Elastic-Plastic Analysis of a Radially Loaded Spherical Shell

1989 ◽  
Vol 111 (1) ◽  
pp. 39-46 ◽  
Author(s):  
G. N. Brooks ◽  
C.-P. Leung
Keyword(s):  
Spherical Shell ◽  
Shallow Shell ◽  
Efficient Solution ◽  
Solution Method ◽  
Yield Condition ◽  
Computationally Efficient ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Plastic Analysis ◽  
Infinite Extent

An elastic-plastic analysis of a spherical shell loaded radially through a rigid inclusion is performed. The sphere is modeled as a shallow shell of infinite extent. The Tresca yield condition is used to derive the elastic-plastic moment-curvature relationship in a simple form. This is used to develop a computationally efficient solution method.

Elastic-Plastic Analysis of a Spherical Shell Loaded Radially Through a Flexible Cylindrical Nozzle

1990 ◽  
Vol 112 (3) ◽  
pp. 296-302 ◽  
Author(s):  
C.-P. Leung ◽  
G. N. Brooks
Keyword(s):  
Spherical Shell ◽  
Efficient Solution ◽  
Yield Condition ◽  
Geometric Parameters ◽  
Plastic Behavior ◽  
Elastic Plastic ◽  
Cylindrical Nozzle ◽  
Tresca Yield Condition ◽  
Failure Loads ◽  
Range Of Values

This study investigates the elastic-plastic behavior of a shallow spherical shell loaded radially through a flexible cylindrical nozzle. Both the sphere and the cylinder can yield and exhibit plastic deformation. The Tresca yield condition is employed to derive elastic-plastic moment-curvature relationship in a simple form which is implemented in an efficient solution scheme. Three geometric parameters represent the relative dimensions of the structure. Numerical results are obtained for a range of values of these parameters. Various situations involving the failure of the sphere and/or the cylinder are studied. The ultimate or failure loads of the structure are plotted as functions of the geometric parameters.

The Elastic-Plastic Analysis of Tubes—II: Variable Loading

1992 ◽  
Vol 114 (2) ◽  
pp. 222-228 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Closed Form Solution ◽  
Yield Condition ◽  
Complex Loading ◽  
Form Solution ◽  
Stress And Strain ◽  
Variable Loading ◽  
Elastic Plastic ◽  
Incremental Method ◽  
Plastic Analysis ◽  
General Program

This paper is concerned with the elastic-plastic analysis of tubes subjected to variable loads. The yield condition for a material having residual stress and strain is first derived. Then by incremental method, the stresses and strains of the tube at any loading stage can be found. A closed-form solution is achieved as an example of tubes incurring ratchetting, and a general program is developed to make the theory applicable to complex loading situations.

Elastic-Plastic Analysis of Pressurized Cylindrical Shells

1987 ◽  
Vol 54 (3) ◽  
pp. 597-603 ◽  
Author(s):  
G. N. Brooks
Keyword(s):  
Shell Theory ◽  
Plastic Region ◽  
Yield Condition ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Axisymmetric Shell ◽  
Bending Stresses ◽  
Principal Directions ◽  
The Moment ◽  
Thin Shell Theory

Plasticity in shells is often contained near the ends of a segment where the bending stresses are significant. Outside of this local neighborhood the behavior is elastic. Thus, an axisymmetric shell can be divided along its axis into a purely elastic region away from an end and the local region where plasticity is present. The moment-curvature relation in the elastic-plastic region is calculated using the Tresca yield condition. Use of the Tresca yield condition greatly simplifies this derivation because the principal directions are known. This moment-curvature relationship is “exact” in the sense that only the standard assumptions of thin shell theory are made. The solutions of the elastic and plastic regions are matched at their intersection for an efficient numerical solution. The technique is used here to study the semi-infinite clamped cylindrical shell with an internal pressure loading.

Development of Alternate Methods for Establishing Design Margins for ASME Section VIII Division 3: Part 2

2009 ◽  
Author(s):  
Susumu Terada
Keyword(s):  
Cylindrical Shell ◽  
Spherical Shell ◽  
High Strength ◽  
Test Results ◽  
Burst Test ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Section Viii ◽  
Lower Ratio ◽  
Design Margin

The design margin against collapse for Division 3 is based on Nadal’s equation. For high strength material this method is adequate. However for material with a lower ratio of Sy/Su this method has additional margin from yielding through the thickness to final collapse or burst. The experimental burst test results for closed-end cylinder show the excessive margin for these materials as stated in former paper. Therefore the development of alternate methods for establishing design margin for all materials is desirable. The design margin of 1.5 in equation for open-end cylindrical shell and spherical shell in current code is different from that of 1.732 for closed-end cylindrical shell. The design margin of elastic-plastic analysis is 1.732. Therefore the consistent design margins of equations and elastic-plastic analysis for open-end cylindrical shells and spherical shells are also desirable. In this paper new equations for design pressure of cylindrical shell and spherical shell are proposed by investigation of burst test results and case studies of various methods.

