bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonlinear Stability Considerations in Thermoelastic Contact
Authors: Pelesko J. A.
Published: February 2008

The behavior of a one-dimensional thermoelastic rod is modeled and analyzed. The rod is held fixed and at constant temperature at one end, while at the other end it is free to separate from or make contact with a rigid wall. At this free end a pressure and gap-dependent thermal boundary condition is imposed which couples the thermal and elastic problems. Such systems have previously been shown to undergo a bifurcation from a unique linearly stable steady-state solution to multiple steady-state solutions with alternating stability. Here, the system is studied using a two-timing or multiple-scale singular perturbation technique. In this manner, the analysis is extended into the nonlinear regime and dynamic information about the history dependence and temporal evolution of the solution is obtained.
Contact Creep of Biphasic Cartilage Layers
Authors: Kelkar R. , Ateshian G. A.
Published: February 2008

Integral transform methods are used to solve the contact creep problem between two identical cylindrical biphasic cartilage layers bonded to rigid impermeable subchondral bone substrates. The biphasic model employed for cartilage consists of a binary mixture of an incompressible porous-permeable solid phase and an incompressible fluid phase. Solutions are obtained as a function of time, from the instantaneous to the equilibrium responses of the tissue. A significant result of this analysis is that under application of a step load, fluid pressurization may support upward of 96 percent of the total applied load for more congruent joints, shielding the solid collagen-proteoglycan matrix of the tissue from excessive stresses during physiological loading durations. The protection imparted by interstitial fluid pressurization to the solid collagen-proteoglycan matrix of cartilage is investigated, and the influence of material properties and osteoarthritic changes on the potential loss of this protective effect is discussed.
The Elastic Field of an Elliptic Cylindrical Inclusion in a Laminate With Multiple Isotropic Layers
Authors: Beom H. G. , Earmme Y. Y.
Published: February 2008

An elliptic cylindrical inclusion with an eigenstrain in an infinite laminate composed of multiple isotropic layers is analyzed. The problem is formulated by using the classical laminated plate theory in which displacement fields in the laminated plate are expressed in terms of in-plane displacements on the main plane and transverse displacement. Employing a method based on influence functions, an integral type solution to the equilibrium equation is expressed in terms of the eigenstrain. Closed-Form solutions for the elastic fields are obtained by evaluating the integrals explicitly for interior points and exterior points of the ellipse. The elastic fields caused by an elliptic cylindrical inhomogeneity with an eigenstrain in the infinite laminate are determined by the equivalent eigenstrain method. Solutions for a finite laminate with an eigenstrain in a circular cylindrical inhomogeneity are also obtained in terms of material and geometric parameters for each layer composing the laminate.
Thermosolutal Convection in the Presence of Both Vertical and Horizontal Temperature Gradients
Authors: Sahai A. K.
Published: February 2008

The occurrence of stationary and oscillatory solutions in a horizontal layer of fluid in the presence of horizontal and vertical temperature gradients and also in the presence of a vertical solute concentration gradient is investigated. The critical Rayleigh number for oscillatory and stationary solutions is derived numerically for a wide range of values of parameters and it is found that the marginal state is of periodic character in almost all the cases except for very small values of horizontal temperature gradient, solute gradient, and Prandtl number. The effect of horizontal gradient of temperature on the stability of the system is both stabilizing as well as destabilizing. For a large value of horizontal temperature gradient the system first exhibits oscillatory motion and in subsequent time oscillations die down.
Analytical Vibration of Spinning, Elastic Disk-Spindle Systems
Authors: Parker R. G.
Published: February 2008

This work develops the dynamic equations of motion for a spinning disk-spindle system and casts them in a structured formulation that reveals the classical gyroscopic nature of the system. The disk and spindle are modeled as elastic continua coupled by a rigid, three-dimensional clamp. The inherent structure of the system is clarified with the definition of extended operators that collect the component disk, spindle, and clamp equations of motion into a compact analytical form. The extended operators are easily identified as the inertia, elastic bending stiffness, gyroscopic, and rotational stiffness operators, and they possess the symmetry and definiteness characteristics that define gyroscopic continua. Consequently, well-known analytical methods for gyroscopic systems are readily applied to disk-spindle systems. Qualitative eigensolution properties, an exact, closed-form response analysis, and the Galerkin discretization that follow naturally from the structured formulation are discussed. A free and forced vibration example is presented.
Load Identification Through Structural Modification
Authors: Mo¨ller P. W.
Published: February 2008

