bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonlinear Corrections for Edge Bending of Shells
Authors: Ranjan G. V. , Steele C. R.
Published: July 2009

Asymptotic expansions for self-equilibrating edge loading are derived in terms of exponential functions, from which formulas for the stiffness and flexibility edge influence coefficients are obtained, which include the quadratic nonlinear terms. The flexibility coefficients agree with those previously obtained by Van Dyke for the pressurized spherical shell and provide the generalization to general geometry and loading. In addition, the axial displacement is obtained. The nonlinear terms in the differential equations can be identified as “prestress” and “quadratic rotation.” To assess the importance of the latter, the problem of a pressurized spherical cap with roller supported edges is considered. Results show that whether the rotation at the edge is constrained or not, the quadratic rotation terms do not have a large effect on the axial displacement. The effect will be large for problems with small membrane stresses.
Effects of Elastic Supports on the Buckling of Circular Cylindrical Shells Under Bending
Authors: Yabuta T.
Published: July 2009

This paper presents the effects of elastic supports on the buckling of circular cylindrical shells under bending. Stability was investigated using Donnell’s equation and the Galerkin method, including the spring constant of the elastic support. The results of this investigation indicate that the effects are similar in the cases of bending and axial compression.
Vibrations of Solid Cylinders
Authors: Hutchinson J. R.
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 vibrations of solid elastic cylinders with traction-free surfaces. The series solution is found to converge to accurate frequencies with the use of very few terms. Results are given for height-to-diameter ratios from zero to two and a frequency parameter ωR/Cs from zero to five and for modes of circumferential order from zero to four. Comparisons of these analytical results with previous experimental results shows excellent agreement.
Exact Equations for the Large Inextensional Motion of Elastic Plates
Authors: Simmonds J. G.
Published: July 2009

The governing equations for plates that twist as they deform are reduced to 14 differential equations, first-order in a single space variable and second-order in time. Many of the equations are the same as for statics. Nevertheless, the extension to dynamics is nontrivial because the natural coordinates to use to describe the deformed, developable midsurface are not Lagrangian. The plate is assumed to have two curved, stress-free edges, one built-in straight edge, and one free straight edge acted upon by a force and a couple. There are 7 boundary conditions at the built-in end and 7 at the free end.
Propagation of Elastic Pulses and Acoustic Emission in a Plate—Part 3: General Responses
Authors: Ceranoglu A. N. , Pao Yih-Hsing
Published: July 2009

In the first part of this paper, the Laplace transformed solutions in terms of the generalized ray integrals for point sources in a plate are presented. The inverse transform and the exact solutions for the epicentral responses together with numerical results were given in Part 2. In this part a modified version of Cagniard’s method is applied to obtain the transient response of the plate at any location due to point sources applied at the surface or the interior of the plate. Numerical results are shown for a concentrated force, a single-couple, a double-force, a double-couple without moment and a center of rotation, at locations up to six plate thicknesses from the source.
Reflection, Refraction, and Absorption of Elastic Waves at a Frictional Interface: P and SV Motion
Authors: Miller R. K. , Tran H. T.
Published: July 2009

An approximate method of analysis is presented for determining the reflection, refraction, and absorption of obliquely incident planar time-harmonic P or SV waves at a frictional interface between dissimilar elastic solids. The solids are pressed together with sufficient pressure to prevent separation, and the angle of incidence is subcritical. General expressions for the amplitudes and phases of all reflected and refracted waves are developed in closed form for a broad class of models for bonding friction. Specific results are presented for the case of identical elastic solids bonded by Coulomb friction, as an example of application of the general approach.
Nonlinear Response of an Elastic Cylindrical Shell to a Transient Acoustic Wave
Authors: Geers T. L. , Yen C.-L.
Published: July 2009

Governing equations are developed for the nonlinear response of an infinite, elastic, circular cylindrical shell submerged in an infinite fluid medium and excited by a transverse, transient acoustic wave. These equations derive from circumferential Fourier-series decomposition of the field quantities appearing in appropriate energy functionals, and from application of the “residual potential formulation” for rigorous treatment of the fluid-structure interaction. Extensive numerical results are presented that provide understanding of the phenomenology involved.
Modeling of Nonholonomic Dynamic Systems With Applications
Authors: Hemami H. , Weimer F. C.
Published: July 2009

A feedback model of nonholonomically constrained dynamic system is presented with applications in analysis, control, and understanding of such systems under impulsive and friction forces.
On the Stability of Equilibrium Paths Associated With Autonomous Systems
Authors: Huseyin K.
Published: July 2009

The postcritical behavior and stability distribution on the equilibrium paths emanating from a divergence point associated with an autonomous system are studied within a state-space formulation. The analysis concerning the stability of equilibrium paths is based on the eigenvalues of the Jacobian evaluated at arbitrary equilibrium points in the vicinity of a critical point. Explicit conditions of stability and instability concerning the initial and postcritical paths are obtained through a perturbation approach. It is shown that at an asymmetric point of bifurcation an exchange of stabilities between two paths occurs in complete analogy with conservative systems. Similarly, a symmetric point of bifurcation involves a postcritical path which is totally stable (unstable) if the initial path is unstable (stable).
Viscoelastic Responses of Finite Bodies by Quadrature Form of Correspondence Principle
Authors: Dasgupta G.
Published: July 2009

