bluuebunny/crossref_metadata_2025 huggingface dataset:
Floquet Theory and Newton’s Method
Authors: Thurston G. A.
Published: November 2010

Application of Newton’s method to nonlinear vibration problems can lead to a sequence of nonhomogeneous ordinary differential equations with periodic coefficients. The form of the complementary solutions are known from Floquet theory. This paper suggests a method for avoiding “secular terms” that grow with time in the particular solution. The method consists of finding a single periodic solution of the complementary solutions and its adjoint. If the periodic solution exists, a frequency correction can be computed that eliminates secular terms. After the frequency correction, the rest of the particular solution is periodic and can be computed by the infinite determinant method or other numerical methods. In oversimplified terms, the procedure is to find the improved approximation to the period by variation of parameters and the next approximation to the amplitudes by undetermined coefficients which is a simpler computation than variation of parameters.
Bounds for Initial Value Problems
Authors: Bell C. A. , Appl F. C.
Published: November 2010

A new method has been developed for finding rigorous upper and lower bounds to the solution of a wide class of initial value problems. The method is applicable to initial value problems of the following type: x(¨t)+f(t,x,x)˙=0,x(0)=X0,x(˙0)=V0, where f is continuous with continuous first derivatives, Lipschitzian, and ∂f/∂x ≥ 0. An original bounding theorem has been formulated and proven and a numerical technique has been developed for finding the bounding functions in analytic form as linear combinations of Tchebyshev polynomials. The method has been applied to several problems of engineering interest.
The Stability Surfaces of a Hill’s Equation With Several Small Parameters
Authors: Rubenfeld L. A.
Published: November 2010

The stability surfaces of a Hill’s equation with three independent small parameters are investigated using an extension of a perturbation method due to Struble. The method is applied up to second order but it is clear that it can be extended to any desired order and to other equations having any number of small parameters.
Vibration of Cable Gridworks With Small Initial Deformation
Authors: Afshari H. , Soler A. I.
Published: November 2010

Governing equations describing small dynamic motions about an initially deformed shape are derived for orthogonal cable gridworks. Dirac delta functions enable exact representation of the discrete tensions and physical property distribution of the system; Galerkin’s method is employed to reduce the field equations to ordinary differential equations in the time domain. It is shown that the effect of initial deformation on system natural frequencies is characterized by a characteristic parameter whch can be non-negligible even for small initial deformations. Numerical results are obtained for a typical system to illustrate the influence of initial sag. A model two-by-two orthogonal net of fine wires is constructed and tested experimentally. Results of the experiments tend to verify the theoretical conclusions.
On Bending of a Crystal to a Cylindrical Surface
Authors: Havner K. S.
Published: November 2010

This paper is concerned with macroscopic aspects of (large deformation) bending of a crystal to a cylindrical surface via slip in a single family of glide planes. The analysis rests upon the involute geometry of bent configurations and upon the adoption of an extended Schmid law. General stress fields required to bend the crystal are investigated considering possible phenomenological effects of (gross) glide plane curvature on local crystal hardening. In the case of linear (easy-glide) hardening of the glide system, an overall, nonlinear moment-curvature relation is developed. This general analytical equation, evaluated for zinc crystals, predicts a critical moment for large deformations and a finite moment with infinite rate of change at maximum bending.
Large Deformations of Circular Rings Under Nonuniform Normal Pressure
Authors: Seide P. , Jamjoom T. M. M.
Published: November 2010

The deformations and static stability of thin elastic circular rings under nonuniform pressures are studied. The investigation takes into account large bending deformations of the ring which is treated as an elastica. The loads considered remain normal to the center line during deformations. Numerical methods are used to solve the ordinary differential equations of equilibrium and of perturbed equilibrium for a particular case of loads which vary as p = p0(1 + q cos 2θ). The ring is found to deform only in a doubly symmetric fashion. Static buckling into an asymmetric deformation pattern does not occur.
Plane Solutions for the Displacement and Traction-Displacement Problems for Anisotropic Elastic Wedges
Authors: Kuo M. C. , Bogy D. B.
Published: November 2010

The plane displacement and traction-displacement problems for anisotropic elastic wedges are solved by use of the complex function representation of the plane solution in conjunction with the Mellin transform. The special forms of the solutions pertinent to orthotropic wedges with a material symmetry axis along the wedge bisector is also presented and the dependence of the order of the stress singularities at the apex on the wedge angle and material parameters is shown graphically for this case.
Incompressible and Linearly Compressible Viscoelastic Creep and Relaxation
Authors: Findley W. N. , Onaran K.
Published: November 2010

It is shown that defining an incompressible material as one whose response to stressing or straining is insensitive to volumetric-type changes in strain or stress allows the derivation of incompressible forms for multiple integral representations, through the third order, which have only three kernel functions both in the creep formulation and the relaxation formulation for small strains. Earlier work had yielded four kernel functions in the relaxation and three in the creep formulation. Linearly compressible formulations are also discussed and compared with available creep data.
Pulse Propagation in Straight and Curved Beams—Theory and Experiment
Authors: Crowley F. B. , Phillips J. W. , Taylor C. E.
Published: November 2010

