Rigid-Plastic Collapse of Cylindrical Shells

1973 ◽  
Vol 95 (1) ◽  
pp. 215-218 ◽  
Author(s):  
H. M. Haydl ◽  
A. N. Sherbourne
Keyword(s):  
Limit Analysis ◽  
Cylindrical Shells ◽  
Numerical Approach ◽  
External Pressure ◽  
Plastic Collapse ◽  
Rigid Plastic ◽  
Limit Loads ◽  
Complex Problems ◽  
Safe Side ◽  
Von Mises

This paper suggests a simple numerical approach to the limit analysis of cantilever cylindrical shells. The loads considered are external pressure and external pressure combined with a moment at the free shell end. It is shown that the collapse loads are within 4.5 percent on the safe side of the exact von Mises limit loads. The extension of the method of analysis to more complex problems is suggested.

Research Note: Limit Loads of Cylindrical Shells under Band Pressures

1974 ◽  
Vol 16 (5) ◽  
pp. 349-350
Author(s):  
H. M. Haydl ◽  
A. N. Sherbourne
Keyword(s):  
Numerical Method ◽  
Limit Analysis ◽  
Cylindrical Shells ◽  
Numerical Approach ◽  
Research Note ◽  
Limit Loads ◽  
Title Problem

The purpose of this brief note is to point out that a numerical approach to the limit analysis of discontinuously-loaded cylindrical shells is simple and appears to be useful for designers and engineers. In particular, we illustrate the numerical method by solving the title problem.

Elastic-plastic collapse of 3-D damaged cylindrical shells subjected to uniform external pressure

2004 ◽  
Vol 10 (4) ◽  
pp. 343-349 ◽  
Author(s):  
X. W. Zhao ◽  
J. H. Luo ◽  
M. Zheng ◽  
H. L. Li ◽  
M. X. Lu
Keyword(s):  
Cylindrical Shells ◽  
External Pressure ◽  
Plastic Collapse ◽  
Uniform External Pressure ◽  
Elastic Plastic

Pure Plastic Behavior and the Assumption of Zero Elasticity at the Limit Load

2019 ◽  
Author(s):  
Pedro V. Marcal ◽  
Robert Rainsberger ◽  
Jeffrey T. Fong
Keyword(s):  
Limit Analysis ◽  
Low Cycle Fatigue ◽  
Limit Load ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Rigid Plastic ◽  
External Work ◽  
Limit Loads ◽  
Vulcanized Rubber ◽  
Area 7

Abstract The authors have introduced an analysis based on a modification of the Mooney Rivlin material to obtain an estimate of the plastic behavior of a structure near its failure point. In this paper we generalize the concept of zero elasticity and pure plastic behavior at the limit loads and beyond [1–2]. The theorems of limit analysis assume rigid plastic behavior that is equivalent to zero elasticity. We are concerned with the regions just beyond the limit load, so it is not unreasonable to again assume zero elasticity in this region. The neglect of elastic behavior allows us to concentrate on large plastic strains that take place at or beyond the limit loads as defined by Limit Analysis [3–4]. We can focus on tearing, Plastic Fracture Mechanics and low-cycle fatigue respectively. In such situations the practice has been adopted to label such state points as ‘Ultimate’ behavior. Here we adopt the same label to refer to behavior at or beyond the limit load, where the full large displacement and work hardening effects can be accounted for by the modified Mooney Rivlin material. The mechanics of fracture has also been applied to the tearing of Vulcanized rubber by Rivlin and Thomas[5]. This study concerned large nonlinear incompressible strains that were modeled by Mooney Rivlin Materials, Mooney[6]. The Fracture is modeled by the balance of internal and external work caused by the advancing crack surface area [7–8]. One final benefit of the assumption of zero elasticity is its simplification of dynamic analysis.

Plastic Collapse Assessment of Thick Vessels Under Internal Pressure According to Various Hardening Rules

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
A. Chaaba
Keyword(s):  
Internal Pressure ◽  
Strain Hardening ◽  
Limit Analysis ◽  
Limit State ◽  
Plastic Behavior ◽  
Plastic Collapse ◽  
Perfectly Plastic ◽  
Von Mises ◽  
Hardening Rules ◽  
Collapse Assessment

This paper aims to deal with plastic collapse assessment for thick vessels under internal pressure, thick tubes in plane strain conditions, and thick spheres, taking into consideration various strain hardening effects and large deformation aspect. In the framework of von Mises’ criterion, strain hardening manifestation is described by various rules such as isotropic and/or kinematic laws. To predict plastic collapse, sequential limit analysis, which is based on the upper bound formulation, is used. The sequential limit analysis consists in solving sequentially the problem of the plastic collapse, step by step. In the first sequence, the plastic collapse of the vessel corresponds to the classical limit state of the rigid perfectly plastic behavior. At the end of each sequence, the yield stress and/or back-stresses are updated with or without geometry updating via displacement velocity and strain rates. The updating of all these quantities (geometry and strain hardening variables) is adopted to conduct the next sequence. As a result of this proposal, we get the limit pressure evolution, which could cause the plastic collapse of the device for different levels of hardening and also hardening variables such as back-stresses with respect to the geometry change.

Experimental Behaviour of Thin-Walled Cylindrical Shells Subjected to External Pressure

1969 ◽  
Vol 11 (1) ◽  
pp. 40-56 ◽  
Author(s):  
P. Montague
Keyword(s):  
Cylindrical Shells ◽  
Small Deformation ◽  
External Pressure ◽  
Elastic Instability ◽  
Rigid Plastic ◽  
Modes Of Failure ◽  
Instability Theory ◽  
Pressure Tests ◽  
Thin Walled ◽  
Deformation Patterns

The paper describes external radial and hydrostatic pressure tests on 12 mild steel, thin-walled cylindrical shells. Radial deflections and surface strains on the inside and outside of the cylinders' walls are related to the conventional small deformation theory. The elastic deformation patterns are found to be similar in shape to the lobar modes which can be predicted by elastic instability theory. The collapse pressures of the shells and their modes of failure are considered in relation to the rigid-plastic theory, the importance of initial imperfections is discussed and an attempt is made to relate the geometric and material properties of the cylinders to modes of failure and to appropriate collapse analyses.

Rigid-Plastic Analysis of Symmetrically Loaded Cylindrical Shells

1954 ◽  
Vol 21 (4) ◽  
pp. 336-342 ◽  
Author(s):  
P. G. Hodge
Keyword(s):  
Geometric Mean ◽  
Cylindrical Shells ◽  
Closed Shell ◽  
External Pressure ◽  
Rigid Plastic ◽  
Uniform External Pressure ◽  
Incipient Velocity ◽  
Limiting Load ◽  
General Method ◽  
Half Thickness

Abstract A general method is presented for finding the stress and incipient velocity distribution in a symmetrically loaded cylindrical shell at collapse. The results are based upon a linearized yield surface, and a method is given for obtaining this linearized surface directly. The techniques are illustrated with reference to open and closed cylindrical shells under uniform external pressure. In each case the shell is specified completely by a single parameter c defined as the ratio of the half-length of the shell to the geometric mean of the radius and half-thickness; c = L / a ! . It is found that for moderately large values of c, the limiting load is greater for the closed shell, while for small c the reverse is true.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

Sign in / Sign up

Export Citation Format

Share Document