The aim of the work is to perform a comparative analysis of the results of analyzing arbitrarily loaded shells of revolution using finite element method in various formulations, namely, in the formulation of the displacement method and in the mixed formulation. Methods. To obtain the stiffness matrix of a finite element a functional based on the equality of the actual work of external and internal forces was applied. To obtain the deformation matrix in the mixed formulation the functional obtained from the previous one by replacing the actual work of internal forces in it with the difference of the total and additional work was used. Results. In the formulation of the displacement method for an eight-node hexahedral solid finite element, displacements and their first derivatives are taken as the nodal unknowns. Approximation of the displacements of the inner point of the finite element was carried out through the nodal unknowns on the basis of the Hermite polynomials of the third degree. For a finite element in the mixed formulation, displacements and stresses were taken as nodal unknowns. Approximation of the target finite element values through their nodal values in the mixed formulation was carried out on the basis of trilinear functions. It is shown on a test example that a finite element in the mixed formulation improves the accuracy of the strength parameters of the shell of revolution stress-strain state.

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The methods of specifying the middle surface of an elliptical cylinder in curvilinear coordinate systems are described. An algorithm for discretization of an elliptic cylinder by high-precision quadrangular finite elements with a set of nodal variable parameters, which includes components of the displacement vector, as well as their partial derivatives of the first and second orders, is described. Nodal unknowns in global and local coordinate systems are described. Two types of interpolation procedure are presented: vector interpolation of displacement fields, scalar interpolation. Interpolation expressions for the components of the displacement vector and their first and second derivatives are obtained using the vector version of the interpolation procedure.