The Stress State in the Boundary Region of a Conical Shell according to a Refined Theory

In this article, on the basis of a refined theory, we study the stress state of a conical shell of the "boundary layer" type. In comparison with the classical theory, the sought displacements of the shell are approximated by polynomials along the coordinate normal to the median surface with a degree two units higher. Based on the equations of the three-dimensional elasticity theory and the Lagrange variational principle, a system of differential equations of equilibrium in displacements with variable coefficients is obtained. The solution of the formulated boundary value problem is carried out by using the methods of finite differences and matrix sweep. The results can be used when assessing the strength and durability of shell structures.