Three-dimensional Stress Concentration around a Spherical Cavity in a Thick Plate under Uniaxial Tension

Abstract

This paper contains an exact solution for the stresses arising in an infinite elastic plate having a symmetrically located spherical cavity and subjected to uniaxial tension. The problem of stress analysis in a plate with a spherical cavity was investigated by several authors. But their solutions were all for the problems of plates subjected to the axisymmetrical loads. The present paper is aimed to present for the asymmetrical cavity problem of the plate. The solution obtained is in integral form and infinite series form, and is deduced with the aid of six harmonic stress functions. Numerical results are included for the stresses on the surface of a spherical cavity and along the z-axis, corresponding to several values of a cavity. The results obtained are compared with the axisymmetric solution.