Alternative forms of the elastic-viscoelastic analogy for numerically obtained frequency response functions have been reported for solids of similarly and dissimilarly viscoelastic in bulk and shear in [1, 2], respectively. It is herein demonstrated that the same integrals can be numerically evaluated to obtain viscoelastic responses of finite bodies even though the harmonic response functions have singularities at the resonance frequencies. Crucial aspects of the algorithm regarding the truncation of numerical quadrature in the neighborhood of the poles are addressed in this Note.
Self-Consistent Determination of Time-Dependent Behavior of Metals
Authors: Weng G. J.
Published: July 2009

Though Kro¨ner’s self-consistent model is not fully consistent in the elastic-plastic deformation of polycrystals, it is found to be perfectly consistent in the time-dependent deformation of such materials. Hill’s model, on the other hand, should be used with a modified constraint tensor containing the elastic moduli of the matrix in that case. Kro¨ner’s model is supplemented with a physically consistent constitutive equation for the slip system; these, together with Weng’s inverse method, form the basis of a self-consistent determination of time-dependent behavior of metals. The kinematic component of the latent hardening law and the residual stress introduced in more favorably oriented grains are the two major driving forces for recovery and the Bauschinger effect in creep. The proposed method was applied to predict the creep and recovery strains of a 2618-T61 Aluminum alloy under pure shear, step and nonradial loading. The predicted results are seen to be in generally good agreement with the test data.
A Finite-Element Singular-Perturbation Technique for Convection-Diffusion Problems—Part 2: Two-Dimensional Problems
Authors: Diaz-Munio Rafael F. , Wellford L. Carter
Published: July 2009

Approximation procedures for the solution of two-dimensional convection-diffusion problems are introduced. In these procedures finite-element techniques are utilized. The developed solution algorithms are based on a variational method of matched asymptotic expansions. When these techniques are used in conjunction with standard Galerkin methods, to solve convection-diffusion equations, highly accurate solutions are obtained. Numerical results for certain two-dimensional problems are presented to establish the accuracy of the proposed procedures.
A Theory of Multiaxial Anisotropic Viscoplasticity
Authors: Eisenberg M. A. , Yen C.-F.
Published: July 2009

A theory of anisotropic viscoplasticity is developed. It is compared with and shown to reduce to existing theories under appropriate restrictions. The theory accommodates anisotropic hardening laws which, by means of Lagrangian mappings in stress space, incorporate experimentally observed yield surface distortion as well as kinematic and isotropic flow-induced changes. The theory is applied to the prediction of flow surfaces in tension-torsion space.
On Thermodynamics and Kinetic Theory of Ideal Rubber Membranes
Authors: Dreyer W.
Published: July 2009

Based on experimental evidence and thermodynamics it will be shown that the stored energy function of an ideal rubber membrane is determined by the entropy alone. The membrane is represented by a two-dimensional surface for the purposes of thermodynamics, and its thickness is taken into account by a scalar parameter so that incompressibility of the membrane can be described. The entropy of the membrane is calculated from a kinetic model and hence results the surface stress as a function of temperature and deformation for arbitrary shape of the membrane.
Elastic Instability of a Heated Annular Plate Under Lateral Pressure
Authors: Tani J.
Published: July 2009

On the basis of the dynamic version of the nonlinear von Karman equations, a theoretical analysis is performed on the elastic instability of a uniformly heated, thin, annular plate which has suffered a finite axisymmetric deformation due to lateral pressure. The linear free vibration problems around the finite axisymmetric deformation of the plate are solved by a finite-difference method. By examining the frequency spectrum with various asymmetric modes, the critical temperature rise under which the axisymmetric deformation becomes unstable due to the bifurcation buckling is determined, which is found to jump up to 7.2 times within a range of very small lateral pressure.
Earthquake Response of Deformable Liquid Storage Tanks
Authors: Haroun M. A. , Housner G. W.
Published: July 2009

A method for analyzing the earthquake response of deformable, cylindrical liquid storage tanks is presented. The method is based on superposition of the free lateral vibrational modes obtained by a finite-element approach and a boundary solution technique. The accuracy of such modes has been confirmed by vibration tests of full-scale tanks. Special attention is given to the cos θ-type modes for which there is a single cosine wave of deflection in the circumferential direction. The response of deformable tanks to known ground motions is then compared with that of similar rigid tanks to assess the influence of wall flexibility on their seismic behavior. In addition, detailed numerical examples are presented to illustrate the variation of the seismic response of two different classes of tanks, namely, “tall” and “broad” tanks. Finally, the significance of the cos nθ-type modes in the earthquake response analysis of irregular tanks is briefly discussed.
On Energy-Release Rates for a Plane Crack
Authors: Golebiewska Herrmann A. , Herrmann G.
Published: July 2009