A load identification problem in structural dynamics has in general multiple solutions. Therefore, additional information, such as the locations of the unknown forces, has to be supplied a priori in order to make a unique solution possible. The present study focuses on cases where such information is not readily available. First, it is shown that, given (tentatively) the spatial shape and position of the load, the Betti reciprocal theorem together with a reference load case may be used to calculate the required magnitude of the unknown load so that the response fits the measurement data as well as possible in a defined sense. In this manner a large number of trial loads may be evaluated with only little computational effort, since no equation system needs to be solved. Second, the situation where several loads, each reproducing the same measurement data, have been identified is investigated. An optimization problem with added discrete masses as design variables is suggested. The solution of this problem yields a structure such that each set of responses generated by each one of the previously identified loads is clearly distinguishable at the transducer positions. The proposed method is a novel approach and should be useful in the load identification problem for an existing structure. A numerical example illustrates the application of the method.
Studies of Elastic-Plastic Instabilities
Authors: Tvergaard V.
Published: February 2008

Analyses of plastic instabilities are reviewed, with focus on results in structural mechanics as well as continuum mechanics. First the basic theories for bifurcation and post-bifurcation behavior are briefly presented. Then, localization of plastic flow is discussed, including shear band formation in solids, localized necking in biaxially stretched metal sheets, and the analogous phenomenon of buckling localization in structures. Also some recent results for cavitation instabilities in elastic-plastic solids are reviewed.
A Geometric Approach for Establishing Dynamic Buckling Loads of Autonomous Potential Two-Degree-of-Freedom Systems
Authors: Kounadis A. N.
Published: February 2008

Nonlinear dynamic buckling of autonomous potential two-degree-of-freedom nondissipative systems with static unstable critical points lying on nonlinear primary equilibrium paths is studied via a geometric approach. This is based on certain salient properties of the zero level total potential energy “surface” which in conjunction with the total energy-balance equation allow establishment of new dynamic buckling criteria for planar systems. These criteria yield readily obtained “exact” dynamic buckling loads without solving the highly nonlinear initial-value problem. The simplicity, reliability, and efficiency of the proposed technique is illustrated with the aid of various dynamic buckling analyses of two two-degree-of-freedom models which are also compared with those obtained by the Verner-Runge-Kutta scheme.
A Reissner’s Mixed Variational Theorem Applied to Vibration Analysis of Multilayered Shell
Authors: Carrera E.
Published: February 2008

A comprehensive model of anisotropic multilayered double curved shells fulfilling a priori the interlaminar continuity requirements for the transverse shear and transverse normal stress as well as the static conditions on the bounding surfaces of the shell is developed in this paper. To this end, Reissner’s mixed variational theorem is employed to derive the equations governing the dynamic equilibrium and compatibility of each layer, while the interlaminar continuity conditions are used to drive the equations at the multilayered level. No assumptions have been made concerning the terms of type thickness to radii shell ratio h/R. Classical displacement formulations and related equivalent single layer equations have been derived for comparison purposes. Comparison of frequency predictions based upon the presented structural model with a number of results spread throughout the specialized literature and obtained via other models reveals that this advanced model provides results in excellent agreement with the ones based on three-dimensional elasticity theory, and better as compared to the ones violating the interlaminar stress continuity requirements and/or transverse normal stress and related effects.
Interaction Between Slow and Fast Oscillations in an Infinite Degree-of-Freedom Linear System Coupled to a Nonlinear Subsystem: Theory and Experiment
Authors: Georgiou I. T. , Schwartz I. , Emaci E. , Vakakis A.
Published: February 2008

The interaction dynamics of a cantilever linear beam coupled to a nonlinear pendulum, a prototype for linear/nonlinear coupled structures of infinite degrees-of-freedom, has been studied analytically and experimentally. The spatio-temporal characteristics of the dynamics is analyzed by using tools from geometric singular perturbation theory and proper orthogonal decompositions. Over a wide range of coupling between the linear beam and the nonlinear pendulum, the coupled dynamics is dominated by three proper orthogonal (PO) modes. The first two dominant PO modes stem from those characterizing the reduced slow free dynamics of the stiff/soft (weakly coupled) system. The third mode appears in all interactions and stems from the reduced fast free dynamics. The interaction creates periodic and quasi-periodic motions that reduce dramatically the forced resonant dynamics in the linear substructure. These regular motions are characterized by four PO modes. The irregular interaction dynamics consists of low-dimensional and high-dimensional chaotic motions characterized by three PO modes and six to seven PO modes, respectively. Experimental tests are also carried out and there is satisfactory agreement with theoretical predictions.
A Three-Dimensional Frictional Contact Element Whose Stiffness Matrix is Symmetric
Authors: Ju S. H. , Rowlands R. E.
Published: February 2008

A three-dimensional contact element based on the penalty function method has been developed for contact frictional problems with sticking, sliding, and separation modes infinite element analysis. A major advantage of this contact element is that its stiffness matrix is symmetric, even for frictional contact problems which have extensive sliding. As with other conventional finite elements, such as beam and continuum elements, this new contact element can be added to an existing finite element program without having to modify the main finite element analysis program. One is therefore able to easily implement the element into existing nonlinear finite element analysis codes for static, dynamic, and inelastic analyses. This element, which contains one contact node and four target nodes, can be used to analyze node-to-surface contact problems including those where the contact node slides along one or several target surfaces.
Analysis of Interaction of Multiple Cracks in a Direct Current Field and Nondestructive Evaluation
Authors: Liu H. , Saka M. , Abe' H. , Komura I. , Sakamoto H.
Published: February 2008

