Analytical solution for stresses in the spherical shell of a thin-wall composite multi-layer vessel under internal pressure by using the classical theory of shells

Obtaining stress values in spherical shell of a thin-walled composite multi-layer vessel in a completely analytical way and independent of numerical methods in solving the equations is a subject that has not been investigated so far. In this article, using a fully analytical solution based on classical shell theory, the stress values in each layer of the spherical shell are obtained. In this solution method, by using equilibrium equations, Hooke's law, strain-displacement and curvature-displacement relations, the governing equations of general composite shells of revolution are extracted and then the governing equations of a symmetric spherical shell are obtained. In the following, using displacement and rotation consistency equations, forces and stresses at the intersection of the spherical and cylindrical composite shell are calculated, and then the longitudinal and circumferential stresses due to internal pressure are extracted in each layer. Finally, the results are compared with the results of the finite element numerical solution and it is shown that the stress values obtained from the analytical results are in good agreement with the results of the numerical solution and it is possible to use the results of this analytical solution to make optimally designed composite vessels.