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RESEARCH PAPERS

J. Appl. Mech. 1977;44(3):372-377. doi:10.1115/1.3424086.

Velocity measurements are reported for steady and unsteady flow in a rectangular cross-section Y-branch of high aspect ratio. Good agreement is found between the experimental results and two-dimensional calculations. Emphasis is placed on flow velocities near and parallel to the outer wall inasmuch as their gradients are proportional to wall shearing stress which may be of influence in atherogenesis. Large variation in flow velocities and hence shearing stress are found in the immediate vicinity of the corner. The results in this region could support theories which propose either high or low shearing stress as an important consideration in the etiology of arteriosclerosis.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):378-384. doi:10.1115/1.3424087.

A theoretical investigation into the linear, spatial stability of plane laminar jets is presented. The three cases studied are: 1. Inviscid stability of Sato’s velocity profile. 2. Viscous stability of the Bickley’s jet using parallel-flow stability theory. 3. Viscous stability of the Bickley’s jet using a theory modified to account for the inflow terms. The integration of stability equations is started from the outer region of the jet toward the jet axis using the solution of the asymptotic forms of the governing equations. An eigenvalue search technique is employed to find the number of eigenvalues and their approximate location in a closed region of the complex eigenvalue plane. The accurate eigenvalues are obtained using secant method. The inviscid spatial stability theory is found to give results that are in better agreement with Sato’s experimental results than those obtained by him after transformation of the temporal theory results. For the viscous case the critical Reynolds number found by using the theory accounting for inflow is in better agreement with the experimental value than that given by the parallel-flow theory, implying thereby that the parallel-flow approximation for a jet is erroneous for the stability analysis.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):385-388. doi:10.1115/1.3424088.

Experiments were performed to measure the size of drops resulting from the capillary breakup of laminar liquid jets. Random noise was used to perturb the jet and an electro-optical instrument was used to measure drop sizes. Drop size distributions show two peaks as predicted by nonlinear theory. The large group has a mean size as predicted by the most unstable perturbation mode, in agreement with the commonly accepted but previously untested assumption.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):389-395. doi:10.1115/1.3424089.

Measurements of wall shear stress fluctuations have been made in a fully developed turbulent duct flow, using a surface heat transfer gauge. Measurements, made over a moderate Reynolds number range, include RMS values, probability density functions, spectra, and zero-crossing frequencies of the wall shear stress fluctuation. The ratio of RMS of the fluctuation to the mean value of the wall shear stress is found to be about 0.25. The zero-crossing frequency computed from the measured spectra using the relation derived by Rice for a Gaussian process is found to be a good approximation to the measured value, although the measured probability density function is not Gaussian. The zero crossing frequency and spectra of wall shear stress fluctuations appear to scale with outer variables for asymptotically large Reynolds numbers.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):396-400. doi:10.1115/1.3424090.

The thermal boundary layer over a semi-infinite flat plate is investigated. For time t < 0 there is the Blasius boundary layer and no thermal boundary layer. At t = 0, a temperature boundary layer is initiated without altering the velocity and the subsequent temperature boundary layer is studied for all time. The resulting linear, singular parabolic partial differential equation is solved using an efficient numerical method. Numerical results for several values of the Prandtl number are compared with analytical and numerical results obtained by previous authors. Because of the large interest shown recently in impulsive problems which result in the solution of singular parabolic equations the method is extended to study some of these problems. In two of the examples considered the governing equations are nonlinear.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):401-408. doi:10.1115/1.3424091.

This paper deals with the dynamics of a cluster of parallel flexible cylinders in a cylindrical channel in the presence of an axially flowing fluid. The equations of motion are derived, taking into account inviscid and viscous hydrodynamic coupling of small arbitrary motions of the cylinders. Solutions of the equations of motion yield the eigenfrequencies and modal shapes of the system. For sufficiently high flow velocities the system loses stability by divergence and flutter, similarly to a solitary cylinder in unbounded flow; however, the critical flow velocities are much lower, as proximity to other cylinders and to the channel wall severely destabilize the system.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):409-412. doi:10.1115/1.3424092.

The classical formula for the pressure in deep bins containing granular material is derived here employing considerably weaker assumptions than previous derivations. Three important points are established in this rigorous derivation. First, it is shown that the classical formula due to Janssen is a lower bound on the average pressure the granular material can exert on a bin wall rather than necessarily the actual stress. Second, it is shown that Janssen’s assumption of constant vertical stress over the bin’s horizontal cross section is not necessary to obtain his classical formula. Third, it is shown that the coefficient introduced by Janssen should be interpreted as the ratio of the horizontal stress averaged over the lateral boundary perimeter to the vertical stress averaged over the horizontal cross-sectional area of the bin.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):413-418. doi:10.1115/1.3424093.

