Stability problem of a spherical shell under circumferential nonuniformly distributed surface load

A thin-walled spherical shell is fixed and pivoted at the upper edge. The bottom edge is closed by a membrane that is rigid in its plane. The shell is loaded by nonuniformly distributed surface forces that are tangent to the circumferential direction. A problem of the loss of stability of the shell is solved with an energetic method. The change in total energy of the shell during the loss of stability is determined. This requires the forms of the deflection function and the force function to be assumed, according to actual boundary conditions. Coefficient of the force function is determined by solving the comparability condition with the Bubnov-Galerkin method. Stability equation of the shell is formulated as a result of application of the Ritz method to the variation of the total energy. It is an algebraic equation serving for determination of the critical load. The paper ends with a numerical example.