Bending of an elastic slab having a spherical cavity

This paper presents the three-dimensional analysis of the stress distribution arising in an isotropic infinite slab with a symmetrically located spherical cavity under a bending moment. To satisfy both boundary conditions on the surface of slab and the surface of the cavity, harmonic functions in rectangular and spherical coordinates are used and double Fourier transform is applied. The problem is reduced to the solution of an infinite set of linear equations which is suitable for numerical solution. Finally some numerical examples are given for various values of the radius of the cavity.