bluuebunny/crossref_metadata_2025 huggingface dataset:
Buckling of an Elastic Elliptical Ring Inside a Rigid Boundary
Authors: Soong T. C. , Choi I.
Published: July 2009

The buckling of a thin, elastic ring confined in an elliptical hole whose circumference is smaller than that of the ring is studied. The effect of post-buckling slippage of the ring along the boundary with a corresponding curvature change is included. Buckling configurations with no friction that are (a) symmetric to one axis, and (b) symmetric to both axes, and (c) buckling configurations with no-slip are presented. Buckling with a strain energy consideration added as a criterion and buckling merely from compatibility alone are discussed. Results include curves for buckling loads of different ellipticities for different radius-to-thickness ratios.
Large Deflection Behavior of Simply Supported Laminated Panels Under In-Plane Loading
Authors: Zhang Y. , Matthews F. L.
Published: July 2009

An analysis is presented for nonbifurcational behavior of flat and curved panels of unsymmetrically laminated composite materials under in-plane loading, either compression or shear. A pair of governing equations in the von Karman sense are solved in conjunction with simply supported boundaries. A series of computations is carried out for panels having different curvatures, different lay-ups, and different materials. The results show that during loading, lateral deflection is involved in panels with unsymmetric cross-ply layers under compression or in those with unsymmetric angle-ply layers under shear. This effect increases deflection of the flat plates under loading and reduces resistance of curved panels against collapse.
A Viscoplastic Theory With Anisotropic Hardening and Its Application to Pressure-Shear Plate Impact Experiments
Authors: Gilat A.
Published: July 2009

An elastic/viscoplastic theory that includes anisotropic strain hardening is presented. The theory is a combination of the elastic/viscoplastic formulation of Perzyna [4] and the anisotropic hardening model for time-independent plasticity of Mroz [6]. The theory is used in the analysis of pressure-shear plate impact experiments on commercially pure alpha titanium. Good agreement between theory and experiment is observed.
The Uniaxial Unloading Behavior of Two Engineering Alloys at Room Temperature
Authors: Krempl E. , Kallianpur V. V.
Published: July 2009

A computer-controlled servohydraulic testing machine was used to study the unloading behavior from the fully plastic region of AISI Type 304 Stainless Steel and of the Ti-7Al-2Cb-1Ta Titanium alloy at room temperature. Load and displacement control were used and in some tests the magnitude of the loading rate was changed by two orders of magnitude at the point of unloading. Unloading behavior from the fully plastic region depends strongly on the control mode (the boundary condition) and is not linearly elastic, but curved. In displacement control, positive slopes larger than the elastic one are obtained leaving the unloading point. Small negative slopes and creeping out may be observed in load control. At some region below the maximum stress and above zero stress the unloading curve attains an elastic slope. At zero stress the slope is less than the elastic one. The observed behavior is influenced by the presence of significant rate dependence of the deformation behavior (viscosity effects).
Scattering of a Rayleigh Wave by an Elastic Quarter Space
Authors: Gautesen A. K.
Published: July 2009

We study the two-dimensional, steady-state problem of the scattering of waves in a homogeneous, isotropic, linear-elastic quarter space. We derive decoupled equations for the Fourier transforms of the normal and tangential displacements on the free surfaces. For incidence of a Rayleigh surface wave, we plot the amplitudes and phases of the surface waves reflected and transmitted by the corner. These curves were obtained numerically.
Asymmetric Problem of Loading Under a Smooth Punch
Authors: Fabrikant V. I. , Selvadurai A. P. S. , Xistris G. D.
Published: July 2009

This paper examines the three-dimensional elastostatic problem related to the interaction between a smoothly indenting rigid circular punch on a transversely isotropic elastic half-space and an internal concentrated force. The localized force acts at an arbitrary point within the half-space region. The analysis of the problem focuses on the evaluation of the resultant displacement and rotation experienced by the rigid punch.
A Study of Dynamic Instability of Plates by an Extended Incremental Harmonic Balance Method
Authors: Pierre C. , Dowell E. H.
Published: July 2009

The dynamic instability of plates is investigated with geometric nonlinearities being included in the model, which allows one to determine the amplitude of the parametric vibrations. A modal analysis allowing one spatial mode is performed on the nonlinear equations of motion and the resulting nonlinear Mathieu equation is solved by the incremental harmonic balance method, which takes several temporal harmonics into account. When viscous damping is included, a new algorithm is proposed to solve the equation system obtained by the incremental method. For this purpose, a new characterization of the parametric vibration by its total amplitude—or Euclidian norm—is introduced. This algorithm is particularly simple and convenient for computer implementation. The instability regions are obtained with a high degree of accuracy.
On the Recursive Determination of Body Frames for Multibody Dynamic Simulation
Authors: Roberson R. E.
Published: July 2009

In multibody dynamic simulation it often is convenient to choose new body axes such that all body frames are parallel to the attitude reference frame when the system of bodies is in a prescribed configuration consistent with the interbody constraints. Computational details are given of how this may be done efficiently using a recursive method.
Coupled Torsional and Transverse Vibration of Unbalanced Rotor
Authors: Cohen R. , Porat I.
Published: July 2009

