An improved version of the analytical solutions by Xue, Hwang and co-workers (1991, “Some Results on Analytical Solution of Cylindrical Shells With Large Opening,” ASME J. Pressure Vessel Technol., 113, 297–307; 1991, “The Stress Analysis of Cylindrical Shells With Rigid Inclusions Having a Large Ratio of Radii,” SMiRT 11 Transactions F, F05/2, 85–90; 1995, “The Thin Theoretical Solution for Cylindrical Shells With Large Openings,” Acta Mech. Sin., 27(4), pp. 482–488; 1995, “Stresses at the Intersection of Two Cylindrical Shells,” Nucl. Eng. Des., 154, 231–238; 1996, “A Reinforcement Design Method Based on Analysis of Large Openings in Cylindrical Pressure Vessels,” ASME J. Pressure Vessel Technol., 118, 502–506; 1999, “Analytical Solution for Cylindrical Thin Shells With Normally Intersecting Nozzles Due to External Moments on the Ends of Shells,” Sci. China, Ser. A: Math., Phys., Astron., 42(3), 293–304; 2000, “Stress Analysis of Cylindrical Shells With Nozzles Due to External Run Pipe Moments,” J. Strain Anal. Eng. Des., 35, 159–170; 2004, “Analytical Solution of Two Intersecting Cylindrical Shells Subjected to Transverse Moment on Nozzle,” Int. J. Solids Struct., 41(24–25), 6949–6962; 2005, “A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments,” ASME J. Pressure Vessel Technol., 127(4), 357–368; 2005, “Theoretical Stress Analysis of Two Intersecting Cylindrical Shells Subjected to External Loads Transmitted Through Branch Pipes,” Int. J. Solids Struct., 42, 3299–3319) for two normally intersecting cylindrical shells is presented, and the applicable ranges of the theoretical solutions are successfully extended from $d/D\u22640.8$ and $\lambda =d/(DT)1/2\u22648$ to $d/D\u22640.9$ and $\lambda \u226412$. The thin shell theoretical solution is obtained by solving a complex boundary value problem for a pair of fourth-order complex-valued partial differential equations (exact Morley equations (Morley, 1959, “An Improvement on Donnell’s Approximation for Thin Walled Circular Cylinders,” Q. J. Mech. Appl. Math. 12, 89–91; Simmonds, 1966, “A Set of Simple, Accurate Equations for Circular Cylindrical Elastic Shells,” Int. J. Solids Struct., 2, 525–541)) for the shell and the nozzle. The accuracy of results is improved by some additional terms to the expressions for resultant forces and moments in terms of complex-valued displacement-stress function. The theoretical stress concentration factors due to internal pressure obtained by the improved expressions are in agreement with previously published test results. The theoretical results discussed and presented herein are in sufficient agreement with those obtained from three dimensional finite element analyses for all the seven load cases, i.e., internal pressure and six external branch pipe load components involving three orthogonal forces and the respective three orthogonal moments.

Skip Nav Destination

Article navigation

June 2010

Research Papers

# An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part I: Theoretical Foundation

Ming-De Xue,

Ming-De Xue

Department of Engineering Mechanics, AML,

Tsinghua University

, Beijing 100084, P.R. China
Search for other works by this author on:

Qing-Hai Du,

Qing-Hai Du

China Ship Scientific Research Center

, Wuxi, Jiangsu 214082, P.R. China
Search for other works by this author on:

Keh-Chih Hwang,

Keh-Chih Hwang

Department of Engineering Mechanics, AML,

Tsinghua University

, Beijing 100084, P.R. China
Search for other works by this author on:

Zhi-Hai Xiang

Zhi-Hai Xiang

Department of Engineering Mechanics, AML,

Tsinghua University

, Beijing 100084, P.R. China
Search for other works by this author on:

Ming-De Xue

Department of Engineering Mechanics, AML,

Tsinghua University

, Beijing 100084, P.R. China
Qing-Hai Du

China Ship Scientific Research Center

, Wuxi, Jiangsu 214082, P.R. China
Keh-Chih Hwang

Department of Engineering Mechanics, AML,

Tsinghua University

, Beijing 100084, P.R. China
Zhi-Hai Xiang

Department of Engineering Mechanics, AML,

Tsinghua University

, Beijing 100084, P.R. China*J. Pressure Vessel Technol*. Jun 2010, 132(3): 031206 (9 pages)

**Published Online:**May 19, 2010

Article history

Received:

June 3, 2009

Revised:

January 17, 2010

Online:

May 19, 2010

Published:

May 19, 2010

Connected Content

A companion article has been published:
An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part II: Design Method

Citation

Xue, M., Du, Q., Hwang, K., and Xiang, Z. (May 19, 2010). "An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part I: Theoretical Foundation." ASME. *J. Pressure Vessel Technol*. June 2010; 132(3): 031206. https://doi.org/10.1115/1.4001199

Download citation file:

### Get Email Alerts

### Cited By

Investigations of In-Plane Fluidelastic Instability in a Multispan U-Bend Tube Array—Part II: Tests in Two-Phase Flow

J. Pressure Vessel Technol (April 2023)

Investigations of In-Plane Fluidelastic Instability in a Multispan U-Bend Tube Array—Part I: Tests in Air Flow

J. Pressure Vessel Technol (April 2023)

Research on the Buckling Load of Clamped Spherical Caps Under External Pressure: Analyzed by the Fourier Series Model With Initial Geometric Imperfections

J. Pressure Vessel Technol (April 2023)

### Related Articles

An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part II: Design Method

J. Pressure Vessel Technol (June,2010)

Theoretical Stress Analysis of Intersecting Cylindrical Shells Subjected to External Forces on Nozzle

J. Pressure Vessel Technol (February,2006)

A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments

J. Pressure Vessel Technol (November,2005)

Leak Before Break Analysis of Steam Generator Shell Nozzle Junction for Sodium Cooled Fast Breeder Reactor

J. Pressure Vessel Technol (April,2012)

### Related Proceedings Papers

### Related Chapters

Openings

Guidebook for the Design of ASME Section VIII Pressure Vessels

Openings

Guidebook for the Design of ASME Section VIII Pressure Vessels, Third Edition

Development of Nuclear Boiler and Pressure Vessels in Taiwan

Companion Guide to the ASME Boiler and Pressure Vessel Code, Volume 3, Third Edition