A method of analysis is proposed for nondestructive evaluation of multiple cracks by means of the d.c. (direct current) potential drop technique. Two and three-dimensional multiple cracks are treated. A methodology for considering interaction of cracks based on the equation for an isolated crack is given to calculate the potential drop between both sides of a crack in multiple cracking in a plate. The inverse problem to evaluate the crack depth is analyzed by comparing the potential drop calculated in this way with the measurement. It is shown that the evaluated crack depth is in good agreement with the actual one.
Biphasic Poroviscoelastic Behavior of Hydrated Biological Soft Tissue
Authors: Suh J.-K. , DiSilvestro M. R.
Published: February 2008

Hydrated biological soft tissue consists of a porous extracellular matrix (ECM) and an interstitial fluid. The poroelastic theory (Biot, 1962), which was originally developed for soil mechanics, has been widely used for mathematical modeling of such hydrated biological tissue. This theory assumes that the ECM is incompressible and purely elastic, and that the interstitial fluid is incompressible and inviscid. The overall viscoelasticity of the tissue is expressed as a result of the frictional interaction between the elastic porous matrix and the interstitial fluid. The poroelastic theory, also known as the biphasic theory (Mow et al., 1980) in the biomechanics field, has served well over the past 20 years as an excellent modeling tool for the interstitial fluid flow-dependent viscoelastic response of hydrated soft tissue. It has been demonstrated that hydrated soft tissue also possesses a significant intrinsic viscoelasticity, independent of the interstitial fluid flow. The biphasic poroviscoelastic (BPVE) theory, which was first introduced by Mak (1986a and 1986b), incorporates a viscoelastic relaxation function into the effective solid stress of the poroelastic theory thus accounting for both intrinsic fluid flow-independent and fluid flow-dependent viscoelasticity. The objective of the present study is to investigate the biphasic poroviscoelastic characteristics of hydrated soft tissue, with an emphasis on the relative contribution of fluid flow-dependent and fluid flow-independent viscoelasticity to the overall viscoelastic behavior of soft tissues.
Reduction of the Sanders-Koiter Equations for Fully Anisotropic Circular Cylindrical Shells to Two Coupled Equations for a Stress and a Curvature Function
Authors: McDevitt T. J. , Simmonds J. G.
Published: February 2008

With the aid of the static-geometric duality of Goldenveizer (1961), Cartesian tensor notation, and nondimensionalization, it is shown that the equations of linear shell theory of Sanders (1959) and Koiter (1959), when specialized to a circular cylindrical shell with stress-strain relations exhibiting full anisotropy (21 elastic-geometric constants), can be reduced, with no essential loss of accuracy, to two coupled fourth-order partial differential equations for a stress function F and a curvature function G. Auxiliary formulas for the midsurface displacement components are also given. For isotropic shells with uncoupled stress-strain relations, the equations reduce to a form given by Danielson and Simmonds (1969). The reduction is achieved by adding certain negligibly small terms to the given stress-strain relations. For orthotropic shells of mean radius R and thickness h with uncoupled stress-strain relations, it is shown that the very short decay length of O(hR) and the very long decay length of O(RR/h) (associated with separable solutions of the form e−Rz sin nθ) depend, respectively, to within a relative error of O(h/R), only on the products of different pairs of the eight possible elastic constants.
Elasticity Solution for a Radially Nonhomogeneous Hollow Circular Cylinder
Authors: Zhang Xiangzhou , Hasebe Norio
Published: February 2008

An exact elasticity solution is developed for a radially nonhomogeneous hollow circular cylinder of exponential Young’s modulus and constant Poisson’s ratio. In the solution, the cylinder is first approximated by a piecewise homogeneous one, of the same overall dimension and composed of perfectly bonded constituent homogeneous hollow circular cylinders. For each of the constituent cylinders, the solution can be obtained from the theory of homogeneous elasticity in terms of several constants. In the limit case when the number of the constituent cylinders becomes unboundedly large and their thickness tends to infinitesimally small, the piecewise homogeneous hollow circular cylinder reverts to the original nonhomogeneous one, and the constants contained in the solutions for the constituent cylinders turn into continuous functions. These functions, governed by some systems of first-order ordinary differential equations with variable coefficients, stand for the exact elasticity solution of the nonhomogeneous cylinder. Rigorous and explicit solutions are worked out for the ordinary differential equation systems, and used to generate a number of numerical results. It is indicated in the discussion that the developed method can also be applied to hollow circular cylinders with arbitrary, continuous radial nonhomogeneity.
Conditions for Dual Compression in Perfectly Elastic Three-Dimensional Collisions
Authors: Batlle J. A.
Published: February 2008

