Page 85 - DP-2-2

Design+

ARTICLE
Closed-form solution for pressurized obround

shells

Yao Jin*
Propak Systems Ltd., Airdrie, Alberta, Canada

Abstract

Pressurized shells with an obround cross-section are common components in the
petrochemical industry. However, the analysis and design of obround components
have been challenging due to their complex shapes. Empirical and numerical
methods are commonly used for their analysis and design. In this study, the obround
shape is divided into curved and straight segments to simplify the geometry and
boundary conditions within each segment. The theoretical analysis of each segment
was performed separately. By combining existing closed-form solutions, a theoretical
solution was developed that partially satisfies the deformation at the junction of
segments. This combined solution can accurately calculate stress and displacement
in obround shells under internal pressure, representing a closed-form theoretical
solution for pressurized obround shells. When the length of the straight segments
approaches zero, the obround shell becomes cylinder, the proposed solution returns
to the solution of cylindrical shell or Lame’s solution. The solution provides a new
theoretical analysis approach that is simpler, more efficient, and more accurate
*Corresponding author: than empirical methods or numerical analyses. It is expected to change the current
Yao Jin
(mtjinyao1@hotmail.com) reliance on empirical formulas and numerical simulations for analyzing obround
components and to promote the development of a new design methodology for
Citation: Jin Y. Closed- obround components.
form solution for pressurized
obround shells. Design+
2025;2(2):025060010.
doi: 10.36922/DP025060010 Keywords: Obround; Pressure vessel; Non-circular; Stress analysis; Theoretical analysis;
Closed-form solution
Received: February 8, 2025
Revised: March 13, 2025
Accepted: April 17, 2025
1. Introduction
Published online: April 30, 2025
Spheres and cylinders are optimal shapes for internal pressure vessels due to their circular
Copyright: © 2025 Author(s).
This is an Open-Access article cross-sections, which allow for smooth and relatively uniform stress and displacement
distributed under the terms distributions under internal pressure. However, in certain applications, these shapes are
of the Creative Commons not suitable, and an obround cross-section may be a more appropriate option.
AttributionNoncommercial License,
permitting all non-commercial use, Theoretical analysis of obround shapes is challenging due to their complex and
distribution, and reproduction in any discontinuous geometry. At present, no theoretical solution exists. The analysis and
medium, provided the original work
is properly cited. design of obround components rely on empirical and/or numerical methods. Designing
an obround enclosure often involves a complex iterative design process. 1,2
Publisher’s Note: AccScience
Publishing remains neutral with One of the most commonly used empirical methods for analyzing and designing
regard to jurisdictional claims in
published maps and institutional members with non-circular cross-sections is based on the concept of an “equivalent
3
affiliations. circular section,” introduced by Blach. In this method, a non-circular cross-section is

Volume 2 Issue 2 (2025) 1 doi: 10.36922/DP025060010