Considered is a plane crack in a homogeneous, static stress field. The component of the Ji integral normal to the plane of the crack (J2) is shown not to be path-independent in the sense of the well-known J integral (≡ J1) parallel to the plane of the crack. The relation between the energy-release rate for rotation L and the integral J2 is established. It is finally suggested that the integrals L and M may provide a more natural description of energy-release rates (or forces) for plane cracks, rather than the integrals J1 and J2.
On Branched, Interface Cracks
Authors: Hayashi K. , Nemat-Nasser S.
Published: July 2009

The problem of branched, external cracks in the interface between two elastic materials is considered under the plane strain condition. A small interface contact region is introduced in the vicinity of each crack tip in order to remove oscillatory singularities. The branches are replaced by continuous distribution of edge dislocations, and, with the aid of Muskhelishvili’s potential method, the problem is reduced to a system of singular integral equations which are defined on the branches and the perfectly bonded region of the interface. The unknown functions of these integral equations are the shear stress acting on the bonded region, and the density functions of the edge dislocations. Stress-intensity factors of the interface cracks and branches are obtained numerically for several branch angles and branch lengths. Finally, the question of kinking from a tip of an interface crack is discussed with the aid of the results.
The Stress Distribution in Orthotropic Rotating Disks
Authors: Genta G. , Gola M.
Published: July 2009

The stress distribution in a rotating orthotropic disk of constant thickness with a central hole is obtained in closed form for the special case of a material satisfying a condition first studied by Wolf [9] in 1935. A more general analytical solution, proposed in 1973, is closely examined and discussed. The solution proposed in this paper, although limited to a particular kind of material, is successfully used to test the accuracy of the numerical procedures which solve a more generalized form of the problem.
On a One-Dimensional Theory of Finite Torsion and Flexure of Anisotropic Elastic Plates
Authors: Reissner E.
Published: July 2009

Equations for small finite displacements of shear-deformable plates are used to derive a one-dimensional theory of finite deformations of straight slender beams with one cross-sectional axis of symmetry. The equations of this beam theory are compared with the corresponding case of Kirchhoff’s equations, and with a generalization of Kirchhoff’s equations which accounts for the deformational effects of cross-sectional forces. Results of principal interest are: 1. The equilibrium equations are seven rather than six, in such a way as to account for cross-sectional warping. 2. In addition to the usual six force and moment components of beam theory, there are two further stress measures, (i) a differential plate bending moment, as in the corresponding linear theory, and (ii) a differential sheet bending moment which does not occur in linear theory. The general results are illustrated by the two specific problems of finite torsion of orthotropic beams, and of the buckling of an axially loaded cantilever, as a problem of bending-twisting instability caused by material anisotropy.
Characteristic Forms of Differential Equations for Wave Propagation in Nonlinear Media
Authors: Ting T. C. T.
Published: July 2009

Characteristic forms of differential equations for wave propagation in nonlinear media are derived directly from equations of motion and equations which combine the constitutive equations and the equations of continuity. Both Lagrangian coordinates and Eulerian coordinates are considered. The constitutive equations considered here apply to a large class of nonlinear materials. The characteristic forms derived here clearly show which components of the stress and velocity are involved in the differentiation along the bicharacteristics. Moreover, the reduction to one-dimensional cases from three-dimensional problems is obvious for the characteristic forms obtained here. Examples are given and compared with the known solution in the literature for wave propagation in linear isotropic elastic solids and isentropic compressible fluids.
On the Applicability of Acoustoelasticity for Residual Stress Determination
Authors: Johnson G. C.
Published: July 2009

Acoustoelasticity has recently been used for the nondestructive evaluation of residual stresses. In making such measurements the assumption has been made that the plastic flow leading to the residual stress state did not change the acoustic response of the material. This paper examines the extent to which that assumption holds for three aluminum alloys. The acoustoelastic theory is summarized and results are presented for tests of specimens under uniaxial tension which are subjected to plastic deformation followed by complete unloading. It is shown that the assumption made does not hold for all materials and that further theoretical development is required for general quantitative residual stress determination.
Stress Field Due to a Cylindrical Inclusion With Constant Axial Eigenstrain in an Infinite Elastic Body
Authors: Takao Y. , Taya M. , Chou T. W.
Published: July 2009

This paper examines an important aspect of the hygrothermal effect in fiber composite materials, the deformation induced by matrix shrinkage. The physical problem is simulated by prescribing a constant axial eigenstrain to the fiber material and the boundary-value problem is then solved in the context of an “inclusion” problem. The complete stress field due to a cylindrical inclusion with constant axial eigenstrain in an infinite elastic body are obtained by representing the eignestrain and displacements in Fourier integral forms. The solutions for stresses are expressed in terms of gamma and hypergeometric functions. The results are also compared with the existing solution of a special case.
Nonlinear Viscoelastic Analysis of a Unidirectional Composite Material
Authors: Schaffer B. G. , Adams D. F.
Published: July 2009

