bluuebunny/crossref_metadata_2025 huggingface dataset:
On Torsion and Transverse Flexure of Orthotropic Elastic Plates
Authors: Reissner E.
Published: July 2009

The equations of transverse bending of shear-deformable plates are used for the derivation of a system of one-dimensional equations for beams with unsymmetrical cross section, with account for warping stiffness, in addition to bending, shearing, and twisting stiffness. Significant results of the analysis include the observation that the rate of change of differential bending moment is given by the difference between torque contribution due to plate twisting moments and torque contribution due to plate shear stress resultants; a formula for shear center location which generalizes a result by Griffith and Taylor so as to account for transverse shear deformability and end-section warping restraint; a second-order compatibility equation for the differential bending moment; a contracted boundary condition of support for unsymmetrical cross-section beam theory in place of an explicit consideration of the warping deformation boundary layer; and construction of a problem where the effect of the conditions of support of the beam is such as to give noncoincident shear center and twist center locations.
Stability Considerations in Thermoelastic Contact
Authors: Barber J. R. , Dundurs J. , Comninou M.
Published: July 2009

A simple one-dimensional model is described in which thermoelastic contact conditions give rise to nonuniqueness of solution. The stability of the various steady-state solutions discovered is investigated using a perturbation method. The results can be expressed in terms of the minimization of a certain energy function, but the authors have so far been unable to justify the use of such a function from first principles in view of the nonconservative nature of the system.
An Instability Theorem for Steady Motions in Free and Restrained Dynamical Systems
Authors: Hagedorn P. , Teschner W.
Published: July 2009

The stability of steady motions in dynamical systems with ignorable coordinates is considered. In addition to the original “free” systems “restrained” systems are defined in such a way that the ignorable velocities remain constant along all motions; the stability behavior of the two systems is compared. A previously established instability theorem is generalized and three examples are given.
On the Extremal Properties of Hamilton’s Action Integral
Authors: Papastavridis J. G.
Published: July 2009

This Note examines the sufficient conditions for the extremization, in particular the minimization, of the action integral in Hamilton’s principle for a one-degree-of-freedom nonlinear conservative system. It is usually stated in analytical mechanics that the action is actually minimized only over a short-time interval. Here the quantification of these statements is achieved by obtaining an upper bound for this minimizing interval. This is attained by combining results from the sufficiency variational calculus theory, with oscillation/comparison theorems from differential equations.
Propagation of Elastic Pulses and Acoustic Emission in a Plate—Part 1: Theory
Authors: Ceranoglu A. N. , Pao Yih-Hsing
Published: July 2009

Transient waves generated by a variety of dynamic nuclei of strains including a concentrated force, a single-couple, a double-force, a double-couple without moment, a center of rotation, and a center of explosion in an elastic plate are analyzed. Some of these sources, or a combination of them, could be used to model the dynamic process of material defects. The analysis is based on the generalized ray theory and Cagniard’s method and the solutions are presented in terms of Green’s dyadics for a plate.
Basic Transport Equations in Ascending Equiangular Spiral Polar Coordinates
Authors: Ali S.
Published: July 2009

Basic transport equations have been expressed in a coordinate system suitable for the analytical study of momentum, heat, and mass transport processes in ascending equinagular spiral tube coils. The chosen coordinate system for the representation of these equations is orthogonal curvilinear possessing proper transformation to the rectangular Cartesian coordinate system. Various tensorial quantities appearing in the tensorial form of the general basic transport equations have been obtained in expanded form in the chosen curvilinear coordinate system. Substitution of these quantities, readily expands all the basic transport equations in their various forms. Illustration has been made for the equation of continuity, the general equation of motion, the Navier-Stokes equation, the equation of energy, and the equation of mass transport. The resulting equations are in forms suitable for analytical and numerical solution.
A Correct Definition of Elastic and Plastic Deformation and Its Computational Significance
Authors: Lubarda V. A. , Lee E. H.
Published: July 2009

The plastic part of an elastic-plastic deformation is that remaining when the stress, and hence the elastic strain, is reduced to zero. Elastic deformation is that produced in this purely plastically deformed material by the action of stresses up to yield. The associated exact finite-deformation kinematics shows the almost universal assumption that the total rate of deformation is the sum of elastic and plastic rates to be in error. An incremental elastic-plastic theory is developed using the nonlinear kinematics. The theory is contrasted with that in common use and anomalies in the latter are discussed.
A Dislocation Model for Fatigue Crack Initiation
Authors: Tanaka K. , Mura T.
Published: July 2009

The slip band formed in a grain on the material surface is a preferential site for crack initiation during low strain fatigue of polycrystalline metals. The forward and reverse plastic flow within the slip band is modeled in the present study by dislocations with different signs moving on two closely located layers, and it is assumed that their movement is irreversible. Based on the model, the monotonic buildup of dislocation dipoles piled up at the grain boundary is systematically derived using the theory of continuously distributed dislocations. This buildup is associated with the progress of extrusion or intrusion. The number of stress cycles up to the initiation of a crack of the grain size order is defined as the cycle when the stored strain energy of accumulated dislocations reaches a critical value. The relation between the initiation life and the plastic strain range derived theoretically is in agreement with a Coffin-Manson type law, and that between the fatigue strength and the grain size is expressed in an equation of the Petch type.
Creeping Viscous Flow Around a Heat-Generating Solid Sphere
Authors: Krenk S.
Published: July 2009