A model of an unbalanced rotor, driven by a torsion-flexible shaft through a constant velocity joint, is used to investigate the combination-resonance effect in coupled torsional-transverse vibration. Analysis of the nonlinear equations of motion by an asymptotic method yields the instability zones of the system. Results are in very good agreement with those obtained by direct numerical solution of the equations of motion.
Effect of Hinge Gap on Aerodynamics of Thin Airfoils Having an Oscillating Flap
Authors: Ando S. , Lee D.-H.
Published: July 2009

Nonsteady load distributions on a thin airfoil in inviscid incompressible flow having an oscillating flap with a narrow hinge gap are investigated. The angle of attack is assumed to be zero in front of the hinge gap. The problem is first attacked numerically through Poisson’s integral equation to compare it with analytical methods derived later. The logarithmic singularity in the kernal function is treated with special care. Secondly the method of matched asympototic expansions is used to analyze the problem. It brings forth simple closed-form expressions. Comparisons of results of the two methods show excellent agreement with each other, when gap width-to-chord ratio is less than 0.1. In the Appendix, a simplified method is presented where no inner solution needs to be considered. It is useful for the gap/chord ratio less than 0.01.
Free Edge Strain Concentrations in Real Composite Laminates: Experimental-Theoretical Correlation
Authors: Herakovich C. T. , Post D. , Buczek M. B. , Czarnek R.
Published: July 2009

The magnitude of the maximum shear strain at the free edge of axially loaded [θ2/–θ2]s and [(± θ)2]s composite laminates was investigated experimentally and numerically to ascertain the actual value of strain concentration in resin matrix laminates and to determine the accuracy of finite element results. Experimental results using moire´ interferometry show large, but finite, shear strain concentrations at the free edge of graphite-epoxy and graphite-polyimide laminates. Comparison of the experimental results with those obtained using several different finite element representations showed that a four-node isoparametric finite element provided the best and most trouble-free numerical results. The results indicate that the ratio of maximum shear strain at the free edge to applied axial strain varies with fiber orientation and does not exceed nine for the most critical angle which is 15 deg.
Eddy Current Flow Near Cracks in Thin Plates
Authors: Hui C. Y. , Ruina A.
Published: July 2009

The problem of magnetically induced eddy current flow in a thin cracked plate is posed and solved for a few special cases. The current density is singular at the tip of a nonconducting crack. The strength of this singularity, denoted M, is found by reducing the eddy current problem to a conduction problem and then using the mathematical methods of fracture mechanics. M is found for a small crack in a current field, a small crack in a round plate with spatially uniform magnetic field, and a half-cracked round plate with spacially uniform magnetic field.
Saint-Venant End Effects for Incremental Plane Deformations of Incompressible Nonlinearly Elastic Materials
Authors: Abeyaratne R. , Horgan C. O. , Chung D.-T.
Published: July 2009

This paper is concerned with assessing the extent of Saint-Venant end effects within the theory of small deformations superposed on a large deformation for plane strain of homogeneous, isotropic, incompressible materials. The problem considered is that of plane deformation of a body which in its undeformed configuration, occupies a semi-infinite strip. The long sides of the strip are free of traction while the short side is subjected to prescribed normal and shear tractions. A purely normal tensile traction is applied uniformly at the remote end. For the case of slightly nonuniform end tractions at the near end, it is shown that the resulting stress distribution differs from that of homogeneous uniaxial tension by an exponentially decaying function of the distance from the end of the strip. The decay rate is characterized explicitly in terms of the strip width, the remotely applied tensile load, and constitutive parameters. Numerical results are provided for the Mooney-Rivlin material and power-law materials which either harden or soften in tension.
Vibration of a Cracked Cylindrical Shell of Rectangular Planform
Authors: Solecki R. , Forouhar F.
Published: July 2009

Harmonic vibrations of a circular, cylindrical shell of rectangular planform and with an arbitrarily located crack, are investigated. The problem is described by Donnell’s equations and solved using triple finite Fourier transformation of discontinuous functions. The unknowns of the problem are the discontinuities of the slope and of three displacement components across the crack. These last quantities are replaced, using constitutive equations, by curvatures and strain in order to improve convergence and to represent explicitly the singularities at the tips. The formulas for differentiation of discontinuous functions are derived using Green-Gauss theorem. Application of the boundary conditions at the crack leads to a homogeneous system of linear algebraic equations. The frequencies are obtained from the characteristic equation resulting from this system. Numerical results for special cases are provided.
Axial Stress-Time History Measurements in Impulsively Loaded Aluminum Rods Using the Double Gauge Technique
Authors: Rosenberg Z. , Mayseless M. , Partom Y.
Published: July 2009