The single-integral nonlinear viscoelastic constitutive equations developed by Schapery from thermodynamic theory have been adapted to analyze the time-dependent response of a unidirectional composite material. This viscoelastic analysis has been combined with an existing time-independent elastoplastic micromechanics analysis, to permit the study of nonlinear time-dependent response of materials loaded beyond their elastic limit. Literature values as well as a brief series of creep-recovery tests on a typical epoxy resin were used to characterize the nonlinear viscoelastic response of the matrix constituent of a composite material. Composite response under transverse loading at various stress levels was then predicted, and the results compared with actual composite creep data.
Theories for Elastic Plates Via Orthogonal Polynomials
Authors: Krenk S.
Published: July 2009

A complementary energy functional is used to derive an infinite system of two-dimensional differential equations and appropriate boundary conditions for stresses and displacements in homogeneous anisotropic elastic plates. Stress boundary conditions are imposed on the faces a priori, and this introduces a weight function in the variations of the transverse normal and shear stresses. As a result the coupling between the two-dimensional differential equations is described in terms of a single difference operator. Special attention is given to a truncated system of equations for bending of transversely isotropic plates. This theory has three boundary conditions, like Reissner’s, but includes the effect of transverse normal strain, essentially through a reinterpretation of the transverse displacement function. Full agreement with general integrals to the homogeneous three-dimensional equations is established to within polynomial approximation.
A Nonlinear Model for the Dynamics of Penetration Into Geological Targets
Authors: Norwood F. R. , Sears M. P.
Published: July 2009

A general theory is developed for predicting stress and force histories for normal impact and penetration of geological targets by conical-nosed projectiles. To account for general material properties, the target medium is described by arbitrary hydrostat and shear failure-pressure relations. Using the cylindrical cavity approximation, the penetration dynamics reduce to a problem of radially symmetric stress wave propagation involving a nonlinear, ordinary, differential equation in terms of similarity variables. This equation is solved numerically by a shooting technique which is initiated by asymptotic values at the wave front. Numerical results are given for the stresses on the penetrator nose for some specific material models.
Inertia Effects on the Ductile Failure of Thin Rings
Authors: Rajendran A. M. , Fyfe I. M.
Published: July 2009

The introduction of inertia terms into a theoretical model of thin ring expansion shows that classical plastic instability concepts, defined in terms of the local strain in the necking region, no longer apply. By introducing the role of void growth in triggering local necking, through a recently proposed constitutive equation for porous plastic materials, it is possible to overcome this difficulty. A criterion based on a critical void volume fraction provides the alternative means to predict failure. This theory was applied to a thin ring configuration, and the results were found to compare favorably with experimental values obtained from statically and dynamically loaded rings. The experimental techniques developed to handle the thin ring configuration are also described.
Line Force in a Two-Phase Orthotropic Medium
Authors: Wu R. S. , Chou Y. T.
Published: July 2009

Based on the generalized method of images, the elastic field of an in-plane line force acting in a two-phase orthotropic medium is analyzed. Several special cases of technological interest are deduced from the general solution, including the case of a line force applied on the free surface of a half space. Application of the results to the determination of the elastic field of an edge dislocation in a semi-infinite orthotropic medium is illustrated.
Plasticity Analysis of Fibrous Composites
Authors: Dvorak G. J. , Bahei-El-Din Y. A.
Published: July 2009

The elastic-plastic behavior of composites consisting of aligned, continuous elastic filaments and an elastic-plastic matrix is described in terms of constituent properties, their volume fractions, and mutual constraints between the phases indicated by the geometry of the microstructure. The composite is modeled as a continuum reinforced by cylindrical fibers of vanishingly small diameter which occupy a finite volume fraction of the aggregate. In this way, the essential axial constraint of the phases is retained. Furthermore, the local stress and strain fields are uniform. Elastic moduli, yield conditions, hardening rules, and overall instantaneous compliances, as well as instantaneous stress concentration factors are derived. Specific results are obtained for the case of a Mises-type matrix which obeys the Prager-Ziegler kinematic hardening rule. Any multiaxial mechanical load may be applied. Comparisons are made between the present results and certain other theories.
Rough Contact Between Elastically and Geometrically Identical Curved Bodies
Authors: Bryant M. D. , Keer L. M.
Published: July 2009

Surface and subsurface stresses and displacements are obtained when two geometrically and elastically identical rough bodies are pressed together by normal and tangential loads. The theories of Cattaneo and Mindlin, who introduce zones of slip and stick within an elliptical contact area, are used. Von Mises yield criterion and maximum principle tensile stresses are used as failure criteria to assess potential failure due to shear or brittle fracture.
Two Analytical Solutions for Dynamic Crack Bifurcation in Antiplane Strain
Authors: Burgers P. , Dempsey J. P.
Published: July 2009

