Energetic method of solving the stability problem of a semi-spherical shell loaded with torque

A thin-walled spherical shell is pivoted at both ends. The upper edge of the shell, loaded with a torque, may rotate around the shell axis. The problem of the loss of stability of the shell is solved with an energetic method. The change in the total energy of the shell while losing stability is determined. This requires the forms of the deflection and force functions to be assumed, according to actual boundary conditions. Coefficients of the force function are determined from the solution to the inseparability equation with the Bubnov-Galerkin method. The stability equation of the shell is formulated as a result of application of the Ritz method to the total energy variation. It is an algebraic equation serving for determination of the critical load. It is equal to the minimal value of the load. The work ends with a numerical example.