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RESEARCH PAPERS

J. Appl. Mech. 1989;56(4):737-743. doi:10.1115/1.3176166.

This theoretical analysis of an elastoplastic cantilever examines the effects of linear strain-hardening and the development of partial elastic unloading when deflections become large. For a vertical force at the tip, unloading modifies the distribution of curvature in a substantial internal segment after the deflections become very large, but it has a negligible effect on the tip displacement. The analysis uses a bilinear stress-strain constitutive relation that results in slightly better agreement with previous experiments than a corresponding bilinear approximation for the moment-curvature relation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):744-750. doi:10.1115/1.3176167.

An elastically-anisotropic sedimentary rock is modeled by a simple cubic packing of identical, contacting spherical particles. The connected pore space is filled with an inviscid, compressible fluid. A set of averaged equations is derived to relate the constitutive and dynamic coupling coefficients, and hence also the effective wave speeds in any given direction explicitly to the microstructural properties of the rock considered. Simple, explicit results are obtained when the propagation of either a purely longitudinal or a purely transverse wave is considered.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):751-755. doi:10.1115/1.3176168.

The large deflection of an elastomeric dome is studied using the finite element method. The material properties of the elastomer are described by a hyperelastic model in order to capture the strain energy stored in the dome during deformation. The nonlinear responses are determined by the modified Riks procedure, and the calculated load-deflection curve agrees well with experimental results. In addition, a pressurized thick-walled spherical hyperelastic shell is analyzed and the stress results obtained by the finite element method are in excellent agreement with the closed-form solutions. The results provide a better understanding of the mechanical behavior of elastomeric keyboard domes and demonstrate the feasibility of using the finite element method to design such structures.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):756-762. doi:10.1115/1.3176169.

Singular thermal stress fields in bonded viscoelastic quarter planes are studied with the use of the viscoelastic analogy. The order of the singularity is shown to depend on the material properties, indicating that it will vary with time in viscoelastic materials. This is studied in detail for Maxwell materials, and it is shown that the order of the singularity generally increases with time. This evolution of the singularity can, for certain combinations of material properties, lead to initial increases in the stress levels near the edge of the interface before relaxation occurs.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):763-779. doi:10.1115/1.3176170.

In Part I we found that although the near tip fields of cracks on bimaterial interfaces do not have a separable form of the HRR type, they appear to be nearly separable in an annular zone within the plastic zone. Furthermore, the fields bear strong similarities to mixed mode HRR fields for homogeneous medium. Based on our numerical results, we have been able to identify a clear mathematical structure. We found that the small-scale yielding crack tip fields are members of a family parameterized by a near tip phase angle ξ, and that the fields nearly scale with the value of the J -integral. In Part II, the original derivation of the mathematical structure of the small-scale yielding fields is elaborated upon. The issue of crack face contact is addressed and the phenomenology is described in terms of the phase parameter ξ. Crack tip plastic deformation results in an open crack for a range of ξ which is nearly symmetric about the state corresponding to pure remote tension. Plane-strain plastic zones and crack tip fields for the complete range of ξ are presented. Over distances comparable to the size of the dominant plastic zone, the stress levels that can be achieved are limited by the yield stress of the weaker (lower yield strength) material. On the other hand, the stresses well within the plastic zone are governed by the strain-hardening behavior of the more plastically compliant (lower strain-hardening) material. We observe that the extent of the annular zone where the fields are nearly separable (i.e., of the HRR form) is dependent on the remote load combinations and the material combination. When the tractions on the interface are predominantly tensile, there are no indications of crack face contact over any length scale of physical relevance. Instead, the crack tip opens smoothly and crack tip fields as well as the crack opening displacement are scaled by the J -integral. The paper concludes with a discussion on the range of load combinations which could be applied to two fracture test specimen geometries to obtain valid fracture toughness data.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):780-785. doi:10.1115/1.3176171.