The jamb (self-locking) process in single-point three-dimensional rough collisions in multibody systems may lead to a dual compression: a second compression phase develops after an initial compression-expansion one. In such a case the usual energetical restitution coefficient ew is ill defined. This article presents a thorough analysis, by means of the incremental Routh ’s model, of the conditions leading to dual compression in the case of perfectly elastic collisions. For a given general collision configuration and for each value of the friction coefficient greater than the threshold value for jamb, there is always a domain of directions of the incident velocity leading to dual compression. An application example is presented.
Finite Elastic Behavior of Flexible Fabric Composite Under Biaxial Loading
Authors: Luo S.-Y. , Mitra A.
Published: February 2008

A new modeling technique has been introduced to predict the large deformation of flexible composites reinforced by plain-weave fabrics under biaxial loading. The only input required for calculations are the mechanical properties of the constituents and the fabric geometry. The constitutive equations are derived based on a strain energy approach, where fiber and matrix are accounted separately and the curved yarns are assumed to be in sinusoidal shape. Both material and geometrical nonlinearities are considered in the formulation. Good agreement has been found between predictions and experiments under various biaxial loading.
A Stability Criterion for Parameter-Dependent Gyroscopic Systems
Authors: Hryniv R. O. , Lancaster P. , Renshaw A. A.
Published: February 2008

A stability criterion for parameter-dependent gyroscopic systems is established and three examples are used to illustrate its application to typical engineering problems. In a number of practical situations, the criterion can be used to predict system stability with little actual computation and without solving any eigenvalue problem or approximating the eigenvalue locus. Thus, the criterion provides designers with a quick and accurate tool for assessing the stability consequences of potential design changes.
Half-Space Green’s Functions for Transversely Isotropic Piezoelectric Solids
Authors: Dunn M. L. , Wienecke H. A.
Published: February 2008

We obtain explicit closed-form solutions for the half-space Green’s functions for a transversely isotropic piezoelectric solid. The boundary of the half-space is taken to be a plane normal to the unique material axis. The Green’s functions are obtained using a formulation where general solutions in transversely isotropic piezoelectricity are expressed in terms of two potential functions; one satisfying a weighted triharmonic equation and the other satisfying a weighted harmonic equation. By assuming a series solution for the potentials we derive explicit expressions for the Green’s functions.
A Model for Mechanically Induced Densification of Glassy Polymers
Authors: Drozdov A. D.
Published: February 2008

Constitutive equations are derived for the isothermal viscoelastic response of glassy polymers at small strains. An amorphous polymer is modeled as a composite material consisting of a temporary network of long chains, immobile voids, and free volume gas diffusing through the network. The model is applied to analyze stress-induced densification of polymers in tensile and compressive relaxation tests. It is demonstrated that the stress-strain relations adequately predict a decrease in the specific volume observed in uniaxial experiments on polycarbonate.
On Thermal Stress in a Bituminous Pavement: Analytic Solutions and Applications
Authors: Dai H.-H. , Wu G.
Published: February 2008

In this paper, the analytic solution for simulating the thermal stress field in a bituminous pavement is put forward based on a two-dimensional thermoviscoelastic layered system. The numerical analysis is made for the thermal stress field under the typical weather conditions in the north of China. Some new results are obtained. A discussion on the optimum thickness design for the bituminous pavement is given in the final section.
Transmission of SH Waves Through an Elastic Layer Between Two Solids With Frictional Contact Interfaces
Authors: Wang Y.-S. , Yu G.-L.
Published: February 2008

The propagation of SH waves in a three-layered medium containing an interlayer between two semi-infinite solids with frictional contact interfaces is studied. The incident wave, which propagates through the layer from one half-space to another with subcritical angle, is assumed to be strong enough so that friction may be broken, and the local slip may take place at the interfaces. The mixed boundary conditions involving inequalities and unknown intervals lead to a set of recurrence relations. Special examples are given for the case of identical materials to illustrate the mathematical procedure to obtain final results. The interface tractions and relative slip velocities are presented. The interaction between the two interfaces is discussed. It is shown that the slip of the interface near the incident wave may restrain the slip of the interface far from the incident wave, while that the latter may facilitate the former. We also find the instability of the system for similar values of the two interface friction coefficients. Finally, the energy transmitted through the interlayer and dissipated by the friction of the two interfaces are examined.
Dynamic Analysis of Rotating Nonuniform Timoshenko Beams With an Elastically Restrained Root
Authors: Lin S. M.
Published: February 2008

