An Analytical Solution to the Problem of Thin-walled Pressure Vessel with Circular-arc Cross-section

Design procedure of pressure vessels is very important due to their vast applications in many industries. This procedure is mainly based on determining the stress and strain distribution, which is resulted from the internal pressure. In this paper a thin-walled pressure vessel of circular-arc cross-section is analytically studied. The vessel is a surface of revolution generated by rotating a circular arc about an axis that neither intersects the arc nor necessarily passes through the arc center. Both convex and concave vessels with open- and closed-end conditions are considered. The equilibrium equations for a proper element of the vessel surface are derived and solved analytically. Assuming small deformation and elastic behavior for the vessel, the integral constant is determined based on the end boundary conditions of the vessel. Since this type of pressure vessel was not studied in the previous literature, the results of present model are compared with similar ABAQUS Finite Element (FE) simulation. A very close agreement was observed. This evidently implies the validity of the presented model.