Discontinuous Load Research Articles

Singular stress concentrations in second-grade materials

The problems of a second-grade elastic half-space deformed in plane strain and subject to a concentrated load, a discontinuous load, and a double force, acting at a point on the free surface are solved. The nature of the stress singularity is found in each case. Although the strengths of the stress singularities are the same as for both classical elasticity and conventional couple-stress materials, the detailed forms are different and depend on a certain combination of the five new elastic constants. The displacement field produced by a point load is bounded in the neighbourhood of the point of application of the force, in contrast to both earlier theories where it is singular.

Cracked Pavement Slabs With Nonuniform Support

The analysis of plates and pavement slabs is examined and a method is presented which is not limited by the simplifying assumptions needed for closed-form solutions. The technique is based on a physical model of the problem which is described mathematically. The principal features are (1) representation of the plate or slab by a finite-element model of beam-column elements with freely discontinuous stiffness and load; (2) a rapid, direct solution of individual beams using recursive techniques; (3) an alternating-direction iteration method for combining the solution of the individual beams into a coordinated slab solution. All properties and loads can be freely variable from point to point. Concentrated or distributed loads can be handled including transverse loads, in-plane forces and external couples. Elastic restraints are provided by vertical support springs. A computer program which solves the equations implicitly for the deflection patterns has been developed. The method has application to a broad variety of complex plate and slab problems which cannot be solved by any other existing methods. Applications to complex pavement design problems are of particular interest.

Certain two-dimensional problems of stress distribution in wedge-shaped elastic solids under discontinuous load

In this paper we consider the problem of distribution of stress in an infinite wedge of homogeneous elastic isotropic solid under the usual assumptions pertaining to plane strain in classical (infinitesimal) theory of elasticity. The wedge is supposed to occupy the region 0 ≤ ρ ≤ ∞, − α ≤ θ ≤ α (in plane polar coordinates) where the pole is taken on the apex of the wedge with the line bisecting the wedge angle as the initial line. We report here the investigations of two types of stress fields: (i) the stress field which is set up by the application of known pressure to inner surfaces of a crack situated on the bisector of the wedge angle, and (ii) the stress field generated by the indentation of the plane faces of the wedge by the rigid punch. The corresponding boundary-value problems are shown to be equivalent to the problem of solving dual integral equations involving inverse Mellin-transforms. Similar equations have been discussed by Srivastav ((l)) in a recent paper. The method of (1) is easily modified to reduce the dual equations to single Fredholm equations of the second kind which are best solved numerically. The boundary-value problems discussed here are of the mixed type and appear to have been considered only recently by Matczynski ((2)) who has investigated a contact problem. He identifies the problem with a Wiener-Hopf integral equation and solves the integral equation approximately using a method due to Koiter ((3)). The method presented here seems to have the advantage that it requires no elaborate tools of analysis which are necessary for resolving the problem of Wiener-Hopf and numerical results may be obtained comparatively easily.

Fundamental Research on Gear Lubrication : 3rd Report, Theoretical Analysis on the Effect of Discontinuous Load, and Correlation between the Gear Test and the Roller test

By investigating the correlation between the gear test and the roller test, the possiblity and the limit of using rollers in the experimental study on gears will be clarified. In this paper, the influence of a discontinuous load upon the lubrication characteristics, which is thought to be one of the causes of the difference between both tests, was theoretically analyzed taking into consideration the squeeze-effect of oil-film, and the transient performance of oil-film was induced. The correlation between both lubrication characteristics of gears and rollers was synthetically investigated referring to the experimental results in the previous reports. If the various factors, having influence upon the difference, are well taken into consideration, both lubrication characteristics show a good coincidence from the average point of view, but the roller test will be not very effective to the investigation on the variation of lubrication characteristics with the movement of mating point.

On the Role of Bending in the Dynamic Response of Thin Shells to Moving Discontinuous Loads

An infinite cylindrical shell symmetrically loaded by a step pressure wave is used to study the importance of bending in a dynamic system with a moving, discontinuous load. The case of an acoustically loaded thin steel shell in water is discussed at length. A parameter study is run to determine the effect on shell behavior of changes in load speed, external damping, and shell thickness. I t is found that bending plays quite different roles in static (or quasi-static) and dynamic systems. In a static system, discontinuities in displacements and stresses appear at points of load discontinuity unless bending is taken into account. Also, the bending stresses themselves are significant in the neighborhood of such points. Similar results hold when a quasi-static system is considered—i.e., when the inertial reaction of the shell is neglected but the load is allowed to move. In the dynamic system, however, membrane theory alone is sufficient to yield a continuous solution. The importance of bending in such a system is closely linked to the speed of the load and the thickness of the shell. I t is shown that, contrary to the impression gained from a static analysis, it is often possible to neglect bending provided the load speed is fairly large (three or four times the acoustic speed of air), and the shell is sufficiently thin (thickness-radius ratio < l / 3 0 ) . V =

Fundamental Research on the Gear Lubrication : 5th Report, The Relation between Roller Test and Gear Test

The experimental study of gear lubrication was carried out with the tests, using rollers or gears, but the relation between the both tests has not been clarified yet. It is the purpose of this study to find out the lubricating characteristics at the any point on gear-tooth surface and to investigate the correlation between the both tests. The fundamental equations are induced for the frictional characteristcs under a discontinuous load. By the application of these results to load variation on the gear-tooth surface, the influence of load variation is derived for the any meshing point. Considering the influence by the difference of the both tests upon the test results accurately, the roller test gives coincidence with gear test on the average lubricating characteristcs.

Fundamental Research on the Gear Lubrication : 4th Report, The Theoretical Analysis on the Influence of Discontinuous Load

Discontinuity of load is one of the characteristic properties in the gear lubrication. In order to investigate the influence of discontinuous load upon the lubricating performance on the gear-tooth surface, the wedge- and squeeze-effects of the lubricating oil-film are theoretically analyzed and the fundamental relations among the parameters indicating the influence of load discontinuity are induced. By means of these relations the estimations under the unsteady state are derived for the pressure distribution, the minimum thickness and the load-carring capacity of the lubricating oil-film. The continual length of the unsteady state caused by discontinuous load is also given. These results may be able to give some good suggestions to the consideration of the lubricating characteristics on the gear-tooth surface.