Stress intensity factors are represented by path independent integrals for linear elastic materials. Two types of representation are given. The first type of integrals are expressed by integration over contours surrounding a crack tip. Those of the second type are integrated over contours enclosing a finite crack. The path independent integrals are applied to determine the stress intensity factors due to a body force and a dislocation for a finite crack in an infinite anisotropic body.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):786-790. doi:10.1115/1.3176172.

There is a strange feature of plane elasticity that seems to have gone unnoticed: The stresses in a body that contains rigid inclusions and is loaded by specified surface tractions depend on the Poisson ratio of the material. If the Poisson ratio in this stress field is set equal to +1 for plane strain, or +∞ for plane stress, the rigid inclusions become cavities for elastic constants within the physical range. The paper pursues this circumstance, and in doing so also produces several useful by-products that are connected with the stretching and curvature change of a boundary.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):791-797. doi:10.1115/1.3176173.

The present paper discusses an analytical method for an inverse problem of three-dimensional transient thermoelasticity in a transversely-isotropic solid. The inverse thermoelastic problem consists of the determination of the condition of heating when the conditions of displacements and stresses are given at some points of the solid considered. Applying the Laplace and Fourier transforms as well as the new potential function method, the temperature, displacements, and stresses are represented by the potential functions alone, and they are determined from the prescribed conditions. The heating condition is obtained from the boundary condition for the temperature field. As a practical example of an inverse problem, the heating temperature of a transversely-isotropic infinite circular cylinder is determined in the case where the radial displacement is given at an arbitrary cylindrical section and the radial and shear stresses are free on the lateral surface of the cylinder. Numerical calculations are carried out to illustrate the heating temperature of the cylinder as well as the temperature and stresses on the lateral surface of the cylinder.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):798-806. doi:10.1115/1.3176174.

The contact of a flat, simply-connected axisymmetric indenter with a layered elastic half space is examined. The problem is mathematically formulated using integral transforms to derive singular integral equations for the contact pressure. The solution of these equations is obtained by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with multiple contact regions. A parameter space is divided into zones for single and multiple contact solutions and comparisons are made with the solutions for the analogous plane-strain problem.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):807-813. doi:10.1115/1.3176175.

In Part I, the multiple contact region solutions for an axisymmetric indenter were presented. The solution technique utilized integral transforms and singular integral equations. The emphasis there was the study of the conditions of contact as a function of the physical parameters of the indenter and the layered elastic half space. The method and results were similar to those for the analogous plane-strain problem that was studied in Shield and Bogy (1989). However, several differences in detail were required for the analysis of the axisymmetric geometry. In this Part II, the solution of Part I is used to study some related problems that have been considered previously in the literature for homogeneous half spaces. First we solve the problem of the axisymmetric annular indenter for the layered half space. Multiple contact region solutions are studied and the problem of an axisymmetric punch with internal pressure is solved for the layered half space and also for the special case of a layer with a traction-free lower surface. Finally, the problem of an annular crack in a homogeneous or layered structure is solved.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):814-820. doi:10.1115/1.3176176.

A numerical technique has been developed to deal with three-dimensional rolling contact problems with an arbitrary contact region under an arbitrary pressure. Results of this technique are checked against existing solutions for cases of Hertzian contact. A solution for a case of non-Hertzian contact is also presented. This numerical technique works satisfactorily for cases with small spin creepage. For cases of large spin creepage, we utilize a recent work (by the authors) for the limiting case of fully developed sliding contact.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):821-827. doi:10.1115/1.3176177.

The viscoelastic analysis of tape systems composed of rate-dependent materials is presented. Histories for winding, winding-pause, and winding-pause-unwinding are considered. The winding problem is reduced to determining the appropriate Green’s function by numerical solution of a Volterra integral equation of the second kind. This Green’s function and integral superposition permits the evaluation of the stress and displacement fields in the tape system for any winding history. Viscoelastic unwinding is treated by the superposition of two-states — one determined from the initial condition of the tape when unwinding begins and the second state given in terms of an arbitrary external pressure evaluated by solving an integral equation. Numerical results are presented for several histories and representative material properties.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):828-836. doi:10.1115/1.3176178.

