Thermal stresses in an elastic sphere containing conical cuts

An axisymmetric thermoelastic problem for a sphere with conical cuts in the poles under the action of a quasi-stationary temperature field depending on the meridional angle and on the sphere radius is solved by a method based on the Castigliano variational principle. Orthonormalized systems of polynomials are used as the coordinate functions. Results of numerical calculations of the stress state of a spherical solid are presented.