bluuebunny/crossref_metadata_2025 huggingface dataset:
Steady-State Point-Source Excitation of a Laminated Composite
Authors: Beaupre G. S. , Herrmann G.
Published: July 2009

Steady-state periodic excitation at a point of an extended, periodically laminated, elastic composite is considered in antiplane strain. The curves of constant phase are determined in the geometric optics approximation. The associated distribution of group velocity is also calculated.
Experimental Determination of Stresses in Damaged Composites Using an Electric Analogue
Authors: Batdorf S. B.
Published: July 2009

Inadequate knowledge of the local stress distributions in damaged composites has been a major obstacle to progress in the understanding of damage accumulation and ultimate failure of such materials. Theoretical treatments of three-dimensional uniaxially reinforced composites are difficult, and direct experimental observations of stresses around interior flaws are not feasible. An experimental determination of stress distributions can be made using an electric analogue. A scaled model of the composite including the damage is made with the fibers replaced by conducting rods and the matrix replaced by an electrolyte. The resistivity ratio of rods to electrolyte is taken equal to the elastic modulus ratio of matrix to fiber. A tensile force applied in the fiber direction is modeled by applying a potential gradient in the rod direction. The displacement distribution in the composite is then modeled by the potential distribution in the analogue to an accuracy somewhat better than that given by shear lag theory. Thus stress distributions can be found by measuring potentials in the analogue with the aid of an electric probe.
Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity
Authors: Oden J. T. , Pires E. B.
Published: July 2009

The use of the classical Coulomb law of friction in the formulation of contact problems in elasticity leads to both physical and mathematical difficulties; the former arises from the fact that this law provides a poor model of frictional stresses at points on metallic surfaces in contact, and the latter is due to the fact that the existence of solutions of the governing equations can be proved only for very special situations. In the present paper, nonclassical friction laws are proposed in an attempt to overcome both of these difficulties. We consider a class of contact problems involving the equilibrium of linearly elastic bodies in contact on surfaces on which nonlocal and nonlinear friction laws are assumed to hold. The physics of friction between metallic bodies in contact is discussed and arguments in support of the theory are presented. Variational principles for boundary-value problems in elasticity in which such nonlinear nonlocal laws hold are then developed. A brief discussion of the questions of existence and uniqueness of solutions to the nonlocal and nonlinear problems is given.
Flow Inside a Pneumatic Tire: A Peristaltic-Pumping Analysis for the Thin-Tire Limit at Very Low Forward Speed
Authors: Rae W. J.
Published: July 2009

The flow inside a pneumatic tire is analyzed in the limit where the cross-sectional diameter of the tire is small in comparison to the wheel diameter, and where the forward speed is sufficiently low that centrifugal pressure gradients can be neglected. The movement of the contact point around the circumference of the tire produces an internal flow by a mechanism analogous to peristaltic pumping in long flexible ducts. Analytic expressions for the flow velocities and pressures predicted by this model are derived, and are related to tire velocity and load.
Initial Strain Field and Fatigue Crack Initiation Mechanics
Authors: Lin S. R. , Lin T. H.
Published: July 2009

On single aluminum crystals under cyclic loadings, fresh slip lines appeared during the reversed loading, lying very close to, but not coincident with the slip lines formed in the forward loading. These slip lines indicate the start of extrusion or intrusion as commonly observed in fatigue specimens. An initial stress field is present in all metals. The initial stress field favorable to the aforementioned sequence of slip is one having a positive shear stress in one thin slice P and a negative one in a closely located thin slice Q. A forward loading causes a positive shear stress, which is of the same sign as the initial shear stress in P, but of opposite sign to that in Q. Hence the shear stress in P will reach the critical value first to cause slip. Due to the continuity of the stress field, slip in P relieves not only the positive shear stress in P but also in Q. This has the same effect as increasing negative shear stress in Q. During the reversed loading, Q has the highest negative shear stress and hence slides. Similarly, this slip causes P to be more ready to slide in the next forward loading. This process is repeated to cause a monotonic alternate sliding in P and Q. In this way, an extrusion or intrusion is nucleated. A crack can be started from an intrusion. The thin slices P and Q are considered to be in a most favorably oriented crystal located at a free surface. An initial stress field giving positive shear stress in P and negative in Q is calculated from an assumed initial inelastic strain field which, in turn, can be caused by distribution of dislocations. The buildup of plastic shear strain in P and Q causing the start of extrusion or intrusion is shown.
Transient Response of an Elastic Medium to Torsional Loads on a Cylindrical Cavity
Authors: Parnes R. , Banks-Sills L.
Published: July 2009

The transient response of an elastic medium to torsional line loads acting as a step function in time on the surface of an infinite cylindrical bore is obtained. The solution is seen to be composed of a superposition of space-harmonic applied tractions. Integral representations of the resulting displacement and stress fields are derived and numerical results are presented. The behavior in the vicinity immediately behind the outward propagating S-wave fronts is studied and analytic expressions for the resulting singularities and jumps across the fronts are given. These solutions may be used as the Green’s functions for more general spatial loading systems. The response is compared with the known static solution to determine the relative contribution of the transient effect.
Dynamics of a Cluster of Flexibly Interconnected Cylinders, Part 2: In Axial Flow
Authors: Paidoussis M. P. , Chaubernard J.-P. , Genadry M. R. , El Barbir K. N.
Published: July 2009