The purpose of this Brief Note is to present experimental stress-time histories along the centerline of impulsively loaded aluminum rods. The measurement is based on the double gauge technique in which we use both a manganin stress gauge and a constantan strain gauge at the same location in the rod. The strain gauge record enables one to eliminate the strain contribution to stress gauge resistance change and have a stress-time history. The measured stress history is compared to a calculated one using two-dimensional Lagrangian code and the agreement between them is good.
Some Stability Results for General Linear Lumped-Parameter Dynamic Systems
Authors: Ahmadian M. , Inman D. J.
Published: July 2009

A technique is presented for stability of equilibrium of general, linear, lumped-parameter dynamic systems. Liapunov functions are used to develop stability conditions that are direct in terms of the mass, damping, and stiffness matrices. The significance of what is presented here is twofold. First, this technique can be applied to general asymmetric systems. Second, it offers direct conditions that can easily be programmed on a digital computer to handle high-order systems. Many previously developed results, such as the KTC theorem and its extensions, are mentioned. Next, it is shown that the present study may provide broader applications because general systems are included and a more convenient approach is offered. Examples are used to illustrate the validity and applications of the presented results.
The Mechanisms of Determining Shock Locations in One and Two Dimensional Transonic Flows
Authors: Nixon D. , Liu Y.
Published: July 2009

The mechanism that locates a shock wave in a transonic flow in one and two dimensions is examined. It is found that in one dimension the shock is located by specifying the downstream pressure whereas in two dimensions the shock is located by the application of an entropy condition at the sonic line.
An Analysis of Large Strain Viscoplasticity Problems Including the Effects of Induced Material Anisotropy
Authors: Chandra A. , Mukherjee S.
Published: July 2009

This paper examines the modeling of large shearing of solids that exhibit induced anisotropy during inelastic deformation. The “traditional” approach uses integration of material rates of certain tensors which are obtained from Jaumann rates of these tensors delivered by a material constitutive model. This leads to erroneous results (spurious oscillations) in a simple shear example. Several previous authors have suggested resolutions to this dilemma based on modification of the constitutive model — usually based upon changing the interpretation of the tensor rates delivered by a constitutive model. This paper draws attention to another aspect of the modeling process — that of obtaining the components of tensors such as the Cauchy stress in a global, space-fixed basis, from the objective rates of these tensors as delivered by the material constitutive model. In essence, it is suggested here that the elastic rotation rather than the spin should be used to achieve the above objective. The rotation idea is first discussed in the context of a simple shear example. This philosophy is then incorporated in a general purpose two-dimensional boundary element method (BEM) formulation and computer program. Numerical results for the simple shear problem, using the rotation idea, are obtained both by direct integration and from the general BEM computer program.
Mechanism of Surface Crack Growth in Lubricated Rolling/Sliding Spherical Contact
Authors: Kaneta M. , Suetsugu M. , Murakami Y.
Published: July 2009

A possible mechanism of the crack growth is described by calculating stress intensity factors for a semicircular surface crack under a spherical Hertzian contact moving over a cracked elastic half-space surface. In the analysis the crack is assumed to be inclined at an angle of 45 deg from the surface. In particular, the effects of surface traction, frictional force between crack faces, and oil hydraulic pressure caused by oil penetrated into the crack are discussed.
A Model for the Flow of a Chopped Fiber Reinforced Polymer Compound in Compression Molding
Authors: Barone M. R. , Caulk D. A.
Published: July 2009

The flow of a chopped fiber reinforced polymer compound in compression molding is modelled as a two-dimensional membrane-like sheet which extends uniformly through the cavity thickness with slip at the mold surface. The model is consistent with both the kinematic mechanisms observed in actual flow and the three-dimensional anisotropy caused by the arrangement of fibers in the sheet. The material resistance to extension is expressed in a constitutive equation for the two-dimensional stress resultant formed by integrating the planar stress components through the thickness of the cavity. This stress resultant is assumed to be a linear function of the corresponding planar rate of deformation in the molding compound. Through a mechanism of fiber-resin interaction, the material resistance to extension can be characterized by a single scalar function of the transverse temperature distribution. Three alternatives are considered for the friction response at the cavity surface: (i) constant magnitude, (ii) proportional to the relative velocity (hydrodynamic), and (iii) proportional to the normal component of the stress vector (Coulomb). These three assumptions are compared by considering their general implications on the flow-front progression. The latter two are examined in some detail for thin charges in which the material resistance to extension is negligible compared to the effect of friction. Analytical solutions for an elliptical charge are obtained for both hydrodynamic and Coulomb friction. By comparing these solutions with experimental results, we conclude that the hydrodynamic model for the friction response is the best of the three proposed alternatives.
A Green’s Function Solution for Plane Anisotropic Contact Problems
Authors: Miller G. R.
Published: July 2009

An analytical expression for the stresses in contacting anisotropic cylinders containing a singularity is derived, including the effects of sliding friction. The solution is obtained using complex variables, and is expressed in terms of piece-wise analytic functions. Concentrated force and edge dislocation type singularities are both considered, providing a solution useful for various boundary integral applications.
A Constitutive Model of Cyclic Plasticity for Nonlinear Hardening Materials
Authors: Ohno N. , Kachi Y.
Published: July 2009

