bluuebunny/crossref_metadata_2025 huggingface dataset:
Analysis of Orthogonally Cracked Laminates Under Tension
Authors: Hashin Z.
Published: July 2009

The problems of stiffness reduction and stress analysis of cross-ply fiber composite laminates, where all plies are cracked in fiber directions, are treated by a variational method on the basis of the principle of minimum complementary energy. The Young’s modulus obtained is a strict lower bound but is expected to be close to the true value on the basis of experience with a previous analysis. Approximate values of Poisson’s ratio and internal stresses have been obtained. The latter reveal important tendencies of continued failure by delamination.
Effective Medium Approach to Matrix-Inclusion Type Composite Materials
Authors: Nomura S.
Published: July 2009

This paper addresses a problem of finding the effective medium that exhibits the same overall response as a given composite material reinfored by unidirectional short-fibers (chopped fibers). The expression for the displacement field in composites is obtained by converting the equilibrium equation into an integro-differential equation using the quasi-static Green’s function for a homogeneous medium. The “effective medium” is chosen that the ensemble averaged displacement field for the composite is equal to that of an equivalent homogenous medium. The “effective stiffness” and the “effective mass density” are defined as those properties of the effective medium. This is a first preliminary attempt to analyze the elasto-dynamic effect of matrix-inclusion type of composites. The obtained result for the effective stiffness is new and is not symmetrical with the interchange of the matrix phase and the fiber phase, unlike previous models. The result is also favorably compared with experimental data for spherical-inclusion reinforced composites.
The Wrinkling of Thin Membranes: Part II—Numerical Analysis
Authors: Roddeman D. G. , Drukker J. , Oomens C. W. J. , Janssen J. D.
Published: July 2009

Using a weighted residual method, a geometrically and physically nonlinear membrane element is derived, which can be used in the analysis of anisotropic membranes. What is special about the formulation is that the wrinkling behavior of the element is incorporated. If wrinkling occurs the stress situation in the element is determined by making use of a modified deformation tensor. A structure may have completely slack regions, leading to a singular stiffness matrix. Because of this we have chosen to use a restricted step method for the iterative solution procedure. A simple shear test is used to compare numerical and analytical results which show good agreement.
A Method to Improve the Modal Convergence for Structures With External Forcing
Authors: Gu Keqin , Tongue Benson H.
Published: July 2009

The traditional approach of using free vibration modes in the assumed mode method often leads to an extremely slow convergence rate, especially when discete interactive forces are involved. By introducing a number of forced modes, significant improvements can be achieved. These forced modes are intrinsic to the structure and the spatial distribution of forces. The motion of the structure can be described exactly by these forced modes and a few free vibration modes provided that certain conditions are satisfied. The forced modes can be viewed as an extension of static modes. The development of a forced mode formulation is outlined and a numerical example is presented.
Coupled Gas-Liquid-Structure Systems: Part 1—Theory
Authors: Joos F. M. , Huber P. W.
Published: July 2009

A complex hydrodynamic transient due, for example, to the injection of gas into a liquid, creates pressure forces on adjacent structures. These structures, together with gas cavities in the liquid itself, represent flexible boundaries to the distributed, time-varying liquid mass. The response of the gas-liquid-structure system depends on the intrinsic flexibility of the gas cavities and on the flexibility of structural boundaries. In this paper we analyze the dynamics of such systems where the liquid is incompressible. We present systematic procedures for driving the response of one system from the known response of a geometrically identical system with different flexibility. Finally, we outline the analysis for the compressible case.
Finite Deformation and Nonlinear Elastic Behavior of Flexible Composites
Authors: Luo Shen-Yi , Chou Tsu-Wei
Published: July 2009

The flexible composites discussed in this paper are composed of continuous fibers in an elastomeric matrix. The usable range of deformation of these composites is much larger than that of conventional rigid composites. Due to the material as well as geometric factors, the stress-strain relations for these composites are generally nonlinear under finite deformations. A constitutive model has been developed based upon the Eulerian description. The material nonlinear stress-strain relation is derived by using the stress energy density referring to the deformed volume. The stretching-shear coupling and the effects of the in-plane reorientation of fibers are also considered in the theoretical analysis. Comparisons are made between predictions of the present theory and experimental data for tirecord/rubber and Kevlar/silicone-elastomer flexible composite laminae; very good correlations have been found.
Nonlinear Composite Beam Theory
Authors: Bauchau O. A. , Hong C. H.
Published: July 2009