In this paper the dynamical characteristics are discussed of a cluster of cylinders, the extremities of which are interconnected by beam-like connectors, modeled here by sets of linear springs as formulated in Part 1 of this study; resistance to both in-plane and out-of-plane deformation of the connectors is taken into account. The cylinders are subjected to axial flow, and hydrodynamic coupling in cylinder motions is taken into account. The system eigenfrequencies and modal shapes are calculated for different conditions of structural and hydrodynamic coupling. The effect of increasing flow on the dynamics of the system is also studied, up to and beyond the threshold of fluid-elastic instabilities.
Application of Wiener-Hermite Expansion to Nonstationary Random Vibration of a Duffing Oscillator
Authors: Jahedi A. , Ahmadi G.
Published: July 2009

Nonstationary random vibration of a Duffing oscillator is considered. The method of Wiener-Hermite series expansion of an arbitrary random function is reviewed and applied to the analysis of the response of a Duffing oscillator. Deterministic integral equations for the Wiener-Hermite kernel functions are derived and discussed. For the special case of a shaped white-noise excitation, the system of integral equations are solved by an iterative scheme and the mean square responses of a Duffing oscillator for various values of nonlinearity strength and damping coefficient are calculated and the results are elaborated in several graphs.
Limit Plasticity Approach to Piping in Bins
Authors: Drescher A.
Published: July 2009

The plastic limit analysis method is adopted to derive a criterion for piping in particulate solids discharged from prismatic and cylindrical bins. Plane, rectangular, and circular cross sections of empty channels (pipes) are considered. Utilizing the kinematic approach, various mechanisms of failure of the material surrounding an empty channel are discussed. The geometry of a stable channel is related to the material strength parameters c and φ, specific weight γ, and geometry of the bin; safe estimate to the piping criterion is given.
Stress Analysis for Anisotropic Hardening in Finite-Deformation Plasticity
Authors: Lee E. H. , Mallett R. L. , Wertheimer T. B.
Published: July 2009

Kinematic hardening represents the anisotropic component of strain hardening by a shift of the center of the yield surface in stress space. The current approach in stress analysis at finite deformation includes rotational effects by using the Jaumann derivatives of the shift and stress tensors. This procedure generates the unexpected result that oscillatory shear stress is predicted for monotonically increasing simple shear strain. A theory is proposed that calls for a modified Jaumann derivative based on the spin of specific material directions associated with the kinematic hardening. This eliminates the spurious oscillation. General anisotropic hardening is shown to require a similar approach.
Ductile Fracture of Rapidly Expanding Rings
Authors: Johnson J. N.
Published: July 2009

Heterogeneous plastic deformation (necking) of thin ductile rings given an initial outward impulse is described in terms of the ordinary differential equations of thermoplasticity and the partial differential equations of mass and momentum conservation in one spatial dimension (circumference) and time. Flaws in cross-sectional area and porosity are introduced and the resulting plastic deformation is calculated numerically for a prescribed initial radial velocity. Plastic deformation is initially homogeneous but soon concentrates in the weakest region, which then thins rapidly and fractures. Effects of flaw wavelength, work-hardening rate, thermal softening, and rate-dependent plastic flow on the flaw growth rate are studied.
Incremental Harmonic Balance Method With Multiple Time Scales for Aperiodic Vibration of Nonlinear Systems
Authors: Lau S. L. , Cheung Y. K. , Wu S. Y.
Published: July 2009

An incremental harmonic balance method with multiple time scales is presented in this paper. As a general and systematic computer method, it is capable of treating aperiodic “steady-state” vibrations such as combination resonance, etc. Moreover, this method is not subjected to the limitation of weak nonlinearity. To show the essential features of the new approach, the almost periodic free vibration of a clamped-hinged beam is computed as an example.
The Evolution of Computational Methods in Aerodynamics
Authors: Jameson A.
Published: July 2009

This paper surveys the evolution of computational methods in aerodynamics. Improvements in high-speed electronic computers have made it feasible to attempt numerical calculations of progressively more complex mathematical models of aerodynamic flows. Numerical approximation methods for a hierarchy of models are examined in ascending order of complexity, ranging from the linearized potential flow equation to the Reynolds averaged Navier Stokes equations, with the inclusion of some previously unpublished material on implicit and multigrid methods for the Euler equations. It is concluded that the solution to the Euler equations for inviscid flow past a complete aircraft is a presently attainable objective, while the solution to the Reynolds averaged Navier Stokes equations is a possibility clearly visible on the horizon.
Stability of Dynamic Systems
Authors: Leipholz H. H. E.
Published: July 2009