A semi-infinite crack is subjected to constant magnitude, dynamic antiplane loading at time t = 0. At the same instant the crack is assumed to bifurcate and propagate normal to its original plane or to propagate without branching. For constant crack-tip velocities the stresses and particle velocity are functions of r/t and θ only, which allows Chaplygin’s transformaton and conformal mapping to be used to obtain two Riemann-Hilbert problems which can be solved analytically. Expressions for the elastodynamic Mode III stress-intensity factors are then computed as functions of the crack-tip velocity and some conclusions concerning crack initiation are drawn.
Eddy Current Flows Around Cracks in Thin Plates for Nondestructive Testing
Authors: Mukherjee S. , Morjaria M. A. , Moon F. C.
Published: July 2009

The boundary element method is used to calculate the induced electric current flow around cracks in thin conducting plates. A low frequency approximation leads to a Poisson equation for the current density potential or stream function. A kernel is used which produces the correct singularity at the crack tip. The boundary condition on the crack, derived from Faraday’s law, requires the line integral of the current density around the crack to be zero. Numerical results for induced currents due to a circular induction coil ore given. These results show that hot spots, due to Joule heating, can occur at the tips of the crack. Comparison of numerical results with infrared scanning experiments of eddy currents in a cracked plate are given. It is hoped that the numerical method presented here will provide a tool to simulate both new and conventional nondestructive eddy current testing techniques.
Nonlinear Theory for Flexural Motions of Thin Elastic Plate, Part 3: Numerical Evaluation of Boundary Layer Solutions
Authors: Sugimoto N.
Published: July 2009

The boundary layer solutions previoulsy obtained in Part 2 of this series for the cases of the built-in edge and the free edge are evaluated numerically. For the built-in edge, a characteristic penetration depth of the boundary layer toward the interior region is given by 0.13 εh, εh being the normalized thickness of the plate, while for the free edge, it is given by 0.32 εh. Thus the boundary layer for the free edge penetrates more deeply toward the interior region than that for the built-in edge. The first-order stress distribution in each boundary layer is displayed. For the built-in edge, the stress singularity appears on the edge. It is shown that, in the boundary layer, the shearing and normal stresses become comparable with the bending stresses. Similarly for the free edge, the shearing stress also becomes comparable with the twisting stress. It should be remarked that, in the boundary layer, the shearing or the normal stress plays a primarily important role as the bending or the twisting stress. But the former decays toward the interior region and remains higher order than the latter. Finally owing to these numerical results, the coefficients involved in the “reduced” boundary conditions for the built-in edge are evaluated for the various plausible values of Poisson’s ratio.
Uniqueness for Elastic Crack and Punch Problems
Authors: Shield R. T.
Published: July 2009

Uniqueness of solution is shown for equilibrium states for elastic bodies in smooth contact. The cases considered include a body with a crack that may open only partially under load with parts of the faces in frictionless contact. Indentation of a body by a smooth rigid punch and contact with an elastic foundation are also treated.
Torsional Impact Response in an Infinite Cylinder With a Circumferential Edge Crack
Authors: Atsumi A. , Shindo Y.
Published: July 2009

The problem of torsional impact response in an infinite cylinder with a circumferential edge crack is solved. Using Laplace and Fourier transforms the problem is reduced to a singular integral equation of the first kind that has Cauchy-type, logarithmic and generalized Cauchy-type singularities. The kernel of the integral equation is improved in order that the calculation may be made easy. Dynamic stress-intensity factors are estimated with good accuracy.
Approximate Stability Criteria for Some Second-Order Linear Differential Equations With Stationary-Gaussian Random Coefficients
Authors: Ahmadi G. , Glockner P. G.
Published: July 2009

Approximate sufficiency conditions for almost sure stability of the equilibrium state of some second-order linear systems with stationary-Gaussian random coefficients are obtained in analytical form.
A Unified, Self-Consistent Theory for the Plastic-Creep Deformation of Metals
Authors: Weng G. J.
Published: July 2009

A unified, self-consistent scheme is formulated to determine the plastic-creep behavior of metals under combined stress. It is pointed out that such a deformation involves the transition from the inhomogeneity to transformation problem in the sense of Eshelby. The plastic deformation is studied by the Berveiller and Zaoui modification of Hill’s model. Following plastic deformation the structure of self-consistent relation for subsequent creep is analyzed and found to be independent of prior plastic strains. These self-consistent relations are used in conjunction with one set of unified constitutive equations for slip systems, in which the effect of prior plastic strains on the subsequent creep is considered. This unified, self-consistent scheme is applied to predict the plastic-creep strains of a 304 stainless steel. As compared to the experimental data, the self-consistent scheme is found to consistently provide reasonably accurate estimates for the total inelastic strains, while the predictions by the von Mises theory are seen to be less favorable.
On-Line Control of Nonlinear Flexible Structures
Authors: Masri S. F. , Bekey G. A. , Caughey T. K.
Published: July 2009