Finite Elastic-Plastic Expansion of a Cylindrical Tube

1973 ◽  
Vol 2 (4) ◽  
pp. 216-222
Author(s):  
B. Slevinsky ◽  
J. B. Haddow
Keyword(s):  
Plastic Deformation ◽  
Yield Condition ◽  
Cylindrical Tube ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
End Conditions ◽  
Cylindrical Tubes ◽  
Limiting Case ◽  
Plastic Flow Rule

A numerical method for the analysis of the isothermal elastic-plastic expansion, by internal pressure, of cylindrical tubes with various end conditions is presented. The Tresca yield condition and associated plastic flow rule are assumed and both non-hardening and work-hardening tubes are considered with account being taken of finite plastic deformation. Tubes which undergo further plastic deformation on unloading are also considered. Expansion of a cylindrical cavity from zero radius in an infinite medium is considered as a limiting case.

Elastic-Plastic Ring-Loaded Cylindrical Shells

1988 ◽  
Vol 55 (4) ◽  
pp. 761-766 ◽  
Author(s):  
Gregory N. Brooks
Keyword(s):  
Axisymmetric Problem ◽  
Shell Theory ◽  
Complete Solution ◽  
Yield Condition ◽  
Plastic Ring ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Small Deflection ◽  
Principal Directions ◽  
Long Cylindrical Shell

The elastic-plastic solution for an infinitely long cylindrical shell with an axisymmetric ring load is presented. Except for the material nonlinearity, the standard assumptions of small deflection shell theory were made. Because the principal directions are known for the axisymmetric problem, the Tresca yield condition wasused. This made it possible to obtain closed-form expressions for the elastic-plastic, moment-curvature relations, greatly simplfying the computational task. The actual stress distribution through the thickness was used, making these relations exact. Yielding was contained near the load. Thus, for the analysis the cylinder was divided along its axis into elastic-plastic and purely elastic regions. Solutions were obtained for each region which were then matched at their intersection to give the complete solution. All results are given in dimensionless form so that they may be applied to any shell.

The Elastic, Plastic Bending of a Simply Supported Plate

1961 ◽  
Vol 28 (3) ◽  
pp. 395-401 ◽  
Author(s):  
G. Eason
Keyword(s):  
Yield Condition ◽  
Constant Load ◽  
Flow Rule ◽  
Plastic Bending ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this paper the problem of the elastic, plastic bending of a circular plate which is simply supported at its edge and carries a constant load over a central circular area is considered. The von Mises yield condition and the associated flow rule are assumed and the material of the plate is assumed to be nonhardening, elastic, perfectly plastic, and compressible. Stress fields are obtained in all cases and a velocity field is presented for the case of point loading. Some numerical results are given comparing the results obtained here with those obtained when the Tresca yield condition is assumed.

Approximate Elastic-Plastic Analysis of Intersecting Equal Diameter Cylindrical Shells

1981 ◽  
Vol 103 (1) ◽  
pp. 111-115
Author(s):  
D. P. Updike
Keyword(s):  
Plastic Material ◽  
Cylindrical Shells ◽  
Yield Condition ◽  
Pressure Vessels ◽  
Ductile Materials ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Analysis ◽  
Elastic Perfectly Plastic ◽  
Von Mises

Design of connections of pipes and pressure vessels on the basis of a calculated maximum elastic stress often proves to be too conservative in the case of ductile materials. Elastic-plastic analysis by the finite element method proves to be too costly. This paper presents an alternative method which reduces the calculations to those of a rotationally symmetric shell subjected to axisymmetric loading. Using this approach approximate elastic-plastic deformations on the meridian passing through the crotch of a tee branch connection of cylindrical shells of equal diameter and thickness are determined. The method is limited to cases of the normal intersection of very thin shells of identical diameter, thickness, and material and to internal pressure loading. Numerical results for the intersection of two shells of R/t equal to 100 are given for an elastic-perfectly plastic material satisfying the von Mises yield condition.

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