A systematic solution procedure for studying the dynamic response of a rotating nonuniform Timoshenko beam with an elastically restrained root is presented. The partial differential equations are transformed into the ordinary differential equations by taking the Laplace transform. The two coupled governing differential equations are uncoupled into two complete fourth-order differential equations with variable coefficients in the flexural displacement and in the angle of rotation due to bending, respectively. The general solution and the generalized Green function of the uncoupled system are derived. They are expressed in terms of the four corresponding linearly independent homogenous solutions, respectively. The shifting relations of the four homogenous solutions of the uncoupled governing differential equation with constant coefficients are revealed. The generalized Green function of an nth order ordinary differential equation can be obtained by using the proposed method. Finally, the influence of the elastic root restraints, the setting angle, and the excitation frequency on the steady response of a beam is investigated.
Free Vibration of Axially Loaded Laminated Conical Shells
Authors: Tong L.
Published: February 2008

Analytical solutions for the three displacements are obtained, in the form of power series, directly from the three governing equations for free vibration of laminated conical shells under axial load. Numerical results are presented for free vibration of axially loaded laminated conical shells with different geometric parameters and under two types of boundary conditions. It is found that an axial tension increases the frequencies while an axial compression decreases the frequencies. For the shells studied, the effect of axial load on the lowest frequency of the shell is found to be not sensitive to change in semivertex angle when the applied axial load is kept as a constant fraction of the critical buckling load. However, the axial load effect becomes very sensitive to variation in semivertex angle when a constant axial load is applied.
Moment Value at the Center of Circular Plates Under Central Point Load
Authors: Wang C. M. , Ang C. H.
Published: February 2008

It is a well-known fact that the bending moment at the center of a circular plate under a central point load becomes infinite. So, “what is a sensible finite moment value, that one may adopt, at the center of a circular plate under a central point load?” This study addresses this interesting and fundamental question. In order to obtain a finite value to the bending moment, we draw upon the exact deflection expressions from the classical and higher-order plate theories of Mindlin and of Reddy, and make some reasonable assumptions such as the maximum deflection of Mindlin plate being equal to the maximum deflection of the corresponding Reddy plate and the constancy of the Mindlin shear correction factor.
A Generalization of Cattaneo-Mindlin for Thin Strips
Authors: Ja¨ger J.
Published: February 2008

In this paper, a generalization of the Cattaneo-Mindlin solution is derived for thin bonded layers with arbitrary surfaces. We assume that equal layers are in contact, and show that the normal and tangential stress displacement equations are uncoupled and of the same form. In this case the stick condition for tangential shift is identical with the contact condition in normal direction, and the tangential problem can be reduced to the normal problem. Finally, a recursive algorithm for general load cases is proposed. We believe that this model illustrates typical features of elastic bodies with friction. It can also serve as a model for memory effects, employing the elastic superposition technique.
On the Imperfectly Bonded Spherical Inclusion Problem
Authors: Zhong Z. , Meguid S. A.
Published: February 2008

An exact solution is developed for the problem of a spherical inclusion with an imperfectly bonded interface. The inclusion is assumed to have a uniform eigenstrain and a different elastic modulus tensor from that of the matrix. The displacement discontinuity at the interface is considered and a linear interfacial condition, which assumes that the displacement jump is proportional to the interfacial traction, is adopted. The elastic field induced by the uniform eigenstrain given in the imperfectly bonded inclusion is decomposed into three parts. The first part is prescribed by a uniform eigenstrain in a perfectly bonded spherical inclusion. The second part is formulated in terms of an equivalent nonuniform eigenstrain distributed over a perfectly bonded spherical inclusion which models the material mismatch between the inclusion and the matrix, while the third part is obtained in terms of an imaginary Somigliana dislocation field which models the interfacial sliding and normal separation. The exact form of the equivalent nonuniform eigenstrain and the imaginary Somigliana dislocation are fully determined using the equivalent inclusion method and the associated interfacial condition. The elastic fields are then obtained explicitly by means of the superposition principle. The resulting solution is then used to evaluate the average Eshelby tensor and the elastic strain energy.
An Analysis of Intersonic Crack Growth Under Shear Loading
Authors: Needleman A.
Published: February 2008

Crack growth in a homogeneous elastic solid under impact shear loading conditions is analyzed numerically, with the crack constrained to grow along a weak plane directly ahead of the initial crack tip. The configuration analyzed is a plane-strain model of that used in the experiments of Rosakis et al. (1999). A cohesive surface constitutive relation is specified along the weak plane that relates the tractions and displacement jumps across it and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any additional failure criterion. The effect of cohesive strength and impact pulse time on the response is explored. In a certain parameter regime, the calculations reproduce, at least qualitatively, the type of crack speed histories seen in the experiments. For other parameter values, an abrupt transition from crack growth at the Rayleigh wave speed to a value above 2 times the shear wave speed is seen. This transition involves microcrack nucleation ahead of the main crack. At intersonic crack speeds, shock-like gradients in the near-tip stress field are found as seen in the experiments.
An Energy Method for Analyzing Magnetoelastic Buckling and Bending of Ferromagnetic Plates in Static Magnetic Fields
Authors: Yang W. , Pan H. , Zheng D. , Cai Q.
Published: February 2008

