Buckling of Imperfect, Axisymmetric, Homogeneous Shells of Variable Thickness: Perturbation Solution

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Dennis K. Williams ◽  
James R. Williams ◽  
Yogeshwar Hari
Keyword(s):  
Cylindrical Shell ◽  
Variable Thickness ◽  
Large Diameter ◽  
Compressive Load ◽  
Thin Wall ◽  
Shells Of Revolution ◽  
Equilibrium Equations ◽  
Asme Code ◽  
Section Viii ◽  
Ultimate Objective

This paper presents the first of a series of solutions to the buckling of imperfect cylindrical shells subjected to an axial compressive load. The initial problem is the case of a homogeneous cylindrical shell of variable thickness that is of an axisymmetric nature. The equilibrium equations as first introduced by Donnell over 70 years ago are thoroughly presented as basis for a solution employing perturbation methods. The ultimate objective of these calculations is to achieve a quantitative assessment of the critical buckling load considering the small axisymmetric deviations from the nominal shell wall thickness. Clearly in practice, large diameter thin wall shells of revolution that form stacks (as found in flue gas desulphurization absorber assemblies) are never fabricated with constant diameters and thicknesses over the entire length of the assembly. As such, ASME Boiler and Pressure Vessel Code Section VIII shell thickness tolerances as supplemented by ASME Code Case 2286-1 are reviewed and addressed in comparison to the resulting solutions with respect to the critical buckling loads. The method and results described herein are in stark contrast to the “knockdown factor” approach currently utilized in ASME Code Case 2286-1. Recommendations for further study of the imperfect cylindrical shell are also outlined in an effort to improve on the current rules regarding column buckling of large diameter shells designed in accordance with ASME Section VIII, Divisions 1 and 2 and ASME STS-1 in combination with the suggestions contained within Code Case 2286-1.

scholarly journals Buckling of Imperfect, Axisymmetric, Homogeneous Shells of Variable Thickness: Perturbation Solution

2005 ◽  
Author(s):  
Dennis Williams
Keyword(s):  
Cylindrical Shell ◽  
Variable Thickness ◽  
Large Diameter ◽  
Compressive Load ◽  
Thin Wall ◽  
Shells Of Revolution ◽  
Equilibrium Equations ◽  
Asme Code ◽  
Current Design ◽  
Section Viii

This paper presents the first of a series of solutions to the buckling of imperfect cylindrical shells subjected to an axial compressive load. In particular, the initial problem reviewed is the case of a homogeneous cylindrical shell of variable thickness that is of an axisymmetric nature. The equilibrium equations as first introduced by Donnell over seventy years ago are thoroughly presented as a basis for embarking upon a solution that makes use of perturbation methods. The ultimate objective of these calculations is to achieve a quantitative assessment of the critical buckling load considering the small axisymmetric deviations from the nominal shell wall thickness. Clearly in practice, large diameter, thin wall shells of revolution that form stacks (as found in flue gas desulphurization absorber assemblies) are never fabricated with constant diameters and thicknesses over the entire length of the assembly. As such, ASME Boiler and Pressure Vessel Code Section VIII fabrication tolerances as supplemented by ASME Code Case 2286-1 are reviewed and addressed in light of the findings of the current study and resulting solutions with respect to the critical buckling loads. The method and results described herein are in stark contrast to the “knockdown factor” approach currently utilized in ASME Code Case 2286-1. Recommendations for further study of the imperfect cylindrical shell are also outlined in an effort to improve on the current design rules regarding column buckling of large diameter shells designed in accordance with ASME Section VIII, Divisions 1 and 2; and ASME STS-1 in combination with the suggestions contained within Code Case 2286-1.

Buckling of Axisymmetric Cylindrical Shells of Variable Thickness: Finite Difference Solution

2007 ◽  
Author(s):  
Gurinder Singh Brar ◽  
Yogeshwar Hari ◽  
Dennis K. Williams
Keyword(s):  
Cylindrical Shell ◽  
Finite Difference ◽  
Variable Thickness ◽  
Cylindrical Shells ◽  
Finite Difference Methods ◽  
Large Diameter ◽  
Buckling Load ◽  
Thin Wall ◽  
Shells Of Revolution ◽  
Equilibrium Equations

This paper presents the third of a series of solutions to the buckling of imperfect cylindrical shells subjected to an axial compressive load. In particular, the initial problem reviewed is the case of a homogeneous cylindrical shell of variable thickness that is of an axisymmetric nature. The equilibrium equations as first introduced by Donnell over seventy years ago are discussed and reviewed in establishing a basis for embarking upon a solution that utilizes finite difference methods to solve the resulting equilibrium and compatibility equations. The ultimate objective of these calculations is to achieve a quantitative assessment of the critical buckling load considering the small axisymmetric deviations from the nominal cylindrical shell wall thickness. Clearly in practice, large diameter, thin wall shells of revolution that form stacks are never fabricated with constant diameters and thicknesses over the entire length of the assembly. The method and results described herein are in stark contrast to the “knockdown factor” approach currently utilized in ASME Code Case 2286-1. The results obtained by finite difference method agree well with those published by Elishakoff and Williams for the prediction of buckling load.

