A compact form for the static Green’s function for symmetric loading of an elastic
sphere is derived. The expression captures the singularity in closed form using
standard functions and quickly convergent series. Applications to problems involving
contact between elastic spheres are discussed. An exact solution for a point load on
a sphere is presented and subsequently generalized for distributed loads.
Examples for constant and Hertzian-type distributed loads are provided,
where the latter is also compared to the Hertz contact theory for identical
spheres. The results show that the form of the loading assumed in Hertz
contact theory is valid for contact angles up to about ten degrees. For larger
angles, the actual displacement is smaller and the contact surface is no longer
flat.