On the numerical solution of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity

In the present report, we investigate the formulation, for the numerical evaluation of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity. Some simple formulas are given for the numerical solution of the general case of the multidimensional singular integrals. Moreover a numerical technique is also established for the numerical solution of some special cases of the multidimensional singular integrals like the two - and three - dimensional singular integrals. An application is given to the determination of the fracture behaviour of a thick, hollow circular cylinder of viscoelastic material restrained by an enclosing thin elastic ring and subjected to a uniform pressure.

Buckling of an Elastic Elliptical Ring Inside a Rigid Boundary

The buckling of a thin, elastic ring confined in an elliptical hole whose circumference is smaller than that of the ring is studied. The effect of post-buckling slippage of the ring along the boundary with a corresponding curvature change is included. Buckling configurations with no friction that are (a) symmetric to one axis, and (b) symmetric to both axes, and (c) buckling configurations with no-slip are presented. Buckling with a strain energy consideration added as a criterion and buckling merely from compatibility alone are discussed. Results include curves for buckling loads of different ellipticities for different radius-to-thickness ratios.

Analysis of a Planet Bearing in a Gear Transmission System

This paper develops a general theory whereby the effects of the elastic distortions of a planet bearing outer ring due to gear loads and inertial forces on the bearing load distribution and fatigue life can be considered. The analysis makes use of a recently developed solution for a thin elastic ring under an arbitrary system of loads. A numerical example for a planet gear roller bearing under heavy gear loads and operating at a high speed is presented.

Analysis of a Thin Elastic Ring Under Arbitrary Loading

This paper presents a general solution for a thin ring under a self-equilibrating loading system comprising any combination of radial, tangential, and moment loads. The formulations are applicable to concentrated loads as well as to distributed load functions. Closed-form solutions are obtained for each case for engineering applications. Comparisons with recent published results for some special cases are demonstrated in some of the sample problems.