0


RESEARCH PAPERS

J. Appl. Mech. 1972;39(2):321-326. doi:10.1115/1.3422678.

This paper shows the calculation of the initial yield surface of a unidirectionally reinforced composite subjected to longitudinal normal, transverse normal, and longitudinal shear loadings. The composite is composed of boron filaments arranged in a periodic square array and embedded in a matrix of 6061 aluminum alloy. A finite-element method is employed to obtain solutions for stresses throughout the composite. The von Mises yield criterion is used to calculate the elastic limit of the local microscopic combined stresses in the composite.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):327-336. doi:10.1115/1.3422679.

The propagation of harmonic elastic waves through composite media with a periodic structure is analyzed. Methods utilizing the Floquet or Bloch theory common in the study of the quantum mechanics of crystal lattices are applied. Variational principles in the form of integrals over a single cell of the composite are developed, and applied in some simple illustrative cases. This approach covers waves moving in any direction relative to the lattice structure, and applies to structures of the Bravais lattice groups which include, for example, parallel rods in a square or hexagonal pattern, and an arbitrary parallelepiped cell. More than one type of inclusion can be considered, and the elastic properties and density of the inclusion and matrix can vary with position, as long as they are periodic from cell to cell. The Rayleigh-Ritz procedure can be applied to the solution of the variational equations, which provides a means of calculating dispersion relations and elastic properties of specific composite materials. Detailed calculations carried out on layered composites confirm the effectiveness of the method.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):337-344. doi:10.1115/1.3422680.

The linearized problem of an infinite steady flow about a thin cambered hydrofoil with a jet flap is solved. The flow is assumed to be inviscid and incompressible and the cavitation number is taken to be zero. It is also assumed that the profile of the foil can be expressed in terms of a polynomial function. Expressions have been obtained for lift, drag, pressure distribution, pitching moment, the jet shape, and the cavity shape. Numerical results are presented for a general “polynomial” foil, and, in particular, Tulin’s low drag foil to show the effects of the geometric parameters of the foil on these hydrodynamic characteristics.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):345-350. doi:10.1115/1.3422681.

Laminar flow of an incompressible, Newtonian fluid is considered, in a narrow space between two stationary surfaces of revolution having a common axis of symmetry. The method of free parameters is used to investigate the existence of similarity solutions. It is found that there are no surface shapes for which similarity solutions exist, when the full Navier-Stokes equations are used to describe the flow. After order-of-magnitude arguments are employed to reduce the equations surface shapes are found for which similarity solutions exist; the shapes are delineated and the similarity problems are formulated. Finally, a method for solving the similarity problem is discussed and the solution is tabulated from the results of calculations conducted on a digital computer.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):351-358. doi:10.1115/1.3422682.

The steady, two-dimensional, constant properly flow and temperature distribution are calculated for turbulent flow in a square cavity over which there is a bounded flow with an initially uniform velocity. This is done by solutions of the finite-difference equations, stabilized for iteration by taking the first derivatives in the “upstream” direction. When such a solution incorporates corrections for the large truncation error produced by taking the derivatives in this way, results are obtained which compare favorably to many aspects of the available experimental data at a Reynolds number of 1.5 × 105 . Velocity and temperature distribution are well predicted within the cavity and the shear layer, and wall temperatures are in excellent agreement with experiment over a considerable fraction of the wall area.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):359-366. doi:10.1115/1.3422683.

A common objective in designing a postmortem type of plate-impact experiment is to be able to attribute the observable residual effects (such as residual strain, hardness, or dislocation density) primarily to the conditions which existed while the material was in a state of uniaxial strain. In the past it has generally been assumed that effects due to radial stress release phenomena, which are always present in such an experiment, are of secondary importance. In order to test the validity of this assumption, a two-dimensional Lagrangian finite-difference computer program is used to model physical experiments representative of common practice. Target plate dimensions, the target and flyer plate material, and the impact velocity are systematically varied for circular target plates with, and without, guard rings. The results show that in many cases the effects of radial release phenomena are too large to ignore. Conclusions are presented which serve as guidelines for designing experiments to minimize radial release effects.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):367-371. doi:10.1115/1.3422686.