The modeling of naturally curved and twisted beams undergoing arbitrarily large displacements and rotations, but small strains, is a common problem in numerous engineering applications. This paper has three goals: (1) present a new formulation of this problem which includes transverse shearing deformations, torsional warping effects, and elastic couplings resulting from the use of composite materials, (2) show that the small strain assumption must be applied in a consistent fashion for composite beams, and (3) present some numerical results based on this new formulation to assess its accuracy, and to point out some distinguishing feature of anisotropic beam behavior. First, the predictions of the formulation will be compared with experimental results for the large deflections and rotations of an aluminum beam. Then, the distinguishing features of composite beams that are likely to impact the design of rotating blades (such as helicopter blades) will be discussed. A first type of extension-twisting coupling introduced by the warping behavior of a pretwisted beam is discussed, then, a shearing strain squared term, usually neglected in small strain analyses, is shown to introduce a coupling between axial extension and twisting behavior, that can be significant when the ratio E/G is large (E and G are Young’s and shearing moduli of the beam, respectively). Finally, the impact of inplane shearing modulus changes and torsional warping constraints on the behavior of beams exhibiting elastic couplings is investigated.
Representation of Mechanical Behavior in the Presence of Changing Internal Structure
Authors: Onat E. T. , Leckie F. A.
Published: July 2009

The paper is concerned with the representation of the relationship that exists, for a given material and temperature and for small deformations, between histories of applied stress and the observed strain and the accompanying changes in internal structure of the material. Emphasis is given to creep damage in metals as a vehicle for illustration of the main ideas introduced in the paper. In particular, the role played by irreducible even rank tensors in the representation of internal structure is discussed and clarified. The restrictions placed by thermodynamics on constitutive equations are considered and the use of potentials in these equations is examined and criticized.
Continuum Damage Mechanics: Part I—General Concepts
Authors: Chaboche J. L.
Published: July 2009

Continuum Damage Mechanics (C.D.M.) has developed continuously since the early works of Kachanov and Rabotnov. It constitutes a practical tool to take into account the various damaging processes in materials and structures at a macroscopic continuum level. The main basic features of C.D.M. are considered in the first part together with its present capabilities, including damage definitions and measures, and its incorporation into a thermodynamic general framework. Practical damage growth equations will be reviewed in the second part of the paper.
Laser-Induced Heating of a Multilayered Medium Resting on a Half-Space: Part I—Stationary Source
Authors: Kant R.
Published: July 2009

Laser induced heating of a multilayered medium resting on a homogeneous half-space is considered. The transient heat transfer equation is solved by employing the Laplace transform in the time domain and the Hankel transform in the space domain (r direction). Numerical inversion of the Laplace transform is obtained by using a technique developed by Crump. For the time intervals of interest, inversion of the Hankel transform is obtained by the Simpson rule. Application to magneto-optical recording is discussed.
Elastic Fracture Mechanics Concepts for Interfacial Cracks
Authors: Rice J. R.
Published: July 2009

Elastic fracture mechanics concepts are reexamined for a crack on the interface between dissimilar solids. A derivation by function theory is given of the form of stress and displacement fields in the vicinity of the crack tip, equivalent to complete Williams expansions of both inner and outer (external to a nonlinear or contact zone) type. The complex stress intensity factor K associated with an elastic interface crack, for which contact is ignored, is discussed and, specifically, its validity as a crack tip characterizing parameter is noted for cases of small scale nonlinear material behavior and/or small scale contact zones at the crack tip. That is, similar values of K for two cracked bodies then imply similar states as the crack tip, so that conditions for crack growth can be phrased in terms of K reaching a critical failure locus in a complex plane. The maintenance of a similar state at a crack tip under change of crack length is shown to require alteration of both the magnitude and phase angle of a combined tension and shear loading. Some possible definitions of stress intensity factors KI and KII of classical type associated with interface cracks are discussed. Also, the scaling of interface crack tip plastic zone size with load under small scale yielding conditions is found to deviate from classical scaling, in proportion to the square of the applied load level, and dependences of the field on distance from the tip and on load phase angle are found to be linked together.
Some Exact and Approximate Solutions for the Modified von Mises Yield Criterion
Authors: Lee J. H.
Published: July 2009

The effects of Strength Differential (SD) and plastic compressibility for materials obeying the modified von Mises yield criterion were exemplified by solving two boundary-value problems. The assumptions of associated plasticity (leading to maximum plastic volume increase) and nonassociated plasticity (leading to zero plastic volume increase) were used for comparative studies on the effects of plastic compressibility. The solutions for compression processes showed that SD effects increased the pressure at initial yielding and at failure, as well as increased the capacity of the materials to withstand plastic deformations. The opposite was true for tension processes. For associated and nonassociated plasticity, upper and lower bounds for stresses and strains for load and stroke-controlled situations were indicated. The results also showed unrealistic restrictions on the Poisson’s ratio and C/T for nonassociated plasticity under certain conditions. Hence, plastic volume increase, although small, should be incorporated into a more realistic plasticity model.
Dynamic Spherical Cavity-Expansion in a Compressible Elastic-Plastic Solid
Authors: Forrestal M. J. , Luk V. K.
Published: July 2009