A constitutive model is proposed for cyclic plasticity of nonlinear hardening materials. The concept of a cyclic nonhardening range, which enables us to describe the dependence of cyclic hardening on the amplitude of cyclic straining or stressing, is employed together with the idea of a two-surface plasticity model. Results of the proposed model are compared with experiments of 304 and 316 stainless steels in several cases of cyclic loading in which mean strain is zero or nonzero and strain limits are fixed or variable. Thus, it is shown that the model successfully describes both the cyclic hardening phenomenon and the transient elastoplastic behavior after initial and reverse yields of these materials. The capability of the model to provide nonlinear cyclic stress-strain curves is also discussed.
Effect of Yield Surface Curvature on Necking and Failure in Porous Plastic Solids
Authors: Becker R. , Needleman A.
Published: July 2009

The effect of material path dependent hardening on neck development and the onset of ductile failure is analyzed numerically. The calculations are carried out using an elastic-viscoplastic constitutive relation that has isotropic hardening and kinematic hardening behaviors as limiting cases and that accounts for the weakening due to the growth of micro-voids. Final material failure is incorporated into the constitutive model by the dependence of the plastic potential on void volume fraction. Results are obtained for both axisymmetric and plane strain tension. Failure is found to initiate by void coalescence at the neck center in axisymmetric tension and within a shear band in plane strain tension. The increased curvature of flow potential surfaces associated with the kinematic hardening solid leads to somewhat more rapid diffuse neck development than occurs for the isotropic hardening solid. However, a much greater difference between the predictions of the two constitutive models is found for the onset of ductile failure.
Fatigue Crack Initiation Under Cyclic Torsion
Authors: Cooley W. U. , Lin T. H.
Published: July 2009

Lin’s ratchet mechanism developed by Lin and his associates for fatigue crack initiation under tension and compression loading is here applied to fatigue under torsional loadings. Under the former loading, the most favorable slip system has a slip plane and a slip direction, both making 45 deg with the free surface; while under the latter the most favorable slip system has a slip direction parallel to the free surface. High cycle fatigue loading is considered. A slip direction parallel to the free surface does not produce extrusion or intrusion. A surface crystal with a slip plane normal to the shaft axis and with a slip direction making an angle β with the free surface was considered. Displacement component normal to the free surface is considered to be a measure of the amount of intrusion, which, in turn, is taken as a measure of crack initiation. It was found that the angle β, giving a maximum displacement component normal to the free surface, varies with the torsional stress. Under the same maximum range of shear stress (zero mean stress), the growth of the displacement component normal to the free surface is much larger in the tension and compression specimen than in torsional ones.
Scattering of Love Waves by a Surface-Breaking Crack
Authors: Angel Y. C.
Published: July 2009

The interaction of Love waves with a surface-breaking crack normal to the free surface is investigated. By the use of Fourier transform techniques, the mixed-boundary value problem is reduced to a singular integral equation which is solved numerically. It is shown that the reflected and transmitted displacement fields at some distance from the crack are the superposition of a finite number of Love-wave modes. The reflection coefficients for the first three modes and the transmission coefficient are plotted versus the frequency. Several sharp resonances are observed. Each resonance corresponds to the vanishing of the amplitude of a particular Love-wave mode.
Stress Analysis of Sandwich Plates With Unidirectional Thickness Variation
Authors: Paydar N. , Libove C.
Published: July 2009

A small deflection theory is presented for the stresses and deformations in variable thickness elastic sandwich plates that are symmetric about a middle surface. In this analysis the face sheets are treated as membranes; the core is assumed to be inextensible in the thickness direction, to carry only transverse shear stress on its cross sections normal to middle surface, and to be deformable in transverse shear. The theory takes into account the contribution of the face sheet membrane forces (by virtue of their slopes) to the transverse shear.
Effects of Axial Imperfections on Vibrations of Anti-Symmetric Cross-Ply, Oval Cylindrical Shells
Authors: Hui David , Du I. H. Y.
Published: July 2009

This paper examines the effects of axial geometric imperfections on the fundamental vibration frequencies of cross-ply simply-supported oval cylindrical shells. It is found that the presence of such imperfection with small amplitudes may significantly raise or lower the fundamental frequencies, depending on the wave numbers of the imperfection and vibration mode. The effects of oval eccentricity, bending-stretching coupling of the material, the reduced-Batdorf parameter and Young’s moduli ratio are examined. It appears that the present problem has not been examined, even in the simplified case of oval cylindrical shells made of isotropic-homogeneous material.
Thermal Stress in a Coated Short Fibre Composite
Authors: Mikata Yozo , Taya Minoru
Published: July 2009