The elastic strain waves resulting from the impact of two 3/4-in-dia 6061-T6 aluminum bars are studied experimentally and analytically. Experimental data are obtained from strain gages on the center line and outer surface of the bar, located at various distances from the impact end of the bar. Experimental data are compared to numerical results obtained from integrating the exact equations of two-dimensional motion. In general, agreement between the numerical and experimental results is very good.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):372-377. doi:10.1115/1.3422687.

The nature of the singularity in the stresses produced near the front of a progressing step load of pressure on the surface of an elastic half space is investigated for the case when the velocity of the front coincides with that of Rayleigh waves in the elastic medium. The technique is based on the assumption of the basic form of the solution and the demonstration that this assumption is correct. It is found that for the particular velocity of the front considered here, unusually large stresses are produced in the medium.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):378-384. doi:10.1115/1.3422688.

The problem of propagation of guided elastic waves near curved surfaces and in layers of nonconstant thickness is investigated. Rigorous solutions for such problems are not available, and a method is shown for the construction of high frequency asymptotic solutions for such problems in two dimensions. The method is applied to Love waves, which are SH-waves in an elastic layer, Rayleigh waves, which are elastic waves guided by a single free surface, and Lamb waves, which are SV-waves guided in a plate or layer with two free surfaces. The procedure shown breaks the second-order boundary-value problems which have to be solved into successions of simpler problems which can be solved numerically. Some numerical examples for Rayleigh waves are carried out in order to demonstrate the utility of our method. The method shown is useful for a large variety of guided wave problems, of which the ones we treat are just examples.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):385-389. doi:10.1115/1.3422689.

Simple perturbation solutions are given for the propagation of stress waves in an elastic cylindrical shell subjected to transient, axisymmetric, longitudinal excitations. The solutions are shown to be accurate even at rather large distances from the boundary at which the excitation is applied. Convergence of the series solutions is examined and application of the technique to related problems is discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):390-394. doi:10.1115/1.3422690.

A compressive pulse applied to the base of a cone develops a tensile tail as it propagates toward the cone apex. This tension can cause fracture of the cone perpendicular to the cone axis before the leading edge of the pulse reaches the tip. It is shown that the elementary one-dimensional wave-propagation theory for cones and a time-independent critical tensile stress fracture criterion adequately describe the fracture of lucite cones subjected to narrow rectangular compressive pulses between 1 and 7 kilobars in magnitude.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):395-400. doi:10.1115/1.3422691.

A transient stress analysis for the problem of a torque applied suddenly to the surface of a penny-shaped crack in an infinite elastic body is carried out. The singular solution is equivalent to that of the sudden appearance of a crack in a body under torsion. Using an integral transform technique developed for this class of transient problems, the dynamic stresses near the periphery of the crack are found to have the same angular distribution and inverse square root singularity as in the static case. This character of the local solution prevails for all time only in a toroidal region extremely close to the crack border. Within this region, the stress intensity is found to vary with time, reaching a peak greater than the static value and subsequently oscillating about that value with decreasing amplitude. The dynamic crack-opening displacement field is also given for any instant of time after loading.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):401-406. doi:10.1115/1.3422692.

By applying the correspondence principle, the Laplace transform solutions of spherical waves in viscoelastic model are derived in this study. The numerical inversion of Laplace transform developed by Bellman is introduced to invert the transform solution of spherical waves into time domain. A modification of the numerical inversion is particularly shown to enable one to obtain the viscoelastic waves adequately. The accuracy of the numerical inversion is proven by comparing the results calculated from series solution and Papoulis’ method. The efficiency of the numerical inversion is demonstrated by studying the wave parameters in 6-element and 5-element models. By examining the behavior of wave responses in time domain, it is found that the 5-element model behaves as a viscous liquid and the 6-element model as a solid.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):407-415. doi:10.1115/1.3422693.

