bluuebunny/crossref_metadata_2025 huggingface dataset:
Dynamic Fracture of an Idealized Fiber-Reinforced Cantilever
Authors: Mannion L. F.
Published: July 2009

The dynamic fracture of a double cantilever beam of fiber-reinforced material is discussed. The material is modeled by assuming that the fibers are inextensible and continuously distributed. The examples considered reduce to the solution of the wave equation on a time-dependent interval; the method of characteristics is used. Two fracture criteria are used to calculate the crack speed. One of these criteria is the energy release rate commonly used in elastic fracture mechanics. In the present model some fibers can carry a finite force; the second criterion is based on the force in the fiber through the crack tip. Three simple examples are given to illustrate the model.
On the Asymptotic Continuum Analysis of Quasistatic Elastic-Plastic Crack Growth and Related Problems
Authors: Drugan W. J.
Published: July 2009

The present work provides rigorous substantiation of certain crucial asymptotic expressions which constitute the basis of a number of previous near-tip analyses of quasistatic elastic-plastic crack growth. This is accomplished as part of an investigation of the general features of two-dimensional near-tip continuum fields for quasistatic elastic-plastic crack growth, under general unsteady conditions, for a broad class of constitutive behavior and crack loading conditions. The approach employed and results obtained are also applicable to a number of geometrically similar problems, such as the plane strain analysis of the continuum fields near the leading and trailing edges of a quasistatically moving distributed surface load.
Prediction of Impact Force and Duration Due to Low-Velocity Impact on Circular Composite Laminates
Authors: Shivakumar K. N. , Elber W. , Illg W.
Published: July 2009

Two simple and improved models — energy-balance and spring-mass — were developed to calculate impact force and duration during low-velocity impact of circular composite plates. Both models include the contact deformation of the plate and the impactor as well as bending, transverse shear, and membrane deformations of the plate. The plate was a transversely isotropic graphite/epoxy composite laminate and the impactor was a steel sphere. In the energy-balance model, a balance equation was derived by equating the kinetic energy of the impactor to the sum of the strain energies due to contact, bending, transverse shear, and membrane deformations at maximum deflection. The resulting equation was solved using the Newton-Raphson numerical technique. The energy-balance model yields only the maximum force; hence a less simple spring-mass model is presented to calculate the force history. In the spring-mass model, the impactor and the plate were represented by two rigid masses and their deformations were represented by springs. Springs define the elastic contact and plate deformation characteristics. Equations of equilibrium of the resulting two degree-of-freedom system, subjected to an initial velocity, were obtained from Newton’s second law of motion. The two coupled nonlinear differential equations were solved using Adam’s numerical integration technique. Calculated impact forces from the two analyses agreed with each other. The analyses were verified by comparing the results with reported test data.
Laminar Start-Up Flow in a Pipe
Authors: Otis D. R.
Published: July 2009

A numerical solution is presented for the laminar start-up flow in a circular pipe. It is an extension of the Szymanski solution to include a parameter accounting for the head that must be devoted to the acceleration of the flow. Velocity profiles, wall shear stress, mean velocity history, and start-up time constants are given as a function of the new parameter.
Falkner-Skan Solution for Gravity-Driven Film Flow
Authors: Andersson H. I. , Ytrehus T.
Published: July 2009

It is demonstrated that the development of a viscous film flow down along a vertical wall can be described by the classical Falkner-Skan equation from aerodynamic boundary layer theory for the particular parameter-value m = 1/2. This leads to a well-known exact solution for the velocity field, as long as the viscous boundary layer can be considered not to interact with the free surface of the film. An exact reference solution for developing film flow is thus made available, against which approxiate solutions may be tested for accuracy.
An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading, Part 1: Theory
Authors: Ponter A. R. S. , Karadeniz S.
Published: July 2009

The paper describes an extension of classical shakedown theory for structural problems involving constant mechanical loads and cyclic variations in temperature. The objective of the theory is to provide a simple means of distinguishing between circumstances where thermal cycling can cause structural ratchetting for small or zero mechanical loads from those where very substantial thermal stresses can occur with no danger of ratchetting. This distinction is of particular importance in the design of Liquid Metal Fast Breeder Reactors and current design codes do not address this problem directly. An extended definition of material shakedown is described that provides a conservative theory, taking into account cyclic strain hardening. Some simple experiments on a two-bar structure demonstrates the relevance of the theory to observed structural behavior.
Free Vibration of a Point-Supported Spherical Shell
Authors: Irie T. , Yamada G. , Muramoto Y.
Published: July 2009

An analysis is presented for the free vibration of an elastically or a rigidly point-supported spherical shell. For this purpose, the deflection displacements of the shell are written in a series of the products of the associated Legendre functions and the trigonometric functions. The dynamical energies of the shell are evaluated, and the frequency equation is derived by the Ritz method. For a rigidly point-supported shell, the Lagrangian multiplier method is conveniently employed. The method is applied to a closed spherical shell supported at equispaced four points located along a parallel of latitude; the natural frequencies and the mode shapes are calculated numerically, and the effects of the point supports on the vibration are studied.
Dynamics of Viscoelastic Structures—A Time-Domain, Finite Element Formulation
Authors: Golla D. F. , Hughes P. C.
Published: July 2009