The equations from Morley’s one-dimensional theory governing the motion of a curved beam subjected to an arbitrary pulse are solved numerically using the method of characteristics. Propagation of initially longitudinal pulses in beam assemblages with both straight and curved sections is investigated. Simulated isochromatic fringe patterns are constructed by a Calcomp plotter and are compared with actual photoelastic patterns. Remarkably good agreement is found between theory and experiment in all the cases investigated. It is concluded that Morley’s theory can be applied to pulse propagation problems of the type investigated.
Analysis of Narrow Porous Journal Bearing Using Beavers-Joseph Criterion of Velocity Slip
Authors: Prakash J. , Vij S. K.
Published: November 2010

Analytical solution for performance characteristics of a narrow journal bearing is obtained. The analysis takes account of the velocity slip at the surface of a porous medium by using Beavers-Joseph criterion [1]. Results are presented for various bearing characteristics and compared with earlier results obtained by using no-slip condition. A comparison is also made with an earlier approximate analysis [8] which considers the slip effects but assumes the bearing wall thickness to be infinitesimally small.
Delay-Bond Graph Models for Geared Torsional Systems
Authors: Tsai N. T. , Wang S. M.
Published: November 2010

The dynamic responses of geared torsional systems are analyzed with the delay-bond graph technique. By transforming the power variables into torsional wave variables, the torsional elements are modeled as transmission line elements. The nonlinear elements, e.g., varying tooth stiffness, gear-tooth backlash, and nonlinear damping, are incorporated into the ideal transmission line element. A computational algorithm is established where the state variables of the system are expressed in terms of wave scattering variables and the dynamic responses are then obtained in both time and space domains. The simulation results of several simple examples of linear and nonlinear geared torsional systems are presented to demonstrate the feasibility of this algorithm.
A Statistical Theory for the Fracture of Brittle Structures Subjected to Nonuniform Polyaxial Stresses
Authors: Batdorf S. B. , Crose J. G.
Published: November 2010

A weakest link theory for macroscopically homogeneous isotropic materials containing randomly oriented microcracks uniformly distributed in location is developed under the assumption that fracture depends only on the macroscopic stress normal to a crack plane. The function representing the number of cracks per unit volume failing at each value of normal stress is expanded as a Taylor series with coefficients determined from tensile test data. This function is used without additional assumptions to determine the probability of fracture under arbitrary (but not predominantly compressive) stress conditions. The results can be readily incorporated into a finite-element code to predict the failure probability of any structure to which the code applies.
Response of Long, Unconstrained, Thin-Walled Circular Cylinders to Lateral Time-Dependent Thermal Irradiation
Authors: Cooper L. Y.
Published: November 2010

This work investigates the response of initially uniform temperature, long, unconstrained, thin-walled, circular cylinders to a constant and uniform lateral thermal flux. The results are used to study the response of such cylinders to a time-varying thermal radiation delivery. The particular response variables studied are those of temperature, axial elongation, lateral deflection, and stress. Time histories of these are obtained in a dimensionless form. For the case of an energy delivery which is characteristic of a nuclear weapon burst, these responses are computed and presented for the full range of dimensionless parameter tmax, this being the ratio of a characteristic time of thermal flux delivery to a natural time of heat diffusion around a cylinder of interest.
Simple Methods for Determining the Virtual Origin of Turbulent Boundary Layers in Hypersonic Flow on Sharp-Edged Flat Plates
Authors: Hopkins E. J.
Published: November 2010

For hypersonic Mach numbers up to about 8, the virtual origin for turbulent skin-friction calculations is shown to be close to the beginning of boundary-layer transition. A simple relationship between the beginning and end of boundary-layer transition is presented.
On the Stability of Plane Parallel Flow Between Differentially Heated, Tilted Planes
Authors: Ayyaswamy P. S.
Published: November 2010

The linear and energy theories of stability of a plane parallel, antisymmetric flow between differentially heated, tilted planes are examined. The linear and energy results do not coincide indicating that subcritical motion may be possible. Also, it is seen that the energy stability limit corresponds to solutions independent of the coordinate in the direction of the flow. An interesting application of Busse’s theorem in this context is demonstrated.
Computation of Two-Dimensional and Axisymmetric Steady Laminar Boundary Layers by Quadrature
Authors: Bhatia J. C.
Published: November 2010