In this paper the theory of the hodograph transformation is developed in a systematic way for one-dimensional wave propagation in elastic-plastic solids. The material is assumed to have isotropic strain-hardening characteristics with no Bauschinger effect. It is shown that in the hodograph plane it is possible to obtain a Riemann solution for the Cauchy problem. The mappings of different kinds of shock fronts and the elastic-plastic boundary onto the hodograph plane are derived. Two problems are solved using the hodograph method. The first one is related to a long rod subjected to a square pulse loading in stress at the free end. Although this problem is well known it provides a good illustration for the method. The second is related to a square pulse loading in stress followed by loading in reversal at the free end of a long rod. It is shown that under certain conditions the shock wave originated by loading in reversal penetrates the progressing plastic waves indefinitely. The region behind the shock front is plastic again but does not belong to the class of simple waves as the region ahead of the shock. The characteristics with positive slope in the region behind the shock in the X-t plane are concave toward the X-axis. The hodograph method is used to investigate if the condition of plastic loading is satisfied behind the shock and to find the first part of the elastic-plastic boundary.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):416-421. doi:10.1115/1.3422694.

Following the derivations of Koiter, who gave a general proof of Melan’s shakedown theorem for elastic-plastic systems under quasi-static reversible parametric loadings, it is shown here that the inclusion of the inertia force due to dynamic loadings does not change the basic tendency for the system to shakedown, if it can. Because of the validity of this shakedown theorem, the problem of designing a system under dynamic loadings and with only a finite amount of allowable plastic work can be transformed into a quasi-static, elastic counterpart. For the case of proportional loadings, two methods for solving the “compounded” shakedown load are proposed. One is called the “Method of Zero Work;” the other, involving a systematic numerical procedure, is called the “Method of Direct Search.” The concept of “optimum preloading” is also introduced.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):422-430. doi:10.1115/1.3422695.

Upper and lower bounds are found for limit loads on nonsymmetrically loaded spherical shells. The influence of geometrical and load parameters are discussed. The analytical results are compared with the results of tests on four steel models.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):431-437. doi:10.1115/1.3422696.

This analysis seeks three-dimensional instabilities of uniaxial compressive flow in isotropic, strain-hardening, rigid-plastic materials of the Mises and maximum shear stress types. No instabilities are found for Mises materials. Maximum shear materials display axisymmetric, “deflectional”, and “higher-order” buckling. For increasingly slender specimens, the deflectional buckling process merges into that of the Shanley theory. The axisymmetric mode raises the possibility that instabilities contribute to the double axial bulging of ductile compression specimens reported by Nádái.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):438-444. doi:10.1115/1.3422697.

The stability of a basic stationary motion is investigated. The problem is posed as an initial boundary-value problem of partial differential equations in the perturbations. The spectral representation of the Green’s function matrix for the linearized problem is obtained and employed to generate a generalized energy function which is then used for the stability investigation of linearized and certain nonlinear problems. The results are applied to the stability of linearized aerodynamic panel flutter problem and to a nonlinear equation with conic nonlinearity.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):445-450. doi:10.1115/1.3422698.

This paper presents an exact analysis for the buckling value of a concentrated load applied to a shallow circular arch. The effects of load offset and initial imperfections with the same form as the buckling mode are included. The results are displayed graphically and a comparison is made with experimental values that are available in the literature.

Topics: Arches , Stress , Buckling
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):451-455. doi:10.1115/1.3422699.

When a plate of magnetically soft material is supported with its wide surface normal to a uniform magnetic field, it will buckle when the field reaches a critical value. This paper formulates the problem quite generally for thin plates (including beams) and carries the solution as far as can be done without making specific assumptions as to plate geometry and constraints. The special case of wide cantilever beam, considered earlier by Moon and Pao, is carried through in detail. It is shown that if their theoretical result is modified to take account of the increased field intensity caused by the plate, agreement with experiment is within 20 percent.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):456-460. doi:10.1115/1.3422700.

A theory of rolling contact is presented which deviates from past theories in two respects: (a) the contacting surfaces are not assumed to be topographically smooth, and (b) Coulomb’s law of friction is replaced by a law describing the behavior of interfacial friction junctions. Numerical results for the slip as a function of the normal and tangential loads are shown to depend on a roughness parameter D, which, in turn, depends on surface topography, the gross geometry of the contacting bodies and on the normal load. It is found that when D is large (i.e., the surfaces are very rough, or the normal load is small), the slip-force relationship differs considerably from that predicted by the smooth-surface (or classical) theory. When D tends to zero, the two theories coincide. The dependence of D on topographical parameters is shown explicitly. Numerical examples indicate that for cylinders of small radius, surface-roughness effects may be important. Their importance decreases as the cylinder radius or the maximum contact pressure is increased, or the surface is made smoother.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):461-468. doi:10.1115/1.3422701.