Mathematical models of elastic structures have become very sophisticated: given the crucial material properties (mass density and the several elastic moduli), computer-based techniques can be used to construct exotic finite element models. By contrast, the modeling of damping is usually very primitive, often consisting of no more than mere guesses at “modal damping factors.” The aim of this paper is to raise the modeling of viscoelastic structures to a level consistent with the modeling of elastic structures. Appropriate material properties are identified which permit the standard finite element formulations used for undamped structures to be extended to viscoelastic structures. Through the use of “dissipation” coordinates, the canonical “M, K” form of the undamped motion equations is expanded to encompass viscoelastic damping. With this formulation finite element analysis can be used to model viscoelastic damping accurately.
Three-Dimensional Dynamic Response of Buried Pipelines to Incident Longitudinal and Shear Waves
Authors: Datta S. K. , O’Leary P. M. , Shah A. H.
Published: July 2009

An exact analysis is presented here for the three-dimensional dynamics of a long continuous pipeline embedded in an elastic medium. A shell model of the pipe has been used here. It is shown that the dynamic amplification of axial and hoop stresses induced in the pipe due to incident plane longitudinal and shear waves depends crucially on the ratio of rigidities of the surrounding soil and the pipe. Induced stresses are also found to have appreciable frequency dependence for certain combinations of material properties and angles of incidence. Results presented here are also applicable to buried tunnels.
Asymptotic Modal Analysis and Statistical Energy Analysis of Dynamical Systems
Authors: Dowell E. H. , Kubota Y.
Published: July 2009

A new derivation of the results commonly referred to as Statistical Energy Analysis (SEA) is given by studying the asymptotic behavior of classical modal analysis for a general, linear (structural) system. It is shown that, asymptotically, the response at (almost) all points of the system is the same. A numerical example is used to illustrate the way in which the asymptotic limit is approached. Both random and sinusoidal loadings are considered; for the latter an extension of the usual SEA result is obtained.
Temperature Distributions and Thermal Stresses in Asymmetrically Heat Radiated Tubes
Authors: Fett T.
Published: July 2009

The transient and stationary temperature distributions in a tube wall caused by an asymmetrical heat flux distribution are evaluated. The results are represented for the case of a heat radiating half-space. In addition, the accompanying stress distributions are computed.
On the Wave Propagation in an Elastic Hollow Cylinder With Long-Range Cohesion Forces
Authors: Nowinski J. L.
Published: July 2009

After a brief derivation of the formula for the nonlocal moduli, Fourier transforms of the stress components in their nonlocal aspect are established. Satisfaction of the traction-free boundary conditions leads to the frequency equation of the problem. A particular case involving longitudinal Lame´ modes is analyzed in more detail. A numerical example solved shows a considerable decrease of the speed and the frequency of the short waves as compared with those of long waves studied in the classical theory.
Rectangular Plates on Unilateral Edge Supports: Part 1—Theory and Numerical Analysis
Authors: Dempsey J. P. , Li Hui
Published: July 2009

The corners of a simply supported, laterally loaded rectangular plate must be anchored to prevent them from lifting off the supports. If no such anchors are provided, and the supports are unilateral or capable of exerting forces in one direction only, parts of the plate will bend away from the supports upon loading. The loss of contact when uplift of laterally loaded rectangular plates is not prevented is examined in this paper. Arbitrary centrally symmetric loading is considered. Finite integral transforms convert the coupled dual-series equations that result from the Levy-Nadai approach to two coupled singular integral equations. Different solution methods are applicable for sagged and unsagged supports; these two numerical approaches are discussed in detail.
Pipe Bend Analysis by Thin Shell Theory
Authors: Whatham J. F.
Published: July 2009

Thin shell theory is applied to pipe bends terminated by flanges or flange-ended tangent pipes and subjected to any end loading, either in-plane or out-of-plane. Graphs of flexibility factor versus pipe bend characteristic are presented for in-plane bending of a wide range of pipe elbows terminated by flanges or short flange-ended tangents. Experimental results verify the thin shell solutions for in-plane and out-of-plane bending of a flanged pipe elbow. The capabilities of a computer program BENDPAC are also described.
The Stability of Oscillatory Hagen-Poiseuille Flow
Authors: Tozzi J. T. , von Kerczek C. H.
Published: July 2009

The linear stability theory of the nonzero mean, sinusoidally oscillating flow in a tube of circular cross section is examined. It is found that the relevant axisymmetric disturbances in the oscillatory flow are more stable (i.e., have larger decay rates) than the axisymmetric disturbances of the mean flow alone. This result holds for values of the cross-sectional average oscillation velocity amplitude at least as large as seven-tenths the average mean-flow velocity amplitude. Although the instantaneous velocity profile contains generalized inflection rings for a substantial portion of the oscillation period, the disturbances do not become instantaneously unstable at any time, even for very low frequency oscillations.
A One-Dimensional Numerical Model of a Drop-On-Demand Ink Jet
Authors: Adams R. L. , Roy J.
Published: July 2009

