bluuebunny/crossref_metadata_2025 huggingface dataset:
Wavefront Analysis in the Nonseparable Elastodynamic Quarter-Plane Problems, I—Part 1: The General Method
Authors: Miklowitz J.
Published: July 2009

This work concerns the transient response in elastodynamic quarter-plane problems. In particular, the work focuses on the nonseparable problems, developing and using a new method to solve basic quarter-plane cases involving nonmixed edge conditions. Of initial interest is the classical case in which a uniform step pressure is applied to one edge, along with zero shear stress, while the other edge is traction free. The new method of solution is related to earlier work on nonseparable wavequide (semi-infinite layer) problems in which long time, low-frequency response was the objective. The basic idea in the earlier work was the exploitation of a solution boundedness condition in the form of an infinite set of integral equations. These equations were generated by eliminating the residues at an infinite set of poles stemming from the zeros of the Rayleigh-Lamb frequency equation. These poles were associated with exponentially unbounded contributions. The solution of the integral equations determined the unknown edge conditions in the problem, hence giving the long time solution. In the new method for the quarter-plane problems the analog of the Rayleigh-Lamb frequency equations is the Rayleigh function that yields just three zeros, i.e., say the squares of cR1, cR2, and cR3 speeds for the Rayleigh surface waves. Of these six roots (and corresponding poles) only one is physical, i.e., cR1. The other five are eliminated since they correspond to: (1) exponentially unbounded waves, or (2) waves with speeds cR2 > cd, cR3 > cd, all inadmissible. They analogously (to the layer case) give four integral equations for the edge unknowns, hence the formal solution for the problems. To date the method has been successful in obtaining all the wavefront expansions for the uniform step pressure case mentioned earlier. The dilatational and equivoluminal wavefronts were obtained for the interior and both edges and the Rayleigh wavefronts for both edges. This asymptotic solution has been verified and hence establishes the credibility of the new method.
A Variable Parameter Incrementation Method for Dynamic Instability of Linear and Nonlinear Elastic Systems
Authors: Lau S. L. , Cheung Y. K. , Wu S. Y.
Published: July 2009

A variable parameter incrementation method is proposed and then applied to the determination of parametric instability boundary of columns. Attention is particularly paid to the geometrically nonlinear problems including the instability of nonlinear vibrations. Although only beam and column problems are treated at present, the approach is believed to be general in methodology. This method is not subjected to the limitations of small exciting parameters and weak nonlinearity.
Compact Probabilistic Representation of Random Processes
Authors: Masri S. F. , Miller R. K.
Published: July 2009

A method is given for representing analytically defined or data-based covariance kernels of arbitrary random processes in a compact form that results in simplified, analytical, random-vibration transmission studies. The method uses two-dimensional orthogonal functions to represent the covariance kernel of the underlying random process. Such a representation leads to a relatively simple analytical expression for the covariance kernel of the linear system response which consists of two independent groups of terms: one reflecting the input characteristics, and the other accounting for the transmission properties of the excited dynamic system. The utility of the method is demonstrated by application to a covariance kernel widely used in random-vibration studies.
Vibration of a Free Rectangular Parallelepiped
Authors: Hutchinson J. R. , Zillmer S. D.
Published: July 2009

A series solution of the general equations of linear elasticity is used to determine accurate natural frequencies for the vibrations of a rectangular parallelepiped with traction-free surfaces. The series solution is found to converge to accurate frequencies with the use of very few terms. Resulting frequences are tabulated for comparison with previous experimental results and are shown graphically for comparison with elementary rod, beam, and plate solutions. The comparisons with elementary solutions show good agreement, and comparisons with the experiment results shows excellent agreement.
Theory of Viscoplastic Shells for Dynamic Response
Authors: Atkatsh R. S. , Bieniek M. P. , Sandler I. S.
Published: July 2009

A viscoplastic shell model is formulated that utilizes the shell membrane strains and curvatures as the kinematic variables and the shell stress resultants (membrane forces and moments) as the dynamic variables. The viscoplastic shell model combines the concepts of Perzyna’s viscoplastic constitutive equations with Bieniek’s shell stress resultant formulation. The model is incorporated into the Elastoplastic Shell Analysis code (EPSA) for the analysis of shells in an acoustic medium subjected to dynamic loadings that produce moderately large elastoviscoplastic deformations in the shell. An example is presented to demonstrate the effect of material rate dependence on structural response.
A Linear Theory for Pretwisted Elastic Beams
Authors: Krenk S.
Published: July 2009

A linear theory for pretwisted elastic beams subjected to general loads is developed from the potential energy functional. The longitudinal strain distribution is that of a similar beam without pretwist supplemented by terms from the warping function and its longitudinal derivative. The paper contains a general system of differential equations and gives explicit solutions for homogenous extension, torsion, and bending. The theory accounts explicitly for the shear center, the elastic center, and the axis of pretwist. The resulting torsion-extension coupling is in agreement with a recent asymptotic result from three-dimensional elasticity apart from the limitation imposed by neglecting deformations of the cross sections in their own plane.
The Interface Crack Behavior in Dissimilar Anisotropic Composites Under Mixed-Mode Loading
Authors: Wang S. S. , Choi I.
Published: July 2009