Buckling of Axisymmetric, Homogeneous Cylindrical Shells With Random Imperfections: Monte Carlo Method

2005 ◽  
Author(s):  
Dennis Williams
Keyword(s):  
Monte Carlo ◽  
Cylindrical Shell ◽  
Pressure Vessel ◽  
Cylindrical Shells ◽  
Large Diameter ◽  
Buckling Load ◽  
Problem Solution ◽  
Critical Buckling Load ◽  
Asme Code ◽  
Section Viii

This paper presents the second of a series of solutions to the buckling of imperfect cylindrical shells subjected to an axial compressive load. In particular, the current problem reviewed is the case of a homogeneous cylindrical shell with random axisymmetric imperfections. The problem solution for the determination of the critical buckling load utilizes a statistical approach to define the random imperfections as opposed to the deterministic methods most often employed in the pressure vessel industry. The imperfections are treated as a random function of the axial (i.e., longitudinal) position on the shell. The Monte Carlo technique is utilized to create a large sample of random shell geometries from which to eventually calculate a critical buckling load for each randomly generated shell geometry. Having matched or predefined the statistical parameters (including the co-variance) of interest as determined from actual manufacturing statistics to the Monte Carlo simulation of shell geometries, the reliability of the critical buckling load is then calculated for the set of cylindrical shells with the random axisymmetric imperfections. The ASME Boiler and Pressure Vessel Code Section VIII fabrication tolerances as supplemented by ASME Code Case 2286-1 are reviewed and addressed in light of the findings of the current study and resulting solutions with respect to the critical buckling loads. The method and results described herein are in stark contrast to the “knockdown factor” approach currently utilized in ASME Code Case 2286-1. Recommendations for further study of the imperfect cylindrical shell are also outlined in an effort to improve on the current design rules regarding column buckling of large diameter shells designed in accordance with ASME Section VIII, Divisions 1 and 2 and ASME STS-1 in combination with the suggestions contained within Code Case 2286-1.

Analysis of Shells of Noncircular Cross Section

2004 ◽  
Author(s):  
Jack E. Helms ◽  
Michael W. Guillot
Keyword(s):  
Experimental Data ◽  
Cross Section ◽  
Thin Wall ◽  
Element Analysis ◽  
Noncircular Cross Section ◽  
Division 1 ◽  
Asme Code ◽  
Minimum Requirements ◽  
Section Viii ◽  
Tank Design

Minimum requirements for the design of shells of noncircular cross section are given in Appendix 13 of Section VIII, Division 1 of the ASME Code. The ASME Section XII Committee is re-examining the design of noncircular shells as part of their activities on cargo tank design. In this study finite element analysis is used to model a thin-wall noncircular shell. The results of the analysis are compared to experimental data provided by RTL, Inc.

Design Formulas of Blind End Closures for High Pressure Vessels

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
R. D. Dixon ◽  
E. H. Perez
Keyword(s):  
High Pressure ◽  
Fatigue Life ◽  
Maximum Stress ◽  
Accurate Determination ◽  
Pressure Vessels ◽  
Stress Distributions ◽  
Fatigue And Fracture ◽  
Asme Code ◽  
Section Viii

The available design formulas for flat heads and blind end closures in the ASME Code, Section VIII, Divisions 1 and 2 are based on bending theory and do not apply to the design of thick flat heads used in the design of high pressure vessels. This paper presents new design formulas for thickness requirements and determination of peak stresses and stress distributions for fatigue and fracture mechanics analyses in thick blind ends. The use of these proposed design formulas provide a more accurate determination of the required thickness and fatigue life of blind ends. The proposed design formulas are given in terms of the yield strength of the material and address the fatigue strength at the location of the maximum stress concentration factor. Introduction of these new formulas in a nonmandatory appendix of Section VIII, Division 3 is recommended after committee approval.