When a coated short fibre composite is subjected to temperature change, thermal stresses in and around the coated fibres are induced due to the mismatch of thermal expansion coefficients of the constituents, resulting in a possibility of cracking in the coating. The problem of the above thermal stresses in a coated short fibre composite is solved by using the Boussinesq-Sadowsky stress functions. The present results are compared with Eshelby’s solutions for an extreme case and good agreement between the two methods is obtained. A parametric study is then conducted to examine the effect of the geometry and thermo-mechanical properties of the coating on the stress field in and around a coated short fibre. It is found in this study that the stress field in the coating is sensitive to the properties and geometry of the coating.
Modeling and Analysis of the Dynamics of a Drill Penetrating a Thin Plate
Authors: Reinhall P. G. , Storti D. W.
Published: July 2009

We propose a simplified model of the drilling process which is useful in understanding the problem of noncircular hole production. The dynamics of a drill penetrating a circular hole in a rigid plate are studied analytically, and numerical methods are then used to include the effects of material removal. We show that certain drill trajectories which lead to noncircular holes can be stabilized by material removal. Based on these findings, we recommend careful drill speed selection as a means of minimizing the probability of noncircular hole production, and explain why even this solution may not be sufficient for the case of very soft or composite plate materials.
The Effect of Surface Depressions on Conformal and Nonconformal Contact Pressure Distributions
Authors: Chen H. H. , Marshek K. M.
Published: July 2009

This paper presents a numerical method for analyzing the stress concentration around one or several shallow longitudinal surface depressions. The modified iterative method and modified influence function are used in conjunction with an automatic mesh generation technique to avoid solving the ill-condition of the large scale linear system and therefore a wide range of contact problems having multiply-connected regions can be solved. The effect of the blending radius and the pit size on the stress concentration for a pitted copper cylinder contacting an elastic half space are examined. The conformal pressure distributions for a smooth steel journal contacting a self-lubricated bearing with various radial clearances and material properties are also determined. The numerical results show that the smaller the blend radii, the higher the stress concentration for a given pit size. A large deviation from the Hertzian solution is observed for a surface with large pits because of the loss of pressure supporting area. The results of the analysis provides a design tool for predicting the magnitude and location of the peak stress for the rolling and sliding contact elements.
Longitudinal Shear Problem for an Elastic Body With Two Fixed Edges
Authors: Hasebe N. , Sugimoto T. , Nakamura T.
Published: July 2009

A semi-infinite elastic body with an arbitrary shape and an infinite one with a hole under uniform longitudinal shear load are investigated. These bodies have a boundary with two fixed parts. The respective complex stress functions are obtained in closed form by using a conformal mapping function. Doubly connected elastic bodies with symmetry can also be treated. Examples of the stress distribution and expressions for the stress intensity factor are shown.
Elastodynamic Formulation of the Eulerian-Lagrangian Kinematic Description
Authors: Koh H. M. , Haber R. B.
Published: July 2009

An extension of the Eulerian-Lagrangian kinematic description (Haber, 1984) to elastodynamic problems is presented. Expressions are derived for field variables and material time derivatives using the new kinematic description. The variational equation of motion is written in a weak form suitable for use with isoparametric finite elements. The new kinematic model allows a finite element mesh to continuously adjust for changes in the structural geometry, material interfaces, or the domain of the boundary conditions without a discrete remeshing process. Applications of the new model to mode I dynamic crack propagation demonstrates its advantages over moving mesh methods based on conventional Lagrangian kinematic models. Numerical results show excellent agreement with analytic predictions.
Damped Response of Shells by a Constrained Viscoelastic Layer
Authors: El-Raheb M. , Wagner P.
Published: July 2009

Vibration absorbers are introduced into an asymmetric configuration of thin cylinders and tori enclosing an acoustic medium. The absorbers consist of thin axial strips bonded to the cylinder with a thin viscoelastic layer. The constrained layer dissipates the energy of relative motions between strip and cylinder. The absorber is most effective on response modes with two or more circumferential waves. The use of transfer matrices is extended to the coupled cylinder-absorber system.
Boundary Element Method by Dislocation Distribution
Authors: Sheng C. F.
Published: July 2009

The method of dislocation distribution has been applied extensively to crack related problems by many people in the last fifteen years. It has been proved to be very successful in terms of accuracy and versatility. However, the potential of applicability of this method has not been fully explored. This paper shows a way to apply this method to plane stress problems with any geometry and loading conditions. The method of dislocation distribution is similar to the Boundary Element Method in spirit, but has the advantage of enjoying the fully developed numerical schemes in solving the formulated system of singular integral equations. Without extensive investigation, it is hard to tell whether this new approach will produce better results than the traditional BIE method. However, as demonstrated by the excellent results from the numerical examples, this method should be competitive and have the potential to become one of the best candidates for the type of elasticity problems where local stress evaluation is needed.
An Experimental Study of the Reflection and Transmission of Flexural Waves at an Arbitrary T-Joint
Authors: Doyle J. F. , Kamle S.
Published: July 2009

Further developments of an experimental methodology for analyzing the effect of structural joints on wave propagation are presented. Experimental results for an arbitrary T-joint are discussed as well as improved ways of characterizing the incident wave.
A Rate-Independent Constitutive Theory for Finite Inelastic Deformation
Authors: Carroll M. M.
Published: July 2009

