STRESS CONCENTRATION DUE TO A HEMISPHERICAL PIT AT A FREE SURFACE OF A THICK PLATE UNDER ALL-AROUND TENSION.

Abstract

A three dimensional solution is presented for the stresses around a hemispherical pit at a free surface of an elastic plate. At infinity the plate is subjected to all-around tension parallel to the free surface. In the analysis, the method of Boussinesq's two harmonic functions approach is used and these functions are expressed in simple forms of cylindrical and spherical harmonics. The boundary conditions both on the upper surface and at infinity are satisfied automatically, while the remaining boundary conditions on the lower surface and on the surface of the pit are satisfied with aid of the Hankel transform and relations between the cylindrical harmonics and the spherical ones. Numerical calculations are carried out for four different values of radius of the hemispherical pit.