In this study, a stability concept in terms of the properties of an effective force field is introduced. A criterion for determining certain infinitesimal disturbances which may amplify with time in an elastic-plastic body subject to prescribed initial, kinematic, and time-dependent traction boundary conditions is introduced and developed. The body may be made of a general work-hardening continuum having a piecewise continuous motion and finite deformation. The transition from the dynamic criterion to Hill’s quasi-static bifurcation criterion is indicated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):419-423. doi:10.1115/1.3424094.

Numerically integrable wave (characteristic) equations governing quasi-linear material motion are derived in generalized spatial curvilinear coordinates. The material under consideration is assigned an isentropic hypoelastic/compressible visco-perfectly plastic flow behavior where geometrical nonlinearities prevail throughout, while finite strains correspond only to the anelastic component of the constitutive equation. The characteristics formulation for the flow is derived under a tensor approach, based on those discontinuity relations that are compatible with the geometric description of hyperbolic partial differential equations. Results for spatial multidimensional integration schemes are presented in the form of nonlinear characteristic equations along their orthogonal path of integration (bicharacteristic curves) varying according to wave speed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):424-430. doi:10.1115/1.3424095.

The purpose of this paper is to draw attention to the fact that the routine application of Saint-Venant’s principle in the solution of elasticity problems involving highly anisotropic or composite materials is not justified in general. This is illustrated in the context of the plane problem of elasticity for an anisotropic rectangular strip loaded only on the short ends. For highly anisotropic transversely isotropic materials, the slow decay of end effects is demonstrated using a method involving self-equilibrating eigenfunctions. For a graphite/epoxy composite, for example, the characteristic decay length is shown to be approximately four times that for an isotropic material. The results have implications in the accurate measurement of mechanical properties of anisotropic materials.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):431-436. doi:10.1115/1.3424096.

In this paper, we describe a general treatment for plane thermoelastic problems in multiply connected orthotropic bodies, and provide an example of its application to be a practical problem. In the first part of the paper, the modified Michell’s conditions are derived for the finite domain of orthotropic bodies with many holes. In the second part, the new transient thermal stress solution method is illustrated by application to an orthotropic hollow circular disk under an instantaneous point heat source.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):437-441. doi:10.1115/1.3424097.

The antiplane strain problem of an elliptic inclusion in an anisotropic medium with one plane of symmetry is solved. Explicit expressions of compact form are obtained for the elastic field inside the inclusion, the stress at the boundary, and the strain energy of the system. The perturbation of an otherwise uniform stress field due to an elliptic inhomogeneity is studied, and explicit solutions are given for the extreme cases of an elliptic cavity and a rigid elliptic inhomogeneity. It is found that both the stress magnification at the edge of the inhomogeneity and the increase of strain energy depend only on the component P23A of the applied stress for an elongated cavity; and depend only on the component E13A of the applied strain for a rigid line inhomogeneity.

Topics: Stress , Cavities
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):442-448. doi:10.1115/1.3424098.

The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement field in a finite geometry bar containing a variable depth rectangular surface crack under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Using the obtained displacement field, normal stresses, and the stress-intensity factor variation along the crack periphery are calculated for different crack depth to bar thickness ratios. Crack opening displacements and stress-intensity factors are also obtained for a through-thickness, center-cracked bar with variable thickness. The reported results show a considerable potential for using this method in calculating stress-intensity factors for commonly encountered surface crack geometries in finite solids.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):449-454. doi:10.1115/1.3424099.

By considering the stress interaction between an inhomogeneity embedded in an elastic brittle-like solid and the preexisting microcracks (“Griffith cracks”) inherent to the solid, several puzzling phenomena concerning the apparent anomalous “size effect” on the fracture strength of solids weakened (strengthened) by a cutout (reinforcement) are explained quantitatively. The various conditions under which a cylindrical inhomogeneity in an otherwise homogeneous body enhances the strength of the body or weakens it when the body is subjected to load normal to the cylindrical axis are revealed and discussed. In particular it is shown that uniaxial tensile and compressive critical loads required to fracture material with various hole sizes are predictable as confirmed by experiments with quasi-isotropic composite materials, rocks, and high strength alloys found in the open literature. The entries to these predictive functions are the two independent fracture properties of the material; tensile strength and toughness of the virgin material, or the typical size of the Griffith cracks. As a by-product, the extremely high compressive strength of a material (with respect to its tensile strength) with vanishingly small inhomogeneity emerges.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):455-461. doi:10.1115/1.3424100.

Polymethylmethacrylate (PMMA) plates with angled elliptic notch are experimentally investigated under monotonic tension. The major interests of this investigation are the direction of crack initiation on the boundary of the notch and the critical stress that causes the crack initiation. It is found that the “fracture angle” in this investigation is generally smaller than that obtained from PMMA plate with slit crack which was reported in the literature. Furthermore, the paths of crack propagation are experimentally determined and “lance-like” fracture surface is observed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):462-468. doi:10.1115/1.3424101.

