Application and accuracy of shell theory in the analysis of stress and deformations in cylindrical pressure vessels

The presented study focusses on the application of the analytical shell theory to the problems of stresses and deformations in cylindrical pressure vessels. Two standard types of dished ends are investigated, torispherical and ellipsoidal. To solve the problem the membrane theory and edge effect theory is applied. The equations of deformations are formulated to calculate the forces in the shells junction. The orthotropic material model is taken into account. Two known solutions of the homogeneous Reissner– Meissner differential equations are studied. The resolved stress and deformation are compared with the numerical results of the finite element method. The accuracy of the analytical solution is highly dependent on the thickness of the pressure vessel, as well as on the shape of the dished end. According to the results discussed, the solution for the structure with torispherical dished ends is accurate only for exceptionally small thickness, beyond the typical values for industrial pressure vessels. This shortcoming has been proven to be the result of the limitations of the membrane theory, despite the thin-walled nature of the shells studied.