Research of the Stress-Strain State of Conical Shell Under the Action of Local Load Based on the Non-Classical Theory

The version of a refined theory of stress-strain computation of a conical shell under axially symmetric load is considered in the paper. The required displacements of the shell are represented in the form of polynomials in the normal coordinate, made for the middle surface two degrees higher with respect to the Kirchhoff – Love classical theory. Based on the equations of the three-dimensional theory of elasticity and the Lagrange variation principle, the equilibrium equations in displacements and the corresponding boundary conditions are obtained. The solution of laid down boundary value problem is carried out by the successive application of finite-difference and matrix sweep methods. Examples of calculating an isotropic conical shell rigidly restrained at two edges are given using a computer program. A significant contribution of additional transverse normal stresses in the boundary zone to the general stress state of the shell is shown. The influence of size of the local loading band on the stress state of the shell is studied. The results can be used to assess the strength and durability of structural elements in engineering facilities for various purposes.