Dynamic Responses of Buried Pipelines Under Impact Loading Caused by Landslide

2012 ◽  
Vol 204-208 ◽  
pp. 3476-3479 ◽  
Author(s):  
Xiu Xing Zhu ◽  
Shi Feng Xue ◽  
Xing Hua Tong ◽  
Chuan Qi Liu
Keyword(s):  
Impact Loading ◽  
Impact Force ◽  
Large Diameter ◽  
Influence Factors ◽  
Dynamic Responses ◽  
Thin Wall ◽  
Buried Pipelines ◽  
Steel Pipes ◽  
Mountainous Regions ◽  
The Impact

Cases of pipeline damage caused by landslide are common in coastal or mountainous regions, where the design of buried pipelines should be improved in order to reduce the risk of damage or failure. Dynamic responses of large diameter thin wall steel pipes under impact loading were analyzed using a nonlinear contact model of pipe-soil coupling in this paper. Several influence factors were studied, such as the impact velocity of rockfall, buried depth of pipeline, ratio of diameter to thickness and style of soil. The results show that an ellipsoid induces much more impact force than a sphere which has the same volume, and the larger one in volume have greater impact force for two spheres. Dangerous compressive areas of pipeline occupy 1/6 of the whole area, so the pipelines subject to landslide occur local failure. Based on results, some useful suggestions for the design of pipelines in landslide region are given

Comparison of International Codes for a Fatigue Crack Growth Flaw Tolerance Sample Problem

2021 ◽  
Author(s):  
Gary L. Stevens
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Large Diameter ◽  
Sample Problem ◽  
Pressurized Water ◽  
Typical Application ◽  
Flaw Tolerance ◽  
Asme Code ◽  
The Impact

Abstract As part of the development of American Society of Mechanical Engineers Code Case N-809 [1], a series of sample calculations were performed to gain experience in using the Code Case methods and to determine the impact on a typical application. Specifically, the application of N-809 in a fatigue crack growth analysis was evaluated for a large diameter austenitic pipe in a pressurized water reactor coolant system main loop using the current analytical evaluation procedures in Appendix C of Section XI of the ASME Code [2]. The same example problem was previously used to evaluate the reference fatigue crack growth curves during the development of N-809, as well as to compare N-809 methods to similar methods adopted by the Japan Society of Mechanical Engineers. The previous example problem used to evaluate N-809 during its development was embellished and has been used to evaluate additional proposed ASME Code changes. For example, the Electric Power Research Institute investigated possible improvements to ASME Code, Section XI, Nonmandatory Appendix L [3], and the previous N-809 example problem formed the basis for flaw tolerance calculations to evaluate those proposed improvements [4]. In addition, the ASME Code Section XI, Working Group on Flaw Evaluation Reference Curves continues to evaluate additional research data and related improvements to N-809 and other fatigue crack growth rate methods. As a part of these Code investigations, EPRI performed calculations for the Appendix L flaw tolerance sample problem using three international codes and standards to evaluate fatigue crack growth (da/dN) curves for PWR environments: (1) ASME Code Case N-809, (2) JSME Code methods [5], and (3) the French RSE-M method [6]. The results of these comparative calculations are presented and discussed in this paper.

Investigation of Nozzle on Knuckle Region of Dished Head

2021 ◽  
Author(s):  
Sujay S. Pathre ◽  
Ameya M. Mathkar ◽  
Shyam Gopalakrishnan
Keyword(s):  
Stress Pattern ◽  
Design Specification ◽  
Specific Location ◽  
Bending Effect ◽  
Division 1 ◽  
User Design ◽  
Asme Code ◽  
Section Viii ◽  
Design Requirements ◽  
Induced Stresses

Abstract ASME Code Section VIII Division 1 [1] provides rules for the shape of openings, size of openings, strength and design of openings, however, the existing rules do not provide any restrictions on the specific location of the nozzle on the dished head knuckle region. Many corporate guidelines/ user design requirements meant for pressure vessel design and specification suggest avoiding placement of any type of nozzle in the knuckle area of a dished head and generally state in their design specification to limit the placement of a nozzle including its reinforcement within the crown area. This applies to Torispherical and Ellipsoidal dished heads. Code [1] rule UG-37(a) provides the benefit in reinforcement by reducing the required thickness (tr) of the dished head when the nozzle is in the spherical portion of the dished head for the Ellipsoidal and Torispherical dished head. High stresses occur in the knuckle region of the dished head due to the edge bending effect caused as the cylinder and head try to deform in different directions. For various reasons the user design requirements insist on placing the nozzle in the knuckle region, further compounding the complexity of the stress pattern in the knuckle area. The work carried out in this paper was an attempt to check whether it is safe to locate a nozzle in the knuckle region of the dished head since the knuckle portion is generally subjected to higher stresses in comparison to the crown portion of a dished head and the Code [1] and [2] does not impose any restrictions for the placement of nozzles in the knuckle region. Also, in this paper an attempt was made to evaluate the induced stresses when equivalent sizes of nozzles are placed in the crown as well as the knuckle portion of the dished head.

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