The contact problem of a symmetric rigid punch pressed at the midspan of a simply supported viscoelastic beam is studied. This is equivalent to a cantilever beam loaded at the free end against a rigid smooth surface. Explicit solutions are obtained for the length of the contact region, the contact pressure, the contact force at the contact boundary, and the curvature of the beam outside of the contact regions. As in other contact problems, the solution does not depend on the entire loading history.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):469-474. doi:10.1115/1.3422702.

Numerical solutions for the time history of motion of a shallow viscoelastic spherical shell are presented under large deformations. Axisymmetric motion is considered due to uniform pressure with arbitrary time variation. The dynamic viscoelastic buckling load is established by comparing long-time equilibrium states due to small changes in the applied pressure. The problem is formulated as a coupled pair of nonlinear integro-differential equations which is solved by Newton’s method.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):475-482. doi:10.1115/1.3422703.

This paper deals with the analysis of plane and axisymmetric problems with concrete-like material behavior where nonuniform transient temperature fields and time-dependent cracking are considered. The material is treated as an aging viscoelastic isotopic substance characterized in its uncracked state by the constant Poisson’s ratio and the uniaxial creep function which is shown to obey an extended form of the time-temperature shift. A cracking criterion is postulated whose ingredients are a failure surface expressed in terms of principal strains and an interactive curve which takes stresses and strains into account. The stress-strain relations are formulated for discontinuous material behavior permitting crack formation in three orthogonal directions with arbitrary crack histories. The numerical analysis is obtained within the framework of the finite-element method and a step-by-step integration procedure. The method is applied to a concrete model and comparisons between analysis and experiment are given.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):483-490. doi:10.1115/1.3422704.

This paper is concerned with a method for calculating the stress distribution in the medium which undergoes elastic and temperature-dependent creep deformation due to heating and loading. It is a method for time increments and using four creep displacement functions similar to the Neuber-Papkovitch stress ones. Following this method, the solution is derived for calculating the relief of the stresses in a disk with the heated stamps on the external surface. A numerical example is shown for a disk made of steel.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):491-494. doi:10.1115/1.3422705.

A general approach to the numerical solutions for axially symmetric membrane problem is presented. The formulation of the problem leads to a system of first-order nonlinear differential equations. These equations are formulated such that the numerical integration can be carried out for any form of strain-energy function. Solutions to these equations are feasible for various boundary conditions. In this paper, these equations are applied to the problem of a bonded toroid under inflation. A bonded toroid, which is in the shape of a tubeless tire, has its two circular edges rigidly bonded to a rim. The Runge-Kutta method is employed to solve the system of differential equations, in which Mooney’s form of strain-energy function is adopted.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):495-500. doi:10.1115/1.3422706.

A numerical method for stress analysis of three-layered, honeycomb-type sandwich plates and shells of arbitrary thickness is illustrated by application to a thick conical frustum. Results are demonstrated in a numerical example. The method features an exact elasticity analysis of the core including transverse shear and transverse normal stress. The facings are treated by classical shell theory. The numerical method used is forward integration.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):501-506. doi:10.1115/1.3422707.

The problem of stress analysis of a circular cylinder is considered under conditions which give rise to stress singularities. Such stresses can be produced by circular boundary discontinuities or when boundaries are subject to mixed displacement and force conditions. General solutions are obtained using transformation of the cylindrical coordinates and these solutions converge in the singular region. The results predict exactly the singular behavior and the analysis generates solutions which can be used over a finite region of the cylinder. A numerical example is given showing the application of this analysis to a circular cylinder completely clamped at one end and loaded axially at the other. In this example the stresses and displacements from the present solution are matched with the corresponding quantities obtained from a finite-element analysis. The matching is performed at a finite distance from the stress singularity. Good agreement is obtained between the two solutions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):507-512. doi:10.1115/1.3422708.

The problem of a thin isotropic elastic plate containing an axisymmetric hole, under simple tension at infinity is considered. The method used is to extend the plate theories which have appeared in recent years, which employ asymptotic expansion techniques to determine systematic approximations to the three-dimensional equations of elastostatics.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):513-520. doi:10.1115/1.3422709.

