Stresses in a Thick Plate Containing an Eccentric Spherical Cavity under Transverse Bending

Abstract

This paper presents an exact solution for the stresses in an elasic thick plate having an eccentrically located spherical cavity under transverse bending. In the analysis six harmonic stress functions approach is used. The solution is expressed by a combination of the cylindrical and spherical harmonics in infinite integral form and infinite series respectively. The boundary conditions on the surfaces of the plate and the surface of a spherical cavity are well satisfied with the aid of the relations between cylindrical and spherical harmonics. Numerical results are given for the eccentric distance c = 0.25, 0.5 with the ratios of cavity diameter to plate thickness varying 0.05-0.45 and 0.05-0.35 respectively and the stress distributions around a spherical cavity are shown graphically.