A simple yet efficient method is presented for the on-line control of nonlinear, multidegree-of-freedom systems responding to arbitrary dynamic environments. The control procedure uses pulse generators located at selected positions throughout a given system. The degree of system oscillation near each controller determines the controller’s activation time and pulse amplitude. The direct method of Liapunov is used to establish that the response of the controlled nonlinear system is Lagrange stable. Simulation studies of three example systems (conducted with digital and analog computers) demonstrate the feasibility, reliability, and robustness of the proposed active-control method. These systems, which include one with a hysteretic nonlinearity, are structures representative of modern tall buildings; they are subjected to nonstationary random excitation representative of earthquake ground motions.
Solution to the Backward-Kolmogorov Equation for a Nonstationary Oscillation Problem
Authors: Solomos G. P. , Spanos P-T. D.
Published: July 2009

The solution of a backward-Kolmogorov equation is presented. This equation is associated with a Markov approximation of the response amplitude of a lightly damped linear oscillator driven by an evolutionary random excitation.
An Effective Dispersion Theory for Layered Composites
Authors: Delph T. J. , Herrmann G.
Published: July 2009

A new approximate theory for wave propagation in a periodically layered elastic body is proposed. In its present state, the theory is valid for either propagation normal to the layering or for propagation under antiplane strain conditions. The theory is based on microstructural theories of elasticity, and makes use of a collocation technique in conjunction with the exact solution for wave propagation in an unbounded elastic body. The results are considered to hold promise for formulating accurate approximate solutions to certain types of boundary-initial value problems for composite bodies.
Dynamics of Asymmetric Nonconservative Systems
Authors: Inman D. J.
Published: July 2009

This work examines a linear, asymmetric lumped parameter system. Results on the qualitative behavior of a certain subclass of such systems are presented. In particular, necessary and sufficient conditions for the existence of a linear transformation that transforms an asymmetric system into an equivalent symmetric system are derived. Results on the stability and instability of such systems are presented and stated in terms of the original asymmetric system’s coefficient matrices. This work is compared with that of other authors and numerical examples illustrating the utility and correctness of the results are presented.
On the Estimation of Energy Release Rates
Authors: Abeyaratne R.
Published: July 2009

The energy release rate associated with the Mode I and Mode III crack problems for an infinite, nonlinearly elastic, incompressible body are estimated. The calculation adopts an approximation that is a natural extension of the small-scale yielding concept to problems involving moderate levels of loading. The results are compared with available exact and numerical solutions and the agreement is found to be remarkably good. The scheme used here, based on the theory of small deformations superposed on a finite deformation, can be utilized to estimate the energy release rate in many other crack problems.
Diffusive, Electrostatic, and Gravitational Deposition of Suspensions in the Entrance of a Nozzle
Authors: Korjack T. A.
Published: July 2009

An analytical investigation of the mechanics of deposition affected by gravity, electrostatic charge, and Brownian motion in an effuser from the nozzle inlet to a distance where incompressible effects are still valid has been made and a mathematical model developed for the deposition process. The analysis was restricted to laminar flow of dilute, nonreactive suspensions contained within an incompressible, viscous carrier. The results show that increasing the nozzle angle causes a decrease in deposition rate regardless of the diffusive Peclet number and gravity flow parameter. Furthermore, an increase in gravity field causes an increase in bottom deposition rate and decrease in top deposition rate.
Thermal Stress in a Transversely Isotropic Medium Containing a Penny-Shaped Crack
Authors: Tsai Y. M.
Published: July 2009

The thermal stress problem for a penny-shaped crack contained in a transversely isotropic medium is investigated using the techniques of Hankel transforms and double integrations. Symmetrical thermal loadings are applied over the crack surfaces. For constant temperature and heat flux over the crack surfaces, expressions for the crack shapes and the thermal stresses in the crack plane are obtained in closed forms. The stress intensity factors are also obtained and shown to be dependent on the material properties.
Axisymmetric Singular Stresses in a Thick-Walled Spherical Shell With an Internal Edge Crack
Authors: Atsumi A. , Shindo Y.
Published: July 2009

The paper considers the elastostatic axisymmetric problem for a thick-walled spherical shell containing a circumferential edge crack on the inner surface. The ring-shaped edge crack and the inner surface of the spherical shell are subjected to internal pressure. Using an integral transform technique we obtain a singular integral equation of the first kind which has a generalized Cauchy kernel as the dominant part. The integral equation is solved numerically, and the influence of the geometrical configuration on the stress-intensity factor and the crack-opening displacement is shown graphically in detail.
On the Unsymmetric Eigenproblem for the Buckling of Shells Under Pressure Loading
Authors: Mang H. A. , Gallagher R. H.
Published: July 2009