The velocity field for creeping viscous flow around a solid sphere due to a spherically symmetric thermal field is determined and a simple thermal generalization of Stokes’ formula is obtained. The velocity field due to an instantaneous heat source at the center of the sphere is obtained in closed form and an application to the storage of heat-generating nuclear waste is discussed.
Stability of Developing Flow in a Pipe—Nonparallel Effects
Authors: Garg V. K. , Gupta S. C.
Published: July 2009

A theoretical investigation into the linear, spatial instability of the developing flow in a rigid circular pipe, incorporating the effects of nonparallelism of the main flow, has been made at several axial locations. The velocity profile in the developing flow region is obtained by a finite-difference method assuming uniform flow at the entry to the pipe. For the stability analysis, the continuity and momentum equations have been integrated separately using fourth-order Runge-Kutta integration scheme and applying selectively the Gram-Schmidt orthonormalization procedure to circumvent the parasitic error-growth problem. It is found that the critical frequency, obtained from different growth rates, decreases first sharply and then gradually with increasing X, where X = x/aR = X/R; x being the streamwise distance measured from the pipe inlet, a being the radius of the pipe, and R the Reynolds number based on a and average velocity of flow. However, the critical Reynolds number versus X curves pass through a minima. The minimum critical Reynolds number corresponding to gψ(X, O), the growth rate of stream function at the pipe axis, to gE(X), the growth rate of energy density, and to the parallel flow theory are 9700 at X = 0.00325, 11,000 at X = 0.0035, and 11,700 at X = 0.0035, respectively. It is found that the actual developing flow remains unstable over a larger inlet length of the pipe than its parallel-flow approximate. The first instability of the flow on the basis of gψ(X, O), gE(X) and the parallel flow theory, is found to occur in the range 30 ≤ X ≤ 36, 35 ≤ X ≤ 43, and 36 ≤ X ≤ 45, respectively. The critical Reynolds numbers obtained on the basis of gψ(X, O) are closest to the experimental values.
Rotating Compressible Flow Over the Edge of a Finite Disk
Authors: Toren M. , Solan A.
Published: July 2009

Numerical and asymptotic solutions of the similarity equations governing the laminar compressible rotating flow near the edge of a finite disk are presented for a wide range of the Prandtl and Eckert numbers and the disk-to-external flow ratios of azimuthal velocity and temperature. By appropriate transformations, the compressible flow is reduced to a formulation similar to that of the incompressible flow. Wall heating and dissipation effects are shown to be equivalent to an increment of the velocity of the disk in the sense opposite to that of the outer flow. In the limit of small velocity or temperature difference between the disk and the outer flow, the solutions show how an Ekman layer is started at the edge.
Infiltration of a Fluid Into a Dry Poro-Elastic Body
Authors: Yamagami K. , Kurashige M.
Published: July 2009

The infiltration of a fluid into a dry poro-elastic body, of infinite extent, from its cylindrical or spherical cavity and the resulting mechanical behaviors are investigated. Since the problem is a moving boundary problem, and therefore, an essentially nonlinear one, the finite-difference scheme with the aid of the boundary fixing method is applied to obtain the solution. The results thus obtained for sandstone are compared with those for a porous rigid body as well as with those in a situation where a fluid pervades the whole body from the outset. These comparisons show that the extent of the infiltration front into the body is adequately predicted by the rigid skeleton model and that the actual stress distribution is remarkably different from that which exists if fluid pervades the whole body from the outset.
A Finite-Element Singular-Perturbation Technique for Convection-Diffusion Problems—Part 1: The One-Dimensional Case
Authors: Diaz-Munio Rafael F. , Wellford L. Carter
Published: July 2009

Approximation procedures for the solution of convection-diffusion equations, occurring in various physical problems, are considered. Several finite-element algorithms based on singular-perturbation methods are proposed for the solution of these equations. A method of variational matched asymptotic expansions is employed to develop shape functions which are particularly useful when convection effects dominate diffusion effects in these problems. When these shape functions are used, in conjunction with the standard Galerkin method, to solve convection-diffusion equations, increased solution accuracy is obtained. Numerical results for various one-dimensional problems are presented to establish the workability of the developed methods.
Crack Path Prediction for a Kinked Crack in the Neighborhood of a Circular Inclusion in an Infinite Medium
Authors: Sheng C.-F. , Wheeler L.
Published: July 2009

In this paper, we study the effects of the elasticity and proximity of a circular inclusion upon the fracture angle of a bent crack in the surrounding matrix. The medium is assumed to be in plane strain, and loaded in uniaxial tension by stresses acting perpendicular to the main branch of the crack. A comparison is made of fracture-angle predictions based upon current theories governing the initial fracture angle.
Boussinesq-Papkovich Functions for Creep Around a Spherical Cavity or a Rigid Inclusion in a Gravity-Loaded Half Space
Authors: Anderson C. A.
Published: July 2009