A study of an interlaminar crack between dissimilar, anisotropic composites under mixed-mode loading is presented. Based on the theoretical development in [1], the problem is modeled by using a partially closed interface crack model for the closed tip and an approximate model for the other tip. Solutions are obtained for the interlaminar crack between dissimilar composites with various degrees of anisotropy under general mixed-mode loading conditions. Crack closure, contact stresses, crack-tip stress intensity factors, and energy release rates are determined for each case.
Quantitative Determination of Stress and Strain Distributions During High Axial Compression of Aluminium With the Aid of Small Ruby Particles
Authors: Hoekstra S. , Munnig Schmidt-van der Burg M. A. , Galenkamp H. , van Wijngaarden H.
Published: July 2009

Line shift measurements of the sharp R1 ruby fluorescence line with respect to a neon reference line are used for the determination of quantitative stress distributions during high axial compression of cylindrical samples of aluminium between two transparent sapphire anvils. At the sample-anvil interface small ruby particles are embedded in the aluminium surface as optomechanical sensors for local stress and strain measurements. The experimental results are used to verify computer calculations based on the finite element method. The measurement technique was recently described by Brouha et al. [5, 6]. In this paper some modifications and new results will be presented and the use of pure sapphire anvils with a stress-sensitive top layer of ruby obtained by implantation of Cr3+ ions will be discussed.
Interaction of a P-Wave With a Laterally Stiffened Slot
Authors: Ryan R. L. , Mall S.
Published: July 2009

The interaction of a longitudinal wave with a narrow cavity or slot that contains an inclusion is considered. A singular integral equation is derived for the scattered field and the integral equation is solved numerically by a Gauss-Chebyshev technique. The stress intensity at the ends of the slot is obtained as a function of frequency and inclusion stiffness for both a continuous and discrete element inclusion.
An Educational Elasticity Problem With Friction, Part 3: General Load Paths
Authors: Dundurs J. , Comninou M.
Published: July 2009

This concluding paper treats general load paths when the two components of the concentrated force are allowed to change independently with time. It is shown that there are two kinds of dependence on the load path. For certain directions of the forward tangent, the dependence is strict in that the deformations depend on the full details of the path. For other directions, however, the dependence is loose, and the deformations do not depend on the exact nature of the path as long as the forward tangent falls within given bounds. The problem also shows that, given an initial state, the load space can be subdivided into different regions each corresponding to a certain mode of deformations.
On Transverse Secondary Flows in Wave Channels
Authors: Johnson R. E.
Published: July 2009

The viscous boundary layer analysis for the sidewalls of a wave tank is presented for the case of two-dimensional waves of small amplitude traveling along the channel length. The second-order transverse streaming motion induced in the interior of the channel by the sidewall layers is determined. The calculations extend the work of Mei and Liu [1] which examined the effect of sidewalls on the longitudinal streaming motion. The intensity of the transverse streaming flow is found to increase as the depth to wavelength ratio decreases, and is found to be significant for typical wave tanks that generally have a depth to width ratio between one-half and one-fourth. The present results are useful if accurate conclusions concerning mass transport in the open ocean are to be made from laboratory studies. Furthermore, the results may offer an explanation for some of the laboratory observations already in the literature.
Perturbation Procedures for Nonlinear Viscous Flows
Authors: Nixon D.
Published: July 2009

The perturbation theory for transonic flow is further developed for solutions of the Navier-Stokes equations in two dimensions or for experimental results. The strained coordinate technique is used to treat changes in location of any shock waves or large gradients.
A Free Boundary Value Problem in Plate Theory
Authors: Villaggio P.
Published: July 2009

In this paper the equilibrium configuration of a thin rectangular plate, supported on an elastic foundation that reacts in compression only, is studied. It is assumed that the foundation is described by the Winkler model in the contact region. The plate is supposed to be weightless and subjected to a concentrated load in its midpoint. The shape of the free boundary, where the plate loses contact with the foundation, is determined.
The Viscous Collapse of Thick-Walled Tubes
Authors: Geyling F. T. , Walker K. L. , Csencsits R.
Published: July 2009

The collapse of glass tubes, as used in the manufacture of optical fiber preforms, constitutes a problem involving Stokes flow, driven by surface tension and applied pressure. Undesirable, noncircular modes of deformation may grow or decay, depending on initial tube dimensions, radial viscosity variations, and the pressure differential across the tube wall. A two-dimensional model of the collapse process has been developed. Numerical results show trends that agree with experimental observations and are useful in the control of actual, three-dimensional collapse.
Instability Analysis of Pressure-Loaded Thin Arches of Arbitrary Shape
Authors: Ye T. Q. , Gallagher R. H.
Published: July 2009