Based on momentum and energy integral equations of the boundary layer an approximate method is developed for computing two-dimensional and axisymmetric steady laminar flows. Simple quadrature formulas have been obtained to determine energy thickness and a shape parameter. Various characteristics of the boundary layer, e.g., different thicknesses, shearing stress at the wall, position of separation, etc., for Howarth and Tani flows, flow past a circular cylinder, a sphere, and a spheroid for various thickness ratios are computed. A comparison with other known solutions indicates that the present quadrature formulas yield closer approximation than do most other approximate methods. A few results for the compressible case (adiabatic wall) have also been presented.
A New Slip Theory of Plasticity
Authors: Lin T. H. , Ito Y. M. , Yu C. L.
Published: November 2010

A slip theory is presented for the calculation of the incremental stress-strain relations of a face-centered cubic polycrystal such as aluminum and its alloys, from its experimental uniaxial curves. This theory satisfies the conditions of equilibrium, condition of continuity of displacement as well as the slip characteristics of the component crystals. Numerical calculations based on this theory give results which are in good agreement with known experimental data on thin wall cylinders subject to different ratios of incremental axial and torsional loadings after being compressed beyond the elastic range.
Plastic Analysis of Shallow Spherical Shells
Authors: Haydl H. M. , Sherbourne A. N.
Published: November 2010

Rigid-plastic yielding and postyielding of pressurized shallow spherical shells is considered. The analysis includes the contribution of the transverse shear to yielding. Two approximate numerical solutions are given for several shell configurations. The yield surface used is based on the von Mises criterion. The results show that the effects of geometry changes lead to “geometrical strengthening” and “geometrical weakening” of the shallow shells.
Efficient Pulse Shapes to Plastically Deform Beams
Authors: Stronge W. J.
Published: November 2010

The transient motion of a simply supported, rigid-plastic beam in response to uniformly distributed pressure pulses of arbitrary shape is considered. The objective is to determine the pulse shape that will maximize the residual deflection at the center of the beam subject to certain load constraints. Results for two constraints are determined. When a specified impulse is applied to the beam an impulsive load causes the largest deflection. When a specified amount of work is done on the beam the deflection is maximized by limiting the maximum pressure so only the static collapse deformation mode occurs. This result is independent of pulse shape. These conclusions are supported by comparisons of the deformation due to triangular, exponentially decreasing and double rectangular pressure pulses.
On the First-Passage Distribution for the Envelope of a Nonstationary Narrow-Band Stochastic Process
Authors: Lennox W. C. , Fraser D. A.
Published: November 2010

A narrow-band stochastic process is obtained by exciting a lightly damped linear oscillator by wide-band stationary noise. The equation describing the envelope of the process is replaced, in an asymptotic sense, by a one-dimensional Markov process and the modified Kolmogorov (backward) equation describing the first-passage distribution function is solved exactly using classical methods by reducing the problem to that of finding the related eigenvalues and eigenfunctions; in this case degenerate hypergeometric functions. If the exciting process is white noise, the analysis is exact. The method also yields reasonable approximations for the first-passage time of the actual narrow-band process for either a one-sided or a symmetric two-sided barrier.
The Problem of Edge Cracks in an Infinite Strip
Authors: Gupta G. D. , Erdogan F.
Published: November 2010

The elastostatic plane problem of an infinite strip containing two symmetrically located internal cracks perpendicular to the boundary is formulated in terms of a singular integral equation with the derivative of the crack surface displacement as the density function. The solution of the problem is obtained for various crack geometries and for uniaxial tension applied to the strip away from the crack region. The limiting case of the edge cracks is then considered in some detail. The fundamental function of the integral equation is obtained and a numerical technique for solving the singular integral equations with this particular type of fundamental function which is characteristic of the edge cracks is described. The stress-intensity factor for the complete range of net ligament-to-width ratio 0 ≤ a/h ≤ 1 is calculated. The results also include the solution of the edge crack problem in an elastic half plane.
Contact Problem for an Elastic Reinforcement Bonded to an Elastic Plate
Authors: Erdogan F. , Civelek M. B.
Published: November 2010

The contact problem for a thin elastic reinforcement bonded to an elastic plate is considered. The stiffening layer is treated as an elastic membrane and the base plate is assumed to be an elastic continuum. The bonding between the two materials is assumed to be either one of direct adhesion or through a thin adhesive layer which is treated as a shear spring. The solution for the simple case in which both the stiffener and the base plate are treated as membranes is also given. The contact stress is obtained for a series of numerical examples. In the direct adhesion case the contact stress becomes infinite at the stiffener ends with a typical square root singularity for the continuum model and behaving as a delta function for the membrane model. In the case of bonding through an adhesive layer the contact stress becomes finite and continuous along the entire contact area.
Finite-Element Analysis of Vibration and Flutter of Cantilever Anisotropic Plates
Authors: Rossettos J. N. , Tong P.
Published: November 2010