Boussinesq-Papkovich stress functions are used to determine three-dimensional closed form solutions for steady creep around a spherical cavity or rigid inclusion in a half space under gravity loading. The ratio of cavity depth to radius is assumed to be greater than 5, and the flow law of the half space is linear, which allows for solution in terms of a finite number of spherical harmonics. Numerical results are given to show the influence of the lateral stress component at infinity, the stabilizing effect of internal cavity pressure, and buoyancy forces associated with the motion of a rigid inclusion.
On Stiffness and Strength of an Aligned Short-Fiber Reinforced Composite Containing Fiber-End Cracks Under Uniaxial Applied Stress
Authors: Taya M. , Mura T.
Published: July 2009

One of the experimental findings on short-fiber reinforced composite materials is that the fiber-ends act as a crack initiator. The effect of the fiber-end crack on the overall stiffness and the strength of the composite are investigated here. A particular emphasis is placed upon the weakening longitudinal Young’s modulus by the fiber-end crack which is assumed to be penny-shaped. The energy release rate of the penny-shaped crack at the fiber-end under a uniaxial applied stress is also calculated for a fracture criterion. It is assumed in our theoretical model that short-fibers are all aligned in the loading direction and the penny-shaped crack at the fiber-end extends in the direction perpendicular to the fiber axis. Our analytical technique is a combination of Eshelby’s equivalent inclusion method and Mori-Tanaka’s back stress analysis so that our results are valid even for large volume fraction of fibers.
Nonlinear Theory for Flexural Motions of Thin Elastic Plate—Part 2: Boundary-Layer Theory Near the Edge
Authors: Sugimoto N.
Published: July 2009

This paper deals with, as a continuation of Part 1 of this series, the boundary-layer theory for flexural motions of a thin elastic plate. In the framework of the higher-order theory developed in Part 1, three independent boundary conditions at the edge of the plate are too many to be imposed on the essentially fourth order differential equations. To overcome this difficulty, a boundary layer appearing in a narrow region adjacent to the edge is introduced. Using the matched asymptotic expansion method, uniformly valid solutions for a full plate problem are sought. The boundary-layer problem consists of the torsion problem and the plane problem. Three types of the edge conditions are treated, the built-in edge, the free edge, and the hinged edge. Depending on the type of edge condition, the nature of the boundary layer is characterized. After solving the boundary-layer problem, “reduced” boundary conditions relevant to the higher-order theory are established.
Dynamic Response of a Beam With a Geometric Nonlinearity
Authors: Masri S. F. , Mariamy Y. A. , Anderson J. C.
Published: July 2009

Analytical and experimental studies were made of the dynamic response of a system with a geometric nonlinearity, which is encountered in many practical engineering applications. An exact solution was derived for the steady-state motion of a viscously damped Bernoulli-Euler beam with an unsymmetric geometric nonlinearity, under the action of harmonic excitation. Experimental measurements of a mechanical model under harmonic as well as random excitation verified the analytical findings. The effect of various dimensionless parameters on the system response was determined.
A Numerical Solution for Gas-Particle Flows at High Reynolds Numbers
Authors: Laitone J. A.
Published: July 2009

Predicting the fluid mechanical characteristics of a gas-solid two-phase flow is critical for the successful design and operation of coal gasification systems, coal fired turbines, rocket nozzles, and other energy conversion systems. This work presents a general grid-free numerical solution which extends a numerical solution of the Navier-Stokes equations developed by Chorin to a solution suitable for unsteady or steady dilute gas-solid particle flows. The method is applicable to open or closed domains of arbitrary geometry. The capability of the method is illustrated by analyzing the flow of gas and particles about a cylinder. Good agreement is found between the numerical method and experiment.
Approximate Description of Crack Kinking and Curving
Authors: Karihaloo B. L. , Keer L. M. , Nemat-Nasser S. , Oranratnachai A.
Published: July 2009

An approximate description is given of the slightly out-of-plane growth of a straight crack under mixed-mode loading and in the presence of an in-plane stress. By using a perturbation technique, conditions are derived for the deviation of the crack from straightness. The allowance for the possible curvature of the quasi-statically growing crack, and the effect of the finite length of the main crack are included in the analysis, which retains second-order terms. In particular, it is shown that the curvature of the crack path depends on the in-plane stress and the derivatives of the stress-intensity factors with respect to the length of the main crack. The influence of the in-plane stress on the stability of the crack growth is also studied and the conclusions are the same as those reported by Cotterell and Rice.
Transient Response of a Finite Crack in a Half Plane Under Impact Load
Authors: Itou S.
Published: July 2009