The vibration and stability of plates with mixed edge conditions are considered in this paper. A simply supported rectangular plate which is clamped along the central portion on two opposite edges and a plate with partial clamping along one edge are analyzed. The problems are formulated as dual series equations and reduced to homogeneous Fredholm integral equations of the second kind. Comparisons with numerical results obtained by other investigators are made. Vibration and buckling mode shapes are illustrated. A vibration analysis of a plate simply supported adjacent to the corners is also made. This case is formulated as a coupled system of dual series equations which is reduced to a system of homogeneous integral equations. In all of the solutions given, the singularity is isolated and treated analytically.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):521-526. doi:10.1115/1.3422710.

The dynamic response of a ring-stiffened circular cylindrical shell, immersed in a fluid and subjected to a suddenly applied radial load, is investigated. The shell is infinitely long, the stiffening rings are periodically spaced and identical, and the applied load is uniformly distributed. In the analysis, the authors employ a technique involving the superposition of steady-state solutions which they have found, in previous applications, to be more suitable for problems involving complex interaction conditions than the customary transform approaches. The shell response is computed for an applied step pulse. Displacements and stress histories, and variations in their peak levels, are presented for values of ring flexibility, mass, and spacing, varying over a broad range. The response to the dynamic load is also compared to the response obtained for a static load of equal amplitude. It is found, for example, that for a given ring spacing and flexibility, increase in ring mass above a certain level can lead to dynamic stresses and displacements that exceed their static counterparts by large amounts. Such a situation also makes the existence of an oscillating response more likely. When the ring mass has a negligible influence of the shell response, the trends followed by the peak dynamic displacement and stress with ring flexibility are not appreciably different from those followed by the corresponding static quantities. A similar observation can be made concerning the variation of the peak dynamic displacement with ring spacing.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):527-534. doi:10.1115/1.3422711.

The problem of determining the response of a rigid strip footing bonded to an elastic half plane is considered. The footing is subjected to vertical, shear, and moment forces with harmonic time-dependence; the bond to the half plane is complete. Using the theory of singular integral equations the problem is reduced to the numerical solution of two Fredholm integral equations. The results presented permit the evaluation of approximate footing models where assumptions are made about the interface conditions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):535-538. doi:10.1115/1.3422712.

An estimator for the standard deviation of a natural frequency in terms of second-order statistical properties of the parameters of the system is derived. Results for one simple example is presented in this part and are compared with theoretical and Monte Carlo results. Further results and discussion will be presented in Part 2, ASME Paper No. 71-WA/APM-8.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):539-544. doi:10.1115/1.3422713.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):545-550. doi:10.1115/1.3422714.

A statistical linearization approach is applied to problems of the stationary random response of nonlinear multidegree-of-freedom dynamical systems. The approach is formulated in such a way that the resulting linear system parameters have a simple physical interpretation and can often be determined analytically. The accuracy of the approach is investigated by means of examples.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):551-558. doi:10.1115/1.3422715.

Given in this paper is the development of a theory for dynamical systems subjected to periodic impulsive parametric excitations. By periodic impulsive parametric excitation we mean those excitations representable by periodic coefficients which consist of sequences of Dirac delta functions. It turns out that for this class of periodic systems the stability analysis can be carried out in a remarkably simple and general manner without approximation. In the paper, after giving the general theory, many special cases are examined. In many instances simple and closed-form analytic stability criteria can be easily established.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):559-562. doi:10.1115/1.3422716.

This paper presents an approach which provides a particularly simple and direct way of determining the instantaneous correlation matrices for the stationary random response of multidegree-of-freedom linear systems subjected to excitations of nearly arbitrary spectral density. In the special case of white excitation, the instantaneous correlation matrices are determined directly from a set of linear algebraic equations. When the excitation is nonwhite, some integrals must be evaluated before solving a system of linear algebraic equations. However, the form of these integrals is considerably simpler than that encountered in other common approaches.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):563-568. doi:10.1115/1.3422718.

The exact solution for the steady-state motion of a dynamic vibration neutralizer with motion-limiting stops attached to a sinusoidally excited primary system is derived analytically, and its asymptotically stable regions are determined. Simulated motion on a digital computer and experimental studies with an analog computer corroborate the predictions of the theory. Results of the analysis are applied to modified vibration neutralizers, Lanchester dampers, and impact dampers. It is shown that the incorporation of properly designed motion-limiting stops into the auxiliary mass system will enhance the performance of the foregoing dampers.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):569-576. doi:10.1115/1.3422719.