MacCormack’s predictor-corrector algorithm is used to solve one-dimensional model equations of drop development from a drop-on-demand ink jet. The calculation is done in Lagrangian coordinates, and the results are compared with calculations reported in which an axisymmetric marker-and-cell algorithm is used. The comparison indicates that, although drop velocities differ in the two cases, good qualitative results can be obtained with the less complex one-dimensional approach.
The Response of Elastic and Viscoelastic Surfaces to a Turbulent Boundary Layer
Authors: Gad-el-Hak Mohamed
Published: July 2009

The unstable response of elastic and viscoelastic surfaces to a turbulent boundary layer was experimentally investigated in an 18-m towing tank. The compliant surface deformation was measured using a remote optical technique. The “Laser Displacement Gauge” employs a Reticon camera equipped with a linear array of 256 photodiodes spaced 25 microns apart. The device was used to measure the characteristics of two classes of hydroelastic instability waves that form on elastic or viscoelastic surfaces as a reuslt of the interaction with a turbulent boundary layer. The instability waves developing on an elastic surface are symmetric and have a relatively high phase speed and a small wavelength, as compared to the slow and highly nonlinear “static-divergence” waves observed on the viscoelastic surface. The experimentally determined wave characteristics are compared to existing theories on compliant surface instabilities.
A Time-Domain Method for Identifying Modal Parameters
Authors: Wang Zhen-ni , Fang Tong
Published: July 2009

A time-domain method for identifying the modal parameters of a vibration system is presented. It is shown that system eigenvectors can be effectively estimated through the multivariate AR model representation of the system response to white noise excitation. In contrast to the usual ARMA model approach, in this method only a linear least square algorithm is required, so that a great amount of calculation is saved. Results of digital simulations support the identification method.
A Natural Modes Model and Modal Identities for Damped Linear Structures
Authors: Vigneron F. R.
Published: July 2009

A modal model is derived for a passive elastic structure with linear viscous damping, from a first-order state variable arrangement of the physical parameters model. The state variable form of the model is composed using the equations Kq˙ − Kq˙ = 0 and Mq¨ + Cq˙ + Kq = f. An attribute of the particular formulation is that it facilitates a straightforward derivation of mass-properties-related modal identities for the associated damped natural modes. Transfer functions and normalizations used in experimental modal parameter estimation are also given special attention.
On the Transverse Vibration of Beams of Rectangular Cross-Section
Authors: Hutchinson J. R. , Zillmer S. D.
Published: July 2009

An exact solution for the natural frequencies of transverse vibration of free beams with rectangular cross-section is used as a basis of comparison for the Timoshenko beam theory and a plane stress approximation which is developed herein. The comparisons clearly show the range of applicability of the approximate solutions as well as their accuracy. The choice of a best shear coefficient for use in the Timoshenko beam theory is considered by evaluation of the shear coefficient that would make the Timoshenko beam theory match the exact solution and the plane stress solution. The plane stress solution is shown to provide excellent accuracy within its range of applicability.
Radial Dependence of Near-Tip Continuum Fields for Plane Strain Tensile Crack Growth in Elastic-Ideally Plastic Solids
Authors: Drugan W. J.
Published: July 2009

This paper is an extension of work by Drugan et al. (1982) who derive the stress and deformation fields at the tip of a plane strain tensile crack that grows quasi-statically, under general nonsteady conditions, in an elastic-ideally plastic solid. Here I perform a higher-order analysis of the near-tip fields for this growing crack problem. My principal objectives are to determine the radial variation of the near-tip stress field and elucidate the structure of the deformation fields in the 90-deg sector ahead of the growing crack; this information was not provided by the lowest-order solution of Drugan et al. (1982). I also derive a crucial asymptotic expression for the normal radial component of the deformation rate tensor in a moving “centered fan” plastic sector, which was given without complete proof by Rice (1982). The analysis presented herein differs from typical perturbation analyses in that I am able to derive the higher-order structure of the continuum fields rather than having to assume expansions for them. Among the results, normal polar components of deviatoric stress are shown to vary as (ln r)−1, while the in-plane polar shear component varies as (ln r)−2, for small r > 0 in moving “centered fan” plastic sectors, r denoting distance from the (moving) crack tip. Further, in-plane strains proportional to ln|ln r| as r → 0 appear not to be precluded in the 90-deg sector ahead of the growing crack.
Three-Dimensional Stress Singularities at Conical Notches and Inclusions in Transversely Isotropic Materials
Authors: Somaratna Nihal , Ting T. C. T.
Published: July 2009