The governing differential equations and the virtual work expressions for the large displacement analysis of thin arches of arbitrary shape, subjected to pressure loads, are derived. The virtual work expressions are employed as the basis for formulation of finite element stiffness equations. Classical solutions are obtained, from the differential equations, for the buckling of circular rings under uniform “follower” (hydrostatic) and “dead” (constant direction) pressure loadings. Finite element solutions are calculated for elliptical rings for a wide range of axis ratios.
Inertial Effects in Poroelasticity
Authors: Bowen R. M. , Lockett R. R.
Published: July 2009

The dynamic behavior of a chemically inert, isothermal mixture of an isotropic elastic solid and an elastic fluid is studied. Geometrically, this mixture is assumed to comprise a layer of fixed depth, bounded below by a rigid, impervious surface, and above by a free surface to which loads are applied. The resulting boundary-initial value problem is solved by use of a Green’s function. Two different loading conditions are used to demonstrate the effect of including inertia terms in the equations of motion. In the first example of a constant compressive load, our result is found to agree with the inertia-free solution only for a certain long-time approximation. The second example shows that for a harmonically varying compression, resonance displacements occur at certain loading frequencies, whereas the solution obtained by neglecting inertia does not predict this behavior.
Stability of Steady Frictional Slipping
Authors: Rice J. R. , Ruina A. L.
Published: July 2009

The shear resistance of slipping surfaces at fixed normal stress is given by τ = τ(V, state). Here V = slip velocity, dependence on “state” is equivalent to functional dependence with fading memory on prior V(t), and ∂τ(V, state)/∂V>0. We establish linear stability conditions for steady slip states (V(t), τ(t) constant). For single degree-of-freedom elastic or viscoelastic dynamical systems, instability occurs, if at all, by a flutter mode when the spring stiffness (or appropriate viscoelastic generalization) reduces to a critical value. Similar conclusions are reached for slipping continua with spatially periodic perturbations along their interface, and in this case the existence of propagating frictional creep waves is established at critical conditions. Increases in inertia of the slipping systems are found to be destabilizing, in that they increase the critical stiffness level required for stability.
On the Nonequivalence of the Stress Space and Strain Space Formulations of Plasticity Theory
Authors: Casey J. , Naghdi P. M.
Published: July 2009

Yoder and Iwan [7] have recently claimed that the stress space and strain space formulations of plasticity are equivalent. This conflicts with the results of Casey and Naghdi [6]. The main objective of the present paper is to demonstrate, with the use of fairly general constitutive equations of the type employed in [7], that the stress space and strain space formulations of plasticity theory are not equivalent. It is also shown that if the loading criteria of strain space are adopted as primary, then the main features of [7] may be obtained by specializing the results of [6].
Dynamics of a Cluster of Flexibly Interconnected Cylinders, Part 1: In Vacuum
Authors: Paidoussis M. P. , El Barbir K. N. , Genadry M. R. , Chaubernard J.-P.
Published: July 2009

This paper presents an analytical model for the dynamics of a cluster of flexible cylinders, the extremities of which are structurally interconnected, e.g., through “end plates” or other kinds of structural connectors. These connectors are modeled by sets of translational and rotational springs, such that resistance to both in-plane and out-of-plane deformation of the connectors is fully taken into account. The dynamics of the system in vacuum is examined here, and especially the effect of varying the different spring stiffnesses on the system eigenfrequencies. This provides a reference base and the necessary analytical tools for the study of the system in axial flow, which is presented as Part 2 of this work.
Observations on the Steady-State Solution of an Extremely Flexible Spinning Disk With a Transverse Load
Authors: Benson R. C.
Published: July 2009

The steady deflection of a transversely loaded, extremely flexible, spinning disk is studied. Membrane theory is used to predict the shapes and locations of waves that dominate the response. It is found that waves in disconnected regions are possible. Some results are presented to show how disk stiffness moderates the membrane waves, the most important result being an upper bound on the highest ordered wave of significant amplitude. A hybrid system of differential equations and boundary conditions is developed to replace the pure membrane formulation that is singular, and the full fourth-order plate formulation that is numerically sensitive. The hybrid formulation retains the salient features of the flexible disk response and facilitates calculations for very small disk stiffnesses.
Postbuckling Behavior of Inelastic Inextensional Rings Under External Pressure
Authors: Kyriakides S. , Arikan E.
Published: July 2009

This paper deals with the problem of predicting the postbuckling configuration of a thin, inextensional, inelastic ring under external pressure. Previous work has shown that the postbuckling configuration of such a ring is unstable up to the point where the first two diametrically opposite points on the ring’s circumference first come into contact. The presented analysis deals with ring configurations past the first contact. It is shown that the configuration is stable and that for plastic materials, multiple contact points tend to develop. Collapse experiments on thin tubes are consistent with the analytical predictions.
Creep and Plastic Strains Under Stress Reversal in Torsion With and Without Simultaneous Tension for 304 Stainless Steel at 593°C
Authors: Cho U. W. , Findley W. N.
Published: July 2009