It is shown how stability theory of dynamic systems, emerging from various beginnings strewn over the realm of mechanics, developed into a unified, comprehensive theory for dynamic systems with a finite number of degrees of freedom. It is then demonstrated, how such theory could be adapted over the last five decades to the specific nature of stability problems involving continuous elastic systems. The need for such adaption is stressed by pointing to systems with follower forces. The difficulties arising from the fact that continuous systems are systems with an infinite number of degrees of freedom are emphasized, and an adequate approach to a unified stability theory including also continuous systems is outlined.
Crystal Plasticity
Authors: Asaro R. J.
Published: July 2009

Significant progress has been made during the past decade in incorporating micromechanics in continuum descriptions of inelastic deformation. This has led to the development of a rather comprehensive constitutive theory for rate-dependent and idealized rate-independent crystalline materials that deform plastically by crystalline slip. This theory is reviewed in some detail and examples are presented which illustrate how complex slip phenomena involving localized plastic flow and nonuniform crystallographic texture can be analyzed. The paper concludes by suggesting that it is now possible to develop accurate models for rate-dependent polycrystals undergoing arbitrarily large strains. Such models would have as principal aims the prediction of texture development and the rigorous assessment of such anisotropy on constitutive behavior. An example of how this would be of immediate value in analyzing strain-hardening behavior of metal polycrystals at large strains is provided.
Influence of the Yield Function Nonlinearity and Temperature in Dynamic Buckling of Viscoplastic Cylindrical Shells
Authors: Wojewo´dzki W. , Bukowski R.
Published: July 2009

A viscoplastic theory of dynamic buckling is developed for cylindrical shells subjected to uniform radially inward impulses. The influence of the yield function nonlinearity and elevated temperature on the magnitude of displacements, buckling mode, and threshold impulse is investigated. Asymmetrical and axisymmetrical modes of buckling are considered. The asymmetrical mode is proved to exist. The obtained theoretical results are compared with existing experiments.
48 Hour Multiaxial Creep and Creep Recovery of 2618 Aluminum Alloy at 200°C
Authors: Ding J.-L. , Findley W. N.
Published: July 2009

Data are reported from 48 hour constant multiaxial stress creep followed by 48 hour creep recovery with the magnitudes of the effective stress ranging from 34.5 MPa (5.00 ksi) to 175.5 MPa (25.46 ksi). They differed from a previous data set in the much longer constant-stress durations and the inclusion of data from low stress creep, compression creep, and short term aging tests. Data were represented by a viscous-viscoelastic model in which the time-dependent strain was resolved into recoverable and nonrecoverable components. Previous stress-strain relations for constant stress creep and recovery were modified to include the current experimental observations of the nonexistence of creep limits, negligible aging effects, and symmetry in tension and compression. The time dependence was represented by a power of time with different exponents for the recoverable and nonrecoverable components. A homogeneous function of maximum shear stress was developed to represent the full range of stress dependence of the nonrecoverable time-dependent components; the third-order multiple integral representation was used for the recoverable component.
Nonlinear Bending and Collapse of Long, Thin, Open Section Beams and Corrugated Panels
Authors: Benson R. C.
Published: July 2009

Long, thin, open section beams and corrugated panels undergo a cross section flattening when bent longitudinally. This leads to a “soft” nonlinear moment-curvature response and geometrical instability. The problem is analyzed by means of a closed, convergent sequence of algebraic and integral equations which are tractable on modern microcomputers. The shape of the cross section is unrestricted, save that it be thin, symmetrical, and not self-penetrating. Results for circular section and angle section beams are obtained and compared with the existing literature. Example results for a wide, corrugated panel are also obtained. Bifurcations in the deformed cross section are found to occur.
Eigenvalues and Stable Time Steps for the Uniform Strain Hexahedron and Quadrilateral
Authors: Flanagan D. P. , Belytschko T.
Published: July 2009

Simple formulas for bounding the maximum eigenvalues or computing them exactly are obtained for the uniform strain eight-node hexahedron and the four-node quadrilateral. The development is based on a novel technique that reduces the size of the eigenproblem to where it can be managed analytically. These formulas are useful for explicit time integration applications since they provide conserative estimates of stable time steps. The eigenvalue analysis is limited to linear, isotropic materials but the results are also useful in nonlinear problems since the linerized material properties may be used.
Resonance Effects for a Crack Near a Free Surface
Authors: Keer L. M. , Lin W. , Achenbach J. D.
Published: July 2009

Stress intensity factors are computed for a horizontal subsurface crack that is subjected to time harmonic excitation. The problem is analyzed by determining displacement potentials that satisfy reduced wave equations and specified boundary conditions. The formulation of the problem leads to a system of coupled integral equations for the dislocation densities. The numerical solution of the integral equations leads directly to the stress intensity factors. Curves are presented for the ratios of the elastodynamic and the corresponding elastostatic Mode-I and Mode-II stress intensity factors. At specific values of the frequency, a resonance effect is observed and a correlation with the natural frequencies calculated by a Timoshenko plate theory for the layer between the crack and the free surface is noted.
Transient Stress Intensity Factors of an Interfacial Crack Between Two Dissimilar Anisotropic Half-Spaces, Part 1: Orthotropic Materials
Authors: Kuo A.-Y.
Published: July 2009

