Theoretical Solution of Square Shell Under Internal Pressure

Abstract Pressurized enclosures with square cross sections are common components in the petrochemical industries. Since no theoretical solutions are available, analysis and design of such components mainly rely on empirical or numerical analysis methods. In engineering practice, determination of shell wall thickness requires complex iterations. In this study, the square shape is divided into curved and straight segments to simplify the geometry and boundary conditions. With corresponding boundary conditions, theoretical analysis of each segment was performed separately. By combining the existing closed-form solutions, a theoretical solution that partially satisfies the deformation coordination at the junction of curved and straight segments is obtained. The proposed combined solution accurately describes stress and displacement distributions of the square shells under internal pressure. Considering the uniqueness of the elastic solution, this solution is the closed-form theoretical solution for pressurized square shells. The determination of the minimum required thickness of the square shells becomes possible. After the introduction of the concept of virtual square, the application of the solution is extended to the analysis and design of welded squares. The solution provides a new theoretical analysis method. It is simpler, more efficient, and more accurate than empirical methods and numerical analysis. It is expected to change the current situation of square component analysis relying on empirical formulas and numerical analysis and develop a new square component design method.