We developed an analytical model for the elastic-plastic response of a compressible material from the uniform expansion of a spherically symmetric cavity. Previous models consider the material as incompressible. Numerical results from both models showed the effect of compressibility.
Generalized Coupled Transient Thermoelastic Plane Problems by Laplace Transform/Finite Element Method
Authors: Chen Tei-Chen , Weng Cheng-I
Published: July 2009

A general finite-element model is proposed to deal with dynamic theromelastic problems especially with longer transient period. The method consists of formulating and solving the problem in the Laplace transform domain by the Finite Element Method (FEM) and then numerically inverting the transformed solution to obtain the time-domain response. Therefore, the transient solutions at any time could be evaluated directly. A number of examples are presented which demonstrate the accuracy, efficiency, and versatility of the proposed method, and show the effects of relaxation times, inertia, and thermoelastic coupling terms.
A Fast Eigenfunction Approach for Computing Spinning Disk Deflections
Authors: Cole Kevin A. , Benson Richard C.
Published: July 2009

Due to a complicated spectrum of natural modes of vibration, flexible spinning disks are very sensitive to transverse loading, and deflections have been difficult to compute. Developed in this paper is an efficient technique for determining the forced response from space fixed loads. Using an eigenfunction expansion, we are able to identify, a priori, those modes which are most important to the overall response. By ignoring unimportant modes we are able to coverge upon a numerical solution with a speed that is orders of magnitude faster than other commonly used techniques.
Stochastic Sample Stability of Oscillatory Systems
Authors: Ariaratnam S. T. , Xie W.-C.
Published: July 2009

A method of obtaining a sufficient almost-sure asymptotic stability condition for second-order, linear oscillatory systems with an ergodic damping coefficient is presented. In this method, the probabilistic property of the derivative process of the damping coefficient is taken into account. A sufficient condition for almost-sure asymptotic stability is derived and numerical results are presented for the case of a Gaussian noise coefficient. The results are found to be an improvement over previously available results for oscillatory systems with stochastic damping.
A Continuum Damage Model for Viscoelastic Materials
Authors: Weitsman Y.
Published: July 2009

This paper presents a continuum damage model for viscoelastic materials. “Damage” is expressed by two symmetric, second rank tensors which are related to the total areas of “active” and “passive” microcracks within a representative volume element of the multifractured material. Viscoelasticity is introduced through scalar valued internal state variables that represent the internal degrees-of-freedom associated with the motions of long chain polymeric molecules. The constitutive relations are established from basic considerations of continuum mechanics and irreversible thermodynamics, with detailed expressions derived for the case of initially isotropic materials. It is shown that damage causes softening of the material moduli as well as changes in material symmetry. The special cases of uniaxial damage under uniaxial stress and the interaction of damage with moisture diffusion are also considered.
Stresses in Dual-Coated Optical Fibers
Authors: Suhir E.
Published: July 2009

We examine several problems related to the mechanical behavior of dual-coated optical fibers: low temperature microbending, evaluation of spring constant due to coating layers, strength of the end portions of fibers clamped in termination fixtures, and prediction of stresses caused by the misalignment of the openings in the frame and the termination fixture. The developed formulas are simple, easy-to-use and clearly indicate the role of the major factors affecting the mechanical behavior of the fibers. The obtained results can be of help in physical design of dual-coated fibers and optical interconnections.
Effect of Interface Layers on Scattering of Elastic Waves
Authors: Paskaramoorthy R. , Datta S. K. , Shah A. H.
Published: July 2009

Scattering of elastic waves by spheroidal elastic inclusions has been studied in this paper. Particular attention has been focused on the effect of interface layers between the inclusions and the matrix on the scattering cross-sections. It has been assumed that properties of each layer is constant through its thickness. For spheroidal inclusion this problem cannot be solved by exact means. We have used a hybrid finite element and wave function expansion technique to analyze the problem. It is shown that solutions thus obtained for spherical inclusions and cavities agree well with analytical solutions. For spheroidal inclusions we show that when the interface layer properties are intermediate between those of the particles and the matrix the scattering cross-section increases. These results can be useful in characterizing interface layer properties.
The Normal Impact of a Rod-Mass System on a Viscoelastic Layered Half Space
Authors: Downey H. A. , Bogy D. B.
Published: July 2009