This study examines analytically the possible existence of stress singularities of the form σ = ρδf(θ,φ) at the apex of axisymmetric conical boundaries in transversely isotropic materials. (ρ, θ, φ) refer to spherical coordinates with the origin at the apex. The problems of one conical boundary and of two conical boundaries with a common apex are considered. The boundaries are either rigidly clamped or traction free. Separation of variables enables the general solution to be expressed in terms of Legendre functions of the first and second kind. Imposition of boundary conditions leads to an eigenequation that would determine possible values of δ. The degenerate case that arises when the eigenvalues of the elasiticity constants are identical is also discussed. Isotropic materials constitute only a particular case in this class of degenerate materials and previously reported eigenequations corresponding to isotropic materials are shown to be recoverable from the present results. Numerical results corresponding to a few selected cases are also presented to illustrate the solution procedure.
Nonlinear Analysis of Crazes
Authors: Weitsman Y.
Published: July 2009

This paper concerns the nonlinear mechanical behavior of a single craze of finite length contained in an extended linear elastic medium. The craze is modeled as a distributed spring with a nonlinear force-displacement relation, which exhibits a hysteresis loop upon unloading. Stresses, displacements, and energy release rates are computed and compared against results for a linear craze. The case of a central crack within the craze is also considered.
Linear Analysis of Uniformly Stressed, Orthotropic Cylindrical Shells
Authors: Wilson J. F. , Orgill G.
Published: July 2009

Within the framework of classical elasticity, the nonbuckled deformations are calculated for orthotropic, right circular, thin-walled cylinders under uniform load conditions. The principle direction of orthotropy follows parallel constant angle helices. Nondimensional system parameters involving four material constants and three loading conditions (internal pressure, longitudinal load, and pure torque) are identified. Through parametric studies deformation patterns are calculated that are unique to orthotropy. Numerical examples illustrate that the proper selection of cylinder orthotropy can lead to designs with optimal deformations or load-carrying capacity. Results may be used for the design of robotic actuators driven by internal pressure.
Finite Deformations of Nonlinear, Orthotropic Cylindrical Shells
Authors: Orgill G. , Wilson J. F.
Published: July 2009

The nonbuckling finite deformations of an orthotropic, thin wall cylinder are investigated. The cylinder is made of a nonlinear material and subjected to internal pressure, end load and torque. Initially the stresses and strains in the cylinder are assumed to be axially homogeneous. The model is then extended to include axially nonhomogeneous stresses and strains that may arise due to particular displacement boundary conditions such as radial confinement at the edges. The loads are applied to the cylinder incrementally, the finite strains are computed, and adjustments are made in cylinder dimensions and the constitutive law to account for geometric and material nonlinearities. Parametric studies show how the deformation behavior is influenced by the orientation of the angle of material orthotropy. Results may be applied to the design of pressure controlled robotic actuators and manipulators.
A Curved C0 Shell Element Based on Assumed Natural-Coordinate Strains
Authors: Park K. C. , Stanley G. M.
Published: July 2009

A curved C0 shell element is presented, which corrects several deficiencies in existing quadratic shell elements. The improvements realized in the present element include rank sufficiency without transverse shear locking, consistent membrane strain interpolation that admits inextensional bending without reduced integration, and adequate representation of curvature effects to capture the important membrane-bending coupling. The element can be constructed either by a nine-point integration rule or by a four-point integration rule with the proper rank compensating terms. Numerical experiments with the present element on several benchmark problems indicate that the element yields accurate and reliable solutions without any ostensible deficiency. The element is recommended for production analysis of shell structures.
Accelerating Vector Iteration Methods
Authors: Papadrakakis M.
Published: July 2009

This paper describes a technique for accelerating the convergence properties of iterative methods for the solution of large sparse symmetric linear systems that arise from the application of finite element method. The technique is called partial preconditioning process (PPR) and can be combined with pure vector iteration methods, such as the conjugate gradient, the dynamic relaxation, and the Chebyshev semi-iterative methods. The proposed triangular splitting preconditioner combines Evans’ SSOR preconditioner with a drop-off tolerance criterion. The (PPR) is attractive in a FE framework because it is simple and can be implemented at the element level as opposed to incomplete Cholesky preconditioners, which require a sparse assembly. The method, despite its simplicity, is shown to be more efficient on a set of test problems for certain values of the drop-off tolerance parameter than the partial elimination method.
The Extent of the Stress Intensity Factor Field During Crack Growth Under Dynamic Loading Conditions
Authors: Ma C. C. , Freund L. B.
Published: July 2009