A rate-independent constitutive theory for finite inelastic deformation is formulated in terms of the symmetric Piola-Kirchhoff stress, the Lagrangian strain, and a kinematic tensor which describes inelastic or microstructural effects. Assumptions of (a) continuity in the transition from loading to neutral loading, (b) consistency, and (c) nonnegative work in closed cycles of deformation, lead to simplification of the theory. The response is described by two scalar functions — a stress potential and a loading function. The theory can describe isotropic or anisotropic response, and allows for hardening, softening, or ideal behavior. It may also be appropriate to describe the response of porous materials, such as metals, rocks and ceramics, and also the evolution of damage.
A Composite Plate Theory for Arbitrary Laminate Configurations
Authors: Toledano A. , Murakami H.
Published: July 2009

In order to improve the accuracy of in-plane responses of shear deformable composite plate theories, a new laminated plate theory was developed for arbitrary laminate configurations based upon Reissner’s (1984) new mixed variational principle. To this end, across each individual layer, piecewise linear continuous displacements and quadratic transverse shear stress distributions were assumed. The accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by Pagano (1969). A comparison with the exact solutions obtained for symmetric, antisymmetric, and arbitrary laminates indicates that the present theory accurately estimates in-plane responses, even for small span-to-thickness ratios.
Cumulative Plastic Flow in Rolling and Sliding Line Contact
Authors: Hearle A. D. , Johnson K. L.
Published: July 2009

Rollers loaded above their shakedown limit are known to undergo cumulative plastic shearing of their surface layers. An approximate analysis of this deformation by Merwin and Johnson (1963) was in good accord with experiments, but a recent finite-element calculation by Bhargava et al. (1984) predicted much larger deformations. This paper investigates the discrepancy and presents an alternative analysis which supports that by finite-elements.
The Modified Mixture Theory for Fluid-Filled Porous Materials: Applications
Authors: Katsube N. , Carroll M. M.
Published: July 2009

The recently established modified mixture theory for fluid-filled porous materials is applied to two steady state boundary value problems; also, how the newly developed theory provides more general solution than Biot’s theory is examined. The velocity profiles in steady state boundary value problems are found to depend on the ratio of a characteristic length of the microstructure to a characteristic length defined by the boundary conditions. As opposed to Biot’s theory, the zero fluid velocity condition on the boundary are satisfied and the existence of a non-Darcy flow closer to the boundary are shown.
The Stress Field Induced by Normal Contact Between Dissimilar Spheres
Authors: Hills D. A. , Sackfield A.
Published: July 2009

The stress field induced by the mutual compression of two spheres having dissimilar elastic constants is deduced. Solutions are found assuming full slip, full stick, and partial slip at the interface, but coupling between the shear traction and vertical displacement of the surfaces is neglected. It is shown that significant modifications to the Hertzian stress field occur at the surface, and that these decay rapidly with depth.
Optimal Beam and Plate Foundations for Minimum Compliance
Authors: Plaut R. H.
Published: July 2009

Uniform beams and circular plates on nonuniform elastic foundations are considered. They are subjected to a uniformly distributed load and have various boundary conditions. For a specified total stiffness of the foundation, the distribution of foundation stiffness is determined which minimizes the compliance (i.e., the work done by the applied load). The optimal solutions for the beams consist of either a single elastic support or a region of uniform foundation bounded by elastic supports (except at free ends). For the plates, there is a central, circular region with a uniform foundation, bounded by a circular elastic support. In comparison to a uniform foundation, the decrease in compliance may be substantial.
Design of Material Properties That Yield a Prescribed Global Buckling Response
Authors: Antman S. S. , Adler C. L.
Published: July 2009

In the context of the large buckling of a nonlinearly elastic column under end thrust, this paper treats the design of (constitutive) functions appearing in bifurcation problems so as to produce a prescribed first bifurcating branch (e.g., a branch having a prescribed number of wiggles, which produce a prescribed pattern of hysteresis with snap bucklings in loading-unloading processes). The solution of this design problem also yields a method for determining a constitutive function from a single buckling experiment. A dual variational formulation is used to reduce the design problem to the solution of a linear Volterra integral equation of the first kind with a singular kernel. Effective numerical methods for the solution of such ill-posed equations are described and then applied to some physically interesting examples. Generalizations are discussed.
General Solutions for the Inelastic Behavior of Pressurized Membranes
Authors: Neale K. W. , Chater E.
Published: July 2009

The small-deflection behavior of inelastic membranes supported along arbitrary contours and subjected to lateral pressure is considered. Hill and Stora˚kers’ (1980) solution for isotropic power-law hardening membranes is extended to a wide class of anisotropic material response. Applications to circular membranes are given for anisotropic materials characterized by Budiansky’s (1984) general transversely isotropic yield function. Specific results corresponding to the yield functions proposed by Hill (1979) and Bassani (1977) are also presented.
Effects of Nonconstant Spin Rate on the Vibration of a Rotating Beam
Authors: Kammer D. C. , Schlack A. L.
Published: July 2009