Results of creep experiments under stress reversals in torsion with and without constant tension are reported. Constitutive equations based on data for single step creep and creep recovery tests previously reported are used to describe the test results. A viscous-viscoelastic model with aging effects and modifications for step-down stress changes and stress reversals predicted the creep behavior reasonably well. The prediction of time-independent plastic strains is also described.
Internal and Edge Cracks in a Plate of Finite Width Under Bending
Authors: Boduroglu H. , Erdogan F.
Published: July 2009

In this paper the title problem is studied by using Reissner’s transverse shear theory. The main purpose of the paper is to investigate the effect of stress-free boundaries on the stress intensity factors in plates under bending. Among the results found particularly interesting are those relating to the limiting cases of the crack geometries. The numerical results are given for a single internal crack, two collinear cracks, and two edge cracks. Also studied is the effect of Poisson’s ratio on the stress intensity factors.
Forced Nonlinear Oscillations of an Autoparametric System—Part 2: Chaotic Responses
Authors: Hatwal H. , Mallik A. K. , Ghosh A.
Published: July 2009

Chaotic oscillations arising in forced oscillations of a two degree-of-freedom autoparametric system are studied. Statistical analysis of the numerically integrated nonperiodic responses is shown to be a meaningful description of the mean square values and the frequency contents of the responses. Some qualitative experimental results are presented to substantiate the necessity of performing the statistical analysis of the responses even though the system and the input are deterministic.
Constraint to Side Flow in Plates
Authors: Liss J. , Goldsmith W. , Hauser F. E.
Published: July 2009

An experimental program was conducted to determine the increase in flow stress relative to simple uniaxial compression for 2024-0 aluminum plates subjected to symmetric quasistatic compression by steel punches and to dynamic compression using the Kolsky (split Hopkinson-bar) technique. An average constraint factor of 2 was determined experimentally for a ratio of specimen thickness to bar diameter of 0.5 for the quasi-static case. This correlated well with the value predicted theoretically. Under dynamic conditions the constraint factor at yield stress was found to be slightly lower at a value of 1.75 and appeared to be nearly independent of strain rate over the test range from 103 to 1.5 × 104s−1.
Fluid Flow Through a Crack Network in Rocks
Authors: Englman R. , Gur Y. , Jaeger Z.
Published: July 2009

A network of cracks pervading a rock is modeled by a random distribution of two-dimensional intersecting, complex, narrow cracks. The percolation properties of the resulting network are studied as functions of the crack-area density and size of the medium. Gas flow commences at a finite value of the crack density which in Arkansas Novaculite rocks amounts according to our model to 670 cracks per cm2. The mean probability of finding at least one crack intersecting another is 0.57 at the threshold density. Above that, the rock gas-flow permeability increases superlinearly with crack density due to the enhancement of short percolative paths.
Variation Principles and Bounds for the Approximate Analysis of Plane Membranes Under Lateral Pressure
Authors: Stora˚kers B.
Published: July 2009

A first-order consistent approximation for the analysis of small deflections of membranes is given several variational formulations. Lower and upper bounds are derived for the volume enclosed by deformed and undeformed membranes. The power of the principles is discussed and their application is illustrated by some cases of practical interest. Explicit analytical results are given for linear elastic membranes having circular, elliptic, and rectangular contours.
Effects of Geometric Imperfections on Vibrations of Biaxially Compressed Rectangular Flat Plates
Authors: Hui David , Leissa A. W.
Published: July 2009

This paper deals with the effects of geometric imperfections on the vibration frequencies of simply supported flat plates under in-plane uniaxial or biaxial compression. The analysis is based on a solution of the nonlinear von Ka´rma´n equations for finite deflections, incorporating the influence of an initial geometric imperfection. It is found that significant increase in the vibration frequencies may occur for imperfection amplitude of the order of a fraction of the plate thickness, even in the absence of in-plane forces.
Numerical Simulation of Transient Finite Deformations of Thin Beams
Authors: Rodal J. J. A. , Steigmann D. J. , Witmer E. A.
Published: July 2009

The formulation of the problem of finite elastic-viscoplastic deformation of thin beams is described. The finite element analysis of a representative problem is presented and various solution methods are surveyed.
The Penny-Shaped Interface Crack With Heat Flow, Part 2: Imperfect Contact
Authors: Barber J. R. , Comninou Maria
Published: July 2009

The penny-shaped crack with heat flux is investigated for the case in which the heat flux is into the material with the lower distortivity. A harmonic potential function representation is used to reduce the problem to a boundary value problem which is solved by an integral equation method. If a sufficiently high tensile traction is applied, a solution is obtained involving a central circle of separation and surrounding annuli of imperfect and perfect thermal contact. For lower tractions, or higher heat fluxes, the crack closes completely and a closed-form solution is obtained in which the division of the crack face into imperfect and perfect contact regions is unaffected by further changes in heat flux or traction. Multiple solutions are obtained in an intermediate range.
The Stress Field in an Elastic Half Space Having a Spheroidal Inhomogeneity Under All-Around Tension Parallel to the Plane Boundary
Authors: Tsuchida E. , Mura T.
Published: July 2009

