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RESEARCH PAPERS

J. Appl. Mech. 1984;51(1):1-5. doi:10.1115/1.3167573.

The one-dimensional isothermal flow of viscous-liquid fibers displays draw resonance instability when a constant-velocity winder condition is applied. This instability is removed when a constant-force condition occurs at the winder. The instability mechanism is examined and used to explain the stability trends when the effects of gravity, surface tension, inertia, and wind stress are included.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):6-12. doi:10.1115/1.3167599.

Steady laminar flows of a newtonian fluid in the vicinity of a spherical ball located inside a spherical cavity are studied. Two methods were employed: a method involving a finite element calculation and an experimental method based on measurements of local velocities by means of laser Doppler anemometry using the Bragg cell. The influences of the Reynolds numbers and of the ball positions in the cavity have been analyzed and compared.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):13-18. doi:10.1115/1.3167557.

Many metallurgical applications of magnetohydrodynamics (MHD) involve open-channel liquid-metal flows with magnetic fields. This paper treats the three-dimensional, variable-depth flow in a rectangular open channel having an electrically insulating bottom and perfectly conducting sides. A steady, uniform magnetic field is applied perpendicular to the channel bottom. Induced magnetic fields and surface tension effects are neglected, while the applied magnetic field is sufficiently strong that inertial effects are negligible everywhere. Viscous effects are confined to boundary layers adjacent to the bottom, sides, and free surface. Solutions are presented for the inviscid core and the boundary layers. The locations of the free surface above the core and above the boundary layers adjacent to the sides are obtained. The side-layer variables are rescaled into universal profile functions which depend on the coordinates in the channel’s cross section and on a parameter related to the local slopes of the bottom and the free surface. The solutions for the side layers in open channels are compared to the side-layer solutions for certain rectangular closed ducts in order to reveal the effects of the free surface. This comparison leads to a qualitative correspondence principle between open-channel and closed-duct side-layer solutions. The similarities and differences between corresponding open-channel and closed-duct side layers are discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):19-26. doi:10.1115/1.3167572.

Steady, inviscid, planar and constant density shear flows past thin airfoils have strongly coupled thickness and camber flowfields which can be simply analyzed using some invariant properties of Euler’s equations. In this paper, both the nonlinear vorticity generation term in Poisson’s disturbance stream-function equation and the Bernoulli constant (which varies from streamline to streamline) are explicitly evaluated in terms of the known plane parallel flow far upstream, recognizing that vorticity convects unstretched and unchanged along streamlines; this produces a governing differential equation with an explicitly available right side plus a Bernoulli integral with a true constant fixed throughout the entire flow field. Using these results, the inverse problem, which solves for the shape that induces a prescribed pressure, is formulated as a nonlinear boundary value problem with mixed Dirichlet and Neumann surface conditions; here, trailing edge shape constraints are directly enforced by controlling jumps in the stream-function or its streamwise derivative through the downstream wake (analogies with potential flows past axisymmetric ringwings showing similar source and vortex interactions are also described). For flows with arbitrary profile curvature, we show that the linearized stream-function equation can be put in conservation form, thus leading to new and more general Cauchy-Riemann conditions which extend the notion of the velocity potential; the analysis problem, which determines the flow past a known shape subject to Kutta’s condition, is shown to satisfy a simple boundary value problem for a “super-potential” identical to the irrotational planar formulation except for an axisymmetric-like change to the Cartesian form of Laplace’s equation. For flows with uniformity vorticity, closed-form solutions are given which clearly illustrate the interaction between thickness and camber; also, for arbitrary thin airfoils, a particularly simple expression shows that the lift due to thickness varies directly as the product of vorticity and enclosed area. With more general shears, numerical approaches are especially convenient; these require only simple code changes to existing algorithms, for example, established potential function methods readily available for analysis problems, or “direct stream-function methods” for inverse problems recently developed by this author. Numerical methods and results that cross-check and extend derived analytical solutions are given for both analysis and design problems with vorticity. Also, extensions of the basic theory to three-dimensional constant density and planar compressible shear flows are given.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):27-34. doi:10.1115/1.3167593.

The gas mixture produced by coal gasifier contains components that have serious corrosive effects on the walls of the pipe flow system. To reduce these, a non-corrosive gas is injected into the stream of the coal gas products, in a direction parallel to the pipe wall. The interaction between the injected stream and the original pipe flow is investigated analytically and is an example of the so-called Wall Jet Problem.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):35-40. doi:10.1115/1.3167594.