A rod with a lumped mass attached to its trailing end travels axially with a uniform velocity and strikes an elastic half space that is covered with an adhering viscoelastic layer. The problem is reduced to integral equations for the average contact stress and the displacement of the rod tip into the contact surface. The kernels of these integral equations are composed of temporal Green’s functions for the rod and the layered half space, which represent the response of each to an impulsive uniform normal traction. The Green’s function for the rod is obtained in closed form, while that for the layered half space is obtained through a numerical Laplace transform inversion. The integral equations are solved numerically with a second-order stable scheme. Solutions are computed for a wide variety of materials and configurations, providing the stress and displacement history, as well as the stress-displacement response. The results show the effects of changes in rod material and length, lumped mass, layer material, substrate material, and viscoelastic material parameters.
Some Observations on the Random Response of an Elasto-Plastic System
Authors: Paparizos L. G. , Iwan W. D.
Published: July 2009

The nature of the response of strongly yielding systems subjected to random excitation, is examined. Special attention is given to the drift response, defined as the sum of yield increments associated with inelastic response. Based on the properties of discrete Markov process models of the yield increment process, it is suggested that for many cases of practical interest, the drift can be considered as a Brownian motion. The approximate Gaussian distribution and the linearly divergent mean square value of the process, as well as an expression for the probability distribution of the peak drift response, are obtained. The validation of these properties is accomplished by means of a Monte Carlo simulation study.
The Meniscus Instability of a Thin Liquid Film
Authors: Koguchi H. , Okada M. , Tamura K.
Published: July 2009

This paper reports on the instability for the meniscus of a thin film of a very viscous liquid between two tilted plates, which are separated at a constant speed with a tilt angle in the normal direction of the plates. The disturbances on the meniscus moving with movement of the plates are examined experimentally and theoretically. The disturbances are started when the velocity of movement of the plates exceeds a critical one. The wavelength of the disturbances is measured by using a VTR. The instability of the meniscus is studied theoretically using the linearized perturbation method. A simple and complete analytical solution yields both a stability criterion and the wave number for a linear thickness geometry. These results compared with experiments for the instability show the validity of the stability criterion and the best agreement is obtained with the wave number of maximum amplification.
Structural Decomposition Approach for the Stability of Uncertain Dynamic Systems
Authors: Chen Y. H. , Hsu Chieh
Published: July 2009

The stability property for a class of dynamic systems with uncertain parameter variation is studied. The uncertainty can be fast time-varying and unpredictable. A new approach for stability study is proposed. The only required information on the uncertain variation is its possible bound as well as structure. That is, no a priori knowledge on the realization of the variation is needed.
A Generalization of the Upper Bound Method With Particular Reference to the Problem of a Ploughing Indenter
Authors: Azarkhin A. , Richmond O.
Published: July 2009

An algorithm based on a combination of the upper bound method and finite element repesentation has been developed. The algorithm is applied to the problem of a rigid indenter ploughing through a rigid/perfectly-plastic material. Numerical examples are given and the results are compared with previous approximate solutions. Limitations of the upper bound method are discussed.
Buckling of Edge Damaged, Cylindrical Composite Shells
Authors: Sabag M. , Stavsky Y. , Greenberg J. B.
Published: July 2009

The stability of thin composite layered anisotropic cylindrical shells under axial compression is considered for the case of nonuniform boundary conditions. Such conditions are employed to model the situation where there is edge damage to the shell. The influence of weakening or a crack at an edge on the critical buckling load of a variety of single and multilayered shells is investigated. Results indicate that isotropic shells exhibit a rather sudden steep reduction in the critical buckling load for relatively small edge damage. However, some anisotropic composite shells may not be so sensitive and, in contrast, only a gradual reduction may be brought about by the edge damage. The degree of sensitivity to edge damage appears to be dependent, in some complex fashion, on the various geometric and physical shell parameters.
An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems
Authors: Cameron T. M. , Griffin J. H.
Published: July 2009

A method is proposed for analyzing the steady-state response of nonlinear dynamic systems. The method iterates to obtain the discrete Fourier transform of the system response, returning to the time domain at each iteration to take advantage of the ease in evaluating nonlinearities there—rather than analytically describing the nonlinear terms in the frequency domain. The updated estimates of the nonlinear terms are transformed back into the frequency domain in order to continue iterating on the frequency spectrum of the steady-state response. The method is demonstrated by solving a problem with friction damping in which the excitation has multiple discrete frequencies.
On the Stability Behavor of Bifurcated Normal Modes in Coupled Nonlinear Systems
Authors: Pak C. H.
Published: July 2009

The stability of bifurcated normal modes in coupled nonlinear oscillators is investigated, based on Synge’s stability in the kinematico-statical sense, utilizing the calculus of variations and Floquet’s theory. It is found, in general, that in a generic bifurcation, the stabilities of two bifurcated modes are opposite, and in a nongeneric bifurcation, the stability of continuing modes is opposite to that of the existing mode, and the stabilities of the two bifurcated modes are equal but opposite to that of the continuing mode. Some examples are illustrated.
Analysis of Steady Compaction Waves in Porous Materials
Authors: Powers J. M. , Stewart D. S. , Krier Herman
Published: July 2009

