Equilibrium problems of spherically isotropic bodies

In this paper the displacements and body-forces are resolved, respectively, and the 3-dimensional equilibrium problems of spherically isotropic bodies with body-forces are transferred into a two-order differential equation and a four-order differential equation. Based on the series expansion technique and properties of spherical functions, the series solutions are obtained for the corresponding homogeneous equations, which can be adapted to solve equilibrium problems oj whole spheres or spherical shells. The special solution for a revolving sphere is also given.