Showing papers in "Journal of Applied Mechanics in 1967"

A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks

Abstract: : An integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elastic- plastic type (treated through a deformation rather than incremental formulation) , with a linear response to small stresses followed by non-linear yielding, the integral may be evaluated in terms of Irwin's stress intensity factor when yielding occurs on a scale small in comparison to notch size. On the other hand, the integral may be expressed in terms of the concentrated deformation field in the vicinity of the notch tip. This implies that some information on strain concentrations is obtainable without recourse to detailed non-linear analyses. Such an approach is exploited here. Applications are made to: Approximate estimates of strain concentrations at smooth ended notch tips in elastic and elastic-plastic materials, A general solution for crack tip separation in the Barenblatt-Dugdale crack model, leading to a proof of the identity of the Griffith theory and Barenblatt cohesive theory for elastic brittle fracture and to the inclusion of strain hardening behavior in the Dugdale model for plane stress yielding, and An approximate perfectly plastic plane strain analysis, based on the slip line theory, of contained plastic deformation at a crack tip and of crack blunting.

The Elastic Contact of Rough Spheres

Abstract: The Hertzian theory of elastic contact between spheres is extended by considering one of the spheres to be rough, so that contact occurs, as in practice, at a number of discrete microcontacts. It is found that the Hertzian results are valid at sufficiently high loads, but at lower loads the effective pressure distribution is much lower and extends much further than for smooth surfaces. The relevance to the physical-contact theory of friction and electric contact is considered.

Jet Noise and Shear Flow Instability Seen From an Experimenter’s Viewpoint

Abstract: Similarity laws for jet noise, model line emitter, near field pressure covariances and spectra, phase coherence of near pressure fields, and nonlinear coupling in turbulence

Imperfection Sensitivity of Externally Pressurized Spherical Shells

Abstract: Initial postbuckling behavior of spherical shell under external pressure determined using Koiter theory, analyzing effects of imperfections on buckling strength of structures

Measurement of Laminar Flow Development in a Square Duct Using a Laser-Doppler Flowmeter

Abstract: A system for precision measurement of fluid velocity is developed and applied to determine the laminar flow distribution in a square duct. The experimental technique consists of measuring the Doppler shift of laser radiation scattered by particles moving with the fluid. From this frequency shift, the fluid velocity is inferred. Measurements in the entrance region and fully developed flow region of a square duct indicate that the velocity profile development takes place in a somewhat longer section of the duct than had been predicted. Measurements of the fully developed flow indicate that the optical technique used is capable of measuring velocity within an accuracy of at least 0.1 percent.

Experimental and Theoretical Studies of Liquid Sloshing at Simulated Low Gravity

Abstract: Liquid sloshing at simulated low gravity in rigid cylindrical tank, noting analytical model and experimental results

Generalized Hypergeometric Function Solutions on the Transverse Vibration of a Class of Nonuniform Beams

Abstract: With simple beam theory, solutions of normal functions for transverse vibration of a tapered beam are obtained in terms of generalized hypergeometric functions by the method of Frobenius. For the beams considered, the cross-sectional area and the area moment of inertia vary along the beam according to any two arbitrary powers of the longitudinal coordinate. The frequency equation is formulated, and the numerical results for many different tapered cantilever beams are presented.

Normality relations and convexity of yield surfaces for unstable materials or structural elements.

Abstract: : The stress-strain relations for materials and the load-deflection relations for structural elements play corresponding roles in the analysis of three-dimensional continua and of structures respectively. Mathematically equivalent and phenomenologically quite similar, they are treated simultaneously here. As in previous treatments of stable (rising) plastic stress-strain curves, unstable (falling) curves in simple shear or tension are generalized to all states of stress through the exploration of the work done in a cycle of stress (Drucker) and in a cycle of strain (Ilyushin). The plastic increment of strain is found to be normal to the current yield surface for a wide class of unstable materials in which a continuous variation of strain produces a unique continuous variation of stress and of the shape and position of the yield surface. In the absence of any significant alteration in the (stable) elastic response, each yield surface then is shown to be convex. The degree of concavity possible when the elastic response is stable but is non-linear and does alter appreciably due to plastic deformation is illustrated by a non-linear elastic spring and a plastic block in parallel. Such concavity would not be observable in the yield surfaces of common structural metals, but might be found for soils, rocks or concrete and can be quite pronounced for structural elements. (Author)

Compound-Compressible Nozzle Flow

Abstract: : A one-dimensional theory based upon fundamental flow relationships is presented for analyzing the behavior of one or more gas streams flowing through a single nozzle. This compound-compressible flow theory shows that the behavior of each stream is influenced by the presence of the other streams. The theory also shows that the behavior of compound-compressible flow is predicted by determining how changing conditions at the nozzle exit plane affect conditions within the nozzle. It is found that, when choking of the compound-compressible flow nozzle occurs, an interesting phenomenon exists. The compound-compressible flow is shown to be choked at the nozzle throat, although the individual stream Mach numbers there are not equal to one. This phenomenon is verified by a wave analysis which shows that, when choking occurs, a pressure wave cannot be propagated upstream to the nozzle throat even though some of the individual streams have Mach numbers less than one. Algebraic methods based on this compound-compressible flow theory are used to demonstrate the usefulness of this approach in computing the behavior of compound-compressible flow nozzles.

The Kinematics of Motion Through Finitely Separated Positions

Abstract: A rigid body is studied in a series of finitely separated positions, in order to determine those points which lie on a special locus (a sphere, circle, plane, line, or cylinder). Equations governing these special points are derived and their numerical evaluation is discussed. Several numerical examples are presented. In a companion paper [21], these results are applied to the synthesis of spatial linkages, and special motions (e.g., planer and spherical) are incorporated into the general theory presented herein.