The hybrid stress finite element method is used to study the effects of filament angle, θ, and orthotropicity parameter, EL/ET, on the vibration and flutter characteristics of cantilevered anisotropic plates. The results indicate a generally strong lack of monotonic dependence on θ. Also, the natural frequency in certain cases involving the first few modes, can become relatively insensitive to both θ and EL/ET for a range of θ beyond 70 deg. Values of critical dynamic pressure are obtained by a modal approach, in which the mode shapes are obtained by the hybrid stress method. Convergence of the modal method is rather rapid for the configurations analyzed, and a comparison of the method with an exact solution for the case of an isotropic simply supported plate shows that use of six modes gives excellent agreement.
Interfacial Stresses for Bonded Rubber Blocks in Compression and Shear
Authors: Gent A. N. , Henry R. L. , Roxbury M. L.
Published: November 2010

When a rubber block is compressed between two rigid surfaces, to which it is bonded, both compressive and shear stresses are set up at the interfaces. These interfacial stresses have been measured for small compressions of four relatively-thin, flat rubber blocks of square and circular cross section. Maximum compressive stresses, nearly twice the average value, were developed in the center of the bonded surfaces. Shear stresses were found to increase continuously from zero at the center to maximum values at the edges. No evidence was detected of a singularity at the edges. For all of the blocks examined, the observed stress distributions agreed satisfactorily with theoretical predictions based on incompressibility of the rubber and a simple superposition of two deformation states. Measurements were also made of the shear stress distribution associated with an overall shear displacement of the block.
An Instability of Shear Field-Buoyancy Field Interactions Leading to Vortex Formation
Authors: Garris C. A. , Lee S. L.
Published: November 2010

With the object of gaining a better understanding of the mechanism involved in the formation of vortices in buoyancy-driven systems interacting with ambient vorticity, a mathematical approach based upon the hydrodynamical instability theory is employed. For simplicity, the mathematical model consists of an infinite horizontal line heat source with uniform ambient vorticity supplied. A governing stability equation analogous to the Orr-Sommerfeld equation is derived and solved by a Newton-Raphson iterative technique employing special matching conditions just outside the plume and symmetry conditions enabling analysis in a half plane. The solution predicts a standing-wave-type instability of the class suggestive of incipient vortices. Neutral stability curves are generated and a critical Reynolds number based on plume thickness is obtained for Prandtl numbers of 5/9 and 2. Based on neutrally stable disturbances, a representative perturbed flow streamline pattern is shown. The theory predicts a critical elevation above which unstable modes exist. An optimization analysis was performed in the domain of unstable disturbance modes which suggested an overall selection process. It was found that at one particular elevation in the plume, one particular mode of disturbance grows much more rapidly than all others at any location. This property is then related to the vortex periodicity in the observed phenomenon. An attempt is made to relate the analytical results to relevant field observations of various classes of geophysical vortices.
Transient Thermal Stresses in a Sphere by Local Heating
Authors: Cheung J. B. , Chen T. S. , Thirumalai K.
Published: November 2010

The problem of transient thermal stresses in a solid, elastic, homogeneous, and isotropic sphere is solved for uniform and nonuniform, local surface heating. The temperature solutions are obtained by using separation of variables and integral transformation. The corresponding thermal stresses are derived by superposing a particular displacement potential function on Boussinesq solutions. Numerical solutions for two particular cases of localized heating of a typical brittle spherical solid have been obtained and presented. The results indicate a tensile stress concentration in the interior of the solid below the heated zone.
Thermoelasticity of an Anisotropic Half Space
Authors: Padovan J.
Published: November 2010

The thermoelasticity of an anisotropic Hookean half space is studied herein. A solution based on successive integral transforms is developed. The solution can handle arbitrary thermal and mechanical boundary conditions together with distributed body forces and heat sinks or sources. To illustrate the substantial effects of material anisotropy, a specific boundary-value problem is solved. Numerical results based on the solution are presented. These illustrate the significant effects of both thermal and mechanical material anisotropy.
Shock Wave Structure in a Linear Elastic Mixture With Binary Chemical Reactions
Authors: Nunziato J. W. , Walsh E. K. , Amos D. E.
Published: November 2010

In this paper we consider the propagation of small-amplitude, one-dimensional shock waves in a linear elastic mixture with binary chemical reactions. The effects of heat conduction and diffusion are neglected. Using a numerical technique, along with the results of a singular surface analysis, the behavior of a compressive wave generated by a constant velocity suddenly applied to the boundary of a half space is determined. The influence of the type of chemical reaction and of the underlying state of thermochemical equilibrium on the wave behavior is discussed. In the case of exothermic reactions the results are found to be in qualitative agreement with some recent experimental observations on solid explosives.
Nonlinear Torsional Vibrations of Thin-Walled Beams of Open Section
Authors: Kameswara Rao C.
Published: November 2010

An attempt has been made to derive and solve the governing differential equation of large amplitude torsional vibrations of simply supported doubly symmetric thin-walled beams of open section. Graphs indicating the influence of large amplitudes on nonlinear period of torsional vibrations for various nondimensional beam constants are presented.
Photoelastic Investigation of a Thick Plate With a Transverse Crack
Authors: Villarreal G. , Sih G. C. , Hartranft R. J.
Published: November 2010