Transient response of an interfacial crack between two dissimilar elastic, orthotropic solids is investigated. The interfacial crack is excited by tractions suddenly applied on the crack surfaces. Governing equations, boundary conditions, and continuity conditions along the interface are reduced to a singular integral equation. Solution of the singular integral equation is obtained by the use of Jacobi polynomials. Expressions for stress intensity factors at the crack tip are given. As a sample problem, an interfacial crack in a 0 deg/90 deg fiber-reinforced composite solid excited by a suddenly applied uniform pressure on the crack surfaces is studied.
Deformations and Stress Intensities Due to a Craze in an Extended Elastic Material
Authors: Walton J. R. , Weitsman Y.
Published: July 2009

This paper presents an analytical solution, accompanied by a numerical scheme, to determine the displacement and stress fields in an extended elastic medium due to a thin craze of finite length directed transversely to the load at infinity. Crazes are thin elongated defects containing fine fibrils that connect their opposite interfaces. These fibrils are modeled as a distributed spring, leading to a formulation in terms of a singular integrodifferential equation. The paper also contains a treatment of central cracks within the craze and time-dependent craze response, and includes a discussion of “tip zone” correction.
Constitutive Restrictions for Idealized Elastic-Viscoplastic Materials
Authors: Naghdi P. M.
Published: July 2009

This paper is concerned mainly with restrictions on constitutive equations of idealized elastic-viscoplastic materials in the presence of finite deformation. The development is confined to the purely mechanical theory utilizing a constitutive model that includes unloading and allows for suitable definition of plastic strain. With the use of a physically plausible assumption concerning non-negative work in a closed cycle of deformation, two local inequalities are derived which place restrictions on the nonlinear constitutive response functions of the idealized material. Further implications of these inequalities relating the various response functions are dicussed. In the absence of rate effects in the stress response, the results correspond to those appropriate for rate-independent plasticity.
Bifurcation Theory Applied to Oil Whirl in Plain Cylindrical Journal Bearings
Authors: Myers C. J.
Published: July 2009

An analysis of the self-excited oscillations of a rotor supported in fluid film journal bearings is presented. It is shown that Hopf bifurcation theory may be used to investigate small-amplitude periodic solutions of the nonlinear equations of motion for rotor speeds close to the speed at which the steady-state equilibrium position becomes unstable. A numerical investigation supports the findings of the analytic work.
The Analysis of Multilayer Elastomeric Bearings
Authors: Simo J. C. , Kelly J. M.
Published: July 2009

When a multilayer elastomeric bearing is sheared by end loads, the top and bottom surfaces of a typical plate are subjected to a shear stress distribution which causes bending of the plate. A new approach to the analysis of these bearings is presented which systematically takes into account the flexibility and subsequent warping of the plates. First, the displacement field of the bearing and the shear stress distribution are derived, within the framework of classical linear elasticity, from compatibility conditions between rubber pad and steel plate. Next, use of a second-order approximation to the nonlinear equilibrium equations leads to a new expression for the critical load of the bearing which depends on the bending stiffness of the plate. Under the assumption of perfectly rigid plates, this expression is in agreement with previous formulations. For flexible plates, however, the proposed expression shows that previous formulations lead to an overestimate of the buckling load which might become important for extremely thin plates and low values of the shear modulus of the rubber.
On Symmetric Buckling of a Finite Flat-Lying Heavy Sheet
Authors: Wang C. Y.
Published: July 2009

An elastic sheet with non-negligible density and finite length lies horizontally on the ground. The ends are clamped and subjected to compressive forces. Depending on the force, the sheet may be regarded as “long” or “short” with different characteristics. The critical buckling load, redefined as the force below which the sheet will always return to the horizontal state under any finite disturbance, is higher than the Euler buckling load of a weightless sheet. When deflections are small and finite the sheet is stable for given end displacement, but is unstable for given force. Approximate analytic solutions compare well with the results of exact numerical integration.
The Sliding With Coulomb Friction of a Rigid Indentor Over a Power-Law Inhomogeneous Linearly Viscoelastic Half-Plane
Authors: Walton J. R.
Published: July 2009

In a previous paper, the title problem was solved for a homogeneous power-law linearly viscoelastic half-plane. Such material has a constant Poisson’s ratio and a shear modulus with a power-law dependence on time. In this paper, the shear modulus is assumed also to have a power-law dependence on depth from the half-plane boundary. As in the earlier paper, only a quasi-static analysis is presented, that is, the enertial terms in the equations of motion are not retained and the indentor is assumed to slide with constant speed. The resulting boundary value problem is reduced to a generalized Abel integral equation. A simple closed-form solution is obtained from which all relevant physical parameters are easily computed.
On Elastodynamic Diffraction of Waves From a Line-Load by a Crack
Authors: Gautesen A. K.
Published: July 2009

