The revised method for calculating the stability of shells of rotation in the axisymmetric case

The problems of stability of spherical and toroidal shell in axially symmetric case are considered. For the problem solution variational approach is used. The elastic energy is determined by changing the coefficients of the first and second quadratic forms with the deformation of the shell. To determine the work of the external forces of normal pressure the accurate thermodynamic formula in accordance with the theorem of Euler - Bernoulli (the product of the pressure on the volume) is used.The position of the equilibrium total energy equal to the elastic energy minus the work of external forces, takes a minimum value. Total energy, equal to the elastic energy minus the work of external forces, takes a minimum value being in the position of the equilibrium. For finite-dimensional approximation of displacements interpolation cubic splines are applied. The resulting optimization problem is solved by the method of the conjugate gradient. Dependence of the maximum displacement of the outer shell on the normal pressure is built and the value of the critical force when the movement starts to rise sharply is determined. The results are compared with experimental data.