A two-phase continuum mixture model is used to analyze steady compaction waves in porous materials. It is shown that such a model admits both subsonic and supersonic steady compaction waves in response to a piston-driven boundary condition when a Tait equation is used to describe a solid matrix material and a generic static compaction relation is used to describe collapse of the matrix. Parameters for the Tait equation are chosen to match shock and compaction wave data. The model is able to predict compaction wave speed, final pressure, and final volume fraction in porous HMX. The structure of the compaction wave is also studied. A shock preceding the compaction wave structure is predicted for compaction waves travelling faster than the ambient sound speed of the solid. For subsonic compaction waves no leading shock is predicted. The compaction zone length is studied as a function of initial volume fraction, piston velocity, and compaction viscosity.
Response and Stability of a Random Differential Equation: Part I—Moment Equation Method
Authors: Benaroya H. , Rehak M.
Published: July 2009

A linear stochastic differential equation of order N excited by an external random force and whose coefficients are white noise random processes is studied. The external force may be either white or colored noise random process. Given the statistical properties of the coefficients and of the force, equivalent statistics are obtained for the response. The present solution method is based on the derivation of the equation governing the response autocorrelation function. The simplifying assumption that the response is stationary when the coefficients and input force are stationary is introduced. Another simplification occurs with the assumption that the response is uncorrelated from the random coefficients. Closed-form solutions for the response autocorrelation function and spectral density are derived in conjunction with a stability bound.
Response and Stability of a Random Differential Equation: Part II—Expansion Method
Authors: Benaroya H. , Rehak M.
Published: July 2009

A linear stochastic differential equation of order N with colored noise random coefficients and random input is studied. An approximate expression for the autocorrelation of the response is derived in terms of the statistical properties of the random coefficients and input. This is achieved by using an expansion method known as the Born expansion (Feynman, 1962). Feynman diagrams are used as a short hand notation. In the particular case where the coefficients are white noise processes, the expansion method yields identical results to those obtained using an alternate method in a companion paper (Benaroya and Rehak, 1989). The expansion method is also used to demonstrate that white noise coefficients are statistically uncorrelated from the response.
An Asymptotic Analysis of Cold Sheet Rolling
Authors: Smet Robert P. , Johnson Robert E.
Published: July 2009

We examine the plane strain cold rolling problem of thin strip implementing a perturbation scheme upon the governing equations. The analysis accounts for transverse variations in the flow and inhomogeneous work hardening. We establish deformation regimes based upon the parameters μ, the friction coefficient, τ, the ratio of the initial yield stress and the maximum roll pressure, and δ, a measure of the small gap reduction. We see that the inclusion of these inhomogeneous effects gives mildly different results for values of μ/τ > 0(1) or τ δ/μ = 0(1). We gauge these effects by examining the roll pressure, shear stress, longitudinal stress, yield stress, front and back tensions and torque to see how they are affected by the inclusion of inhomogeneous flow effects.
A Mesomechanical Model for Brittle Deformation Processes: Part I
Authors: Krajcinovic Dusan , Sumarac Dragoslav
Published: July 2009

The discussion centers on the formulation of a constitutive model for brittle solids satisfying two conflicting requirements: simplicity and accuracy. Owing to the inherent complexity oif the problem, stemming from the random distribution of interacting defects, analytical expressions relating macrofields are possible only under some restrictive conditions emphasizing modest levels of defect concentrations.
The Hemispheroidal Inhomogeneity at the Free Surface of an Elastic Half Space
Authors: Kouris D. , Tsuchida E. , Mura T.
Published: July 2009

A series solution is presented for a hemispheroidal elastic inhomogeneity at the free surface of an elastic half space. The loading is either all around tension at infinity, perpendicular to the axis of symmetry of the inhomogeneity, or uniform, nonshear type eigenstrains sustained by the inhomogeneity. The displacement potentials of Boussinesq are used to represent the solution and several numerical calculations are performed to illustrate the results.
Wedge-Apex Crack in an Angularly Inhomogeneous Wedge
Authors: Wu Chein H. , Chen Chao-Hsun
Published: July 2009

An edge crack surrounded by a slender, triangularly-shaped elastic inclusion is used to represent an experimentally-observed crack layer generated by constant amplitude fatigue conditions. Approximate but explicit formula is derived for the stress-intensity factor. As a byproduct, the exact stress-intensity factor for the title problem is explicitly obtained.
Multiple Region Contact Solutions for a Flat Indenter on a Layered Elastic Half Space: Plane-Strain Case
Authors: Shield T. W. , Bogy D. B.
Published: July 2009