For the two-dimensional problem of elastodynamic diffraction of waves by a crack of finite width, we assume that the solution corresponding to incidence of a plane wave of either longitudinal or transverse motions under a fixed angle of incidence is known. We first show how to construct the solution corresponding to an in-plane line-load (the Green’s function) from this known solution. We then give a simple relation between the far field scattering patterns corresponding to a plane wave incident under any angle and the far field scattering patterns corresponding to the known solution. This relation is a generalization of the principle of reciprocity.
Investigation of Stress Wave Propagation Through Intersecting Bars
Authors: Simha K. R. Y. , Fourney W. L.
Published: July 2009

A general formulation is presented for the analysis of stress wave propagation through the junction of rectangular bars. The analysis is applied to the case of two bars meeting at right angles and is used to theoretically predict the passage of longitudinal waves through the junction. An experimental investigation of the phenomenon, using dynamic photoelasticity is conducted with a high-speed multiple spark gap camera of the Cranz-Schardin type. Three different geometries are tested to represent the most common types of junctions encountered in practice. In each of the cases, experimentally obtained results are observed to be very consistent with the theoretical predictions.
Finite Amplitude Vibrations of a Body Supported by Simple Shear Springs
Authors: Beatty M. F.
Published: July 2009

The exact solution of the problem of the undamped, finite amplitude oscillations of a mass supported symmetrically by simple shear mounts, and perhaps also by a smooth plane surface or by roller bearings, is derived for the class of isotropic, hyperelastic materials for which the strain energy is a quadratic function of the first and second principal invariants and an arbitrary function of the third. The Mooney-Rivlin and Hadamard material models are special members for which the finite motion of the load is simple harmonic and the free fall dynamic deflection always is twice the static deflection. Otherwise, the solution is described by an elliptic integral which may be inverted to obtain the motion in terms of Jacobi elliptic functions. In this case, the frequency is amplitude dependent; and the dynamic deflection in the free fall motion from the natural state always is less than twice the static deflection. Some results for small-amplitude vibrations superimposed on a finely deformed equilibrium state of simple shear also are presented. Practical difficulties in execution of the simple shear, and the effects of additional small bending deformation are discussed.
The Origin of Stability Indeterminacy in a Symmetric Hamiltonian
Authors: Hyams M. R. , Month L. A.
Published: July 2009

The stability and bifurcation of periodic motions in a symmetric two-degree-of-freedom Hamiltonian system is studied by a reduction to a two-dimensional action-angle phase plane, via canonical perturbation theory. The results are used to explain why linear stability analysis will always be indeterminate for the in-phase mode in a class of coupled nonlinear oscillators.
Dynamics of Gyroelastic Continua
Authors: D’Eleuterio G. M. T. , Hughes P. C.
Published: July 2009

This paper introduces the idea of distributed gyricity, in which each volume element of a continuum possesses an infinitesimal quantity of stored angular momentum. The continuum is also assumed to be linear-elastic. Using operator notation, a partial differential equation is derived that governs the small displacements of this gyroelastic continuum. Gyroelastic vibration modes are derived and used as basis functions in terms of which the general motion can be expressed. A discretized approximation is also developed using the method of Rayleigh-Ritz. The paper concludes with a numerical example of gyroelastic modes.
The Incremental Strain Growth of an Elastic-Plastic Body Loaded in Excess of the Shakedown Limit
Authors: Ponter A. R. S. , Cocks A. C. F.
Published: July 2009

This paper considers the problem of a body composed of an elastic/perfectly plastic solid that is subjected to constant applied load P and a time-varying cyclic temperature distribution, characterized by a maximum thermoelastic stress σt. For sufficiently large P and σt, in excess of the shakedown limit, the body will begin to suffer incremental growth. A linearized theory is used to obtain a relationship between the increase in displacement Δu per cycle and the increase in ΔP and Δσt, above the shakedown limit. From the result, a simple lower bound is derived for Bree-type problems, which for kinematically determinate structures shows that for moderate thermal loading the displacement increment per cycle is four times the elastic displacement of the body if it were subjected only to the increase ΔP. From a practical point of view the analysis indicates that ratchet rates are always high, in the sense that only a small increase of load above shakedown will produce substantial ratcheting within relatively few cycles.
Analysis of Clamped Plates on Elastic Foundation by the Boundary Integral Equation Method
Authors: Katsikadelis J. T. , Armena`kas A. E.
Published: July 2009

In this investigation the boundary integral equation (BIE) method with numerical evaluation of the boundary integral equations is developed for analyzing clamped plates of any shape resting on an elastic foundation. A numerical technique for the solution to the boundary integral equations is presented and numerical results are obtained and compared with those existing from analytical solutions. The effectiveness of the BIE method is demonstrated.
Simple Waves and Shock Waves Generated by an Incident Shock Wave in Two-Dimensional Hyperelastic Materials
Authors: Li Yongchi , Ting T. C. T.
Published: July 2009

