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

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Keh-Chih Hwang ◽  
Zhi-Hai Xiang
Keyword(s):  
Internal Pressure ◽  
Design Method ◽  
Cylindrical Shells ◽  
Theoretical Method ◽  
Combined Loads ◽  
Stress Components ◽  
Bending Stresses ◽  
External Forces ◽  
External Loads ◽  
Theoretical Stress

A universal design method for pressurized cylindrical shells with attached nozzles subjected to external forces (moments) and internal pressure are presented, based on theoretical stress analysis. The applicable ranges of the presented design methods are extended to ρ0=d/D≤0.9 and λ=d/(DT)1/2≤12. As a first step of design, the required reinforcement thicknesses, both of the main shell and nozzle due to internal pressure, can be determined by the presented theoretical solutions. When the junction is subjected to external nozzle loads, the next step is to determine the absolute values of dimensionless longitudinal and circumferential, normal and shear, membrane and bending stresses in the shell at the junction subjected to internal pressure, and six external nozzle load components by reading out from a number of sets of curves calculated by the present theoretical method. Then the stress components at eight examination points are calculated and superimposed for the combined loads. Finally, the membrane and primary plus secondary stress intensities can be calculated, respectively, to meet the design criteria.

A Universal Design Method Based on Analysis for Cylindrical Shells With Nozzles Due to Internal Pressure, External Forces and Moments: Part II

2009 ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Keh-Chih Hwang ◽  
Zhi-Hai Xiang
Keyword(s):  
Internal Pressure ◽  
Universal Design ◽  
Design Method ◽  
Cylindrical Shells ◽  
Theoretical Method ◽  
Combined Loads ◽  
Stress Components ◽  
Bending Stresses ◽  
External Forces ◽  
Theoretical Stress

A universal design method for pressurized cylindrical shells with attached nozzles subjected to external forces (moments) and internal pressure are presented based on theoretical stress analysis. The applicable ranges of the presented design methods are extended to d/D≤0.9 and λ=d/(DT)1/2≤12. As a first step of design the required reinforcement thicknesses both of main shell and nozzle due to internal pressure can be determined by the presented theoretical solutions. When the junctions are subjected to external nozzle loads, the next step is to determine the absolute values of dimensionless longitudinal and circumferential, normal and shear, membrane and bending stresses in the main shell at the junction subjected to internal pressure and six external nozzle load components by reading out from a number of sets of curves calculated by the present theoretical method. Then the stress components at eight examination points are calculated and superposed for the combined loads. Finally the membrane and primary plus secondary stress intensities can be calculated, respectively, to meet the design criteria.

A Universal Design Method Based on Analysis for Cylindrical Shells With Nozzles Due to Internal Pressure, External Forces and Moments: Part I

2009 ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Keh-Chih Hwang ◽  
Zhi-Hai Xiang
Keyword(s):  
Internal Pressure ◽  
Design Method ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
External Branch ◽  
Complex Boundary ◽  
Stress Concentration Factors ◽  
Accuracy Of Results ◽  
External Forces ◽  
Complex Valued

An improved version is presented for analytical solution developed by the authors and the applicable ranges of the theoretical solutions for two normally intersecting cylindrical shells are successfully extended from d/D≤0.8 and λ=d/(DT)1/2≤8 up to d/D ≤0.9 and λ≤12. The thin shell theoretical solution is obtained by solving a complex boundary value problem for a pair of 4-th order complex-valued partial differential equations (exact Morley equations) 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 presented theoretical stress concentration factors due to pressure are in agreement with the test results in literatures. The presented theoretical results are in good agreement with those by 3-D finite element method for all the seven load cases, i.e., internal pressure and six external branch pipe load components involving axial tension, two kinds of transverse shear forces, longitudinal and circumferential bending and torsion moments.

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

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Keh-Chih Hwang ◽  
Zhi-Hai Xiang
Keyword(s):  
Analytical Solution ◽  
Internal Pressure ◽  
Stress Analysis ◽  
Pressure Vessel ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
Theoretical Solution ◽  
External Branch ◽  
Complex Valued ◽  
External Loads

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≤0.8 and λ=d/(DT)1/2≤8 to d/D≤0.9 and λ≤12. 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.