Consideration of the dependence of hydrostatic pressure on the displacements may result in significant changes of calculated buckling loads of thin arches and shells in comparison with loads calculated without consideration of this effect. The finite element method has made it possible to quantify these changes. On the basis of a shell theory of small displacements but moderately large rotations, this paper derives consistent incremental equilibrium equations for tracing, via the finite element method, the load-displacement path for thin shells subjected to nonuniform hydrostatic pressure and establishes the buckling condition from the incremental equilibrium equations. Within the framework of the finite element method, the character of hydrostatic pressure as one of a follower load is represented in the so-called pressure-stiffness matrix. For shells with loaded free edges, this matrix is unsymmetric. The principal objective of the present paper is to demonstrate that symmetrization of the pressure stiffness matrix resulting from linearization of the buckling condition yields buckling loads that are identical to the eigenvalues resulting from first-order perturbation analysis of the unsymmetric eigenproblem. A circular cylindrical shell with a free and a hinged end, subjected to hydrostatic pressure, is used as an example of the admissibility of symmetrizing the pressure stiffness matrix and for assessing its effect.
Superpotential Solution for Jet-Engine External Potential and Internal Rotational Flow Interaction
Authors: Chin W. C.
Published: July 2009

For flows with prescribed parallel shear far upstream, the vorticity generation term in the disturbance stream-function (Ψ) equation and the Bernoulli “constant,” both of which vary from stream surface to stream surface, are explicitly evaluated as power series in Ψ with curvature-dependent coefficients, for axisymmetric flows using some invariant properties of vorticity. By casting the linearized stream-function equation in conservation form, extended Cauchy-Reimann conditions are obtained, implying a “superpotential” φ* satisfying a “Laplace-like” equation useful for solving flows past prescribed shapes; the corresponding tangency and Kutta conditions, interestingly, take a “potential form,” so that simple changes to existing potential flow algorithms extend their applicability to strong oncoming shears with arbitrary curvature. The theory, which applies to duct flows behind actuator disks generating shear, is sketched for both “analysis” and “design” formulations; here, we address the interaction between external potential and internal rotational jet-engine flows occurring through both an assumed actuator disk and a trailing edge slipstream, and provide representative numerical calculations.
Some Remarks on Transonic Potential Flow Theory
Authors: Nixon D. , Klopfer G. H.
Published: July 2009

The validity of the commonly used transonic potential equation for flows with shock waves is examined. It is concluded that in such cases the potential formulation is inconsistent with the basis assumptions of the theory because of the nonconservation of momentum across a shock. The relationship of this momentum source to wave drag is also discussed. Another topic examined is the rationalization of means to make solutions of the transonic potential equation agree better with solutions of the Euler equations.
Penetration of Targets Described by a Mohr-Coulomb Failure Criterion With a Tension Cutoff
Authors: Longcope D. B. , Forrestal M. J.
Published: July 2009

A model is developed to estimate the force on a conical-nosed penetrator for normal entry into geological targets that have linear hydrostats and fail according to a Mohr-Coulomb criterion with a tension cutoff. The model is applicable to targets with shear strength which either increases with pressure (dry rocks) or is constant (sea ice, concrete, saturated rocks). For high enough penetrator velocity the target response is elastic-plastic, but at lower velocities stresses exceed the target tensile strength and the response includes an additional cracked region. Parametric results are obtained via a similarity transformation and solution to a nonlinear wave propagation problem. Predicted and measured penetrator decelerations are compared for a field test into a dry rock target and reasonable agreement is shown.
Constitutive Equations for Damaging Materials
Authors: Krajcinovic D.
Published: July 2009

The paper focuses on the derivation of the constitutive law for a material containing flat, planar microcracks. The damage law is derived from the dissipation potential in conjunction with the orthogonality principle. The dissipation potential is shown to exist in the space of conjugate thermodynamic forces related to the stress intensity factors. Both brittle and ductile materials are considered within the framework of the small deformation theory and the time-independent processes.
The Dynamic Stress Intensity Factor Due to Arbitrary Screw Dislocation Motion
Authors: Brock L. M.
Published: July 2009

The dynamic stress intensity factor for a stationary semi-infinite crack due to the motion of a screw dislocation is obtained analytically. The dislocation position, orientation, and speed are largely arbitrary. However, a dislocation traveling toward the crack surface is assumed to arrest upon arrival. It is found that discontinuities in speed and a nonsmooth path may cause discontinuities in the intensity factor and that dislocation arrest at any point causes the intensity factor to instantaneously assume a static value. Morever, explicit dependence on speed and orientation vanish when the dislocation moves directly toward or away from the crack edge. The results are applied to antiplane shear wave diffraction at the crack edge. For an incident step-stress plane wave, a stationary dislocation near the crack tip can either accelerate or delay attainment of a critical level of stress intensity, depending on the relative orientation of the crack, the dislocation, and the plane wave. However, if the incident wave also triggers dislocation motion, then the delaying effect is diminished and the acceleration is accentuated.
Natural Frequencies of In-Plane Vibration of Arcs
Authors: Irie T. , Yamada G. , Tanaka K.
Published: July 2009

The natural frequencies of in-plane vibration are presented for uniform arcs with circular cross section under all combinations of boundary conditions.
Viscoplastic Modeling With Strain Rate-History Dependency
Authors: Ghoneim H. , Matsouka S. , Chen Y.
Published: July 2009