The plane-strain problem of a smooth, flat rigid indenter contacting a layered elastic half space is examined. It is mathematically formulated using integral transforms to derive a singular integral equation for the contact pressure, which is solved by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with two or three contact regions. The parameter space divisions between the one, two, or three contact region solutions depend on the material and geometrical parameters and they are found for both the one and two layer cases. As the modulus of the substrate decreases to zero, the two contact region solution predicts the expected result that contact occurs only at the corners of the indenter. The three contact region solution provides an explanation for the nonuniform approach to the half space solution as the layer thickness vanishes.
A Tension Crack Impinging Upon Frictional Interfaces
Authors: Dollar Anna , Steif Paul S.
Published: July 2009

A crack impinging normally upon a frictional interface is studied theoretically. We employ a solution technique which superposes the solution of a crack in a perfectly-bonded elastic medium with a continuous distribution of dislocations which represent slippage at the frictional interface. This procedure reduces the problem to a singular integral equation which is solved numerically. Specifically, we consider the problem of an infinite sheet subjected to uniaxial tension containing a finite crack which lies normal to the tension axis and has both crack tips impinging normally on frictional interfaces. The limiting problem of a semi-infinite crack impinging on a frictional interface is considered as well. Posed as model problems for cracking in weakly bonded fiber composites, these studies reveal the effective blunting that can result when a weak interface serves to deflect a propagating crack.
The Membrane Shell as an Underconstrained Structural System
Authors: Kuznetsov E. N.
Published: July 2009

Statical-kinematic analysis is employed to provide a new perspective on the structural behavior of membrane shells and the related limitations of the linear membrane theory. The obtained results include a resolution of an apparent paradox in the statics of membranes, a description and explanation of the peculiar behavior of toroidal membranes with an arbitrary cross-section, and a stronger version of a central theorem in the membrane theory.
Thick General Shells Under General Loading
Authors: Donnell Lloyd H.
Published: July 2009

Three equilibrium equations in terms of three displacements are derived in scalar mathematics form, by linear, small-strain elasticity principles, for the case of general thick-walled shells under general loading. These reduce to well-known forms for the particular cases of flat-plates and thick circular cylindrical shells.
Thermal Expansion of Three-Phase Composite Materials
Authors: Dvorak George J. , Chen Tungyang
Published: July 2009

Exact expressions are found for overall thermal expansion coefficients of a composite medium consisting of three perfectly-bonded transversely isotropic phases of cylindrical shape and arbitrary transverse geometry. The results show that macroscopic thermal expansion coefficients depend only on the thermoelastic constants and volume fractions of the phases, and on the overall compliance. The derivation is based on a decomposition procedure which indicates that spatially uniform elastic strain fields can be created in certain heterogeneous media by superposition of uniform phase thermal strains with local strains caused by piecewise uniform stress fields, which are in equilibrium with prescribed surface tractions. The procedure also allows evaluation of thermal stress fields in the aggregate in terms of known local fields caused by axisymmetric overall stresses. Finally, averages of local fields are found with the help of known mechanical stress and strain concentration factors.
An Asymptotic Analysis of Three-Dimensional Extrusion
Authors: Aravas N. , McMeeking R. M.
Published: July 2009

A new method of analysis of three-dimensional metal extrusion using asymptotic perturbation methods is presented in this paper. The plasticity model used depends on the first and second invariants of the stress tensor and covers a wide range of constitutive models commonly used for the analysis of metal-forming operations. It is shown that the three-dimensional extrusion problem can be approximated, to leading order, by a problem of generalized plane-strain. The results of the asymptotic analysis together with the finite element method are used to obtain approximate solutions for extrusions of elliptic or square cross-sections from round billets.
Squeeze Film Behavior for Anisotropic Porous Rectangular Plates
Authors: Wheeler A. B. , Balasubramanyam R.
Published: July 2009

The squeeze film between two rectangular plates when one has a porous facing is analyzed taking into account the anisotropic permeability and slip velocity at the fluid and porous material interface. Modified equations for calculating the pressure, the load carrying capacity, and the film thickness and time relations are presented. The effect of the anisotropic permeability and slip velocity at the fluid and porous material interface on the squeeze film behavior is discussed and found to be important.
Surface Displacements and Stress Field Generated by a Semi-Ellipsoidal Surface Inclusion
Authors: Cox Brian N.
Published: July 2009