The purpose of this investigation was to experimentally test one of the assumptions of a recent modified version of the theory of generalized plane stress. The form postulated by the theory for the stress variation through the thickness of a plate containing a crack will be compared with that obtained by three-dimensional photoelastic analysis. Specimens covering the range from thin to moderately thick plates were examined by the frozen stress technique. The experimentally measured transverse variation of the in-plane stress components σx and σy was in excellent agreement with that postulated by the theory.
Effect of Slip Flow in Narrow Porous Bearings With Arbitrary Wall Thickness
Authors: Murti P. R. K.
Published: November 2010

The experimental work of Beavers, et al., established that velocity slip takes place over a permeable boundary. The Reynolds equation governing the flow of lubricant in a finite porous bearing is appropriately modified to include the effect of velocity slip at the permeable boundary. The performance of a bearing with arbitrary wall thickness is then analyzed adopting the narrow bearing approximation. An exact solution is given for the pressure of the lubricant in the bearing material using modified Bessel functions and the modified Reynolds equation for the problem is solved by the Galerkin method. Numerical results obtained with a digital computer indicate that slip flow adversely affects the load capacity and reduces the friction force on the journal; the attitude angle, however, is not significantly affected. Also, the analysis indicates that the effects of velocity slip are prominent when the bearing operates at a higher eccentricity ratio and/or the bearing matrix has a low permeability. The results are presented in graphical and tabular forms and guidelines are outlined to enable designers in assessing bearing performance using the results.
Constitutive Equations for Elastic-Viscoplastic Strain-Hardening Materials
Authors: Bodner S. R. , Partom Y.
Published: November 2010

A set of constitutive equations has been formulated to represent elastic-viscoplastic strain-hardening material behavior for large deformations and arbitrary loading histories. An essential feature of the formulation is that the total deformation rate is considered to be separable into elastic and inelastic components which are functions of state variables at all stages of loading and unloading. The theory, therefore, is independent of a yield criterion or loading and unloading conditions. The deformation rate components are determinable from the current state which permits an incremental formulation of problems. Strain hardening is considered in the equations by introducing plastic work as the representative state variable. The problem of tensile straining has been examined for a number of histories that included straining at various rates, rapid changes of strain rate, unloading and reloading, and stress relaxation. The calculations were based on material constants chosen to represent commercially pure titanium. The results are in good agreement with corresponding experiments on titanium specimens.
Dynamic Fracture Process in Beams
Authors: Colton J. D. , Herrmann G.
Published: November 2010

The relief waves created by the dynamic fracture of a brittle beam were determined. An experiment was conducted on an effectively infinite beam loaded over a finite area with sheet explosive. The time sequence of deformation and fracture was determined by terminal observation, high-speed framing camera photographs, and strain gages. Beam response was also predicted analytically by numerically integrating the characteristic equations of Timoshenko beam theory. Comparison of calculated and measured strains showed that the effect of an initial fracture in a beam at a location of pure bending can be approximated by a two-stage process that specifies how the bending moment at the fracture point is reduced to zero after fracture. In the first stage, the crack propagates to the neutral axis, and the stress distribution remains unchanged. In the second stage, the crack propagates through the remainder of the beam thickness while the stress continuously redistributes itself.
Response and Stability of Linear Dynamic Systems With Many Degrees of Freedom Subjected to Nonconservative and Harmonic Forces
Authors: Fu F. C. L. , Nemat-Nasser S.
Published: November 2010

Dynamic systems whose response can be characterized by a set of linear differential equations with harmonic coefficients which are proportional to a small parameter ε, are considered. These systems are such that the corresponding autonomous sets of equations which are obtained by setting ε = 0, are defined by nonself-adjoint linear differential operators; i.e., they correspond to dynamic systems subjected to nondissipative nonconservative forces. For these systems, general asymptotic solutions are developed and their stability is examined. An interesting feature of these solutions is that, when the exciting frequency is close to, say, twice of a suitable eigenfrequency, or when it is close to the sum or the difference of two suitable frequencies of the autonomous system, then the asymptotic solution will involve negative fractional powers of ε. Hence, the nonsecular asymptotic solution, in general, may not reduce to the solution of the autonomous system as ε goes to zero. Another interesting feature of the present results is that the addition of small suitable harmonic forces does indeed stabilize an inherently unstable nondissipative nonconservative dynamical system; except when the frequency of the harmonic force resonates with one or several of the frequencies of the autonomous system in either a subharmonic or a combinational-type oscillation.
Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers
Authors: Padgaonkar A. J. , Krieger K. W. , King A. I.
Published: November 2010