Analytical investigation of a half plane weakened by a finite crack is considered. The crack is placed perpendicularly to the stress-free boundary of the half plane. The surfaces of the crack are loaded by a uniform pressure with Heaviside-function time dependence. In the Laplace transform domain, Fourier transformations are utilized to reduce the problem to the solution of a pair of dual integral equations which are solved by using the series expansion method. The Laplace inversion of the dynamic stress-intensity factors is carried out numerically.
Planar Hertz Contact With Heat Conduction
Authors: Comninou M. , Dundurs J. , Barber J. R.
Published: July 2009

The paper discusses the planar Hertz contact problem when the bodies are not only pressed together but also exchange heat by conduction. The nature of the problem and the results depend strongly on the direction of heat flow. If heat flows into the material with the larger distortivity, the common boundary conditions are sufficient to achieve a solution which satisfies the inequalities associated with a contact problem. For heat flowing in the opposite direction, the common boundary conditions by themselves lead to contradictions, but the difficulties can be overcome by introducing a zone of imperfect contact. The formulation is based on a suitable Green’s function, and the problem is reduced to a singular integral equation which must be solved numerically.
On the Irrotational Flow Around a Horizontal Cylinder in Waves
Authors: Chaplin J. R.
Published: July 2009

Milne-Thomson’s circle theorem is used to study the characteristics of the two-dimensional irrotational flow around a horizontal cylinder under long-crested waves. Even when the cylinder diameter is small compared with the wavelength, the circumferential velocity and pressure distributions are unsteady and differ markedly from those corresponding to uniform ambient flow with similar velocity and acceleration vectors.
On the Propagation of Weak Discontinuities Along Bicharacteristics in a Radiating Gas
Authors: Singh R. S. , Sharma V. D.
Published: July 2009

The propagation of weak discontinuities along bicharacteristic curves in the characteristic manifold of the differential equations governing the flow of a radiating gas near the optically thin limit has been discussed. Some explicit criteria for the growth and decay of weak discontinuities along bicharacteristics are given. As a special case, when the discontinuity surface is adjacent to a region of uniform flow, the solution for the velocity gradient at the wave head is specialized to the plane, cylindrical, and spherical waves. For expandng waves, the attenuation induced by geometric factors and the radiative flux, and the growth induced by the upstream flow Mach number are discussed. It is shown that a compressive disturbance steepens into a shock only if the initial disturbance is sufficiently strong.
Pendulum Analogy for Nonlinear Fluid Oscillations in Spherical Containers
Authors: Sayar B. A. , Baumgarten J. R.
Published: July 2009

The nonlinear response of a pendulum model is compared to that of fluid motion in a spherical container undergoing lateral oscillations. It is observed that the pendulum does not duplicate the nonlinear response of the fluid except at a particular fluid height. The strong boundary curvature of the spherical container is blamed for this disagreement. Therefore, a cubic spring is included to provide sufficient elasticity to compensate for the boundary effects. The proper values for the coefficient of the cubic spring are found from an experimental observation of planar fluid motion in a spherical tank. It is also noted that, if the pendulum and the fluid are not constrained to a planar motion, at a certain excitation amplitude and frequency, both depart from the plane of excitation and rotate about a vertical axis. The upper and lower boundaries of this rotational motion of the fluid are obtained by a mathematical analysis of its analog pendulum model and compared to those measured experimentally. Mathematical predictions agreed more favorably with the experimental results after the inclusion of the cubic spring in the pendulum model.
On the Formulation of Strain-Space Plasticity With Multiple Loading Surfaces
Authors: Yoder P. J. , Iwan W. D.
Published: July 2009

An alternative formulation of plasticity is discussed in which strain rather than stress serves as the independent variable. The relationship of the formulation to traditional plasticity is examined for cases of both single and multiple loading surfaces. Conditions are given under which the stress and strain-space formulations are equivalent.
Creep and Creep Recovery of 304 Stainless Steel at Low Stresses With Effects of Aging on Creep and Plastic Strains
Authors: Cho U. W. , Findley W. N.
Published: July 2009

Creep and creep recovery data of 304 stainless steel are reported for experiments at low stress levels under combined tension and torsion at 593°C (1100°F). The data were represented by a viscous-viscoelastic model in which the strain was resolved into five components—elastic, plastic (time-independent), viscoelastic (time-dependent recoverable), and viscous (time-dependent nonrecoverable) which has separate positive and negative components. Only part of the creep strain at low stresses was recovered upon complete unloading following creep (as also found at high stresses), and each time-dependent strain data was well represented by a power function of time. But the stress dependence below a transition stress was approximately a linear relation with no creep limits and no cross effects such as were found in a previous analysis for higher stress levels above a transition stress. The transition stress for nonrecoverable strains agrees with the Frost-Ashby boundary between diffusional flow and dislocation creep. Aging decreased the creep rate and plastic strain. Results for different times of aging at 593°C (1100°F) under pure tension stresses were well represented by power functions of aging time up to 1000 h for each creep component and plastic strain.
The Continuous Damage Theory of Brittle Materials, Part 2: Uniaxial and Plane Response Modes
Authors: Fonseka G. U. , Krajcinovic D.
Published: July 2009

