Airy's stress Solution for Isotropic Rings with Eccentric Hole Subjected to Pressure

摘要

Elasticity solution is obtained for stresses in rings with eccentric holes in bipolar coordinate system. The ring is subjected to internal/external pressure at inner and outer boundaries. Materials of the cylinder is assumed to be isotropic and homogeneous. Symmetrical deformations are included in the analysis, yet it is necessary to calculate stresses with various parameters such as angle between the foci and logarithmic ratio of the foci, both defines the coordinates of the bipolar system appeared in the final formulations. With the help of Airy's stress function approach in bipolar coordinate system, the chosen function satisfies the bi harmonic equations in bipolar coordinate system. The results obtained in this study shows the greater effect of eccentricity on the stresses in bipolar coordinates σβ and σα, the analogous stresses in polar coordinates as radial and hoop stresses for cylinders and rings with concentric holes. Along the boundaries, the stresses σβ coincides with the external applied pressure on the boundaries, shows the valid results in agreement with the formulations.