The phenomenon considered is fracture initiation and crack growth in a plate due to dynamic pressure loading on the faces of a pre-existing crack. The problem is formulated within the framework of two-dimensional elastodynamics, and the system is viewed as a semi-infinite crack in an otherwise unbounded body. At a certain instant of time, a spatially uniform pressure begins to act on the crack faces. The pressure magnitude increases linearly in time for a certain period (the rise time T), and it is constant thereafter. The crack begins to extend at constant speed at some time after the pressure begins to act (the delay time τ). The pressure acts only over the original crack faces, and both τ > T and τ < T are considered. The ratio of the normal stress on the fracture plane to the value due to the singular term in the stress field alone is computed for some point at a small fixed distance ahead of the crack tip, with a view toward establishing the conditions under which the stress intensity factor controlled singular term accurately describes the near tip stress distribution in this highly transient process. Measured and calculated histories compare very well for relatively low crack face pressures, but there is significant disagreement beyond crack growth initiation for higher pressures. Possible reasons for the discrepancies are discussed.
Elastic Wave Scattering From an Interface Crack in a Layered Half Space Submerged in Water: Part I: Applied Tractions at the Liquid-Solid Interface
Authors: Gracewski S. M. , Bogy D. B.
Published: July 2009

In Part I of this two-part paper, the analytical solution of time harmonic elastic wave scattering by an interface crack in a layered half space submerged in water is presented. The solution of the problem leads to a set of coupled singular integral equations for the jump in displacements across the crack. The kernels of these integrals are represented in terms of the Green’s functions for the structure without a crack. Analysis of the integral equations yields the form of the singularities of the unknown functions at the crack tip. These singularities are taken into account to arrive at an algebraic approximation for the integral equations that can then be solved numerically. Numerical results in the form of crack tip stress intensity factors are presented for the cases in which the incident disturbance is a harmonic uniform normal or shearing traction applied at the liquid-solid interface. These results are compared with a previously published solution for this problem in the absence of the liquid. In Part II, which immediately follows Part I in the same journal issue, the more realistic disturbances of plane waves and bounded beams incident from the liquid are considered.
Mechanics of Fatigue Damage and Degradation in Random Short-Fiber Composites, Part I—Damage Evolution and Accumulation
Authors: Wang S. S. , Chim E. S.-M. , Suemasu H.
Published: July 2009

Cyclic fatigue damage in random short-fiber composites is studied experimentally and analytically. In the experimental phase of the study, the fatigue damage is observed to involve various forms of microcracking, originated from microscopic stress concentrators in the highly heterogeneous microstructure. In the analytical portion of the study, a probabilistic treatment of the microcracks is conducted to evaluate the statistical nature of the microscopic fatigue damage. The density and the cumulative distribution of microcrack lengths are found to follow the well known Weibull-form function, and the microcrack orientation density and cumulative distribution have expressions of a fourth-order power form of the cosθ function. Fatigue damage evolution and accumulation in the random short-fiber composite are analyzed in detail through the development of probabilistic microcrack density and distribution functions during the cyclic loading history.
Effects of Interacting Cavities on Damage Parameter
Authors: Stigh U.
Published: July 2009

A numerical study is performed on the influence of interacting spherical cavities on the damage parameter. The material is isotropic, incompressible, power-law creeping. The results show that the nonlinearity of the material has a very small influence on the damage parameter. A simple formula is derived relating the damage parameter to the proximity of the cavities. It is further studied how the concentration and nonlinearity influence the growth of the cavities.
Macrocrack-Microdefect Interaction
Authors: Rubinstein A. A.
Published: July 2009

Elastic interactions (in terms of the stress intensity factor variation) of the macrocrack (represented as semi-infinite crack) with microdefects such as finite size, arbitrarily positioned crack, circular hole or inclusion are considered. A solution for the problem of the interaction with dilational inclusion is also given. The influence of the crack tip geometry on the surrounding stress field is studied by analyzing the case of crack-hole coalescence. Problems are considered in terms of complex stress potentials for linear elasticity and formulated as a singular integral equation on the semi-infinite interval. A stable numerical technique is developed for the solution of such equations. In a particular case, in order to evaluate the accuracy of the numerical procedure, results obtained through the numerical procedure are compared with the available analytical solution and found to be in excellent agreement.
Theoretical Study of the Dynamic Tensile Test
Authors: Regazzoni G. , Johnson J. N. , Follansbee P. S.
Published: July 2009

A numerical investigation of the tensile test using a finite-difference, one-dimensional elasto-viscoplastic code is presented. The influence of strain rate, strain rate sensitivity, and inertia on the development of the axial particle velocity, stress, strain, and strain rate profiles in pure copper is studied. The initial stages of post-uniform deformation and the stabilizing influence of inertia and strain rate sensitivity in this regime are demonstrated. Both inertia and strain rate sensitivity are shown to decrease the rate of unloading of the uniform region of a tensile specimen past the point of instability given by the maximum load criterion. A comparison of numerically predicted and experimentally determined values of the post-uniform elongation is shown.
Thermoplastic Instability for the Transient Contact Problem of Two Sliding Half-Planes
Authors: Azarkhin A. , Barber J. R.
Published: July 2009

