Calculation of the Stress State of a Three-Layer Spherical Shell Based on Exact, Asymptotic Solutions and Solutions According to Some Applied Theories

The stress state of a three-layer spherical shell was calculated on the basis of exact, asymptotic solutions and solutions according to some applied theories. As applied theories, we took theories, based on the theory of a single normal for the entire package on the theory of a broken element, and on the theory that considers transverse shear. A comparative analysis of the stresses, obtained from all five solutions, is given. The asymptotic solution, constructed in the work, based on three-dimensional equations, indicates methods for constructing refined applied theories for inhomogeneous thicknesses, including layered plates and shells.