This part of the paper focuses on the application of the analytical model developed in Part 1 on the uniaxial tension, uniaxial compression, and plane problems (including rotating strain fields and unproportional loading). Identification of the material parameters is discussed in view of the derived results.
Residual Stresses of Czochralski-Grown Crystal
Authors: Iwaki T. , Kobayashi N.
Published: July 2009

The residual stresses in a Czochralski-grown crystal during and after pulling are obtained analytically by using a linear isotropic thermoelastic model. It is assumed that the physical properties of crystal are independent of temperature and that the crystal has a semi-infinite cylindrical shape as it is withdrawn from a melt with a constant pulling rate. Moreover the problem is considered to be a quasi-stationary one. Numerical results show that the Biot number is a prime factor affecting the residual stress and that the maximum residual stress occurs at the cylindrical surface when the Biot number is small and at the center of the crystal when it is large, respectively. An explanation for the experimental results is given.
Scattering of Rayleigh Waves by a Plate Attached to a Half Space Through a Viscous Couplant
Authors: Angel Y. C. , Bogy D. B.
Published: July 2009

The steady time-harmonic problem is reduced to a system of singular integral equations for determining the tractions generated at the interface between the plate and half space where a thin viscous couplant is applied. These equations are found to have different types of singular solutions depending on the parameter values. They are solved numerically for a specific set of physical parameters that includes a wide range of values of the couplant viscosity and incident wavelength. The reflected and transmitted powers are calculated and the reflected power is plotted as a function of incident wavelength for various values of couplant viscosity. The wavelengths at which resonances occur in these functions are found to be strongly dependent on the couplant.
The Annular Membrane Under Axial Load
Authors: Allman D. J. , Mansfield E. H.
Published: July 2009

An exact solution is given of the nonlinear differential equations for the large deflection behavior of an initially unstressed annular membrane under axial load for the case of Poisson’s ratio equal to one third.
Critical Compressive Stress of a Beam-Column to a Second Order
Authors: Chattoraj D. , Bose S. K.
Published: July 2009

Buckling of a beam-column under axial loads at the ends is considered as a three-dimensional stability problem. Displacement and stress fields are written in terms of Neuber-Papkovich potentials. These are then approximated to forms containing one more higher-order term than those corresponding to the Euler-Bernoulli equations. These expressions yield a modified formula for the bending moment. The energy method applied to the equations yield a modified form of Euler critical load and Shanley tangent modulus formula. The effect of the second-order modification is to decrease the critical load. For mild steel this decrease exceeds 5 percent for the slenderness ratio less than 25.
Circumferential Through-Cracks in Cylindrical Shells Under Tension
Authors: Sanders J. Lyell
Published: July 2009

Closed-form expressions for the energy-release rate associated with circumferential through-cracks in infinitely long, thin cylindrical shells under tension loading are obtained. The analysis is valid for complete circular cylinders and is not limited to short cracks.
A Finite Element Formulation for Unbounded Homogeneous Continua
Authors: Dasgupta G.
Published: July 2009

Currently available finite element formulations to model dynamic responses of unbounded continua cannot accommodate the Sommerfeld radiation condition. Discrete numerical techniques explicitly rely on analytical expressions of frequency-dependent field variables to account for the energy loss associated with outgoing waves. In the proposed method, such a dependence is eliminated. For steady dynamic responses, the analog of the quadratic eigenvalue problem (occurring in continuum mechanics) is herein constructed in the form of a quadratic matrix equation. The unknown relates to the desired stiffness matrix pertaining to the infinite or semi-infinite domain. The matrix coefficients are obtained from the conventional mass and stiffness matrices of a suitably chosen, bounded finite element. A benchmark example is included in this paper to demonstrate the very high numerical accuracy and significant computational efficiency of the proposed cloning algorithm.
Finite Element Analysis of Magnetoelastic Buckling of Eight-Coil Superconducting Full Torus
Authors: Miya K. , Takagi T. , Uesaka M. , Someya K.
Published: July 2009

A method of numerical analysis of the magnetoelastic buckling of toroidal field coils is shown on the basis of finite element method. Lagrange’s equation is used to deduce an eigenvalue equation determining the buckling current of the toroidal coils. The Lagrangian consists of elastic strain energy and magnetic energy. Since the coil is unidirectional, fiber-reinforced composite material, the theory of orthotropy is applied to determine elastic constants at 4.2 K. A buckling experiment on the eight superconducting-coil full torus was conducted to verify the numerical method developed here. A comparison of the numerical results with the experimental result is fairly good.
Some Principles of Elastic Shaft Stability Including Variational Principles
Authors: Shieh R. C.
Published: July 2009

Flutter instability problems of (i) a rotating circular elastic shaft subjected to both follower end torque(s) and dead force, and (ii) a rotating elliptical elastic shaft subjected to axial compressive dead force are studied, and some instability and variational principles are established in an “equivalent energy” term.
Vibration Modes of Centrifugally Stiffened Beams
Authors: Wright A. D. , Smith C. E. , Thresher R. W. , Wang J. L. C.
Published: July 2009