This paper presents calculations of the displacement and stress fields generated by semi-ellipsoidal surface inclusions containing uniform transformation strains or eigenstrains. The inclusion is assumed to have the same elastic constants as the rest of the material. This is a reasonable assumption for modeling transformed zones in transformation toughened ceramics and localized plasticity in individual surface grains in alloys. Analytical results are obtained for special cases and numerical results for general cases. The approach is particularly useful for accurately calculating the anomalous fields at the intersection of the boundary of the inclusion and the free surface. It is shown that, in many physically important cases, all components of the stress tensor are zero or constant on the free surface within the inclusion. For shallow inclusions or inclusions of general geometry suffering volume conserving transformation strains, the stress fields are also approximately uniform throughout the inclusion. This result greatly simplifies modeling of localized deformation in certain materials under complex external loads.
Simultaneous Optimization of Beams and Their Elastic Foundations for Minimum Compliance
Authors: Plaut R. H.
Published: July 2009

Nonuniform beams on nonuniform elastic foundations are considered. The beams have sandwich cross-sections with cores of negligible stiffness and are subjected to a uniformly distributed load. The total volume of the beam and the total stiffness of the foundation (which may include elastic supports) are specified. Both the cross-sectional area of the beam and the stiffness distribution of the foundation are design functions. They are chosen to minimize the compliance (or, equivalently, the area displaced by the beam deflection function). The calculus of variations is used to derive optimality conditions, and results are obtained for cantilevers and pinned-pinned beams. Several types of solutions are found, involving a single elastic support or a region of uniform foundation bordered at internal locations by elastic supports. In comparison to a reference uniform beam with uniform foundation, the decrease in compliance is significant.
The Buckling of Thin-Walled Open-Profile Bars
Authors: Ojalvo Morris
Published: July 2009

The theory of buckling for thin-walled open-profile bars is criticized. Its several derivations are faulted for violating statics, using a variational theorem approximately, using an incorrect variational statement, and/or using an inconsistent filament representation of the bar. Significantly, the theory yields buckling loads that contradict engineering expectations. A theory to replace it with general equations for computing buckling loads is presented. A problem solved under the old and new theories shows how torsional buckling is viewed under the new.
Active Parameter Control of Nonlinear Vibrating Structures
Authors: Masri S. F. , Miller R. K. , Dehghanyar T. J. , Caughey T. K.
Published: July 2009

A simple, yet efficient method is presented for the on-line vibration control of nonlinear, multidegree-of-freedom systems responding to arbitrary dynamic environments. The procedure uses nonlinear auxiliary mass dampers with adjustable motion-limiting stops located at selected positions throughout a given nonlinear system. A mathematical model of the system to be controlled is not needed for implementing the control algorithm. The degree of the primary structure oscillation near each vibration damper determines the damper’s actively-controlled gap size and activation time. By using control energy to adjust the damper parameters instead of directly attenuating the motion of the primary system, a significant improvement is achieved in the total amount of energy expended to accomplish a given level of vibration control. In a related paper, the direct method of Lyapunov is used to establish that the response of the controlled nonlinear primary structure is Lagrange stable. Numerical simulation studies of several example systems, as well as an experimental study with a mechanical model, demonstrate the feasibility, reliability, and robustness of the proposed semi-active control method.
On the Sufficiency of the Principle of Virtual Work for Mechanical Equilibrium: A Critical Reexamination
Authors: Papastavridis John G.
Published: July 2009

Starting from the general kinetic principle of d’Alembert/Lagrange, an energetic proof of the sufficiency conditions for equilibrium (known as Principle of Virtual Work) is presented. It is clearly demonstrated why to maintain equilibrium requires that, in addition to the familiar vanishing of the virtual work of the impressed forces on the originally motionless system, its geometrical (holonomic) constraints be explicitly time independent (stationary) and its nonintegrable kinematical (nonholonomic) ones be linear and homogeneous in the generalized velocities (catastatic).
Relaxation of Thermal Stress Singularities in Bonded Viscoelastic Quarter Planes
Authors: Blanchard James P. , Ghoniem Nasr M.
Published: July 2009

Singular thermal stress fields in bonded viscoelastic quarter planes are studied with the use of the viscoelastic analogy. The order of the singularity is shown to depend on the material properties, indicating that it will vary with time in viscoelastic materials. This is studied in detail for Maxwell materials, and it is shown that the order of the singularity generally increases with time. This evolution of the singularity can, for certain combinations of material properties, lead to initial increases in the stress levels near the edge of the interface before relaxation occurs.
The Anomalous Response of an Elastic-Plastic Structural Model to Impulsive Loading
Authors: Yu T. X. , Xu Y.
Published: July 2009

To simulate the response of a pin-ended elastic-plastic beam, a nonlinear structural model, i.e., a double-tier-spring model is analyzed to follow its deformation process after it is subjected to impulsive loading. After examining the first integral of the equation of motion, in the final elastic vibration, combined with other conditions, a region in the parameter’s map is found in which the anomalous behavior (i.e., a negative-negative vibration) appears. This model is proved to be equivalent to the Shanley-type model adopted in previous analyses, but the present approach provides new results in a more complete way.
Dynamics of a Plate in Large Overall Motion
Authors: Banerjee A. K. , Kane T. R.
Published: July 2009