The method of matched asymptotic expansions is employed to solve the singular perturbation problem of the vibrations of a rotating beam of small flexural rigidity with concentrated end masses. The problem is complicated by the appearance of the eigenvalue in the boundary conditions. Eigenfunctions and eigenvalues are developed as power series in the perturbation parameter β1/2 and results are given for mode shapes and eigenvalues through terms of the order of β.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):577-583. doi:10.1115/1.3422720.

Simplified nonlinear governing differential equations proposed by Berger and extended by Nash and Modeer are applied to obtain natural frequencies of a circular plate with concentric rigid part at its center in large amplitude vibrations. A modified Galerkin technique is used to derive a nonlinear differential equation of which the solution is given in terms of elliptic functions. The small amplitude vibration is treated as a special case of large amplitude vibration, while the free, large amplitude vibration of a flat circular plate is studied as a special case of large amplitude vibration of a circular plate with a concentric mass. The numerical results show that the effect of added concentric rigid mass to a circular plate is significant.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):584-590. doi:10.1115/1.3422721.

Techniques are presented for obtaining generalized finite-difference solutions to partial differential equations of the parabolic type. It is shown that the advantages of similarity in the solution of similar problems are generally not lost if the solution to the original partial differential equations is effected in the physical plane by finite-difference methods. The analysis results in a considerable saving in computational effort in the solution of both similar and nonsimilar problems. Several examples, including both the heat-conduction equation and the boundary-layer equations, are given. The analysis also provides a practical means of estimating the accuracy of finite-difference solutions to parabolic equations.

Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Appl. Mech. 1972;39(2):366. doi:10.1115/1.3422684.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):366. doi:10.1115/1.3422685.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1972;39(2):591-593. doi:10.1115/1.3422722.

The distribution of scattered energy due to the interaction of spherical elastic dilatational waves with a spherical cavity is found to differ from that due to plane waves for long wavelengths even when the radius of curvature is much larger than the cavity radius.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):595-597. doi:10.1115/1.3422724.

Asymptotic expressions for the eigenvalues and the corresponding eigenfunctions for the free vibrations of an inhomogeneous elastic rod with a finite length are derived. The derivation is based on the assumption that the elastic parameters and their derivatives vary continuously along the rod. A method which consists of a perturbation about the solutions of the homogeneous cases is used.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):598-600. doi:10.1115/1.3422726.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):600-601. doi:10.1115/1.3422727.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):601-602. doi:10.1115/1.3422728.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):602-604. doi:10.1115/1.3422729.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):604-606. doi:10.1115/1.3422730.
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):606-607. doi:10.1115/1.3422731.

The individual normal stresses in a two-dimensional plane-stress wave-propagation problem can be determined directly by using scattered light photoelasticity. The applicability of the method is shown by subjecting a rectangular plate to an explosive load.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):607-609. doi:10.1115/1.3422732.

A generalized isotropic yield criterion of the form,

1−σ2)n+(σ2−σ3)n+(σ1−σ3)n21/n
  = Y
where σ1 ≥ σ2 ≥ σ3 and 1 ≤ n ≤ ∞, is proposed. The corresponding flow rules, Lode variables, and effective strain functions are presented. Experimental and theoretical data on yielding under combined stresses can be described by a single parameter, n.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):609-611. doi:10.1115/1.3422733.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):611-613. doi:10.1115/1.3422734.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):613-615. doi:10.1115/1.3422735.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):615-617. doi:10.1115/1.3422736.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):617-619. doi:10.1115/1.3422737.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):620-621. doi:10.1115/1.3422738.
Abstract
Topics: Vibration
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):621-623. doi:10.1115/1.3422739.
Abstract
Topics: Stress , Buckling
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):625-627. doi:10.1115/1.3422741.
Abstract
Topics: Vibration
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):627-628. doi:10.1115/1.3422742.
Abstract
Topics: Design
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):628-629. doi:10.1115/1.3422743.
Abstract
Topics: Force , Stability
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1972;39(2):629-631. doi:10.1115/1.3422744.
Abstract
Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In