Spherically isotropic, elastic spheres subject to diametral point load strength test

This paper presents an analytic solution for the stress concentrations within a spherically isotropic\ elastic sphere of radius R subject to diametral point load strength test[ The method of solution uses the displacement potential approach together with the Fourier Legendre expansion for the boundary loads[ For the case of isotropic sphere\ our solution reduces to the solution by Hiramatsu and Oka "0855# and agrees well with the published experimental observations by Frocht and Guernsey "0842#[ A zone of higher tensile stress concentration is developed near the point loads\ and the di}erence between this maximum tensile stress and the uniform tensile stress in the central part of the sphere increases with E:E? "where E and E? are the Young|s moduli governing axial deformations along directions parallel and normal to the planes of isotropyrespectively#\ G?:G "where G and G? are the moduli governing shear deformations in the planes of isotropy and the planes parallel to the radial direction#\ and n :n? "where n and n? are the Poisson|s ratios characterizing transverse reduction in the planes of isotropy under tension in the same plane and under radial tensionrespectively#[ This stress di}erence\ in general\ decreases with the size of loading area and the Poisson|s ratio[