We study the time dependent problem of a nonconducting half-plane sliding on the surface of a conductor with heat generation at the interface due to friction. The conducting half-plane is slightly rounded to give a Hertzian initial pressure distribution. Relationships are established for temperature and thermoelastic displacements due to a heat input of cosine type through the surface, and then these are used to obtain the solution in the form of a double Fourier integral. Numerical results show that, if the ratio of the initial size of the area of contact to that in the steady state is less than some critical value, the area of contact and the pressure distribution change smoothly toward the steady state solution. Otherwise the area of contact goes through bifurcation. The bifurcation accelerates the process. Numerical results are compared with previous approximate solutions.
Transient Response of an Interface-Crack in a Layered Plate
Authors: Kundu T.
Published: July 2009

In this paper, the transient response of an interface crack, in a two layered plate subjected to an antiplane stress field, is analytically computed. The problem is formulated in terms of semi-infinite integrals following the technique developed by Neerhoff (1979). It has been shown that the major steps of Neerhoff’s technique, which was originally developed for layered half-spaces, can also be applied to layered plate problems. An improved method for manipulation of semi-infinite singular integrals is also presented here. Finally, the new method is coded in FORTRAN program and numerical results for a sample problem are presented.
The Strain-Energy Density of Rubber-Like Shells of Revolution Undergoing Torsionless, Axisymmetric Deformation (Axishells)
Authors: Simmonds J. G.
Published: July 2009

We consider a shell of revolution made of an incompressible elastically isotropic material. Assuming a torsionless, axisymmetric three-dimensional displacement field that permits large normal strains (i.e., large thickness changes) but small transverse shearing strains, we construct a two-dimensional strain-energy density for a first-approximation shell theory in which the extensional strains may be O(1). The bending strains, however, are small, as in Reissner’s nonlinear theory. An error estimate is given that depends on the undeformed thickness and curvatures, the bending strains, the transverse shearing strain, and the characteristic wavelength of the shell theory solutions.
On the Effect of Transverse Shear Deformability on Stress Concentration Factors for Twisted and Sheared Shallow Spherical Shells
Authors: Reissner E. , Wan F. Y. M.
Published: July 2009

Explicit solutions are obtained, in terms of modified Bessel functions, for the problems of transverse twisting and of tangential shearing of transversely shear-deformable shallow spherical shells with a small circular hole. The relevant stress concentration factors are calculated for the entire range of a rise-to-thickness ratio parameter and a transverse shear deformability parameter. The modification of known results obtained previously by shear deformable plate theory, and by shallow shell theory without consideration of transverse shear deformation effects, is delineated.
Three-Dimensional Vibrations of Twisted Cantilevered Parallelepipeds
Authors: Leissa A. , Jacob K. I.
Published: July 2009

A large number of references dealing with the vibrations of twisted, cantilevered beams and plates exist in the literature. These works show considerable disagreement concerning the effect of twist angle upon frequencies. The present work is the first three-dimensional study of the problem. Displacement components are assumed in the form of algebraic polynomials which satisfy the fixed face conditions exactly, and which are mathematically complete. The Ritz method is then applied. Accurate frequencies are calculated for twisted thick plates and are compared with ones obtained recently by others using beam, shell, and finite element theory.
On Nonlinear Dynamics of Planar Shear Indeformable Beams
Authors: Luongo A. , Rega G. , Vestroni F.
Published: July 2009

The planar forced oscillations of shear indeformabie beams with either movable or immovable supports are studied through a unified approach. An exact nonlinear beam model is referred to and a consistent procedure up to order three nonlinearities is followed. By eliminating the longitudinal displacement component through a constraint condition and assuming one mode, the problem is reduced to one nonlinear differential equation. A perturbational solution in the neighborhood of the resonant frequency is determined and the stability of the steady-state solutions is studied. The dependence of the phenomenon on the geometrical and mechanical characteristics of the system is put into light and the frequency-response curves for different boundary conditions are furnished.
Chaos in a Harmonically Excited Elastic Beam
Authors: Maewal A.
Published: July 2009

Numerical integration of the equations for the evolution of amplitudes of a harmonically forced simply supported elastic beam indicates that for certain values of the frequencies of excitation the response of the beam may be chaotically modulated. In an attempt to confirm the presence of chaos, the Lyapunov exponents have been calculated for two cases in which the broadening of the power spectra around the dominant peaks occurs. In both the cases one of the Lyapunov exponents is positive; this provides further evidence of chaos. The Lyapunov dimension of the attractors in these cases is estimated to be 2.09 and 2.11, respectively.
Free Vibration of a Large-Amplitude Deflected Plate—Reexamination by the Dynamical Systems Theory
Authors: Lee J.
Published: July 2009

For a simply supported large-amplitude deflected plate, Fourier expansion of displacement reduces the nonlinear plate equation to a system of infinitely coupled modal equations. To close off this system, we have suppressed all but the four lowest-order symmetric modes. In the absence of damping and forcing, the four-mode truncation can be recasted into a Hamiltonian of 4 DOF. Hence, the free vibration of nonlinear plate can be investigated by the standard technique of Hamiltonian systems. It has been found that subsystems of 2 DOF are practically stable in that the invariant tori remain on a smooth surface up to total energy of 1000, at which modal displacements can be 40 times the plate thickness. On the other hand, the trajectory of 4 DOF system develops chaos at a much lower energy value of 76, corresponding to modal displacements twice the plate thickness. This has been evidenced by many spikes in the power spectral density of displacement time-series and an erratic pattern that modal energy components cut through an energy sphere.
Laminated Composite Plate Theory With Improved In-Plane Responses
Authors: Murakami H.
Published: July 2009