The computation of angular acceleration of a rigid body from measured linear accelerations is a simple procedure, based on well-known kinematic principles. It can be shown that, in theory, a minimum of six linear accelerometers are required for a complete definition of the kinematics of a rigid body. However, recent attempts in impact biomechanics to determine general three-dimensional motion of body segments were unsuccessful when only six accelerometers were used. This paper demonstrates the cause for this inconsistency between theory and practice and specifies the conditions under which the method fails. In addition, an alternate method based on a special nine-accelerometer configuration is proposed. The stability and superiority of this approach are shown by the use of hypothetical as well as experimental data.
Propagation of Weak Shock Waves in a Vibrational Nonequilibrium, Nonuniform Gas
Authors: Chou D. C. , Maa S. Y.
Published: November 2010

Problems concerned with the propagation of weak planar shock waves in a nonuniform, nonequilibrium gas is theoretically investigated. The medium under consideration is a diatomic thermally perfect gas with excited vibrational energy and is initially inhomogeneous with exponential density and temperature distributions. The systematic characteristic perturbation scheme is employed to render a first-order frozen shock expression. It is shown quantitatively that combined effects of nonequilibrium, nonlinearity, and stratification govern the nature of the shock wave propagation. The uniform gas limit of present theory agrees with previously known results of shock wave propagation in a general relaxing fluid. Numerical examples illustrate the variation of frozen shock strength and speed due to different magnitudes of relaxation rates and inhomogeneity. The interesting competition phenomenon between nonequilibrium effects and nonuniform effects on shock wave propagation is examined.
On an Extremum Principle for Mode Form Solutions in Plastic Structural Dynamics
Authors: Symonds P. S. , Wierzbicki T.
Published: November 2010

An extremum principle of Lee and Martin [2], for mode form solutions of a structure deforming plastically as result of dynamic loading, is discussed with special reference to conditions for the extrema to be stationary, with vanishing first variation of a functional of kinematically admissible velocity fields. Three classes of material behavior are treated: rigid-perfectly plastic, rigid-viscoplastic, and viscous, the last having no yield function. We illustrate various forms of these which are realistic as well as convenient in problems of plastic dynamics of structures. For all three classes of material, we show that stationary extrema occur under certain conditions, but may be regarded as exceptional. The properties of the extrema for structures are illustrated by means of a simple discrete structure model with two masses.
Effect of Sliding Friction on Contact Stresses in a Rectangle Compressed by Rigid Planes
Authors: Prasad S. N. , Dasgupta S.
Published: November 2010

The plane-strain compression of an elastic rectangle by rigid, rough planes with finite coefficient of friction between the surfaces is considered. The contact area is divided into an inner adhesive region in which the surface displacements are known, surrounded by regions in which the friction is limiting and the displacement parallel to the interface is not known. The remaining set of parallel edges of the rectangle is free from tractions. The problem is formulated in terms of Papkovich-Fadle eigenfunctions which lead to the solution of a set of two integral equations of the second kind. Solution of the integral equations which satisfies the finiteness of stresses at the point which separates the adhesive from the slip zone, determines the extent of adhesion. This is found to be independent of the magnitude of load, but depends on the values of frictional coefficients, Poisson’s ratio and the aspect ratio. Numerical results of the quantities of practical interest are reported.
Finite-Element Analysis of Skew Sandwich Plates
Authors: Ng S. S. F. , Kwok W. L.
Published: November 2010

Two finite-element displacement models are presented for the analysis of clamped and simply supported skew and rectangular sandwich plates subjected to uniformly distributed loads. Each finite-element model consists of subelements representing the skins and core of sandwich plates. The parameters considered in this investigation are the aspect ratio of the plate, Poisson’s ratio, angle of skew, and various ratios of bending and shearing stiffnesses.
Stress Concentrations at the Apex of a Plane Indenter Acting on an Elastic Half Plane
Authors: Gdoutos E. E. , Theocaris P. S.
Published: November 2010

The singular stress field at the vicinity of the apex of an elastic plane indenter of various angles compressing an elastic half plane was studied by using a complex variable technique. Three particular cases where the indenter is perfectly bonded, slips or adheres according to the Coulomb’s law of friction, to the half plane were considered. The characteristic equations for the determination of the order of the stress singularity at the vicinity of the apex of the indenter for the above three cases were defined in terms of the angle of the indenter and the two composite material parameters α and β first introduced by Dundurs, depicting the mechanical properties of the two materials. The order of singularity at the vertex of the indenter was determined for all material combinations of the indenter and the half plane. Valuable and interesting results were derived.
A Mechanical Model for Mammalian Tendon
Authors: Beskos D. E. , Jenkins J. T.
Published: November 2010

A theoretical model is proposed to describe the mechanical behavior of mammalian tendon. The tendon is modeled as an incompressible fiber-reinforced composite with continuously distributed inextensible fibers. The fibers describe helices with constant pitch on concentric right circular cylinders. The analysis is, essentially, independent of the material behavior and, for example, applies to nonlinear elastic solids and viscoelastic materials. A boundary-value problem for tendon extension is discussed in detail and, for a particular nonlinear elastic solid, the deformation and stress are determined to be in qualitative agreement with existing experimental results.
Steady Solutions for Moving Loads on Elastic Beams With One-Sided Constraints
Authors: Adams G. G. , Bogy D. B.
Published: November 2010