The method of Frobenius is used to solve for the exact frequencies and mode shapes for rotating beams in which both the flexural rigidity and the mass distribution vary linearly. Results are tabulated for a variety of situations including uniform and tapered beams, with root offset and tip mass, and for both hinged root and fixed root boundary conditions. The results obtained for the case of the uniform cantilever beam are compared with other solutions, and the results of a conventional finite-element code.
Free Vibration Analysis of Stiffened Plates by Including the Effect of Inplane Inertia
Authors: Aksu G.
Published: July 2009

A method based on the variational principles in conjunction with the finite difference technique is applied to determine the dynamic characteristic of eccentrically stiffened plates. The inplane deformations in both directions of the plate have been considered and the inplane inertia has been included into the analysis. The strain and kinetic energy for the plate and the stiffener are expressed in terms of discrete displacement components using the finite difference method. The energy functional is minimized with respect to discretized displacement components and the natural frequencies and corresponding mode shapes are obtained from the solution of a linear eigenvalue problem. The effect of inplane deformations of the plate and the stiffener and also the effect of inplane inertia on free vibration characteristics of uniaxial and cross-stiffened plates have been examined.
On Nonstationary Cumulative Damage Models
Authors: Bogdanoff J. L. , Kozin F.
Published: July 2009

In this paper, we continue our study of embedded Markoff Chain Models of Cumulative Damage. We introduce and discuss a time transformation that leads to a condensation method. This method appears to be unusally comprehensive and a practical way to study nonstationary models of cummulative damage. Further, it allows us to estimate the desired nonstationary transition matrices providing a means of gaining further insights into the cumulative damage process. Examples are presented and further directions of research are indicated.
Complex Stress Intensity Factors in Bent Plates With Cracks
Authors: Theocaris P. S.
Published: July 2009

The experimental method of caustics was applied to the study of asymmetric bending of isotropic cracked plates and to the determination of the complex stress intensity factors (S.I.F’s) at the crack tips. It was shown that the method of reflected caustics is convenient for detecting and evaluating both KI and KII stress intensity factors. Based on the singular approximation of the elastic solution around the crack tip, the theory of formation of the caustics was developed and related to the evaluation of both components of stress intensity factors. It was also shown that the generalized method of caustics, known as the method of pseudocaustics, is a potential and simple method for determining S.I.F’s in cracked plates submitted to bending. Experimental evidence with specimens made either of optically inert materials, such as plexiglass, or of any opaque material like steel, and elastically loaded, has corroborated the theoretical results.
Contact Problems Involving the Flow Past an Inflated Aerofoil
Authors: Vanden-Broeck J.-M.
Published: July 2009

Steady potential flow around a two-dimensional inflated airfoil is considered. The aerofoil consists of a flexible and inextensible membrane which is anchored at both leading and trailing edges. The flow and the aerofoil shape are determined as functions of the angle of attack α, the cavitation number γ, and the Weber number λ. When γ decreases to a critical value γ0 (α, λ), opposite sides of the membrane become tangent to each other at the trailing edge. For γ < γ0 the aerofoil is partially collapsed near the trailing edge. The length of the region of collapse increases as γ decreases and for γ = −∞, the aerofoil is completely collapsed. The shape of the aerofoil and the value of γ0 are determined analytically by a perturbation solution for λ small. Graphs of the results are presented.
A Thermoelastic-Viscoplastic Model With a Rate-Dependent Yield Strength
Authors: Rubin M. B.
Published: July 2009

General nonlinear constitutive equations for a thermoelastic-viscoplastic material that exhibits a rate-dependent yield strength are developed by assuming that the yield function depends explicitly on the total strain rate and temperature rate. Following recent developments in continuum thermodynamics restrictions on the constitutive response functions are imposed to ensure that the moment of momentum and energy equations are identically satisfied and that various statements of the second law of thermodynamics are satisfied for all thermodynamical processes. A particular constitutive equation for a thermoelastic-viscoplastic material is proposed, and an analytical example is considered that examines the rate-dependent plastic response to a deformation history that includes segments of loading, unloading, and reloading, each occurring at varying strain rates.
Two-Dimensional Apparent Masses for Cross-Flow Sections of Wing-Store Configurations
Authors: Huang M.-K.
Published: July 2009

On the basis of the assumption that the external stores are small compared with the wing, an approximate method has been developed for estimation of two-dimensional apparent masses for the cross-flow sections of wing-store combinations. The results obtained may be applicable to the analysis of the effects of the stores on the aerodynamic stability derivatives in slender-body theory. The theory has also been applied to estimate the rolling moment due to sideslip for high-wing configurations. The presented results are in agreement with those of other investigations.
Relaxation of Thick-Walled Cylinders and Spheres
Authors: Ottosen N. S.
Published: July 2009

Using the nonlinear creep law proposed by Soderberg, closed-form solutions are derived for the relaxation of incompressible thick-walled spheres and cylinders in plane strain. These solutions involve series expressions which, however, converge very quickly. By simply ignoring these series expressions, extremely simple approximate solutions are obtained. Despite their simplicity these approximations possess an accuracy that is superior to approximations currently in use. Finally, several physical aspects related to the relaxation of cylinders and spheres are discussed.
Gravity-Induced Density Discontinuity Waves in Sand Columns
Authors: Cowin S. C. , Comfort W. J.
Published: July 2009