Simple formulas for bounding the maximum eigenvalues or computing them exactly are obtained for the uniform strain eight-node hexahedron and the four-node quadrilateral. The development is based on a novel technique that reduces the size of the eigenproblem to where it can be managed analytically. These formulas are useful for explicit time integration applications since they provide conserative estimates of stable time steps. The eigenvalue analysis is limited to linear, isotropic materials but the results are also useful in nonlinear problems since the linerized material properties may be used.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):41-47. doi:10.1115/1.3167595.

A theoretical analysis of transient sound radiation from a clamped circular plate is given using a pressure impulse response method. The vibration response of the plate to a transient point force is obtained. The modal pressure impulse response functions for the plate are derived from the Rayleigh surface integral and numerically convoluted with the modal acceleration response of the plate. The impulse response functions are closely related to the mode shapes and the geometry of the problem. They relate the spatial domain to the temporal domain of the pressure waves. The pressure impulse response waveforms are given for a number of plate modes and the changes in the waveforms with distance from the plate are shown. Sound radiation due to forced and free vibrations of the plate are discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):48-56. doi:10.1115/1.3167596.

We formulate a finite-element reduced integration penalty method applicable to plane-strain problems with incompressible material behavior. This numerical method is employed to generate crack solutions for pure power-hardening solids. For two configurations of interest in applications, an edge cracked panel subject to remote tension and an edge-cracked panel subject to remote bending, we obtain solutions for a wide range of crack lengths and strain-hardening behaviors.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):57-64. doi:10.1115/1.3167597.

Consistency checks, including short and deep crack limiting relations, are applied to the solutions obtained in Part 1. An error measure is introduced to quantify the consistency check. The accuracy of the solutions of Part 1 is discussed in light of these consistency checks and comparison is made with previous solutions. Consistency checks appear useful in ascertaining the accuracy of existing fully plastic crack solutions and of proposed new solutions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):65-70. doi:10.1115/1.3167598.

Stress intensity factors are computed for a horizontal subsurface crack that is subjected to time harmonic excitation. The problem is analyzed by determining displacement potentials that satisfy reduced wave equations and specified boundary conditions. The formulation of the problem leads to a system of coupled integral equations for the dislocation densities. The numerical solution of the integral equations leads directly to the stress intensity factors. Curves are presented for the ratios of the elastodynamic and the corresponding elastostatic Mode-I and Mode-II stress intensity factors. At specific values of the frequency, a resonance effect is observed and a correlation with the natural frequencies calculated by a Timoshenko plate theory for the layer between the crack and the free surface is noted.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):71-76. doi:10.1115/1.3167600.

Transient response of an interfacial crack between two dissimilar elastic, orthotropic solids is investigated. The interfacial crack is excited by tractions suddenly applied on the crack surfaces. Governing equations, boundary conditions, and continuity conditions along the interface are reduced to a singular integral equation. Solution of the singular integral equation is obtained by the use of Jacobi polynomials. Expressions for stress intensity factors at the crack tip are given. As a sample problem, an interfacial crack in a 0 deg/90 deg fiber-reinforced composite solid excited by a suddenly applied uniform pressure on the crack surfaces is studied.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):77-83. doi:10.1115/1.3167601.

The surface motions excited by acoustic emissions produced by fracture processes at the edge of a buried, penny-shaped crack are investigated. Firstly, wave-front approximations to the emissions generated by the sudden growth of a tensile crack in an unbounded elastic solid are reviewed. Then these approximations are Fourier transformed to give the high-frequency portion of their spectra. Secondly, time and frequency-domain approximations to the surface motions excited by this growing crack, when it is buried in a half-space, are calculated. These results are then scrutinized to elucidate what parts of the signals measured at the surface carry information about the crack’s size, its orientation, and the fracture processes near the crack tip.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):84-92. doi:10.1115/1.3167602.

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

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):93-101. doi:10.1115/1.3167603.

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

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):102-106. doi:10.1115/1.3167551.

A cylindrical missile, assumed to be of a rigid-plastic material strikes a nonyielding target normally and end-on. Above a certain (critical) velocity the nose of the missile disintegrates or spatters, and below that velocity the nose flattens to a mushroom form. The contact force decreases with decreasing velocity during impact but experiences a jump as the critical velocity is passed during slowdown. This paper gives a method of calculating the critical velocity and the contact force as function of time, as well as the time variations of the other parameters of the impact process.

Topics: Force , Missiles
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):107-113. doi:10.1115/1.3167552.