An infinite beam resting on a flat rigid foundation is loaded by an upward directed concentrated force, which moves at a constant speed. Both the Euler-Bernoulli and Timoshenko beam models are considered. With force magnitude and speed as parameters, the noncontact lengths, mode shapes and foundation reactions are computed and illustrated graphically.
Transient Response of Nonlinear Systems to Stationary Random Excitation
Authors: Soni S. R. , Surendran K.
Published: November 2010

Transient response of second-order systems with a slightly nonlinear restoring force is analyzed for random inputs using perturbation technique. Mean square responses, up to the second-order of correction, are obtained for white and exponentially decaying correlation functions.
Dynamic Response of Circular Rigid-Plastic Plates Resting on Fluid
Authors: Krajcinovic D.
Published: November 2010

Paper concerns a specific problem in the study of dynamic response of rigid-plastic plates in contact with incompressible and inviscid fluid. The dynamic load is assumed to be of high intensity and short duration. Employing integral transform technique in conjunction with the dual integral equation method this interaction problem is reduced to the problem of plate deforming in vacuum for which the solution is well known.
Wall Shear Stress Inference for Three-Dimensional Turbulent Boundary-Layer Velocity Profiles
Authors: Chandrashekhar N. , Swamy N. V. C.
Published: November 2010

Based on flow similarity in the near-wall region of three-dimensional turbulent boundary layers, three methods have been developed for the prediction of the wall shear stress components, their resultant and its direction. The results from all the methods agree with one another and with available experimental results. It is found that the direction of the wall shear stress vector is not the same as the direction of the limiting wall streamline, except for small crossflows. A simplified procedure for estimating skin friction is also given, by which graphical work, as in the Clauser scheme, is eliminated.
Free Boundary Problem for the Laplace Equation With Application to ECM Tool Design
Authors: Nilson R. H. , Tsuei Y. G.
Published: November 2010

The tool design problem of electrochemical machining (ECM) is formulated by the inverted approach in which the spatial coordinates are treated as the dependent variables on the plane of the complex potential. A general solution of this free boundary problem by analytic continuation provides the basis for a series approximation with correct asymptotic behavior using the method of weighted residues. The procedure is used to determine the noninsulated or partially insulated tool shapes which can be used to machine a prescribed workpiece geometry. The method is generally applicable to inverse (design) problems of potential theory which involve a given equipotential (or streamline) boundary along which a Neumann boundary condition is also prescribed as occurs in heat conduction, ideal flow, and electrostatics. The inverted approach not only eliminates the need for trial-and-error design procedures but also provides the advantage of adjustment in geometry by superposition.
Influence of Deformations Prior to Instability on the Dynamic Instability of Conical Shells Under Periodic Axial Load
Authors: Tani J.
Published: November 2010

The dynamic instability of clamped, truncated conical shells under periodic axial load is studied using the Donnell-type basic equation and considering the effect of bending deformations before instability. Two principal instability regions are determined by combining Bolotin’s method and a finite-difference method. One of these belongs to double the natural frequencies of asymmetrical vibration; the other corresponds to the resonance of symmetrically forced vibrations. The effects of static axial load and end-plate mass on the principal instability regions are also investigated.
On the Phenomenon of Separation During Compression and Frictional Sliding of an Elastic Rectangle
Authors: Dasgupta S. , Prasad S. N.
Published: November 2010

The plane strain compression and sliding of an elastic rectangle is considered whose one set of parallel edges are free from tractions. The remaining set of parallel edges is simultaneously subjected by rigid rough planes to a compressive force P and a sliding force F = μP, where μ is the coefficient of sliding friction. The rigid planes are prevented from rotation and a limiting equilibrium is assumed by taking the contact shear stress to be equal to the product of the normal compressive stress with μ. It is found that the presence of free edges significantly affects the deformation of the rectangle. In particular, it is shown that during sliding the leading edge of the rectangle is compressed most severely against the rigid plane, whereas separation takes place at the trailing edge. The separation occurs at the slightest trace of the application of load and although the magnitude depends upon the level of loading, the extent of the zone depends only on Poisson’s ratio, frictional coefficient, and the aspect ratio. Numerical results of the quantities of practical interest are reported.
Viscid-Inviscid Interaction of Incompressible Separated Flows
Authors: Chow W. L. , Spring D. J.
Published: November 2010