In order to improve the accuracy of the in-plane response of the shear, deformable laminated composite plate theory, a new laminated plate theory has been developed based upon a new variational principle proposed by Reissner (1984). The improvement is achieved by including a zigzag-shaped C0 function to approximate the thickness variation of in-plane displacements. The accuracy of this theory is examined by applying it to a problem of cylindrical bending of laminated plates which has been solved exactly by Pagano (1969). The comparison of the in-plane response with the exact solutions for symmetric three-ply and five-ply layers has demonstrated that the new theory predicts the in-plane response very accurately even for small span-to-depth ratios.
A Cell Mapping Method for Nonlinear Deterministic and Stochastic Systems—Part I: The Method of Analysis
Authors: Hsu C. S. , Chiu H. M.
Published: July 2009

In the past few years as an attempt to devise more efficient and more practical ways of determining the global behavior of strongly nonlinear systems, two cell-to-cell mapping methods have been proposed, namely, the simple cell mapping and the generalized cell mapping. In this first part of the two-part paper we present a different and more efficient cell mapping method for treating nonlinear vibration problems. The vibratory systems may be deterministic or stochastic. The method utilizes compatible simple and generalized cell mapping and it combines the advantages of both. Applications to various systems will be presented in the second part of the paper.
Effect of Tangential Torque on the Dynamics of Flexible Rotors
Authors: Yim K. B. , Noah S. T. , Vance J. M.
Published: July 2009

The effect of tangential load torque on the dynamics of rotors has been studied analytically using both cantilevered and between-bearing rotor models. External damping, distributed shaft mass, and gyroscopic moments are taken into account. A number of analytical approaches, including the classical method and a modified transfer matrix method have been utilized and they all gave results with excellent agreement. For realistic levels of torque, the major effect is found to be on the whirl stability of the system. Stability is found to depend most strongly on the dimensionless ratio of torque to damping, and on the mode shape.
Thermal Expansion of Elastic-Plastic Composite Materials
Authors: Dvorak G. J.
Published: July 2009

Exact relationships are derived between instantaneous overall thermal stress or strain vectors and instantaneous overall mechanical stiffness or compliance, for two binary composite systems in which one of the phases may deform plastically. Also, the local instantaneous thermal strain and stress concentration factors are related in an exact way to the corresponding mechanical concentration factors. The results depend on instantaneous thermoelastic constants and volume fractions of the phases. They are found for fibrous composites with two distinct elastically isotropic or transversely isotropic phases, and for any binary composite with elastically isotropic phases. The results indicate that in the plastic range the thermal and mechanical loading effects are coupled even if the phase properties do not depend on changes in temperature. The derivation is based on a novel decomposition procedure which shows that spatially uniform elastic strain fields can be created in certain heterogeneous media by superposition of uniform phase eigenstrains with local strains, caused by piecewise uniform stress fields which are in equilibrium with prescribed surface tractions. The method is extended to discretized microstructures, and also to the analysis of moisture absorption and phase transformation effects on overall response and on local fields in the two composite materials.
An Efficient Method for the Calculation of Interlaminar Stresses in Composite Materials
Authors: Kassapoglou C. , Lagace P. A.
Published: July 2009

A simple and efficient method is presented to determine the interlaminar stresses in a symmetric composite laminate under uniaxial loading. Expressions for the interlaminar stresses are assumed in terms of exponentials based on shapes that the interlaminar stresses must take in order to assure overall (integral) force and moment equilibrium. The boundary conditions and the traction continuity between plies are satisfied exactly. The exponential terms in the stress expressions are determined by minimizing the laminate complementary energy. Typical results are presented and compared with previous results found in the literature. The current method is shown to efficiently deal with the problem including the ability to perform the analysis of thick laminates (100 plies or more) with relative ease and cost-effectiveness.
The Poisson Function of Finite Elasticity
Authors: Beatty M. F. , Stalnaker D. O.
Published: July 2009

The Poisson function is introduced to study in a simple tension test the lateral contractive response of compressible and incompressible, isotropic elastic materials in finite strain. The relation of the Poisson function to the classical Poisson’s ratio and its behavior for certain constrained materials are discussed. Some experimental results for several elastomers, including two natural rubber compounds of the same kind studied in earlier basic experiments by Rivlin and Saunders, are compared with the derived relations. A special class of compressible materials is also considered. It is proved that the only class of compressible hyperelastic materials whose response functions depend on only the third principal invariant of the deformation tensor is the class first introduced in experiments by Blatz and Ko. Poisson functions for the Blatz-Ko polyurethane elastomers are derived; and our experimental data are reviewed in relation to a volume constraint equation used in their experiments.
Finite Elastic Deformation Governed by Linear Equations
Authors: Keller Joseph B.
Published: July 2009