A first-order perturbation analysis is presented for the configuration of an initially straight crack front which is trapped against forward advance by contact with an array of obstacles (i.e., regions of higher fracture toughness than their surroundings). The problem is important to the micromechanics of crack advance in brittle, locally heterogeneous solids. The formulation is based on a linear perturbation result for the stress intensity factor distribution along the front of a half-plane crack when the location of that front differs moderately from a straight line. The trapping solutions for a periodic array of blocking rectangular obstacles are given using an analogy to the plane stress Dugdale/BCS elastic-plastic crack model. For a periodic array of obstacles with a given spacing and size in the direction parallel to the crack front, the obstacle shape may affect the limit load at which the crack breaks through the array. When such effects are examined within the range of validity of the linear perturbation theory, it is found that obstacles whose cross-sections fully envelop a critical reference area give the maximum limit load while others are broken through at lower load levels. We also formulate a numerical procedure using the FFT technique and adopting a “viscoplastic” crack growth model which, in an appropriate limit, simulates crack growth at a critical stress intensity factor. This is applied to show how a crack front begins to surround and penetrate into various arrays of round obstacles (with a toughness ratio of 2) as the applied load is gradually increased. The limitations of the first-order analysis restrict its validity to obstacles only slightly tougher than the surrounding elastic medium. Recently, Fares (1988) analyzed the crack trapping problem by a Boundary Element Method (BEM) with results indicating that the first-order linear analysis is acceptable when the fracture of toughness of the obstacles differs by a moderate amount from that of their surroundings (e.g., the toughness ratio can be as large as 2 for circular obstacles spaced by 2 diameters). However, the first-order theory is not only quantitatively inaccurate, but can make qualitatively wrong predictions when applied to very tough obstacles.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):837-843. doi:10.1115/1.3176179.

This paper addresses the trapping of the front of a planar crack as it impinges upon a row of periodically-emplaced tough obstacles. The initial penetration of the crack between obstacles, under increasing load, as well as the ultimate unstable joining of penetrating segments so as to surround and by-pass the obstacles, are analyzed. The formulation used for the associated three-dimensional elasticity problems of half-plane cracks with nonuniform, curved fronts is a Boundary Element Method (BEM). This incorporates a specialized fundamental solution for an opening (prismatic) dislocation source ahead of a half-plane crack with a straight front (Rice, 1985a). The implementation of this BEM and associated mesh moving with the front is first discussed after which a series of case studies are carried out. The first two case studies evaluate the accuracy of previously obtained linear perturbation results (Rice (1985b), Gao and Rice (1988)). The last study is a crack growth simulation around a periodic array of circular obstacles with a particle size to spacing ratio of 0.5. The simulation shows in that case that crack trapping achieves an effective toughening ratio of 2.35 when the particle-to-matrix-toughness ratio (Kcp /Kc ) is greater than 3.52. The simulation also gives lower bounds on the net toughening when K cp /K c < 3.52.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):844-849. doi:10.1115/1.3176180.

A solution is presented for the problem of a crack branching off the interface between two dissimilar anisotropic materials. A Green’s function solution is developed using the complex potentials of Lekhnitskii (1981) allowing the branched crack problem to be expressed in terms of coupled singular integral equations. Numerical results for the stress intensity factors at the branch crack tip are presented for some special cases, including the no-interface case which is compared to the isotropic no-interface results of Lo (1978).

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):850-857. doi:10.1115/1.3176181.

The penetration through a two-phase boundary by a biplanar (kinked) crack of arbitrary shape is considered in this paper. The two-phase boundary is modeled as the interface between two perfectly-bonded elastic, isotropic, homogeneous half spaces with different elastic constants. The planar crack on either side of the interface may be arbitrarily orientated with respect to the interface boundary. The body-force method is used to derive a set of coupled two-dimensional singular integral equations which are solved numerically. The solution yields the three crack opening displacements as well as the three modes of stress intensity factors along the crack contour. Numerical results are given for a penny-shaped crack symmetrically oriented with respect to the interface. Mode I stress intensity factors are given for the biplanar crack that experiences a kink when passing through the interface.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):858-864. doi:10.1115/1.3176182.

