energy of Granular Materials in Static Equilibrium
Authors: Shahinpoor M. , Ahmadi G.
Published: November 2010

We employ the continuum theory of granular materials due to Goodman and Cowin and some experimental results due to P. G. Nutting to arrive at a functional from for the free energy of granular materials in static equilibrium. The results obtained indicate the dominance of gravitational effect, modify and enlarge the results previously obtained by J. T. Jenkins.
Generation of Crack Propagation Data on Notched Rotating Beam Specimens by Means of an Interrupted Stressing Technique
Authors: Eisenstadt R. , Fuller Ware D.
Published: November 2010

A simple, inexpensive technique of generating crack propagation data on rotating beam specimens of relatively small dimensions (1/2 in. dia by 3 in. long) has been developed. A recent solution for stress intensity factors on circumferentially notched round specimens [1]2 has made such data comparable with data generated by other specimen geometries. It is the purpose of this paper to develop this approach as an alternative method of generating crack propagation data. This technique should be especially useful for generating crack growth data approaching plane strain conditions under very low stresses where many cycles are required or for those materials where only small volumes are available as composites and powder metallurgy.
Resistance of an Inclined Plate Placed on a Plane Boundary in Two-Dimensional Flow
Authors: Ranga Raju K. G. , Garde R. J.
Published: November 2010

This paper describes the results of an experimental study on the drag coefficient of a two-dimensional sharp-edged plate placed on a plane boundary at different inclinations to the flow. Experimental data were collected to investigate the effects of (i) inclination of the plate to the flow, (ii) the relative submergence of the plate in a turbulent boundary layer, and (iii) the proximity of the tunnel walls to the plate, on the drag coefficient of the plate. Relations have been developed to enable correction for “blockage effect” and also to evaluate the effects of inclination of the plate and the presence of the boundary layer on the drag coefficient of the plate. Data collected by other investigators in wind tunnels of various dimensions have also been used in the development of the foregoing relations.