Formulas are obtained for the speeds of propagation of gravity-induced rarefaction and condensation density discontinuities in vertical sand columns. A rarefaction wave is induced in a column of sand at rest by removing the support at the bottom of the column. A condensation shock is induced by reintroducing the support, which stops the sand from falling. The theoretical prediction of the speed of propagation of the leading edges of the rarefaction wave corresponds well with the speed measurements obtained in a preliminary experiment.
The Large Elastic-Plastic Deflection With Springback of a Circular Plate Subjected to Circumferential Moments
Authors: Yu T. X. , Johnson W.
Published: July 2009

The large deflection elastic-plastic bending of a circular plate subjected to radially outward acting bending moments uniformly distributed around its circumference is analyzed, and computer programs are given to facilitate the determination of the distributions of bending moments, in-plane forces, and displacements during the bending and after unloading or springback. Computed examples are given, and the errors developed by small deflection theory are discussed.
On the Logarithmic Singularity of Free-Edge Stress in Laminated Composites Under Uniform Extension
Authors: Zwiers R. I. , Ting T. C. T. , Spilker R. L.
Published: July 2009

The stress singularities at the free edge of an interface between adjacent layers in a laminated composite are studied. Each layer of the composite is assumed to be of the same orthotropic material with one of the principal axes being the fiber direction. The angle θ, however, which is the fiber orientation, varies from layer to layer. The composite is subjected to uniform extension in the plane of the layers. At the interface between adjacent layers having fiber angles (0/90), (θ/θ′), and a family of special combinations of (θ/θ′) shown in the paper, the singularity of the type k*rδ (δ<0), seems to be the only possibility. For an interface with other combinations of fiber orientations in the the adjacent layers, it is shown that an additional singularity of the form k(ln r) exists. Since the constant k* depends on the stacking sequence of the layers and the complete boundary conditions, and may vanish in some cases, the existence of a k*rδ singularity at a free edge is not certain until a complete problem is solved. In contrast, the constant k, which is called the logarithmic stress-intensity factor, is independent of the stacking sequence of the layers and the complete boundary conditions. Its value is determined once the fiber orientations on both sides of the interface are known. Therefore, at the interface between adjacent layers for which k≠0, the free-edge stress is inherently singular. Moreover, the singularity is logarithmic.
Efficient Pulse Shapes to Deform Beams With Axial Constraints
Authors: Stronge W. J.
Published: July 2009

The transient motion of a simply supported, rigid-plastic beam in response to a uniformly distributed pressure pulse of arbitrary shape is determined. The beam is subject to an axial force in addition to the transverse pressure. This axial force is a parameter that can approximate constraint forces resulting from deformation of beams with fixed or elastically restrained ends. The pulse shape that maximizes deflection at the center of the beam is determined for a specified applied impulse. When a transverse pressure applies a limited amount of impulse to the beam, an impulsive load causes the largest deformation. Axial force decreases the deformation but has no effect on the most efficient pulse shape.
An Improved Semi-Implicit Method for Structural Dynamics Analysis
Authors: Park K. C.
Published: July 2009

A semi-implicit algorithm is presented for direct time integration of the structural dynamics equations. The algorithm avoids the factoring of the implicit difference solution matrix and mitigates the unacceptable accuracy losses which plagued previous semi-implicit algorithms. This substantial accuracy improvement is achieved by augmenting the solution matrix with two simple diagonal matrices of the order of the integration truncation error.
Finite Element Analysis of Vibration of Toroidal Field Coils Coupled With Laplace Transform
Authors: Miya K. , Uesaka M. , Moon F. C.
Published: July 2009

A numerical analysis of a vibration of toroidal field coils in a magnetic fusion reactor is shown here on the basis of the finite element method coupled with Laplace transform. Lagrangian consisting of kinetic, elastic strain, and magnetic energies was utilized to deduce equations of motion of the coils. The equations were solved numerically by applying the Laplace transform to a formulation with respect to time and the finite element method to one with respect to space. The Fast Fourier Transform algorithm was utilized for a calculation of the inverse Laplace transform to obtain a nodal vector of the coil’s displacement in the original domain. Numerical results reasonably explain a dependency of the coil current on a frequency of the coil.
The Steady-State Response of a Class of Dynamical Systems to Stochastic Excitation
Authors: Caughey T. K. , Ma F.
Published: July 2009

In this paper a class of coupled nonlinear dynamical systems subjected to stochastic excitation is considered. It is shown how the exact steady-state probability density function for this class of systems can be constructed. The result is then applied to some classical oscillator problems.
Stress Function Interface and Boundary Conditions in Anisotropic Materials
Authors: Gdoutos E. E. , Kattis M.
Published: July 2009