Branched crack problems are analyzed in two-dimensional, anisotropically elastic homogeneous solids. The method of analysis is based on the complex variable approach of Savin and Lekhnitskii. The Hilbert problem in an anisotropic body is defined, and a pair of singular integral equations are derived for dislocation density functions associated with a branched crack. For both symmetric and nonsymmetric geometries, and under symmetric and antisymmetric loads, the stress intensity factors and the energy release rate are computed numerically by extrapolation for infinitesimally small lengths of branched cracks. The results are compared with those of the isotropic case given in the literature and the effects of anisotropy are discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):865-867. doi:10.1115/1.3176183.

In this paper we discuss a suboptimal method of approximating a desired deflection curve of a simple beam by a given number of force actuators. The spacing between the actuators is allowed to vary as a function of the deflection curve. The method is applied to an example of approximation of a deflection curve of the slice lip on a paper machine headbox for the control of the basis weight profile of paper. The approximation error with variable spacing is compared with that obtained when the spacing is not varied (uniformly-spaced actuators). Significant reduction in error is observed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):868-873. doi:10.1115/1.3176184.

To simulate the response of a pin-ended elastic-plastic beam, a nonlinear structural model, i.e., a double-tier-spring model is analyzed to follow its deformation process after it is subjected to impulsive loading. After examining the first integral of the equation of motion, in the final elastic vibration, combined with other conditions, a region in the parameter’s map is found in which the anomalous behavior (i.e., a negative-negative vibration) appears. This model is proved to be equivalent to the Shanley-type model adopted in previous analyses, but the present approach provides new results in a more complete way.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):874-880. doi:10.1115/1.3176185.

In this paper a dynamic model of a flexible robot is built out of a finite element model of each of its links. The number of degrees-of-freedom of these models is strongly reduced by applying the Component Mode Synthesis technique which involves the preliminary calculation of a limited number of mode shapes of the separate links. As can be seen from examples, the type of boundary conditions thereby imposed in the nodes in which one link is connected to the others, strongly determines the accuracy of the calculated resonance frequencies of the robot. The method is applied to an industrial manipulator. The reduced finite element model of the robot is changed in order to match the numerically and experimentally (modal analysis) determined resonance data. Further, the influence of the position of the robot on its resonance frequencies is studied using the optimized numerical model.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):881-886. doi:10.1115/1.3176186.

We develop the analysis for the propagation of free waves in a general anisotropic plate. We begin with a formal analysis of waves in a plate belonging to the triclinic symmetry group. The calculation is then carried forward for the slightly more specialized case of a monoclinic plate. We derive the secular equation for this case in closed form and isolate the mathematical conditions for symmetric and antisymmetric wave mode propagation in completely separate terms. Material systems of higher symmetry, such as orthotropic, transversely isotropic, cubic, and isotropic are contained implicitly in our analysis. We also demonstrate that the particle motions for Lamb and SH modes uncouple if propagation occurs along an in-plane axis of symmetry. We present numerical free-wave dispersion results drawn from concrete examples of materials belonging to several of these symmetry groups.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):887-892. doi:10.1115/1.3176187.

Equations of motion are formulated for a thin elastic plate that is executing small motions relative to a reference frame undergoing large rigid body motions (three-dimensional rotation and translation) in a Newtonian reference frame. As an illustrative example, a spin-up maneuver for a simply-supported rectangular plate is examined, and the vibration modes of such a plate are used to show that the present theory captures the phenomenon of dynamic stiffening .

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):893-899. doi:10.1115/1.3176188.

An analytical-type solution is developed for the free vibration analysis of rectangular plates with uniform elastic edge support symmetrically distributed about the plate central axes. Both linear elastic rotational and translational support are considered to act simultaneously. Rapid convergence is encountered. Because of the symmetry of the problem, the free vibration modes fall into three distinct families. Eigenvalues are tabulated for the first four modes of vibration of a square plate with identical stiffnesses on each edge and with various ratios of translational to rotational stiffnesses. This represents, to the author’s knowledge, the first comprehensive treatment of this problem.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):900-909. doi:10.1115/1.3176189.