Stress distributions are evaluated for a semi-infinite elastic body having a spheroidal inhomogeneity under an all-around tension (axisymmetric uniform tension) at infinity. Boussinesq’s potential functions are used for the analysis. A special technique is employed for the traction-free condition on the free surface, where the ordinary Legendre functions are expressed in terms of the Bessel functions in cylindrical coordinates. A closed-form expression for the stress concentration factor is found for a special case of a needlelike inhomogeneity.
Index Evaluation for Dynamical Systems and Its Application to Locating All the Zeros of a Vector Function
Authors: Hsu C. S. , Guttalu R. S.
Published: July 2009

An index evaluation method is discussed in this paper. It can also serve as the basis of a procedure to locate all the zeros of a vector function. An application of the procedure is made to a strongly nonlinear point-mapping dynamical system in order to locate all the periodic solutions of period one and period two, 41 in total number.
Deterministic and Stochastic Aspects of Turbulence
Authors: Laufer J.
Published: July 2009

The recent active interest in the deterministic aspects of turbulent flows, referred to as coherent structures is discussed and justified. It is shown that this line of experimental research has yielded some important new results, and has provided new insight to the stochastic character of the flow as well as added new directions for further experimental and theoretical inquiry.
Equilibrium Solutions in Finite Elasticity
Authors: Shield R. T.
Published: July 2009

Some areas in the theory of large deformations of elastic bodies are surveyed. Strain energy functions for isotropic materials are discussed, with emphasis on rubberlike materials, and exact and approximate solutions for equilibrium states are described. The applicability of the energy method for the determination of the stability of elastic systems is reviewed and applications are cited.
The Generalized Finite Element Method—State of the Art and Future Directions
Authors: Zienkiewicz O. C.
Published: July 2009

This contribution reviews the present status of computational procedures in mechanics and indicates some of the areas in which research is active. The generality of the finite element method is stressed as the all-embracing approximation procedure and attention is focused on the need for developing efficient measures of accuracy and adaptive procedures for achievement of a specified precision. Developments aimed at improving the overall efficiency of computation are highlighted and some new areas of application indicated.
Stress Intensity Factors
Authors: Erdogan F.
Published: July 2009

In this paper the concept of the stress intensity factor, the underlying mechanics problem leading to its emergence, and its physical relevance, particularly its relation to fracture mechanics are discussed, the reasons as to why it has become nearly an indispensable tool for studying such important phenomena as brittle fracture and fatigue or corrosion fatigue crack propagation in structural solids are considered, a brief discussion of some of the important methods of solution of elastic crack problems is given, and a number of related special mechanics problems are described.
Regularization and Inverse Problems in Viscoelasticity
Authors: Hedstrom G. W. , Thigpen L. , Bonner B. P. , Worley P. H.
Published: July 2009

The method of constrained regularization is used to invert for retardation spectra and attenuation from the creep data of a commercial-grade lucite material. Four different criteria for choosing a regularization parameter in the solution of the first-kind integral equation are examined. Although the spectra are different, computations using each criterion give essentially the same attenuation curve for a range of frequencies. These results show that reliable estimates of the attenuation may be obtained from inversion of creep data using the method of constrained regularization.
A Nonlinear Theory for Elastic Plates With Application to Characterizing Paper Properties
Authors: Johnson M. W. , Urbanik T. J.
Published: July 2009

A theory of thin plates which is physically as well as kinematically nonlinear is developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a special theory having fewer parameters and being capable of characterizing paper. A procedure is given for matching the special theory to edgewise compressive data of paperboard.
General Characteristics of the Motion of Multiple-Pode Joints
Authors: Lee T. W. , Akbil E.
Published: July 2009

This paper presents an analytical method on the investigation of the motion characteristics of a class of spatial mechanical components involving the ball-and-trunnion type of joint, namely, the multiple-pode joint. Algebraic derivations of the input-output equation and explicit relations for motion parameters are presented for these joints as well as their shaft couplings. From this general displacement analysis, some insights into the basic nature and behavior of the multiple-pode joint are observed and interpreted. The creation of shaft couplings using these joints and their functional analysis are also illustrated in several cases.
Fully Plastic Crack Problems, Part 1: Solutions by a Penalty Method
Authors: Shih C. F. , Needleman A.
Published: July 2009

We formulate a finite-element reduced integration penalty method applicable to plane-strain problems with incompressible material behavior. This numerical method is employed to generate crack solutions for pure power-hardening solids. For two configurations of interest in applications, an edge cracked panel subject to remote tension and an edge-cracked panel subject to remote bending, we obtain solutions for a wide range of crack lengths and strain-hardening behaviors.
Steady Laminar Flows Between a Ball and a Spherical Cavity
Authors: Bellet D. , Ly D. P. , Milleret M.
Published: July 2009