The stress and displacement continuity conditions for interfaces between two different anisotropic media were formulated in terms of the Airy stress functions of the media. It was shown that such formulation greatly facilitates the solution of the problems of composite anisotropic materials by the Airy stress function approach. Two examples were given to demonstrate the potentiality of the method.
Interferometric Determination of Curvatures of Flexed Plate
Authors: Chao Y. J. , Sutton M. A. , Taylor C. E.
Published: July 2009

Two interferometric techniques are proposed that can readily be applied to the measurement of stresses in thin plates. A point-by-point method is presented that allows the analyst to determine either absolute or relative curvatures and twists of thin plates. A full-field method is presented that will determine the absolute curvatures and twists of thin plates. Experiments have been performed that indicate that the methods do provide a simple and accurate means for determining the curvatures and twists of thin plates.
Stability and Vibrations of Compressed, Aeolotropic, Composite Cylindrical Shells
Authors: Greenberg J. B. , Stavsky Y.
Published: July 2009

A general method of solution, based on a complex finite Fourier transform, is adopted for the stability and vibration analysis of compressed, aeolotropic, composite cylindrical shells. A major feature of the solution method is its ability to handle both uniform and nonuniform conditions that hold at the boundaries of finite-length cylindrical shells. For the various shells investigated, an optimum winding angle was found for which a maximum frequency response and highest critical buckling load is attainable. Similar optimization was also discovered to be possible by controlling both/either shell heterogeneity and/or fiber orientation.
Free Out-of-Plane Vibration of a Ring Elastically Supported at Several Points
Authors: Irie T. , Yamada G. , Okada H.
Published: July 2009

An analysis is presented for the free out-of-plane vibration of a circular ring elastically supported against deflection, rotation, and torsion at several points located at equal angular intervals. The equations of out-of-plane vibration of the ring is expressed as a matrix differential equation by using the transfer matrix, the solution to which is conveniently given by infinite series. The vibrations arising in the ring are classified into several types, for each of which the natural frequencies and the mode shapes are calculated numerically up to higher modes.
A Method of Analyzing Generalized Cell Mappings
Authors: Hsu C. S. , Guttalu R. S. , Zhu W. H.
Published: July 2009

In this paper a method for analyzing the global properties of generalized cell mappings involving a very large number of cells is presented. The procedure of the algorithm is devised by taking advantages of certain properties of Markov chains. First, the persistent groups representing the motions to which the system will eventually evolve are determined. Then the absorption probabilities of any transient cell into these persistent groups are evaluated. These two sets of information provide us with the global behavior of the system. After describing the method its viability is illustrated by two examples.
Optimization of Reinforcement for a Class of Openings in Plate Structures
Authors: Dhir S. K.
Published: July 2009

A numerical/analytical procedure has been developed which yields the optimum amount of reinforcement for a given hole shape in a large elastic plate under prescribed boundary stresses. This procedure is based on determining the usual two complex potentials which describe the entire stress field, constructing the strain energy density function in terms of the unknown amount of reinforcement, integrating this function around the opening boundary, and finally minimizing this integral with respect to the reinforcement. The method is first developed for a general hole shape and then demonstrated in some detail for a circular and a square-like opening.
Analysis of Elastic Torsion in a Bar With Circular Holes by a Special Boundary Integral Method
Authors: Caulk D. A.
Published: July 2009

Special boundary integral equations developed in an earlier paper are generalized here for torsion of an elastic bar with circular holes. In this approach, the solution on the boundary of each hole is represented by a series of circular harmonics, and the coefficients in these series are determined by a special system of boundary integral equations. For a cross section with only one hole, the entire system of equations is reduced without approximation to a single integral equation involving only the warping function on the outer boundary. For multiple holes, approximate equations are derived that retain only the first harmonic in the solution representation on each hole. The latter equations are solved analytically for a circular cross section weakened by a concentric ring of circular holes. Simple expressions are derived for torsional rigidity, warping, and maximum stress. The results for torsional rigidity are an improvement over previous ones obtained by another approximate method.
On an Axisymmetric Coupled Thermal Stress Problem in a Finite Circular Cylinder
Authors: Takeuti Y. , Ishida R. , Tanigawa Y.
Published: July 2009

This paper presents a general treatment of the transient thermal stresses of a finite circular cylinder with consideration of the thermomechanical coupling effect using a new technique. The method used is quite useful for the solution of a wide range of transient thermal stress problems in two or three dimensions. From numerical results, we can find that there is a clear effect on the thermal stress distribution when the coupling term is taken into account.
Buckling, Postbuckling, and the Flow Through a Tethered Elastic Cylinder Under External Pressure
Authors: Wang C. Y. , Watson L. T. , Kamat M. P.
Published: July 2009

A thin-walled elastic cylinder is tethered by numerous springs to an outer rigid cylinder. As external pressure is increased, the elastic cylinder will remain circular until a critical pressure difference is attained. The nonlinear governing equations for large deflections are formulated. The stability analysis shows the elastic cylinder may buckle with more than two circumferential waves due to the stiffness of the springs. Postbuckling shapes are integrated numerically by a quasi-Newton method. The flow through such a partially collapsed shape is then computed by a finite element method.