Based on an energy method analyses of magnetoelastic buckling and bending of ferromagnetic thin plates in transverse, oblique, and longitudinal fields are performed in this paper. A general expression of the critical magnetic field of the plate in a transverse field is presented. It is shown that the critical magnetic field is not only related to the ratio of the thickness to the cantilevered length, but also to the susceptibility and the demagnetizing factors that are primarily dependent on the ratios of the thickness to width and the thickness to the total length. In different cases, main factors that affect the critical magnetic field are discussed. Theoretical predictions agree with experimental results reasonably.
Impulsive Squeezing With Suction and Injection
Authors: Hamza E. A.
Published: February 2008

This paper is concerned with the motion of a fluid film squeezed between two parallel plane surfaces with suction or injection at the porous surface. Attention is given to the case of impulsive squeezing. Analytic solutions based on the regular perturbation technique and on the linearized analysis of the resulting nonlinear partial differential equation are presented. The effects of injection and suction on the velocity profiles and on the normal forces which the fluid exerts on the surfaces are studied.
A Thermodynamic Approach to Nonlocal Plasticity and Related Variational Principles
Authors: Borino G. , Fuschi P. , Polizzotto C.
Published: February 2008

Elastic-plastic rate-independent materials with isotropic hardening/softening of nonlocal nature are considered in the context of small displacements and strains. A suitable thermodynamic framework is envisaged as a basis of a nonlocal associative plasticity theory in which the plastic yielding laws comply with a (nonlocal) maximum intrinsic dissipation theorem. Additionally, the rate response problem for a (continuous) set of (macroscopic) material particles, subjected to a given total strain rate field, is discussed and shown to be characterized by a minimum principle in terms of plastic coefficient. This coefficient and the relevant continuum tangent stiffness matrix are shown to admit, in the region of active plastic yielding, some specific series representations. Finally, the structural rate response problem for assigned load rates is studied in relation to the solution uniqueness, and two variational principles are provided for this boundary value problem.
Integration Scheme for Elastic Deformation and Stresses
Authors: Lee S. L. , Ou C. R.
Published: February 2008

The integration scheme is proposed in this paper to solve linear deformation and stresses for elastic bodies. The discretized equations are of the finite difference type such that all of the advantages in the use of a finite difference scheme are preserved. In addition, the boundary traction can be easily converted into Dirichlet boundary condition for the displacement equations without recourse to fictitious points. Three examples are illustrated in this study to examine the performances of the integration scheme. In the case of thermal loading, the integration scheme is seen to provide solution with six-place accuracy while the finite element and the boundary element solutions possess only two- to three-place accuracy at essentially the same number of grid points. A similar situation is believed to exist also in the case of pure mechanical loading, although no exact solution is available for comparison. For a square bimaterial under a thermal loading without boundary traction, the integration scheme is found to successfully predict the existence of the interface zone. Due to its simplicity and efficiency, the integration scheme is expected to have good performance for solid mechanical problems, especially when coupled with heat transfer and fluid flow inside and outside the solid.
Hybrid Stochastic Finite Elements and Generalized Monte Carlo Simulation
Authors: Ghanem R.
Published: February 2008

A procedure is developed to integrate analytical solutions to problems featuring random media with Monte Carlo simulations in order to improve the efficiency of the simulations. This is achieved by developing a common theoretical framework that encompasses Monte Carlo procedures as well as various expansion solution techniques. This framework can be perceived as a natural extension of hybrid deterministic finite element procedures whereby refinement is achieved by simultaneously increasing the number of elements as well as the degree of interpolation within each element.
Asymptotics of Extensional Waves in Isotropic Elastic Plates
Authors: Losin N. A.
Published: February 2008

The long and short-wave asymptotics of order O(η6),η=kh, for free extensional vibrations of an infinite isotropic elastic plate are studied. The asymptotic model for flexural and extensional wave motion applicable for both long and short-wave approximations and for any materials is developed. The velocity and frequency dispersion relations for extensional waves are derived in analytical form from the system of three-dimensional dynamic equations of linear elasticity. All dispersion equations and the group velocity formula are presented as explicit functions in material parameter γ=cs2/cL2 (the ratio of the velocities squared of the flexural and extensional waves) without any correction factors as in the Reissner-Mindlin theory. Variations of the velocity and frequency spectra depending on Poisson’s ratio ν are illustrated graphically. The results are discussed and compared to those obtained and summarized by Mindlin (1960), Mindlin and Medick (1959), Tolstoy and Usdin (1953, 1957), Achenbach (1973), and Graff (1991).
On the Decomposition of Deformation Into Elastic-Plastic Parts
Authors: Shen Li-jun
Published: February 2008

