Showing papers in "Journal of Applied Mechanics in 1964"

The Bending of Plates of Dissimilar Materials With Cracks

Abstract: This paper considers the problem of bending of a plate composed of two plates of materials having dissimilar elastic properties, bonded together along a straight line which sustains a crack. Both materials are assumed to be isotropic and, homogeneous. Upon obtaining stress solutions, it is found that the significant stresses are inversely proportional to the square root of the radial distance from the crack front and have an oscillatory character, which is shown to be confined to the immediate vicinity of the crack tip. A two-parameter set of equations expressing the general form of the stress distribution around the tip of such a crack is provided as it is of primary importance in predicting the strength of cracked plates. Some analogies are also observed between the characteristic equations occurring in the extension and bending of cracked plates composed of dissimilar materials.

An Iterative Method for the Displacement Analysis of Spatial Mechanisms

Abstract: An algebraic method for the displacement analysis of linkages has been the subject of earlier publications [1, 2]. This method, based on the use of a symbolic notation, allows the application of matrix algebra to the study of displacements in linkages, and permits formulation of all the kinematic relations of a linkage in terms of matrix equations. Based on this earlier work, the present paper develops an iterative method for the solution of the matrix equations required in displacement analysis. A complete solution is given for simple-closed linkages consisting of revolute and prismatic pairs (and their combinations). A brief indication of how higher pairs and multiple-closed chains may be handled is also given. Particularly useful in spatial problems, since it does not depend on visualization, this approach is developed in a manner intended for digital-computer operation.

Stability of Flow Between Arbitrarily Spaced Concentric Cylindrical Surfaces Including the Effect of a Radial Temperature Gradient

Abstract: : The stability of Couette flow and flow due to an azimuthal pressure gradient between arbitrarily spaced concentric cylindrical surfaces was investigated. The stability problems are solved by using the Galerkin method in conjunction with a simple set of polynomial expansion functions. Results are given for a wide range of spacings. For Couette flow, in the case that the cylinders rotate in the same direction, a simple formula for predicting the critical speed is derived. The effect of a radial temperature gradient on the stability of Couette flow is also considered. It is found that positive and negative temperature gradients are destabilizing and stabilizing respectively.

Residual Stresses and Fatigue in Metals

Abstract: Residual stresses and fatigue in metals , Residual stresses and fatigue in metals , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

The Inverse Problem in Transient Heat Conduction

Abstract: A general theory is devised for determining the temperature and heat flux at the surface of a solid when the temperature at an interior location is a prescribed function of time. The theory is able to accommodate an initial temperature distribution which varies arbitrarily with position throughout the solid. Detailed analytical treatment is extended to the sphere, the plane slab, and the long cylinder; and it is additionally shown that the semi-infinite solid is a particular case of the general formulation. The accuracy of the method is demonstrated by a numerical example. In addition, a numerical calculation procedure is devised which appears to provide smooth, nonoscillatory results.

Stress and Velocity Fields in the Gravity Flow of Bulk Solids

Abstract: This paper presents the mathematical theory of stress and velocity fields for the steady gravity flow of bulk solids in converging channels. The basic equations based on the concepts of soil mechanics and plasticity are presented along with the appropriate boundary conditions. A simplified stress field (called the “radial stress field” by Jenike), compatible with straight-walled converging channels, is shown by calculated and experimental evidence to approximate closely the physical stress fields occurring in the deforming portions of the solid in plane-strain and axisymmetric straight-walled converging channels.

Theory of Buckling of a Porous Slab and Its Thermoelastic Analogy

Abstract: purpose of the present paper. The existence of a lower and upper buckling load for a porous slab is derived and discussed. The analogy with the viscoelastic behavior of nonporous media is shown to be a consequence of thermodynamic principles. This analogy is applied to the analysis of folding instability of an embedded layer. It is of interest to point out that the physical problem is quite different from that of a viscoelastic continuum since the stresses depend not only on the local strain, but also on the fluid pressure whose value is determined by solving the complete field problem. The simplification which leads to the viscoelastic analogy in the present case is due to the particular nature of the approximation associated with the concept of bending moment. Attention also should be called to the overall perspective, of the problem of buckling of a layered porous medium, which is provided by the simple case analyzed in this paper. A solution is derived for a porous slab embedded in an impervious medium. However, the other extreme case of infinite permeability of the embedding medium is immediately obtained by applying a factor to the relaxation constants in the operator B(p) representing the bending properties of the slab. Hence an estimate can be made for the more complex intermediate case where the finite permeability of the embedding medium enters into play. Another analogy based on thermodynamics leads to the theory of thermoelastic buckling of a purely elastic homogeneous slab. In general the theory is applicable to the case of any two-com

Wave Propagation in a Two-Layered Medium

Abstract: : Elastic wave propagation in a medium consisting of two finite layers is considered. Two types of solutions are treated. The first is a Rayleigh train of waves. For this case, when the wave length becomes short, the waves approach two Rayleigh waves plus a possible Stoneley wave. When the wave length becomes large, there are two waves: a flexural wave and an axial wave. Calculations are presented for this case. The propagation of SH waves is treated, but no calculations are presented. (Author)