LAUSR

The results of a study of the stress-strain state of a conical shell of variable thickness based on a non-classical theory are presented. The sought-for displacements of the shell are approximated by polynomials in the normal coordinate to the median surface two degrees higher in relation to the classical theory of the Kirchhoff-Love type. When developing the theory, the three-dimensional equations of the theory of elasticity, as well as Lagrange variational principle are used as the equation of the shell state. As the result of minimizing the specified value of the total energy of the shell, a mathematical model is constructed, which is a system of differential equations of equilibrium in the displacements with variable coefficients and the corresponding boundary conditions. Two cases are considered: the shell is under the action of symmetric and asymmetric loads. Two-dimensional equations are transformed to the system of ordinary differential equations by means of trigonometric sequences as per circumferential coordinate. To solve the formulated boundary value problem, finite difference and matrix sweep methods are applied. The calculations have been made by means of a computer program. After having determined the displacements, shell deformations and tangential stresses are found from geometric and physical equations, transverse stresses - from the equilibrium equations of the three-dimensional theory of elasticity. As an example, a conical shell rigidly restrained at the two edges, with asymmetrically varying thickness is considered. Compared are the results of the VAT calculations obtained as per the improved and classical theories. The significant contribution of additional stresses in the boundary zone to the total stress state of the shell is shown. The received results can be used in the strength and durability calculations and tests of machine-building facilities of various purposes.