Steady laminar flows of a newtonian fluid in the vicinity of a spherical ball located inside a spherical cavity are studied. Two methods were employed: a method involving a finite element calculation and an experimental method based on measurements of local velocities by means of laser Doppler anemometry using the Bragg cell. The influences of the Reynolds numbers and of the ball positions in the cavity have been analyzed and compared.
The Shear Modulus of Liquid Foam
Authors: Stamenovic D. , Wilson T. A.
Published: July 2009

A strain energy function for liquid foam is formulated by modeling foam as a collection of randomly oriented surfaces with surface tension on the faces. The surfaces are assumed to follow the mean strain. It is assumed that surface forces equilibriate between neighboring elements and hence that the value of surface tension γ is the same on all faces and a function of total surface area. In particular, an expansion of the strain energy function in powers of the strain is used to obtain the value for the shear modulus in the linear elasticity approximation. The predicted value of the shear modulus is 4/15 γS/ V where S/ V is the surface to volume ratio or 2/5 ΔP, where ΔP is the overpressure of the gas trapped in the foam. In rheometric tests, foam was found to behave as a viscoelastic material. The shear modulus that describes the initial elastic response was found to be about 84 percent of the predicted value.
Hydroelastic Instability of Infinite Strips Under Shearing Load on an Elastic Foundation
Authors: Tani J.
Published: July 2009

The paper examines the hydroelastic instability of an infinitely long plate subjected to shearing load with two different boundary conditions, one side of which is exposed to an incompressible inviscid flow, and the other side supported on an elastic foundation. The analysis is based on the small deflection plate theory and the classical linearized potential flow theory. The Galerkin method and Fourier transforms are used. It is found that the effects of the shearing load and the elastic foundation on the divergence velocity can be illustrated by a single curve for both clamped and simply supported cases.
Applications of Fractional Calculus to the Theory of Viscoelasticity
Authors: Koeller R. C.
Published: July 2009

The connection between the fractional calculus and the theory of Abel’s integral equation is shown for materials with memory. Expressions for creep and relaxation functions, in terms of the Mittag-Leffler function that depends on the fractional derivative parameter β, are obtained. These creep and relaxation functions allow for significant creep or relaxation to occur over many decade intervals when the memory parameter, β, is in the range of 0.05–0.35. It is shown that the fractional calculus constitutive equation allows for a continuous transition from the solid state to the fluid state when the memory parameter varies from zero to one.
Notch-Tip Stresses in a Creeping Solid
Authors: Bassani J. L.
Published: July 2009

At high stress levels the creep strain rate for many materials varies as the exponential of stress while at low stresses it varies as stress to some power. An analysis is presented for a sharp notch under antiplane shear loading in a material that deforms by hyperbolic-sine-law creep, ε˙c = ε˙0[sinh(σ/σ0)]n. The asymptotic notch-tip stress intensification is weaker and the strain-rate intensification is stronger than for a power-law creeping material.
An Investigation of Localization in a Porous Elastic Material Using Homogenization Theory
Authors: Abeyaratne R. , Triantafyllidis N.
Published: July 2009

In this work we use a consistent homogenization theory approach to study the overall behavior of a highly porous elastic material at finite levels of strain. Although the matrix material in the problem considered here remains elliptic at all deformations, the resulting “homogenized” material is found to admit a loss of ellipticity at sufficiently high strains, i.e., can fail in a localized shear mode.
Simplified Large Deflection Mode Solutions for Impulsively Loaded, Viscoplastic, Circular Membranes
Authors: Perrone N. , Bhadra P.
Published: July 2009

The title problem is solved by estimating the maximum strain rate field in a circular membrane associated with a modal velocity condition when one-half the kinetic energy in the system has been dissipated. The radial stress may only vary in the radial direction, but is taken as a constant with time at any given location. Internal plastic energy absorbed during the large deformation is found by integrating while accounting for rate sensitivity effects; this absorbed energy is equated to the initial kinetic energy in the system to obtain the final deformed configuration. Correlation of analytically determined results with a series of experiments reported elsewhere is very good. The procedure described here is potentially extendable to any planform membrane shape as well as to axisymmetric shells. The method is applicable to plate problems when membrane effects dominate over bending, that is for deformations of the order of two thicknesses or more. A simple general formula for final plate deformation is devised and also agrees well with experimental results.
Asymptotic Behavior of Heavy Column and Riser Stability Boundaries
Authors: Bernitsas M. M. , Kokkinis T.
Published: July 2009

Columns, marine risers, pipelines, hydraulic columns, and legs of tension leg platforms can be modeled for customary Euler buckling analysis by a single model which, in its most general form, applies to risers. Previous work has shown that numerical algorithms fail to provide stability boundaries for long risers. Asymptotic analyses for long columns have been developed as early as 1941 but the results are either incomplete or incorrect. The goals of this paper are to develop a long-column buckling theory, indicate errors in holding theories, and complete the numerical data available in the literature.
Gas-Gun Experiments Determine Forces on Penetrators Into Geological Targets
Authors: Forrestal M. J. , Lee L. M. , Jenrette B. D. , Setchell R. E.
Published: July 2009

