Tension of an infinite solid containing an elastic spherical inclusion (Mixed boundary-value problem in consideration of interference-fit state)

Abstract

This report deals with the influence of the interference between an elastic sphere and a spherical cavity on the stress distribution and displacement around cavity, which has simply a smooth elastic sphere, in an elastic solid under tension at infinity. The contact stress between the sphere and the cavity is expressed with series of Legendre functions, and the stress and displacement are numerically analyzed by point matching method. Using the numerical results for the elastic solid, the effects of interference and loads are shown on the stresses around the spherical cavity boundary. The main results are as follows: (1) The contact region and stress distribution of the elastic solid are independent of the magnitude of load, when diameter of sphere and spherical cavity are initially the same. (2) When diameters of them are not same, the contact region and stress distribution of the elastic solid vary with a change in magnitude of load.

Keywords

• elasticity
• mixed boundary-value problem
• contact stress
• stress concentration
• spherical inclusion
• infinite elastic solid
• interference