A Stress Analysis Method for Cylindrical Shells With Nozzles Subjected to Internal Pressure, External Forces and Moments

2006 ◽  
Author(s):  
Ming-De Xue ◽  
Qing-Hai Du ◽  
Dong-Feng Li ◽  
Keh-Chih Hwang
Keyword(s):  
Internal Pressure ◽  
Stress Analysis ◽  
Thin Shell ◽  
Cylindrical Shells ◽  
Branch Pipe ◽  
Three Dimensional ◽  
Theoretical Solution ◽  
Analysis Method ◽  
External Forces ◽  
Three Dimensional Finite Element

An identical stress analysis method based on the thin shell theory is carried out for cylindrical shells with normally intersecting nozzles subjected to internal pressure and six kinds of external branch pipe loads involving axial tension, two kinds of transverse shear forces, longitudinal and circumferential bending and torsion moments. The thin shell theoretical solution is obtained based on the Morley equation instead of the Donnell shallow shell equation. The accurate continuity conditions at the intersecting curve, which is a complicated space curve, are adopted. The presented results are verified by three-dimensional finite element method (FEM). The theoretical solution can be applied to d/D ≤ 0.8, λ = d/DT ≤ 12 and d/D ≤ t/T ≤ 2 successfully. The solutions are in good agreement with WRC Bulletin 297 when diameter ratio is small. In the paper some typical design curves calculated by the theoretical solutions are presented and their applicable ranges are greatly expanded in comparison with current design methods.

Strength of a Pipe Mitred Bend

1970 ◽  
Vol 92 (4) ◽  
pp. 767-773 ◽  
Author(s):  
Jaroslaw Sobieszczanski
Keyword(s):  
Internal Pressure ◽  
Maximum Stress ◽  
Cylindrical Shells ◽  
Beam Theory ◽  
The Self ◽  
Design Work ◽  
Stress And Deformation

Single and multiple mitred bends are analyzed for stress and deformation due to inplane bending and internal pressure. Theory of cylindrical shells is used as a tool of analysis. Results show maximum stress at the elbow increased up to more than 400 percent of the stress predicted by elementary beam theory. Influence of the elbow on the self-compensation of the heated pipeline is discussed and the local reinforcements proposed. Solutions are presented as graphs which may be directly applied in design work.

Buckling Design of Axially Compressed Cylindrical Shells Based on Energy Barrier Approach

2021 ◽  
pp. 2150165
Author(s):  
Haigui Fan ◽  
Wenguang Gu ◽  
Longhua Li ◽  
Peiqi Liu ◽  
Dapeng Hu
Keyword(s):  
Experimental Data ◽  
Energy Barrier ◽  
Thin Shell ◽  
Design Method ◽  
Lightweight Design ◽  
Cylindrical Shells ◽  
Design Criterion ◽  
The Other ◽  
Shell Structures ◽  
Buckling Loads

Buckling design of axially compressed cylindrical shells is still a challenging subject considering the high imperfection-sensitive characteristic in this kind of structure. With the development of various design methods, the energy barrier concept dealing with buckling of imperfection-sensitive cylindrical shells exhibits a promising prospect in recent years. In this study, buckling design of imperfection-sensitive cylindrical shells under axial compression based on the energy barrier approach is systematically investigated. The methodology about buckling design based on the energy barrier approach is described in detail first taking advantage of the cylindrical shells whose buckling loads have been extensively tested. Then, validation and discussion about this buckling design method have been carried out by the numerical and experimental analyses on the cylindrical shells with different geometrical and boundary imperfections. Results in this study together with the available experimental data have verified the reliability and advantage of the buckling design method based on energy barrier approach. A design criterion based on the energy barrier approach is therefore established and compared with the other criteria. Results indicate that buckling design based on energy barrier approach can be used as an efficient way in the lightweight design of thin-shell structures.

scholarly journals Calculation of the goffered multilayered composite cylindrical shells by using the finite element method

1999 ◽  
Vol 21 (2) ◽  
pp. 116-128
Author(s):  
Pham Thi Toan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
The Finite Element Method ◽  
Multilayered Composite ◽  
Internal Forces ◽  
External Loads ◽  
Element Method ◽  
Composite Cylindrical Shells

In the present paper, the goffered multilayered composite cylindrical shells is directly calculated by finite element method. Numerical results on displacements, internal forces and moments are obtained for various kinds of external loads and different boundary conditions.

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