The reflection of an oblique plane shock wave from a boundary in a two-dimensional isotropic hyperelastic material is studied. For plane strain deformations, the strain energy function W is a function of two invariants p and q of the deformation gradient. There are, in general, two reflected waves each of which can be a simple wave or a shock wave. For a special class of materials for which the strain energy function W(p, q) represents a developable surface (of which harmonic materials are particular examples), one of the reflected waves is always a shock wave. It is shown that there are materials other than harmonic materials for which the wave speeds are independent of the direction of propagation. Illustrative examples are presented to show how one can determine the reflected waves from a rigid boundary. It is also shown that for certain incident shock waves, there exists only one reflected wave.
On the Nonlocal Theory of Wave Propagation in Elastic Plates
Authors: Nowinski J. L.
Published: July 2009

Propagation of longitudinal waves in isotropic homogeneous elastic plates is studied in the context of the linear theory of nonlocal continuum mechanics. To determine the nonlocal moduli, the dispersion equation obtained for the plane longitudinal waves in an infinite medium is matched with the parallel equation derived in the theory of atomic lattice dynamics. Using the integroalgebraic representation of the stress tensor and the Fourier transform, the system of two coupled differential field equations is solved in the standard manner giving the frequency equations for the symmetric and antisymmetric wave modes. It is found that the short wave speed in the Poisson medium differs by about 13 percent from the speed established in the classical theory. A numerical example is given.
Finite Element Eigenfunction Method (FEEM) for Elastic Wave Scattering by Arbitrary Three-Dimensional Axisymmetric Scatterers
Authors: Su J. H. , Varadan V. V. , Varadan V. K.
Published: July 2009

A finite element eigenfunction method (FEEM) is formulated for elastic wave scattering by bounded three-dimensional axisymmetric regions (cavity, homogeneous, or inhomogeneous) for harmonic waves incident at arbitrary angles. The solutions are hence three-dimensional and no longer axisymmetric. The scattering region is enclosed within a sphere. The scattered field outside the sphere is expanded in outgoing vector spherical functions. Within the sphere, basis-functions are generated by a finite element technique applying the vector spherical harmonics as boundary conditions. The field inside the sphere is then written as a superposition of these basis functions with unknown coefficients which are then solved by matching with the exterior field. Numerical results are obtained for a variety of scatterers and comparisons made with available results.
Special Boundary Integral Equations for Potential Problems in Regions With Circular Holes
Authors: Caulk D. A.
Published: July 2009

An infinite system of special boundary integral equations is derived for the solution of Laplace’s equation in a general two-dimensional region with circular holes. The solution is shown to converge when the number of holes is finite and no two holes are touching. In special cases, these equations are shown to yield the same results as two more restricted methods, which are based on different approaches.
On a Stress Function Method of Plane-Stress Thermoelastic Problem in a Multiply Connected Region of Variable Thickness
Authors: Sugano Y.
Published: July 2009

A plane-stress thermoelastic problem in a multiply connected region of variable thickness is formulated in terms of a stress function by deriving new Michell integral conditions necessary for the assurance of single-valuedness of rotation and displacements. The system of fundamental equations is solved by means of a finite difference method and numerical calculations are carried out for the cases of a rectangular plate of variable thickness with a rectangular hole.
High Shear Stresses in Stiff-Fiber Composites
Authors: Budiansky B. , Carrier G. F.
Published: July 2009

Elastic analysis of two parallel fibers in an infinite matrix subjected to longitudinal shear leads to some exact results for stress concentrations between the fibers. High shear stresses occur when stiff fibers are in close proximity.
Dynamic Stress Intensity Factors for an Inclined Subsurface Crack
Authors: Lin W. , Keer L. M. , Achenbach J. D.
Published: July 2009

Stress intensity factors are computed for an inclined subsurface crack in a half space, whose surface is subjected to uniform time-harmonic excitation. The problem is analyzed by determining displacement potentials that satisfy reduced wave equations and specified boundary conditions. The formulation of the problem leads to a system of coupled integral equations for the dislocation densities. The numerical solution of the integral equations leads directly to the stress intensity factors. Curves are presented for the ratios of the elastodynamic and the corresponding elastostatic Mode-I and Mode-II stress intensity factors for various frequencies and various inclinations of the crack with the free surface. For small angles of inclination with the free surface and large crack length-to-depth ratios, strong resonance vibrations of the layer between the crack and the free surface may arise.
Fluid-Structure Coupling Between a Finite Cylinder and a Confined Fluid
Authors: Garner G. , Chandra S.
Published: July 2009

The dynamic behavior of a finite length cylindrical rod in a fluid filled annulus is considered. The fluid and structure equations are solved simultaneously, with fluid-structure coupling accounted for. Coupled mode shapes and natural frequencies are obtained for various cases. It is found that for short lengths and/or higher modes, the effect of the fluid on the cylinder motion diminishes compared to the infinite cylinder case. In addition, coupled and in-vacuum mode shapes can differ in certain cases.
Optimal Control of a Rotor Partially Filled With an Inviscid Incompressible Fluid
Authors: Hendricks S. L. , Klauber R. D.
Published: July 2009