The effects of a time-dependent angular velocity upon the vibration of a rotating Euler beam are presented. It is assumed that the angular velocity can be expressed as the sum of a steady-state value and a relatively small periodic perturbation. Equations of motion are derived for a beam oriented parallel to the spin axis. Terms with time-dependent coefficients appear in the equations of motion due to the nonconstant spin rate resulting in a nonautonomous system possessing parametric instabilities. A perturbation technique called the KBM method is used to derive general expressions for approximate solutions and instability region boundaries. A simple perturbation function is assumed for the purpose of illustrating the use of the derived general expressions.
Large Amplitude Oscillations of Thin Circular Rings
Authors: Maganty S. P. , Bickford W. B.
Published: July 2009

Using an intrinsic formulation, an accurate set of geometrically nonlinear equations of motion is derived for the large amplitude oscillations of a thin circular ring. Non-dimensionalization of the equations of motion and the compatibility conditions indicates clearly that certain terms involving the extensional deformation, the shear deformation, and the rotatory inertia are relatively small and can be discarded. The resulting equations of motion are analyzed by the method of multiple scales with a single bending mode approximation to the linear problems indicating a softening type of nonlinearity for both the in-plane and the out-of-plane problems with the out-of-plane flexural motion experiencing a greater degree of softening when compared to that of the in-plane flexural motion. The results for the nonresonant case indicate that the frequency of an out-of-plane bending mode is significantly reduced by the presence of a nonzero in-plane bending amplitude, whereas the results for the resonant case indicate the presence of unsteady oscillations with an exchange of energy between the in-plane and the out-of-plane modes.
The Normal Impact on an Elastic Half Space of an Elastic Rod-Mass System
Authors: Downey H. A. , Bogy D. B.
Published: July 2009

The normal impact problem of a one-dimensional elastic rod with a lumped mass on the trailing end onto an elastic half space is solved for the time-dependent interface displacement and stress. This problem is reduced to an integral equation, whose kernel is the solution of a simpler auxiliary problem, which is solved in closed form. After examining the graph of the kernel it is found that a simple linear expression adequately represents its half space contribution. This approximation allows the integral equation to be solved in closed form and provides insight into its solution. Numerical results are presented, which display the impact and rebound of the rod, and illustrate the presence of major effects from the Rayleigh wave in the half space and the reflected wave from the trailing end of the rod. Results are presented for various half-space materials, rod lengths, and masses. It is found that in the absence of the mass the maximum contact stress depends entirely on the rod material, but with the lumped mass added the contact stress can become much greater and depends on the rod, the half space, and the mass.
The Strain-Energy Density of Compressible, Rubber-Like Axishells
Authors: Simmonds J. G.
Published: July 2009

A recent method for deriving, by descent from three dimensions, strain-energy densities in a first-approximation, large-strain theory of incompressible, elastically isotropic shells of revolution undergoing torsionless, axisymmetric deformation (axishells) is adapted to axishells made of compressible material. Application is made to the Blatz-Ko strain-energy densities for a polyurethane (“continuum”) rubber and a foam rubber.
The Shrink Fit with Nonlinearly Hardening Elastic-Plastic Hub
Authors: Gamer Udo
Published: July 2009

Based on Tresca’s yield criterion and the associated flow rule, stresses and displacement in a rotating shrink fit consisting of an elastic disk and a partially plasticized annulus are calculated for an arbitrary nonlinear hardening law. It is shown that the elastic-plastic border radius and the stresses in the elastic region of the hub do not depend on the hardening law.
A Continuum Model for Void Nucleation by Inclusion Debonding
Authors: Needleman A.
Published: July 2009

A cohesive zone model, taking full account of finite geometry changes, is used to provide a unified framework for describing the process of void nucleation from initial debonding through complete decohesion. A boundary value problem simulating a periodic array of rigid spherical inclusions in an isotropically hardening elastic-viscoplastic matrix is analyzed. Dimensional considerations introduce a characteristic length into the formulation and, depending on the ratio of this characteristic length to the inclusion radius, decohesion occurs either in a “ductile” or “brittle” manner. The effect of the triaxiality of the imposed stress state on nucleation is studied and the numerical results are related to the description of void nucleation within a phenomenological constitutive framework for progressively cavitating solids.
Viscoplastic Buckling of Silicon Ribbon
Authors: Tsai C. T. , Dillon O. W.
Published: July 2009

Silicon ribbon grown by the dendritic web process passes through a rapidly changing thermal profile in the growth direction. This rapidly changing profile induces stresses which cause buckling. Based on a viscoplastic material response function (Haasen-Sumino model), the creep buckling behavior of the silicon ribbon is investigated. The lateral deflection speeds describing the viscoplastic buckling behavior are calculated. It is found that the deflections of some modes increase with time while others die out. The role of the residual stresses in viscoplastic buckling is examined.
Buckling of a Rectangular Frame Revisited
Authors: Seide P.
Published: July 2009

