Nowadays there are various calculation methods for solving a wide range of problems in construction, hydrodynamics, thermal conductivity, aerospace research and many other areas of industry. Analytical methods that make up one class for solving problems, and numerical calculation methods that make up another class, including those implemented in computing complexes, are used for the design and construction of various thin-walled structures such as shells. Due to the fact that thin-walled spatial structures in the form of various shells are widely used in many areas of human activity it is useful to understand and know the capabilities of different calculation methods. Research works on the study of the stress-strain state of the torse shell of equal slope with an ellipse at the base are not widely available at the moment. For the first time the derivation of the differential equations of equilibrium of momentless theory of shells to determine the normal force Nu from the action of uniformly distributed load tangentially directed along rectilinear generatrixes to the middle surface of the torse of equal slope with a directrix ellipse is presented in this article. The parameters of the stress state of the studied torse are also obtained by the finite element method and the variational-difference method. The SCAD software based on the finite element method and the program SHELLVRM written on the basis of the variational-difference method are used. The numerical results of the parameters of the stress state of the studied torse are analyzed, and the advantages and disadvantages of the analytical method and two numerical calculation methods are determined.

In a paper, surfaces, recommended for forming hull shapes of river and see ships, are supposed to use in architecture and building construction. These surfaces contain the given main frame from three plane curves in the form of superellipses. The presence of three overall dimensions and six arbitrary exponents in explicit and parametric equations of presented surfaces gives an opportunity to have large quantity of diverse forms of these surfaces, having only three equations. Designers must choose the most optimal surface taking into account architectural demands and strength conditions. In a paper, it is shown and illustrated the principles of geometric modeling of middle surfaces of thin shells of the offered type and an opportunity of their static analysis with the help of FEM is presented.

The author presents the results of a study of the geometry and stress-strain state of a surface with a frame of three flat curves in coordinate planes, which have found application today mainly in the shipbuilding industry. The purpose of the work is to identify from the point of view of the stress-strain state from the action of a constant uniformly distributed load the most optimal shell of a diagonal transfer of a velaroidal type with the same main frame of three superellipses. The static calculation was performed using the SCAD program based on the finite element method, designed to perform strength calculations of various types and purposes of structures. The influence of parametric equations for defining a surface depending on the generative family of the same type of cross sections on the distribution pattern of normal stresses and bending moments is shown. The results obtained can help architects and designers with choosing the shape of shells for new projects.

Works on the study of the stress-strain state of the shell of an equal slope with an ellipse at the base have not been widely performed. The present paper is a part of a series of articles on the analysis of the geometry and stress state of torses of an equal slope with a directrix ellipse by various methods under different loads and support conditions. The derivation of the differential equations of equilibrium of the momentless theory of shells for determining internal forces in the torse with a directrix ellipse under the action of internal pressure is presented. The analytical results are compared with results obtained by the finite element method (FEM) and the variational difference method (VDM). The advantages and disadvantages of three calculation methods are determined, and it is established that VDM results are more accurate compared to FEM, but FEM-based software is a more powerful tool to perform the structural analysis.

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