Optimal control theory is used to stabilize a rotating cylinder partially filled with an inviscid, incompressible fluid. As an example, the theory is used to control a rotor consisting of two discrete masses connected by a flexible shaft. The fluid is inside one of the masses and the control force is applied to the other. The rotor-fluid system which is unstable without controls is shown to be stable when acted upon by a feedback force designed to minimize a suitable performance index.
Asymmetric Flow of a Cylindrical Particle Through a Narrow Channel
Authors: Sugihara M. , Niimi H.
Published: July 2009

The steady flow of a cylindrical particle with a circular or elliptic cross section through a narrow channel is investigated on the basis of the Stokes equation with emphasis on effects of its asymmetric location and orientation. Numerical analyses are carried out by use of the finite element method to determine the drag, lift, and torque acting on the particle as well as the velocity of the particle floating freely in the Poiseuille flow. The numerical results are applied to blood flow in capillaries.
Moire´ Interferometric Study of Dovetail Joints
Authors: Ruiz C. , Post D. , Czarnek R.
Published: July 2009

High sensitivity Moire´ interferometry has been applied to the study of dovetail joints as found in turbomachinery. Without physical measurements, the true contact conditions cannot be known. The benefits to be gained when coupled with a finite element stress analysis are discussed. It is concluded that Moire´ interferometry is of great potential in the study of fixed mechanical joints.
A Simplified Approach to Elastic-Plastic Response to General Pulse Loads
Authors: Symonds P. S. , Mosquera J. M.
Published: July 2009

The paper describes a method for estimating permanent and maximum (elastic plus plastic) deflections of a structure subjected to a force pulse loading of arbitrary shape and duration. The concept of artificially separating the response into purely elastic and purely plastic (i.e., rigid-plastic) stages is adopted. Previous applications have been to very short pulses. When the approach is applied to long pulses of only moderately large force compared to limit load magnitudes the interaction between elastic and plastic effects is more critical. The inclusion of plastic rate sensitivity and the determination of the duration of the initial elastic stage require new approaches. Insight is provided by studying a mass-spring (elastic-perfectly plastic) system of one degree of freedom. The duration of the elastic stage is chosen to maximize a specially defined work function. Comparisons are shown for examples of rate-independent and rate-sensitive frames between deflections given by the simple technique of the paper, final deflections obtained in laboratory tests, and maximum and final displacements furnished by the finite element code ABAQUS.
Reliability of Axially Compressed Cylindrical Shells With General Nonsymmetric Imperfections
Authors: Elishakoff Isaac , Arbocz Johann
Published: July 2009

This paper deals with the effect of general, nonsymmetric random imperfections on the reliability of axially compressed cylindrical shells. Reliability is defined here as the probability of the structure not buckling below some fixed load. The paper is a sequel to an earlier study on cylindrical shells with axisymmetric imperfections. The problem is solved by the Monte Carlo Method. The initial imperfection functions are simulated via a numerical procedure, and the buckling load of each realization of the simulated initial imperfections is found by the Multimode Analysis. It is shown that the results of existing Initial Imperfection Data Banks can be directly incorporated in the reliability analysis. Experimental information and the data derived from it, rather than theoretical assumptions, is used for constructing the reliability-based design curves for shell structures.
The Application of Kinetic Fracture Mechanics to Life Prediction for Polymeric Materials
Authors: Christensen R. M. , Glaser R. E.
Published: July 2009

A recently developed theory of kinetic crack growth is applied to the problem of the time-dependent failure of polymeric materials subject to a timewise constant state of stress. The theory is generalized to include a rather complete treatment of statistical variability. When restricted to the power law range of behavior, it is found that an assumption of a Weibull distribution of static strengths implies rigorously that the corresponding lifetime distributions are also Weibully distributed. In fact, an extremely simple interrelation is found wherby the shape parameter for lifetime is equal to the product of the shape parameter for static strength times the magnitude of the log stress versus log lifetime slope of the scale parameter for the lifetime distribution. These theoretical predictions are compared with the experimental results available from the testing of a particular polymeric fiber composite material, Kevlar 49/epoxy. The theoretical prediction for the lifetime distribution compares favorably with the observed data.
Hydromagnetic Convective Diffusion Between Parallel Plates With Suction
Authors: Annapurna N. , Gupta A. S. , Dandapat B. S.
Published: July 2009

This paper presents an analytical solution for the dispersion of a solute in an electrically conducting fluid flowing between parallel plates with a transverse magnetic field and uniform wall suction. For fixed values of the suction parameter P and Schmidt number Sc, the longitudinal diffusion coefficient K decreases rapidly with increase in the magnetic parameter M. Further, for fixed M and Sc, it is found that K increases with increasing P. The effect of variation of Sc on K is found to be very small.
Flexibility of a Contact Area of an Isotropic Elastic Body
Authors: Szalwinski C. M.
Published: July 2009