It is observed that the equations of motion governing finite elastic deformation are linear if and only if the Piola-Kirchhoff stress tensor is linear in the deformation gradient. Then the three components of displacement satisfy uncoupled linear equations. These equations are used to solve some problems of finite deformation.
Two-Dimensional Strain Cycling in Plasticity
Authors: Naghdi P. M. , Nikkel D. J.
Published: July 2009

Detailed calculations are presented for strain cycling in a homogeneous deformation that can be sustained by a biaxial state of stress in thin-walled specimens of OFHC copper. These calculations are made with a set of relatively simple constitutive equations within the framework of the strain-space formulation of plasticity. The predicted theoretical calculations, carried out in the context of small deformation, are in good agreement with corresponding available experimental results for saturation hardening and erasure of memory in two-dimensional strain cycling. Also, with the use of the calculated results, a scalar quantity that characterizes strain-hardening is plotted as a function of plastic strains. Such plots are likely to be useful for computational purposes.
On Consistency Relations in Nonlinear Fracture Mechanics
Authors: Rodin G. J. , Parks D. M.
Published: July 2009

A simple form of consistency relations between generalized forces and displacements for systems exhibiting power-law behavior is presented. The later discussion focuses on certain details regarding applications of the relations to nonlinear fracture mechanics, emphasizing the finite element analysis of a single edge-cracked strip subjected to remote tension under plane strain conditions.
Stretching and Bending of Rotating Beam
Authors: Stephen N. G. , Wang P. J.
Published: July 2009

The effect of uniform high-speed rotation on the simplest representation of a rotating blade is analyzed according to the linear theory of elasticity. The blade is modeled as a uniform prismatic beam of general cross section rotating about a principal section axis perpendicular to the centroidal axis. This quasi-elastostatic three-dimensional problem is reduced to a two-dimensional boundary value problem to which solutions for the amenable circular and elliptic cross sections are given. For sections not possessing two axes of cross-sectional symmetry, the theory predicts curvature of the blade center line.
Elastic Deformations of Strips and Circular Plates Under Uniform Pressure
Authors: Im S. , Shield R. T.
Published: July 2009

A consistent theory for linear elastic behavior in which the strains are small but in which the displacements and rotations can be large is applied to the bending of a long rectangular plate and of a circular plate by uniform pressure. Within the range of small-strain, linear elastic behavior, the theory provides solutions for all slenderness ratios of the plates and magnitudes of the loading. Thus the theory bridges the gap between the classical theory and the nonlinear structural theory of Fo¨ppl and von Ka´rma´n. The results show that the von Ka´rma´n equations provide accurate solutions for thin plates for which deflections are not small.
Large Deflection Stability of Spherical Shells With Ring Loads
Authors: Cagan J. , Taber L. A.
Published: July 2009

Large deflections of shallow and deep spherical shells under ring loads are studied. The axisymmetric problem is solved through a Newton-Raphson technique on discretized nonlinear shell equations. Comparison of computed load-deflection curves to experimental data from both thick and thin shells generally shows good agreement in peak loads and the type of instability. For a point load, the load increases monotonically with deflection; as the ring radius increases, transition-type (snap-through) and then local buckling occurs. In addition, the pre- and post-buckled mechanical behaviors of the shell are examined.
Clamped Plates on Pasternak-Type Elastic Foundation by the Boundary Element Method
Authors: Katsikadelis J. T. , Kallivokas L. F.
Published: July 2009

A boundary element solution is developed for the analysis of thin elastic clamped plates of any shape resting on a Pasternak-type elastic foundation. The plate may have holes and it is subjected to concentrated loads, line loads, and distributed loads. The analysis is complete, i.e., deflections, stress resultants, subgrade reactions, and reactions on the boundary are evaluated. Several numerical examples are worked out and the results are compared with those available from analytical solutions. The efficiency of the BEM is demonstrated and discussed.
An Experimental Study of the Rapid Flow of Dry Cohesionless Metal Powders
Authors: Craig K. , Buckholz R. H. , Domoto G.
Published: July 2009

This paper studies the rapid shearing flow of dry metal powders. To perform this study, we built and used an annular shear cell test apparatus. In this apparatus the dry metal powders are rapidly sheared by rotating one of the shear surfaces while the other shear surface remains fixed. The shear stress and normal stress on the stationary surface were measured as a function of three parameters: the shear-cell gap thickness, the shear-rate and the fractional solids content. Stresses are measured while holding both the fractional-solids content and the gap thickness at prescribed values. The results show the dependence of the normal stress and the shear stress on the shear-rate. Likewise, a significant stress dependence on both the fractional solids content and the shear-cell gap thickness was observed. Our experimental results are compared with the results of other reported experimental studies.