Equations of motion are formulated for a thin elastic plate that is executing small motions relative to a reference frame undergoing large rigid body motions (three-dimensional rotation and translation) in a Newtonian reference frame. As an illustrative example, a spin-up maneuver for a simply-supported rectangular plate is examined, and the vibration modes of such a plate are used to show that the present theory captures the phenomenon of dynamic stiffening.
An Indirect Boundary Integral Equation Applied to Nonshallow Spherical Shell Problems With Arbitrary Boundary Constraints
Authors: Simos Nikolaos , Sadegh Ali M.
Published: July 2009

The fundamental singular solutions of a complete elastic spherical shell are utilized and, via the superposition principle, an indirect boundary integral equation is formulated. The singular solutions correspond to the action of normal point loads, concentrated tangential loads, and surface moments which apply in a self-equilibrating fashion over the spherical surface. With singular solutions of such property in hand, an arbitrary spherical shell with surface loading and any set of consistent boundary constraints is embedded onto the complete sphere. A set of fictitious load vectors is introduced along the boundary line which, together with the prescribed surface traction, is required to satisfy the constraints at the boundary. The idea of an auxiliary boundary is also introduced and the solution to a number of representative shell problems is shown as compared to the available analytical and finite element method results.
Targeted Retrieval and Analysis of Five Neandertal mtDNA Genomes
Authors: Briggs Adrian W. , Good Jeffrey M. , Green Richard E. , Krause Johannes , Maricic Tomislav , Stenzel Udo , Lalueza-Fox Carles , Rudan Pavao , Brajković Dejana , Kućan Željko , Gušić Ivan , Schmitz Ralf , Doronichev Vladimir B. , Golovanova Liubov V. , de la Rasilla Marco , Fortea Javier , Rosas Antonio , Pääbo Svante
Published: July 2009

Economic Ancient DNA Sequencing

Analysis of ancient DNA is often limited by the availability of ancient material for sequencing.

Briggs
et al.

(p.
318
; see the news story by
Pennisi
) describe a method of ancient DNA sequence retrieval that greatly reduces shotgun sequencing costs while avoiding the many difficulties associated with direct PCR-based approaches. They generated five complete and one near-complete Neandertal mitochondrial DNA genomes, which would have been economically impossible with a simple shotgun approach. Analysis of these genomes shows that Neandertal populations had a much smaller effective population size than modern humans or great apes.
Higher-Order Photon Bunching in a Semiconductor Microcavity
Authors: Aßmann M. , Veit F. , Bayer M. , van der Poel M. , Hvam J. M.
Published: July 2009

A Multiple Photon Pileup

The field of quantum optics began with the observation that two independent photons emitted from a thermal source tend to bunch together. The same is true for any number of bosons, but how do the statistics and correlations evolve experimentally as the number increases?

Aβmann
et al.

(p.
297
) have developed a streak-camera technique that can distinguish the photon number and measure the higher-order correlations between the photons at the detector. The results confirm the predicted “
n
factorial” dependence, showing that the tendency to bunch gets stronger as the number of independent photons is increased.
Modern Riding Style Improves Horse Racing Times
Authors: Pfau Thilo , Spence Andrew , Starke Sandra , Ferrari Marta , Wilson Alan
Published: July 2009

Increased horse race speed over the past century can be attributed to the crouching posture and increased work done by jockeys.
Band Formation from Coupled Quantum Dots Formed by a Nanoporous Network on a Copper Surface
Authors: Lobo-Checa Jorge , Matena Manfred , Müller Kathrin , Dil Jan Hugo , Meier Fabian , Gade Lutz H. , Jung Thomas A. , Stöhr Meike
Published: July 2009

Coupled Copper Surface States

Periodic arrays of quantum dots can create new electronic states that arise from coupling of the states created by confinement.

Lobo-Checa
et al.

(p.
300
) show that the electronic surface-state of copper can be converted into a regular array of quantum dots. An organic overlayer that is created on the copper surface has pores 1.6 nanometers in diameter that trap the surface states. The coupling of these trapped states is revealed in photoemission experiments, in which a shallow dispersive electronic band is formed.
Neutralizing Toxic RNA
Authors: Cooper Thomas A.
Published: July 2009

Oligonucleotides that target aggregates of RNA and protein show potential for treating myotonic dystrophy.
White House Taps Former Genome Chief Francis Collins as NIH Director
Authors: Kaiser Jocelyn
Published: July 2009

President Barack Obama's announcement last week that he had chosen Francis Collins to lead the National Institutes of Health ended months of speculation and ignited a volley of flattering remarks from researchers and biomedical groups.