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.

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.

Dynamic Plastic Response of Cylindrical Shells Under Gaussian Impulse

1980 ◽  
Vol 24 (01) ◽  
pp. 24-30
Author(s):  
S. Anantha Ramu ◽  
K. J. Iyengar
Keyword(s):  
Cylindrical Shells ◽  
Yield Condition ◽  
Longitudinal Axis ◽  
Plastic Behavior ◽  
Plastic Response ◽  
Marine Structures ◽  
Impulsive Load ◽  
Tresca Yield Condition ◽  
Impulsive Loads

The determination of the inelastic response of cylindrical shells under general impulsive loads is of relevance to marine structures such as submarines, in analyzing their slamming damages. The present study is concerned with the plastic response of a simply supported cylindrical shell under a general axisymmetric impulsive load. The impulsive load is assumed to impart an axisymmetric velocity to the shell, with a Gaussian distribution along the longitudinal axis of the shell. A simplified Tresca yield condition is used. The shell response is determined for various forms of impulses ranging from a concentrated impulse to a uniform impulse over the entire length of the shell. Conclusions about the influence of geometry of the shell and the spatial distribution of impulse on the plastic behavior of cylindrical shells are presented.

Limit Analysis for Combined Edge and Pressure Loading on a Cylindrical Shell

1971 ◽  
Vol 93 (4) ◽  
pp. 998-1006
Author(s):  
H. S. Ho ◽  
D. P. Updike
Keyword(s):  
Cylindrical Shell ◽  
Velocity Field ◽  
Axial Force ◽  
Shear Force ◽  
Circular Cylindrical Shell ◽  
Yield Condition ◽  
External Pressure ◽  
Tresca Yield Condition ◽  
Stress States ◽  
Range Of Values

Equations describing the stress field and velocity field occurring in a circular cylindrical shell at plastic collapse are derived corresponding to stress states lying on each face of a yield surface for a uniform shell of material obeying the Tresca yield condition. They are then applied to the case of a shell under combined axisymmetric loadings (moment, shear force, and axial force) at one end and uniform internal or external pressure on the lateral surface. For a sufficiently long shell, complete solutions are obtained for a fixed far end, and for a certain range of values of axial force and pressure, they are obtained for a free far end. All the solutions are represented by either closed form or by quadratures. It is shown that in many cases the radial velocity field is proportional to the shear force.

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.

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.

The Elastic-Plastic Stress Distribution Within a Wide Curved Bar Subjected to Pure Bending

1955 ◽  
Vol 22 (3) ◽  
pp. 305-310
Author(s):  
Bernard W. Shaffer ◽  
Raymond N. House
Keyword(s):  
Stress Distribution ◽  
Convex Surface ◽  
Plastic Material ◽  
Circumferential Stress ◽  
Yield Condition ◽  
Bending Moment ◽  
Stress Distributions ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Plastic Stress

Abstract Analytical expressions are obtained for the radial and circumferential stress distributions within a wide curved bar made of a perfectly plastic material when it is subjected to a uniformly distributed bending moment. The elastic stress distributions are based on the use of the Airy stress function, whereas the plastic stress distributions in this problem of plane strain are based on the use of the Tresca yield condition. It is found that as the bending moment increases in the direction which tends to straighten the initially curved bar, an elastic-plastic boundary develops first around the concave surface. It meets a second boundary, which starts sometime later around the convex surface, when the bar is completely plastic. The elastic region within the bar decreases at a fairly uniform rate as the bending moment increases to within approximately 90 per cent of the fully plastic bending moment but then it degenerates very much more rapidly until it no longer exists when the bar is completely plastic. The position of the neutral surface is independent of the applied bending moment when the stress distribution is within the completely elastic and the completely plastic ranges. Within the elastic-plastic range, however, it moves away from and then toward the center of curvature as the bending moment increases.

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