Effective stress-strain relations for inelastic unidirectional composites developed previously are used to derive the gross constitutive behavior of inelastic laminates in which every lamina is fiber-reinforced. The laminated plate is subjected to stretching and bending deformation and the strain field is described by the Love-Kirchhoff hypothesis. The distribution of the resulting stresses across the thickness is necessarily nonlinear and a Legendre expansion formalism is used to determine the stress field. Results are given for cross-ply symmetric laminates under pure cylindrical bending.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):114-120. doi:10.1115/1.3167553.

A viscoplastic theory of dynamic buckling is developed for cylindrical shells subjected to uniform radially inward impulses. The influence of the yield function nonlinearity and elevated temperature on the magnitude of displacements, buckling mode, and threshold impulse is investigated. Asymmetrical and axisymmetrical modes of buckling are considered. The asymmetrical mode is proved to exist. The obtained theoretical results are compared with existing experiments.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):121-124. doi:10.1115/1.3167554.

The method of constrained regularization is used to invert for retardation spectra and attenuation from the creep data of a commercial-grade lucite material. Four different criteria for choosing a regularization parameter in the solution of the first-kind integral equation are examined. Although the spectra are different, computations using each criterion give essentially the same attenuation curve for a range of frequencies. These results show that reliable estimates of the attenuation may be obtained from inversion of creep data using the method of constrained regularization.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):125-132. doi:10.1115/1.3167555.

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

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):133-140. doi:10.1115/1.3167556.

Creep data of 2618-T61 aluminum alloy under multistep multiaxial proportional loadings at 200°C (392°F) are reported. Two viscoplastic flow rules were developed using constant stress creep and creep recovery data. One was based on the accumulated strain (isotropic strain hardening), and the other on a tensorial state varible (kinematic hardening). Data were represented by two models: a nonrecoverable viscoplastic model, and a viscous-viscoelastic model in which the time-dependent strain was resolved into recoverable (viscoelastic) and nonrecoverable components. The modified superposition principle was used to predict the viscoelastic strain component under variable stress states. The experiments showed that the viscous-viscoelastic model with either isotropic strain hardening or kinematic hardening gave very good predictions of the material responses. Isotropic strain hardening was best in some step-down stress states. The viscoelastic component accounted for not only the recovery strain but also the transient creep strain upon reloadings and step-up loadings.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):141-145. doi:10.1115/1.3167558.

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

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):146-152. doi:10.1115/1.3167559.

A theory of thin plates which is physically as well as kinematically nonlinear is developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a special theory having fewer parameters and being capable of characterizing paper. A procedure is given for matching the special theory to edgewise compressive data of paperboard.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):153-158. doi:10.1115/1.3167560.

Based on a multiple-mode analysis, solutions to the nonlinear equations of motion are presented for elliptical plates in terms of variations of nonlinear periods with amplitudes of vibration. The governing equations are written in terms of lateral displacement w and stress function F and the effects of transverse shear deformation and rotatory inertia are incorporated into these equations. For the multiple-mode approach considered in this paper, an exact solution to the stress function is determined. Effects of geometric nonlinearity, shear deformation, rotatory inertia, plate geometry, and modal interaction on the vibration behaviors of elliptical plates are investigated in detail.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):159-163. doi:10.1115/1.3167561.

Parametric instability of a periodically supported pipe without and with dynamic absorbers is investigated. A method based on the notion of propagation constant is used. This method requires no prior knowledge of the mode shapes and renders the amount of computation independent of the number of spans. Numerical results are presented for single and two-span pipes. Effective control of the instability regions by means of dynamic absorbers is also demonstrated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):164-170. doi:10.1115/1.3167562.

Both particle and rigid body planar collisions are covered in this paper. For particles, the classical equations for oblique impacts are derived using Newton’s laws along with definitions of the coefficient of restitution and equivalent coefficient of friction. A general expression is obtained for the kinetic energy loss explicity containing the two coefficients. This expression for energy loss as a function of the friction coefficient possesses a maximum. The value of the friction coefficient at the maximum is a limiting value which can be used to determine whether or not sliding exists at separation. The maximum energy loss is independent of the physical mechanism of generation of tangential forces (friction) and serves as an upper bound for two-particle collisions. It is shown that to properly formulate and solve the rigid body problem, a moment must be considered at the common “point” of impact. A moment coefficient of restitution must be defined. This leads to six linear algebraic equations from which the six final velocity components can be calculated. An analytical solution is obtained for the general rigid body problem. In a reduced form, it is used to solve the problem of a single rigid body impacting a rigid barrier. This solution is then applied to a classical textbook problem. As shown for particle impacts, the concepts of limiting friction coefficient and maximum energy loss apply to rigid body impacts.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):171-178. doi:10.1115/1.3167563.