The geometrically and constitutively nonlinear response of an infinite, circular, cylindrical shell submerged in an infinite fluid medium to a transverse, transient acoustic wave is analyzed. Circumferential Fourier series solutions are obtained through the numerical integration of coupled ordinary differential equations and convolution integrals. Numerical results are presented in the form of response histories, response snapshots, and iso-damage curves for incident waves of rectangular pressure profile. Response solutions obtained with the first-order doubly asymptotic approximation are compared with their “exact” counterparts. It is found that doubly asymptotic approximations are unsuitable for two-dimensional, shock-response analysis of yielding submerged structures.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):910-917. doi:10.1115/1.3176190.

The present work is a part of the effort toward the development of an efficient method of solution to handle general nonsymmetric time-harmonic end conditions in a cylinder with a traction-free lateral surface. Previously, Kim and Steele (1989a) develop an approach for the general axisymmetric case, which utilizes the well-known uncoupled wave solutions for a mixed lateral wall condition. For the case of a traction-free lateral wall, the uncoupled wave solutions provide: (1) a convenient set of basis functions and (2) approximations for the relation between end stress and displacement which are asymptotically valid for high mode index numbers. The decay rate with the distance from the end is, however, highly dependent on the lateral wall conditions. The present objective was to demonstrate that the uncoupled solutions of the nonsymmetric waves discussed by Kim (1989), which satisfy certain mixed lateral wall conditions, can be utilized in an analogous manner for the asymptotic analysis of the traction-free case. Results for the end displacement/stress due to various end conditions, computed by the present method and by a more standard collocation method, were compared. The present method was found to reduce the computational effort by orders of magnitude.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):918-925. doi:10.1115/1.3176191.

The fundamental singular solutions of a complete elastic spherical shell are utilized and, via the superposition principle, an indirect boundary integral equation is formulated. The singular solutions correspond to the action of normal point loads, concentrated tangential loads, and surface moments which apply in a self-equilibrating fashion over the spherical surface. With singular solutions of such property in hand, an arbitrary spherical shell with surface loading and any set of consistent boundary constraints is embedded onto the complete sphere. A set of fictitious load vectors is introduced along the boundary line which, together with the prescribed surface traction, is required to satisfy the constraints at the boundary. The idea of an auxiliary boundary is also introduced and the solution to a number of representative shell problems is shown as compared to the available analytical and finite element method results.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):926-929. doi:10.1115/1.3176192.

A study is made of the general behavior of a semi-active impact damper. The system consists of an undamped forced torsional oscillator, and a flywheel which can be locked to the oscillator through a clutch. The impact which results during clutch engagement is effective in reducing the vibration amplitude level of the oscillator when it is subjected to bounded excitation. All solutions of the system are shown to be bounded when the input is bounded. Periodic solutions are discussed in the following paper, Part II.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):930-940. doi:10.1115/1.3176193.

All solutions of the semi-active impact damper described in Part I were shown to be bounded when the excitation is bounded. In this part, the existence of periodic solutions is investigated. Emphasis is placed on two impacts/cycle periodic solutions. Exact symmetric and nonsymmetric harmonic solutions are derived analytically and the region of asymptotic stability is determined.

Topics: Stability , Dampers , Cycles
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):941-946. doi:10.1115/1.3176194.

Optimal control of flexible continuous structures subjected to arbitrary time-varying distributed loads is considered. The control is to be implemented by discrete sets of sensors and actuators that monitor the response and apply the necessary forces. The dynamics of the uncontrolled structure is assumed to be governed by a linear, self-adjoint partial differential equation. The control forces at any time are determined on the basis of minimization of the total energy of the system at that time. This leads to a causal optimal algorithm whereby control forces are determined solely on the basis of information available up to the time at which control is being implemented. The effectiveness of the algorithm is demonstrated by applying it to a beam subjected to an impulse.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):947-952. doi:10.1115/1.3176195.