From Cerruti’s solution to the problem of the plane and Cattaneo’s traction distributions, instantaneous and secant flexibilities are derived for an elliptical contact area which includes a region of slip. The results apply to force histories where the tangential component is constantly directed. Some of the results differ from those reported by Mindlin and Deresiewicz [4]. Ellipticity affects normal and tangential flexibilities differently but is independent of the extent of slip.
An Elastic-Plastic Finite Element Model of Rolling Contact, Part 2: Analysis of Repeated Contacts
Authors: Bhargava V. , Hahn G. T. , Rubin C. A.
Published: July 2009

This paper presents finite element analyses of two-dimensional (plane strain), elastic-plastic, repeated, frictionless rolling contact. The analysis employs the elastic-perfectly plastic, cycle and strain-amplitude-independent material used in the Merwin and Johnson analysis but avoids several assumptions made by these workers. Repeated rolling contacts are simulated by multiple translations of a semielliptical Hertzian pressure distribution. Results at p0/k = 3.5, 4.35, and 5.0 are compared to the Merwin and Johnson prediction. Shakedown is observed at p0/k = 3.5, but the comparisons reveal significant differences in the amount and distribution of residual shear strain and forward flow at p0/k = 4.35 and p0/k = 5.0. The peak incremental, shear strain per cycle for steady state is five times the value calculated by Merwin and Johnson, and the plastic strain cycle is highly nonsymmetric.
A Mixture Theory for Wave Propagation in Angle-Ply Laminates, Part 2: Application
Authors: Murakami H. , Akiyama A.
Published: July 2009

A binary mixture theory with microstructure is constructed for symmetric angle-ply laminates with orthotropic laminas for wave motion in arbitrary directions. A numerical study of phase-velocity spectra associated with the resulting theory reveals that dispersion is most prominent in waveguide propagation. Further, it is directionally dependent and may be strong depending on the propagation direction and lay-up angle. Typical results are presented for a graphite/epoxy composite. To assess the accuracy of the mixture model, a finite element eigenvalue analysis has been carried out. The comparisons of exact versus mixture phase-velocity spectra imply that the theory provides a tool with which one may efficiently study the rather extraordinary capability of angle-ply laminates to act as “shock absorbers.”
Response of an Elastic Plate to Localized Transient Sources
Authors: Vasudevan N. , Mal A. K.
Published: July 2009

The surface response of an infinite, homogeneous elastic plate to an internal dislocation across an infinitestimal area is investigated. As a companion problem, the normal displacement of the plate surface due to a time-dependent surface load is also calculated. The first problem is relevant for the detection of crack initiation in structural materials through the analysis of high-frequency elastic waves generated by the event. The solution to the second problem is needed for the calibration of test equipment used in the detection of the waves. The problems are formulated by means of a classical integral transform in the frequency domain and the spectral response of the plate is expressed in terms of the modal contributions due to the real, imaginary, and complex roots of the Rayleigh-Lamb equation. Time histories of the response are obtained through the inversion of the spectra by a Fast Fourier Transform (FFT) routine.
Large Inextensional Deformation of Orthotropic Cantilevered Plates With Distributed Loads
Authors: Darmon P. , Benson R. C.
Published: July 2009

The theory of large inextensional deformation of cantilevered plates, as recently put forth by Simmonds and Libai, is extended to include orthotropic plates and plates with distributed loading. The bending rigidities of the orthotropic plate are calculated in terms of known material constants, and as functions of the single curvilinear coordinate employed in the theory. The constitutive relationships are then reformulated and the equilibrium equations transformed accordingly. The distributed loading that enters into the local equilibrium equations of the Simmonds-Libai theory is, in this paper, carried through to the overall equilibrium equations.
Dissipativeness and Stability of a Class of Distributed Parameter Systems
Authors: Bhat M. S. , Shrivastava S. K.
Published: July 2009

Input-output stability of linear-distributed parameter systems of arbitrary order and type in the presence of a distributed controller is analyzed by extending the concept of dissipativeness, with certain modifications, to such systems. The approach is applicable to systems with homogeneous or homogenizable boundary conditions. It also helps in generating a Liapunov functional to assess asymptotic stability of the system.
Moduluation-Function Technique in Nonuniform Mechanical Systems
Authors: Frostig Y. , Rosenhouse G.
Published: July 2009

This note demonstrates the advantages of the modulation-function technique, proposed here as means of finding efficient solutions for second-order structural systems, the inhomogeneity of which may also vary quickly. The problems dealt with, include buckling of columns, longitudinal vibration of rods, and the dynamic response of time-varying SDF’s. The basic formulas are presented and numerical examples are worked out for buckling.
Counterintuitive Behavior in a Problem of Elastic-Plastic Beam Dynamics
Authors: Symonds P. S. , Yu T. X.
Published: July 2009

In a particular example of short pulse loading on a pin-ended beam, the permanent deflection is predicted by a numerical solution to be in the direction opposite that of the load. Analysis of a Shanley-type model shows that this surprising behavior may occur as a consequence of plastic irreversibility combined with geometric nonlinearity, when the peak deflection produced by the pulse lies in a certain range of small magnitudes. Results from a number of well-known structural dynamics codes are shown. These exhibit a wide spread in the predicted final deflections, indicating strong sensitivities of both physical and computational nature.