This paper analyzes the decomposition of finite deformation into elastic and plastic parts. The analysis argues that Lee’s multiplicative decomposition of the deformation gradient is not the real separation of the total deformation into elastic and plastic parts and that the Green strain cannot be decomposed into elastic and plastic parts. The paper also analyzes the decomposition of the velocity gradient and presents an exact elastic-plastic decomposition of deformation rate.
Stability of Gyroscopic Systems Near Vanishing Eigenvalues
Authors: Renshaw A. A.
Published: February 2008

Renshaw and Mote (1996) proposed a conjecture concerning the growth of vibrating eigensolutions of gyroscopic systems in the neighborhood of a vanishing eigenvalue when the system operators depend on an independent system parameter. Although the conjecture was not proved, it was supported by several examples drawn from well-known continuous physical systems. Lancaster and Kliem (1997), however, recently presented three two-degree-of-freedom counter examples. Unlike the examples tested by Renshaw and Mote (1996), these counter examples lack a definiteness property that is usually found in models derived from physical systems which appears to be essential to the conjecture. This Brief Note revises the original conjecture to include this definiteness criterion and proves the conjecture for general two-degree-of-freedom systems.
Transient Discharge of Entrained Air From a Wound Roll
Authors: Keshavan M. B. , Wickert J. A.
Published: February 2008

As magnetic tape or other web-like material is wound onto a roll, air moving with the incoming stream and the roll becomes forced into the converging wedge at the stream’s point of tangency. The spiral-shaped air bearing so formed can extend many wraps into the roll’s interior. When the roll is subsequently brought to rest, the entrained air discharges from it, and the roll’s radius gradually decreases until all adjacent tape layers have come into direct contact. In the present paper, a model is developed for this transient discharge process, and for the rate at which the roll stabilizes following steady-state winding. Predictions of the model are compared with results from laboratory experiments in which the roll’s radius is measured through laser interferometry during the steady entrainment, and transient discharge, stages of winding. Parametric effects of the tape’s tension, speed, width, and surface roughness are specifically addressed with a view towards reducing the time required for the roll to stabilize.
Study of Residual Stress Distribution by a Combined Method of Moire´ Interferometry and Incremental Hole Drilling, Part II: Implementation
Authors: Wu Zhu , Lu Jian , Han Bongtae
Published: February 2008

An experiment is devised to implement the combined method of moire´ interferometry and incremental hole drilling which was proposed in the companion paper. A unique experimental apparatus is designed to combine an optical set up for moire´ interferometry with an incremental hole-drilling device. The apparatus maintains a constant relative position of a drilling device to the specimen while alternating moire´ interferometry measurements with incremental hole drilling. The drill-bit can reenter the hole for each incremental step. The incremental hole-drilling device produces a precise control of incremental hole depth with an accuracy of 0.1 μm. The method is utilized to measure the residual stresses of two shot-peened materials: AS10U3NG aluminum alloy and the ten percent SiCp reinforced aluminum composite-F3K10S Duralcan with a T6 heat treatment. Moire´ fringe patterns with excellent contrast and high signal-to-noise ratio are obtained, which allows the extraction displacement data at the points very close to a hole boundary. In the experiment, a total number of ten steps of incremental hole drilling with an identical increment of 0.1 mm are performed. The fringe patterns of Ux and Uy displacement fields are recorded after each increment and the displacement data at the points of r = 1.2r0 are extracted consequently. They are used to determine the nonuniform residual stress distributions of surface and subsurface layers of shot-peened materials. The results indicate that the medium level of approximately equibiaxial compressive residual stresses exist within a 0.3 mm layer.
Distortion of a Harmonic Elastic Wave Reflected From a Dry Friction Support
Authors: Leamy M. J. , Barber J. R. , Perkins N. C.
Published: February 2008

This study is motivated by the need to understand the elastodynamic response of belts in frictional contact with pulleys. To this end, a simplified model for belt/pulley contact is used to investigate the dynamic response of a belt subject to a train of harmonic tension waves. Through a nondimensionalization, a single dimensionless parameter Ω is identified which governs the dynamic response. A numerical solution is developed and exercised over a wide range of values of Ω An approximate closed-form solution is derived assuming the belt stretches quasi-statically, and is shown to yield accurate results for small values of Ω Reported results include the distortion of an initially harmonic tension wave, the energy reflected from the frictional support, and the distance harmonic waves penetrate into the support. The results suggest that the quasi-static stretching assumption may be further utilized as a modeling simplification for belt drives characterized by values of Ω <1/3.
Stiff Elastic Tape Wrapped Onto a Drum
Authors: Benson R. C.
Published: February 2008