We developed a convenient laboratory procedure to determine forces on projectiles penetrating geological targets. Gas guns were used to accelerate foundry core targets (a simulated soft sandstone) to steady velocities, and the targets subsequently impacted 20.6-mm-dia penetrators instrumented with piezoelectric accelerometers. Rigid-body acceleration data were recorded for one ogival and two conical nose shapes for impact velocities between 0.2-1.2 km/s.
Axisymmetric Solutions in Elastostatics and Elastic Wave Propagation by Ascent Methods
Authors: Norwood F. R.
Published: July 2009

In the present paper a method of ascent for axisymmetric problems is developed. It is shown that, for problems where the vector or scalar Laplacian operator specifies the space behavior of the potential functions, the three-dimensional axisymmetric problems may be solved by operating on the solution to an associated two-dimensional problem. Hence, the theoretical results presented here may be applied to heat transfer problems, to problems in elastostatics, and to elastic wave propagation problems.
Scattering of Elastic Waves by a Plane Crack of Finite Width
Authors: van der Hijden J. H. M. T. , Neerhoff F. L.
Published: July 2009

A rigorous theory of the diffraction of time-harmonic elastic waves by a cylindrical, stress-free crack embedded in an elastic medium is presented. The incident wave is taken to be either a P-wave or an SV-wave. The resulting boundary-layer problem for the unknown jump in the particle displacement across the crack is solved by employing an integral-equation approach. The jump is expanded in a complete sequence of Chebyshev polynomials, and, writing the Green’s function as a Fourier integral, a system of algebraic equations is obtained. Numerical results are presented in the form of dynamic stress intensity factors, scattering cross sections, and normalized power-scattering characteristics. Some of them deviate from earlier published results.
Observation and Evolution of Chaos for an Autonomous System
Authors: Dowell E. H.
Published: July 2009

Time histories, phase plane portraits, power spectra, and Poincare maps are used as descriptors to observe the evolution of chaos in an autonomous system. Although the motions of such a system can be quite complex, these descriptors prove helpful in detecting the essential structure of the motion. Here the principal interest is in phase plane portraits and Poincare maps, their methods of construction, and physical interpretation. The system chosen for study has been previously discussed in the literature, i.e., the flutter of a buckled elastic plate in a flowing fluid.
An Integral Equation Method for the First-Passage Problem in Random Vibration
Authors: Madsen P. H. , Krenk S.
Published: July 2009

The first-passage problem for a nonstationary stochastic process is formulated as an integral identity, which produces known bounds and series expansions as special cases, while approximation of the kernel leads to an integral equation for the first-passage probability density function. An accurate, explicit approximation formula for the kernel is derived, and the influence of uni or multi modal frequency content of the process is investigated. Numerical results provide comparisons with simulation results and alternative methods for narrow band processes, and also the case of a multimodal, nonstationary process is dealt with.
On Laminar Thin-Film Flow Along a Vertical Wall
Authors: Roy T. R.
Published: July 2009

An accelerating laminar thin-film flow along a vertical wall is investigated in this paper. Using a cubic polynomial for the velocity profile inside the boundary layer the momentum integral equation is solved by a Runge-Kutta method to determine the boundary layer thickness. The corresponding film-thickness is then calculated for the entrance region. These results are compared with the existing results obtained by using a parabolic velocity profile.
Plane Anisotropic Thermoelasticity
Authors: Wu C. H.
Published: July 2009

The problem is formulated in terms of the three pairs of eigenvalues of the elasticity constants and the pair of eigenvalues of the heat conduction constants. Special attentions are given to the cases where the latter eigenvalue pair becomes equal to one or more pairs of the former group. The problem of a crack in an infinite medium is used as an example and solved exactly. This solution, however, is valid only for the case where the four pairs of eigenvalues are distinct.
Theory of Orthotropic and Composite Cylindrical Shells, Accurate and Simple Fourth-Order Governing Equations
Authors: Cheng Shun , He F. B.
Published: July 2009

A pair of complex conjugate fourth-order differential equations that govern the deformation of orthotropic circular cylindrical shells is presented. As shown in the paper, this pair of equations is as accurate as equations can be within the scope of the Kirchhoff assumptions. Also presented for the first time are several pairs of accurate and simple fourth-order equations which can be systematically and explicitly deduced from the previously mentioned pair of equations. Because of their accuracy and simplicity, these simple equations are of practical importance. The advantage in applying those fourth-order equations presented herein is that their solutions can be easily found in simple closed forms. This considerably simplifies calculations for solving problems of orthotropic and composite cylindrical shells as well as isotropic shells as a special case. Unlike other equations known in the literature, their general solutions remain unknown because of the algebraic complexities involved. The present method of deducing simple fourth-order equations improves upon the one used for isotropic shells in the first author’s previous paper entitled “Accurate Fourth-Order Equations for Circular Cylindrical Shells,” Journal of the Engineering Mechanics Division, ASCE, 1972.
Oscillatory Structured Shock Waves in a Nonlinear Elastic Rod With Weak Viscoelasticity
Authors: Sugimoto N. , Yamane Y. , Kakutani T.
Published: July 2009