This paper presents an analytical method on the investigation of the motion characteristics of a class of spatial mechanical components involving the ball-and-trunnion type of joint, namely, the multiple-pode joint. Algebraic derivations of the input-output equation and explicit relations for motion parameters are presented for these joints as well as their shaft couplings. From this general displacement analysis, some insights into the basic nature and behavior of the multiple-pode joint are observed and interpreted. The creation of shaft couplings using these joints and their functional analysis are also illustrated in several cases.

Commentary by Dr. Valentin Fuster

DESIGN DATA AND METHODS

J. Appl. Mech. 1984;51(1):179-181. doi:10.1115/1.3167564.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):182-187. doi:10.1115/1.3167565.
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1984;51(1):188-191. doi:10.1115/1.3167566.
Abstract
Topics: Torsion , Cylinders
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):191-193. doi:10.1115/1.3167567.
Abstract
Topics: Vibration
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):193-194. doi:10.1115/1.3167568.
Abstract
Topics: Eigenvalues
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):202-204. doi:10.1115/1.3167574.

The purpose of this Brief Note is to demonstrate the feasibility of using commercial manganin stress gauges in dynamic uniaxial stress experiments. This was demonstrated by measuring the stress-time histories inside long aluminum rods that were impacted by rigid wall impactors. The experimental records are compared with a two-dimensional Lagrangian calculation using a recently developed constitutive model (the Phases Model) to describe material behavior.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):204-205. doi:10.1115/1.3167575.

The effect of the lubricating film is accounted for by a slip flow boundary condition, and the nonsimilar boundary layer problem is solved by a local nonsimilarity solution method.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):206-207. doi:10.1115/1.3167576.

The complexity of shell analysis stems from the fact that loads are resisted, in general, by both membrane and flexural action. There is a need to develop a suitable shell finite element, but many of those proposed at the present time fail in the context of the “sensitive solutions” coupled with rigid body movements. These “sensitive solutions” refer to known solutions (within the framework of shell theory) of problem in which it is kinematically possible for the shell to deform with no straining of the midsurface. (Purely inextensional solutions were first considered by Lord Rayleigh [1].) In two cases, namely the torsion of a slit cylinder and the application of uniformly distributed moments Mθ and Mx = vMθ to a slit cylinder, the contribution of the membrane forces is identically zero. The second of these two cases is too trivial to be used for comparison with finite element solutions, but the first case exhibits many of the features that current finite elements have difficulty in reproducing. An exact solution within the context of shell theory is not necessarily, of course, an exact three-dimensional solution. However, the torsion of a slit cylinder has also been solved three-dimensionally (Love [2]) and the present Note focuses attention on the exact variation of shear stress through the wall of the shell and on how this compares with shell theory.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):207-210. doi:10.1115/1.3167577.

In this paper nonlinear oscillations of a clamped circular plate of linearly varying thickness have been investigated using von Karman equations expressed in terms of displacement components. Numerical results obtained have been compared and discussed.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):211-213. doi:10.1115/1.3167579.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):213-214. doi:10.1115/1.3167580.
Abstract
Topics: Vibration , Membranes , Shells
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):214-216. doi:10.1115/1.3167581.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):216-220. doi:10.1115/1.3167582.

The present paper deals with the effects of initial geometric imperfections on large-amplitude vibrations of simply supported rectangular plates. The vibration mode, the geometric imperfection, and the forcing function are taken to be of the same spatial shape. It is found that geometric imperfections of the order of a fraction of the plate thickness may significantly raise the free linear vibration frequencies. Furthermore, contrary to the commonly accepted theory that large-amplitude vibrations of plates are of the hardening type, the presence of small geometric imperfections may cause the plate to exhibit a soft-spring behavior. The effects of hysteresis (structural) damping on the vibration amplitude are also examined.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Appl. Mech. 1984;51(1):223. doi:10.1115/1.3167586.
FREE TO VIEW
Abstract
Topics: Solid mechanics
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):224-225. doi:10.1115/1.3167588.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):225. doi:10.1115/1.3167589.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):225-226. doi:10.1115/1.3167590.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(1):226. doi:10.1115/1.3167591.
FREE TO VIEW
Abstract
Topics: Viscoelasticity
Commentary by Dr. Valentin Fuster

ERRATA

Commentary by Dr. Valentin Fuster

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