An investigation of the buckling under uniform beam load of a rectangular frame with columns restrained by linear rotational springs indicates that for certain ranges of bending stiffness ratio, length-height ratio, and support rotational stiffness parameter, the antisymmetrical bifurcation mode of buckling does not exist and buckling occurs at a symmetrical deformation limit load. The ranges of parameters for which this phenomenon may be important are studied.
Periodic Array of Cracks in a Half-Plane Subjected to Arbitrary Loading
Authors: Nied H. F.
Published: July 2009

The plane elastic problem for a periodic array of cracks in a half-plane subjected to equal, but otherwise arbitrary normal crack surface tractions is examined. The mixed boundary value problem, which is formulated directly in terms of the crack surface displacements, results in a hypersingular integral equation in which the unknown function is the crack opening displacement. Based on the theory of finite part integrals, a least squares numerical algorithm is employed to efficiently solve the singular integral equation. Numerical results include crack opening displacements, stress intensity factors, and Green’s functions for the entire range of possible periodic crack spacing.
Integrals of Linearized Differential Equations of Motion of Mechanical Systems; Part II: Linearized Equations of Motion
Authors: Kane T. R. , Djerassi S.
Published: July 2009

Theorems derived in Part I are here applied to differential equations of motion of mechanical systems. The theorems are reformulated in terms of variables appearing in dynamical equations of motion, and their use is illustrated by means of an example.
A New Method for Finding Symmetric Form of Asymmetric Finite-Dimensional Dynamic Systems
Authors: Ahmadian Mehdi , Chou Shui-Hang
Published: July 2009

A subclass of general lumped-parameter dynamic systems which can be transformed into an equivalent symmetric form is considered here. For the purpose of the present study, these systems are divided into two categories: those without velocity dependent forces (pseudo-conservative systems) and those with velocity dependent forces (pseudo-symmetric systems). For each category, the results on symmetrizability of matrices are used to develop an effective, systematic technique for computing the coordinate system in which the system is symmetric. The primary advantages of the technique presented in this study are twofold. First, it is computationally efficient and stable. Second, it can effectively handle systems with many degrees-of-freedom, unlike the trial and error approach suggested in previous studies.
Variational Principles for Some Nonstandard Elastic Problems
Authors: Shield R. T.
Published: July 2009

Variational principles are derived for some nonstandard problems involving elastic bodies in smooth contact. For these problems, the portions of the surfaces where one boundary condition holds rather than another must be determined as part of the solution to the problem. Cases considered include a body containing a crack or delamination, indentation by a rigid punch, and contact with an elastic foundation.
Torsion of Cylinders With Shape Intrinsic Orthotropy
Authors: Cowin S. C.
Published: July 2009

Shape intrinsic orthotropy may be thought of as the type of elastic material symmetry possessed by the wood tissue of a tree. Each year’s new growth rings form a laminate around a central core. The axes of material symmetry lie in the directions tangent and normal to the growth rings or laminates and along the axis of the cylinder. Let Gtz denote the linear elastic orthotropic shear modulus associated with the axial and tangential directions, the tangent plane of a laminate. It is shown here that, for a certain class of elastic cylinders with shape intrinsic orthotropy, the solution to the torsion problem is the same as the solution to the torsion problem for the isotropic cylinder of the same shape if the isotropic shear modulus G were replaced by the orthotropic shear modulus Gtz.
Steady Flow in Porous, Elastically Deformable Materials
Authors: Parker K. H. , Mehta R. V. , Caro C. G.
Published: July 2009

The steady, one-dimensional flow of an incompressible fluid through a deformable porous material is studied theoretically and experimentally. The theoretical model is essentially that of Biot. Assuming that the stiffness and permeability of the matrix are functions of the local strain gradient, the governing equations can be solved and analytical solutions are presented for several simple constitutive relationships. The stiffness and permeability properties of one particular foam are measured and then used to predict the rate of fluid flow and the distortion of the matrix as a function of the applied pressure difference across the material. Comparison of the predictions of the model with experimental observations indicates good qualitative agreement.
A Finite Element Study of Stable Crack Growth Under Plane Stress Conditions: Part I—Elastic-Perfectly Plastic Solids
Authors: Narasimhan R. , Rosakis A. J. , Hall J. F.
Published: July 2009

A detailed finite element study of stable crack growth in elastic-perfectly plastic solids obeying an incremental plasticity theory and the Huber-Von Mises yield criterion is performed under plane stress, small-scale yielding conditions. A nodal release procedure is used to simulate crack extension under continuously increasing external load. It is found that the asymptotic angular extent of the active plastic zone surrounding the moving crack tip is from θ = 0 deg to about θ = 45 deg. Clear evidence of an elastic unloading region following the active plastic zone is found, but no secondary (plastic) reloading is numerically observed. The near-tip angular stress distribution inside the active plastic zone is in good agreement with the variation inside a centered fan, as predicted by a preliminary asymptotic analysis by Rice. It is also observed that the stress components within the plastic zone have a strong radial variation. The nature of the near-tip profile is studied in detail.