A flow model has been devised to deal with the viscid-inviscid interaction of a class of two-dimensional incompressible separated flow problems. It is suggested that the corresponding inviscid flow of these problems is described by the free streamline theory with few unspecified parameters and their values are, in turn, determined by the viscous flow considerations. The problem of a flow past a backward facing step is selected for study in detail. The viscous flow components of turbulent jet mixing, recompression, and reattachment are delineated and studied individually. When they are later combined, it is found that the point of reattachment behaves as a saddle-point-type singularity in the system of differential equations describing the viscous flow process. This feature is employed to the determination of the aforementioned free parameters and thus the establishment of the overall corresponding inviscid flow field. The resulting base pressure coefficient for the specific case agrees reasonably well with the available experimental data. Additional calculations are performed to demonstrate the influence of higher Reynolds numbers and the values of the similarity (or spread rate) parameter σ of the “constant pressure” turbulent jet mixing process. Further studies of redevelopment of the viscous flow after reattachment, the turbulent exchange within the recompression and redevelopment regions, and the effect of wind tunnel-wall interference on the overall flow patterns have been suggested and discussed.
Effect of Velocity Slip in an Externally Pressurized Porous Thrust Bearing Working With an Incompressible Fluid
Authors: Murti P. R. K.
Published: November 2010

A porous thrust pad externally pressurized with an incompressible fluid is analyzed providing for the slip flow at the porous boundary as per the Beavers-Joseph model. The performance characteristics of the bearing are derived in a closed form assuming that the flow is predominantly axial in the bearing matrix. The behavior of the bearing is described in terms of a new dimensionless parameter called the “Bearing Number.” There is near perfect agreement between the theoretical predicted performance and the one experimentally evaluated.
Torsion of a Rigid Cylinder Embedded in an Elastic Half Space
Authors: Luco J. E.
Published: November 2010

A study is made of the axially symmetric torsion of a rigid cylinder partially embedded into a layered elastic half space. The problem is formulated on the basis of perfect bonding between the cylinder and the surrounding material. Integral representations are used to reduce the problem to the solution of two integral equations. Stress singularities of fractional order are obtained along the perimeter of the base of the cylinder. A numerical solution of the integral equations is used to obtain the torque-twist relationship for different embedment depths and for different values of the elastic constants.
Analysis of Elastic-Plastic Impact Involving Severe Distortions
Authors: Johnson G. R.
Published: November 2010

A Lagrangian analysis technique is presented for two-dimensional axi-symmetric impact problems involving elastic-plastic flow. This technique is based on a triangular finite-element formulation rather than the quadrilateral formulation generally used in comparable finite-difference methods. For impact problems involving severe distortions, the triangular element formulation is better suited to represent the severe distortions than is the traditional quadrilateral finite-difference method. Included are the formulation of the technique and illustrative examples.
Creep Buckling of a Complete Spherical Shell
Authors: Jones Norman
Published: November 2010

The creep buckling behavior of a complete spherical shell which is subjected to a uniform external pressure is investigated using a perturbation method of analysis. The spherical shell has an arbitrary initial imperfect shape and is made from a material which creeps according to the generalized Norton’s law. It turns out that the critical mode number of the deformed profile is identical to that obtained previously by various authors for the linear elastic instability of complete spherical shells. It also appears that the resistance to creep buckling of complete spherical shells is greater than the resistance of a long cylindrical shell having the same R/h ratio and material properties.
Dynamics of a Partially Full Cylinder Containing a Magnetic Liquid in a Magnetic Field
Authors: Tichenor D. R. , Avula X. J. R.
Published: November 2010

This study is concerned with the transient motion of an infinitely long thin-walled circular cylinder partially filled with a magnetic liquid under magnetic and nonmagnetic forces. Starting from rest the cylinder is constrained to roll without slipping on a plane surface while the contained fluid with a rectangular free surface is simultaneously subjected to a magnetic field parallel to the plane by activating a magnet located ahead of the cylinder. The nonmagnetic force on the cylinder and its contents is provided by the gravity. Assuming negligible viscous dissipation Lagrange’s equations of motion are derived and solved to obtain the motion of the cylinder and the liquid subsequent to the application of the magnetic field. Results are presented in a nondimensional form for motion on horizontal and inclined planes under different magnetic strengths.
Stress-Intensity Factors for Very Short Cracks in Arbitrary Pressurized Shells
Authors: Simmonds J. G. , Bradley M. R.
Published: November 2010

A pressurized, shallow, elastically isotropic shell containing a crack is considered. The crack is assumed to lie along a line of curvature of the midsurface. The equations governing the essentially equivalent residual problem, in which the only external load is a uniform normal stress along the faces of the crack, are reduced via Fourier transforms to two coupled singular integral equations. The solutions of these equations depend on three parameters: λ, a dimensionless crack length, κ, the dimensionless Gaussian curvature of the midsurface at the center of the crack, and ν, Poisson’s ratio. Perturbation solutions for small values of λ are obtained by expanding the kernels of the integral equations in series. Explicit formulas for stretching and bending stress-intensity factors are obtained. These represent the first-order corrections due to curvature effects of the well-known flat plate results. The connection with the work of Copley and Sanders for cylindrical shells and Folias for spherical and cylindrical shells is indicated.