Nonlinear oscillations of a single-degree-of-freedom, parametrically-excited system are considered. The stiffness involves quadratic and cubic nonlinearities and models a shallow arch or buckled mechanism. The excitation frequency is assumed to be close to twice the natural frequency of the system. Numerical integration is used to obtain phase plane portraits, power spectra, and Poincaré maps for large-time motions. Period-doubling bifurcations and several types of limit cycles and chaotic behavior are observed. Approximate analytical techniques are applied to analyze some of the limit cycles and transitions of behavior. The results are used to estimate the parameter region in which chaos may occur.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):953-959. doi:10.1115/1.3176196.

A probabilistic approach to the torsional vibration problem of a marine diesel engine shafting system has been developed. In this analysis, the shafting shear stress is found to be a Gaussian, harmonizable cyclostationary process with a harmonic series representation consisting of two complex conjugate components. In this paper, the level crossing problem for this stress process is studied. Two methods for estimating the probability that the stress exceeds a specified threshold at least once over a given time interval are presented. In the first method, a local maximum of the process is approximated by the value of the corresponding envelope at the time of occurrence of this maximum. A Markov-type condition is assumed to hold for the local maxima. The second method assumes that the maximum of the process over a reasonable number of cycles is approximately equal to that of the envelope process. The envelope crossings are assumed to constitute a Poisson process. The two methods are applied to estimate the upcrossing probability in various cases. The results of both approaches are found to be in good agreement with those from Monte Carlo simulation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):960-967. doi:10.1115/1.3176197.

Recent theoretical studies indicate that whereas large excitation amplitudes are needed to produce chaotic motions in single-degree-of-freedom systems, extremely small excitation levels can produce chaotic motions in multi-degree-of-freedom systems if they possess autoparametric resonances. To verify these results, we conducted an experimental study of the response of a two-degree-of-freedom structure with quadratic nonlinearities and a two-to-one internal resonance to a primary resonant excitation of the second mode. The responses were analyzed using hardware and software developed for performing time-dependent modal decomposition. We observed periodic, quasi-periodic, and chaotic responses, as predicted by theory. Conditions were found under which extremely small excitation levels produced chaotic motions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):968-974. doi:10.1115/1.3176198.

The motion of inviscid and Newtonian jets issuing from elliptical orifices is analyzed. The analysis is not confined to small departures of the jet free surface from a circular cylindrical mean surface, but rather is fully nonlinear. Two types of behavior are predicted: (1) In the presence of surface tension the major axis of the elliptical jet cross-section alternates between perpendicular directions with distance down the jet. In this case the system is described as a single-degree-of-freedom nonlinear oscillator, conservative for the inviscid elliptical jet in the absence of gravity, and nonconservative for the Newtonian jet. (2) When surface tension is neglected, the transformation occurs only once, after which the jet flattens into a sheet perpendicular to the major axis of the orifice. The effect of gravity is discussed both for downward flowing jets and fountains.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1989;56(4):975-976. doi:10.1115/1.3176199.
Abstract
Topics: Torque , Stress , Deflection
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):976-977. doi:10.1115/1.3176200.

The stress and strain field solutions for the stationary mode III crack in small-scale yielding is obtained from a direct physical picture in which the plastic strain is produced by the motion of infinitesimal dislocations. The analysis is based on a shifting center, cylindrical coordinate system. The nonredundant dislocation density is determined. The ratio of nonredundant to redundant dislocation density within the plastic zone may be a useful measure for placing cracks into a brittle class, a ductile class and semibrittle to semiductile classes.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):977-979. doi:10.1115/1.3176201.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):981-983. doi:10.1115/1.3176203.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):983-985. doi:10.1115/1.3176204.
Abstract
Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Appl. Mech. 1989;56(4):986. doi:10.1115/1.3176205.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1989;56(4):986-987. doi:10.1115/1.3176206.
FREE TO VIEW
Abstract
Topics: Dimensions , Shells
Commentary by Dr. Valentin Fuster

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