A nonlinear analysis is presented to describe the static equilibrium of a long elastic tape wrapped onto a rigid drum. Closed-form results are obtained for the case when the tape can be modeled as an inextensional beam with finite bending rigidity. Strains are assumed to be small, but rotations of the beam may be arbitrarily large. The tape’s stiffness in bending requires the abandonment of a common modeling assumption—that the tape approaches the drum along a perfectly straight tangent. After calculating the actual shape of the elastica, a number of changes are seen to occur in the loading and geometry of the system. Among these are a lower tape tension at the point of tape/drum contact, an increased torque on the drum, and the introduction of an elastic compliance between the drum and distant locations in the tape.
Free and Forced Vibration of an Axially Moving String With an Arbitrary Velocity Profile
Authors: Zhu W. D. , Guo B. Z.
Published: February 2008

The exact response of an axially moving string with an arbitrary velocity profile is determined under general initial conditions and external excitation. In terms of the curvilinear characteristic coordinates, the time-dependent governing equation reduces to one with constant coefficients. The domain of interest in the characteristic coordinate plane is bounded by two monotonic curves with the same shape corresponding to the spatial boundaries of the string. Solutions of the transformed equation are derived for the free and forced responses. The amplitude of the free response is shown to be bounded under arbitrary variation of the transport speed in the subcritical regime. The unbounded displacement of the string predicted by Floquet theory for the spatially discretized models does not occur. The method is demonstrated on two illustrative examples with piecewise constant and sinusoidal accelerations.
Flexibility-Based Finite Element Analysis for Structures With Random Material Properties
Authors: Ren Yongjian , Elishakoff I.
Published: February 2008

In this paper, we propose a flexibility-based finite element formulation for beams with stochastic bending stiffness. We formulate the element-level finite element equilibrium equation in terms of the element flexibility, so that the stochasticity appears on the right side of the equilibrium equation as the random flexibility. As a result, the unknown internal forces, which are dependent on the stochastic bending stiffness for statically indeterminate beams, appear explicitly in the global finite element equilibrium equations. The internal forces associated with the mean stiffness are used to approximate the unknown internal forces in the process of computation. With the new formulation, the mean and covariance of the displacement for stochastic beams can be directly calculated in terms of mean and covariance function of the flexibility, which can be evaluated from one-dimensional probability density function and the correlation function of the stiffness by the Monte Carlo simulation. The numerical example is given to illustrate the advantages of the new formulation over the conventional perturbation solution.
Geometric Stiffening of Timoshenko Beams
Authors: Oguamanam D. C. D. , Heppler G. R.
Published: February 2008

The equations of motion of a prismatic isotropic Timoshenko beam with a tip mass and attached to a rotating hub are derived including the effects of centrifugal forces which appear in the equations of motion as nonlinear functions of the angular speed. The Rayleigh-Ritz method is used to obtain approximate solutions for the cases of a prescribed torque profile and a prescribed hub angular speed profile. In the case of a constant torque input, the effect of the centrifugal forces is not observed until sufficient angular speed is reached. When the system is driven under a constant velocity, it is observed that, for a sufficiently high angular speed, the centrifugal forces reduce the vibration amplitude.
A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations
Authors: Chatterjee A. , Ruina A.
Published: February 2008

We present a geometric representation of the set of three-dimensional rigid-body collisional impulses that are reasonably permissible by the combination of non-negative post-collision separation rate, non-negative collisional compression impulse, non-negative energy dissipation and the Coulomb friction inequality. The construction is presented for a variety of special collisional situations involving special symmetry or extremes in the mass distribution, the friction coefficient, or the initial conditions. We review a variety of known friction laws and show how they do and do not fit in the permissible region in impulse space as well as comment on other attributes of these laws. We present a few parameterizations of the full permissible region of impulse space. We present a simple generalization to arbitrary three-dimensional point contact collisions of a simple law previously only applicable to objects with contact-inertia eigenvectors aligned with the surface normal and initial relative tangential velocity component (e.g., spheres and disks). This new algebraic collision law has two restitution parameters for general three-dimensional frictional single-point rigid-body collisions. The new law generates a collisional impulse that is a weighted sum of the impulses from a frictionless but nonrebounding collision and from a perfectly sticking, nonrebounding collision. We describe useful properties of our law; show geometrically the set of impulses it can predict for several collisional situations; and compare it with existing laws. For simultaneous collisions we propose that the new algebraic law be used by recursively breaking these collisions into a sequence ordered by the normal approach velocities of potential contact pairs.
Adaptive Boundary Control of Out-of-Plane Cable Vibration
Authors: Canbolat H. , Dawson D. , Rahn C. , Nagarkatti S.
Published: February 2008

This paper develops active controllers for the out-of-plane vibration of a flexible cable using boundary actuators and sensors. An exact model knowledge controller exponentially stabilizes the cable displacement assuming known system parameters. An adaptive controller asymptotically stabilizes the cable displacement while compensating for parametric uncertainty in the actuator mass and cable tension. The performance of the controllers is experimentally demonstrated.