The propagation of longitudinal shock waves in a thin circular viscoelastic rod is investigated theoretically as the counterpart of the torsional shock waves previously considered in [1, 2]. Assuming a “nearly elastic” rod, the approximate equation is first derived by taking account of not only the finite deformation but also the lateral contraction or dilatation of rod. The latter gives rise to the geometrical dispersion, which is taken in the form of Love’s theory for an elastic rod. Taking two typical relaxation functions, the structures of the steady shock waves are investigated in detail, one being the exponential function type and the other the power function type. The effect of geometrical dispersion is emphasized. Finally a brief discussion is included on the simplified evolution equations for a far field behavior.
Three-Dimensional Analysis of Axisymmetric Transient Waves in Hollow Elastic Cylinders
Authors: Sva¨rdh P.-A.
Published: July 2009

The axially symmetric problem of a semi-infinite, hollow, linear-elastic circular cylinder with traction-free lateral surfaces initially at rest and subjected to transient end loadings is solved using three-dimensional theory. Two cases are treated: an axial pressure applied to a radially clamped end and a prescribed axial velocity applied to an end that is free from shear stress. A double integral transform technique is used, and asymptotic solutions valid at large distances from the end are given for two types of time variation of the end loadings: step function and finite rise time function. A necessary condition for the validity of the asymptotic result is given.
The Exact Solution to an Ablation Problem With Arbitrary Initial and Boundary Conditions
Authors: Tao L. N.
Published: July 2009

The problem of ablation by frictional heating in a semi-infinite solid with arbitrarily prescribed initial and boundary conditions is investigated. The study includes all convective motions caused by the density differences of various phases of the materials. It is found that there are two cases: (i) ablation appears immediately and (ii) there is a waiting period of redistribution prior to ablation. The exact solutions of velocities and temperatures of both cases are derived. The solutions of the interfacial positions are also established. Existence and uniqueness of the solutions are examined and proved. The conditions for the occurrence of these two cases are expressed by an inequality. Physical interpretation of the inequality is explored. Its implication coincides with one’s expectation. Ablation appears only when the surface temperature is at or above the melting temperature.
Dynamic Stability of a Nonlinear Cylindrical Shell
Authors: Tylikowski A.
Published: July 2009

The stability of the undeflected middle surface of a uniform elastic cylindrical shell governed by Ka´rma´n’s equations is studied. The shell is being subjected to a time-varying axial compression as well as a uniformly distributed time-varying radial loading. Using the direct Liapunov method sufficient conditions for deterministic asymptotic as well as stochastic stability are obtained. A relation between stability conditions of a linearized problem and that of Ka´rma´n’s equations is found. Contrary to the stability theory of nonlinear plates it is established that the linearized problem should be modified to ensure the stability of the nonlinear shell. The case when the shell is governed by the Itoˆ stochastic nonlinear equations is also discussed.
Oscillations of a Self-Excited, Nonlinear System
Authors: Hall S. A. , Iwan W. D.
Published: July 2009

A system of self-excited, nonlinear differential equations exhibiting frequency entrainment is studied. Although similar equations describe electrical oscillators and machine-tool chattering, the results presented herein apply specifically to a model for the vortex-induced oscillation of linear structures. The equations are treated analytically by an approximate method, and two cases — partial nonlinear coupling and full nonlinear coupling — are identified. As applied to vortex-induced oscillations, the partially coupled case describes a structure having a single mode of oscillations, while the fully coupled case approximates continuous systems, such as undersea cables. Solutions for each case are examined for stability, and the results reveal several new types of behavior.
Effects of Warping and Pretwist on Torsional Vibration of Rotating Beams
Authors: Kaza K. R. V. , Kielb R. E.
Published: July 2009

The effect of pretwist and warping on the torsional vibration of short-aspect-ratio rotating beams is examined for application to the modeling of turbofan, turboprop, and compressor blades. The equations of motion and the associated boundary conditions by using both Wagner’s hypothesis and Washizu’s theory are derived and a few minor limitations of the Wagner’s hypothesis, as applied to thick blades, are pointed out and discussed. The equations for several special cases are solved in a closed form. Results are presented indicating the effect of warping, pretwist, and rotation on torsional vibration of beams as aspect ratio is varied. The results show that the structural warping and pretwist terms have a significant effect on torsional frequency and mode shapes of short-aspect-ratio blades whereas the inertial warping terms have negligible effect. Since the torsional frequencies and mode shapes are very important in aeroelastic analyses by using modal methods, the structural warping terms should be included in modeling turbofan, turboprop, compressor, and turbine blades.