The strain rate-history effect on the plastic behavior of some classes of viscoplastic materials is incorporated into the power formula of Bodner’s model by adopting an integral-memory type equation for the “hardening” state variable. The modified model is incorporated into a finite element program. Results on uniaxial loading-unloading-reloading at different rates as well as jump tests show the capability of this modified model in simulating the strain rate-history effects on the yield stress and the plastic hardening for some viscoplastic materials.
Nonlinear Shell Dynamics—Intrinsic and Semi-Intrinsic Approaches
Authors: Libai A.
Published: July 2009

The intrinsic approach to the nonlinear dynamics of shells, which was introduced in [6], is reviewed and extended by the addition of appropriate initial and boundary conditions of the dynamic and kinematic types to the field equations. The alternative semi-intrinsic velocity approaches (where the velocity components supply the connection between the equations of motion and the time rates of the metric and curvature) are also presented. Both linear and rotational velocity forms are included. The relative merits of these approaches to shell dynamics are discussed and compared with extrinsic approaches.
Free Vibration of a Circular Cylindrical Shell Elastically Restrained by Axially Spaced Springs
Authors: Irie T. , Yamada G. , Muramoto Y.
Published: July 2009

An analysis is presented for the free vibration of a circular cylindrical shell restrained by axially spaced elastic springs. The governing equations of vibration of a circular cylindrical shell are written as a coupled set of first-order differential equations by using the transfer matrix of the shell. Once the matrix has been determined, the entire structure matrix is obtained by the product of the transfer matrices and the point matrices at the springs, and the frequency equation is derived with terms of the elements of the structure matrix under the boundary conditions. The method is applied to circular cylindrical shells supported by axially equispaced springs of the same stiffness, and the natural frequencies and the mode shapes of vibration are calculated numerically.
Interaction Between a Rigid Indenter and a Near-Surface Void or Inclusion
Authors: Miller G. R. , Keer L. M.
Published: July 2009

A solution is presented to the two-dimensional problem of a rigid indenter sliding with friction on a half plane containing a near-surface imperfection in the form of a circular void or rigid inclusion. The complex variable formulation of Muskhelishivili is used to reduce the problem to a Fredholm integral equation of the second kind. This integral equation is solved numerically thus enabling the numerical calculation of the stress field. The behavior of the stress field is depicted in plots of the contact stress distribution and the subsurface maximum shear stress field. Results are presented showing location and size effects in the case of an inclusion, and finally, comparisons are made between the disturbances due to inclusions and voids.
Longitudinal Collision of Rod-Rigid Element Systems
Authors: Mioduchowski A. , Faulkner M. G. , Pielorz A. , Nadolski W.
Published: July 2009

One-dimensional wave propagation theory is used to investigate the forces, velocities, and displacements in a series of elastic rods connected to rigid elements. The method is applied to the case of two subsystems that collide. The technique allows the calculations to be done during a short-lived event such as a collision.
An Approach to the First Passage Problem in Random Vibration
Authors: Mason A. B. , Iwan W. D.
Published: July 2009

The first passage problem for the response of a linear oscillator excited by a random excitation is considered. An approximate analytical technique is presented for calculation of the distribution of the time to first excursion across a symmetric double barrier. The approach may be applied to the case of nonstationary response to modulated Gaussian noise with nonwhite spectral density. Results for the limiting decay rate parameter are presented and are compared with those of other analytical methods and simulation results. The first passage probability is calculated for a system subjected to a suddenly applied white noise and the results also compared with those of other methods and computer simulations. The results of the proposed method show generally good agreement with simulation results.
Tresca’s Yield Condition and the Rotating Disk
Authors: Gamer U.
Published: July 2009

The displacement field belonging to the elastic-plastic stress field in a rotating solid disk that can be found with the help of Tresca’s yield condition, in textbooks on plasticity, is discontinuous at the elastic-plastic interface. Tresca’s yield condition cannot be applied to this problem since its associated flow rule predicts a negative plastic strain caused by a tensile stress.
An Elastic Beam Contained in a Frictionless Channel
Authors: Vaillette D. P. , Adams G. G.
Published: July 2009

An infinitely long elastic beam, contained within a frictionless and rigid channel, is subjected to axially compressive forces. It is shown that the elastica theory predicts a maximum permissible axial force that can be supported. This critical force is expressed by a very simple relationship involving the flexural rigidity of the beam and the channel width.
Ablation by Frictional Heating
Authors: Tao L. N.
Published: July 2009

The ablation problem of a semi-infinite solid, moving at a constant speed parallel to its surface, is investigated. The study includes all induced motions caused by the density differences of various phases of the materials. Some appropriate transformations are introduced to reduce the problem to one where all phases behave as if they had the same density. The reduced problem is then solved by similarity transformations. It is found that the exact solution exists if and only if an inequality is satisfied. The physical interpretation of the inequality is examined. A numerical example is given to illustrate the result.