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Abstract
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
10 degrees. For larger angles, the actual displacement is smaller and the contact
surface is no longer flat.