A theory, in the form of a coupled system of reduced parabolic wave equations (equations (42)), is developed for stress wave propagation studies through inhomogeneous, locally isotropic, linearly elastic solids. A parabolic wave theory differs from a complete wave theory in allowing propagation only in directions of increasing range. Thus, when applicable, it is well suited for numerical computation using a range-incrementing procedure. The parabolic theory considered here requires the propagation directions to be limited to a cone, centered about a principal propagation direction, which might be described as narrow-angled. Further, the theory requires that the effects of diffraction, refraction, and energy transfer between the dilatational and distortional modes are gradual enough that coupling between them can be ignored over a range of several wavelengths. Precise conditions for the applicability of the theory are summarized in a series of inequalities (equations (44)).

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):469-474. doi:10.1115/1.3424102.

An inverse procedure is developed for obtaining exact solutions to the one-dimensional inhomogeneous wave equation. Transformations of the independent spatial variable and the dependent variable are introduced so that the wave equation assumes the form associated with a homogeneous material. The resulting transformation relations are nonlinear but of such a nature that they can be easily integrated if the reciprocal of the wave speed distribution can be expressed in terms of elementary functions. One functional form that yields realistic values for material properties of soil layers is investigated in detail. Amplification factors for a sinusoidal seismic shear wave in inhomogeneous and homogeneous layers are derived and illustrations of significantly different characteristics for the two types of layers are shown.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):475-481. doi:10.1115/1.3424103.

Postbuckling behavior of clamped circular cylindrical shells of finite length under uniform axial compression is analyzed using a potential-energy-based, displacement finite-element method. Contour maps of equal radial deflection computed from this analysis for one-tier and two-tier postbuckled, stable equilibrium patterns show very good agreement with experimentally measured contour maps for a polyester shell with L/R = 0.7 and R/h = 405. Developed for these computations, and essential for them, are: (a) A 48 DOF shell element; (b) A method to calculate accurately for the perfect shell the nonlinear fundamental path and its bifurcation points. The lowest such bifurcation point does not correspond to the first observed postbuckle pattern, which is reproduced by calculating the continuous equilibrium path from the sixth bifurcation point. Patterns of successive postbuckling shapes that are formed under additional end-shortening are determined by using a special technique to calculate equilibrium paths extending continuously from still higher bifurcation points on the fundamental path.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):482-486. doi:10.1115/1.3424104.

A solution has been constructed for the transient motion of a viscoelastic cylindrical shell of the arbitrary cross section, surrounded by a fluid medium. The fluid region external to the shell is mapped into the interior of a rectangle. The transformed fluid equation together with the shell equations are expressed in finite-difference form and the time variable suppressed through the application of the Laplace transform. Shell displacements and acoustic pressures are found over the fluid field and at the fluid solid interface.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):487-491. doi:10.1115/1.3424105.

The transient mean-square displacement, slope, and relative motion of a viscously damped shear beam subjected to correlated random boundary excitation is presented. The effects of various system parameters including the spectral characteristics of the excitation, the delay time between the beam support motion, and the beam damping have been investigated. Marked amplifications in the mean-square response are shown to occur for certain dimensionless time delays.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1977;44(3):492-494. doi:10.1115/1.3424106.

A method for studying the behavior of transient longitudinal waves in fiber-reinforced composites, both in high and low frequency ranges, is presented. The results agree well with the solutions obtained by means of the transform method. The dispersive effect of waves to the interpretation of experimental results is also demonstrated by comparing the results obtained from the ultrasonic pulse technique.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):494-496. doi:10.1115/1.3424107.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):496-498. doi:10.1115/1.3424108.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):501-502. doi:10.1115/1.3424111.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):502-504. doi:10.1115/1.3424112.
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):504-505. doi:10.1115/1.3424113.
Abstract
Topics: Stability , Equations
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):506-507. doi:10.1115/1.3424114.
Abstract
Topics: Weight (Mass) , Design , Disks
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):507-509. doi:10.1115/1.3424115.

A simple formula is suggested for the upper bound on the asymptotic pressure in a spherical cavity surrounded by an infinite elasto-plastic medium. The uniaxial stress-strain curve is assumed to be represented by the Ramberg-Osgood equation. Comparison of the proposed upper bound with the exact asymptotic pressure, for a few metals, shows that the average overestimation is around 16 percent.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):509-511. doi:10.1115/1.3424116.

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):511-513. doi:10.1115/1.3424117.
Abstract
Commentary by Dr. Valentin Fuster

ERRATA

DISCUSSIONS

Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Appl. Mech. 1977;44(3):516. doi:10.1115/1.3424122.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):516. doi:10.1115/1.3424123.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):516-517. doi:10.1115/1.3424124.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):517. doi:10.1115/1.3424125.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):517-518. doi:10.1115/1.3424126.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):518. doi:10.1115/1.3424127.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(3):518. doi:10.1115/1.3424128.
FREE TO VIEW
Abstract
Topics: Lasers
Commentary by Dr. Valentin Fuster

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