Lower Bounds to the Collapse Load of a Thick Circular Cylinder Subjected to Internal Pressure and Shear

1977 ◽  
Vol 44 (4) ◽  
pp. 766-768
Author(s):  
N. Inoue ◽  
H. Nakagawa ◽  
T. Nakayama ◽  
M. Shimono ◽  
T. Tanaka
Keyword(s):  
Lower Bound ◽  
General Solution ◽  
Circular Cylinder ◽  
Internal Pressure ◽  
Plane Strain ◽  
Lower Bounds ◽  
Mathematical Theory ◽  
Collapse Load ◽  
Bound Solution ◽  
Lower Bound Solution

A new method for obtaining statically admissible states of stress in plane strain in the mathematical theory of plasticity is presented. After deriving a general solution, the proposed procedure is exemplified by a known solution of a thick circular cylinder subjected to internal pressure. The method is applied to a thick circular cylinder subjected to internal pressure and shear, and a lower-bound solution is given.

Symmetric Deformations of Viscoelastic-Plastic Cylinders

1966 ◽  
Vol 33 (2) ◽  
pp. 327-334 ◽  
Author(s):  
M. J. Crochet
Keyword(s):  
General Solution ◽  
Circular Cylinder ◽  
Internal Pressure ◽  
Plane Strain ◽  
Constitutive Equations ◽  
Plastic State ◽  
Plastic Cylinder ◽  
Loading And Unloading ◽  
Special Case ◽  
Incompressible Cylinder

This paper, in the main, contains a general solution for a viscoelastic-plastic hollow circular cylinder under internal pressure and in the state of plane strain. The medium is assumed to be isotropic and homogeneous, and the constitutive equations used are a special case of those given in [1]. Solutions for both loading and unloading from a viscoelastic-plastic state are considered, and numerical results are obtained for the specific case of an incompressible cylinder under a step pressure. Also discussed briefly is the torsion of a viscoelastic-plastic cylinder, the solution of which is again illustrated by a numerical example.

Upper and Lower Bounds for Incipient Failure in a Body Under Gravitational Loading

2004 ◽  
Vol 71 (4) ◽  
pp. 586-589 ◽  
Author(s):  
J. A. Chamberlain, ◽  
D. J. Horrobin, ◽  
K. A. Landman, and ◽  
J. E. Sader
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Numerical Work ◽  
Bound Solution ◽  
Rectangular Block ◽  
Gravitational Loading ◽  
Lower Bound Solution ◽  
Line Analysis

Recent numerical work has investigated incipient failure of yield stress materials under gravitational loading, for both the rectangular block and cylinder geometries [Chamberlain et al.; 2001, Int. J. Mech. Sci. 43(3):793-815, 2002, Int. J. Mech. Sci. 44(8):1779-1800]. While the rectangular block solution is exact, the cylinder solutions give lower bounds on the height of incipient failure. Consequently, we construct upper bound solutions for the height of incipient failure of a cylinder under gravitational loading. This closes the cylinder problem and quantifies the accuracy of the Haar-Karman hypothesis used in slip-line analysis. For completeness, we also give a simple lower bound solution for the cylinder, as well as upper and lower bound solutions for the two-dimensional rectangular block. These results have the advantage of being analytical, in contrast to the previous purely numerical results.

Stress discontinuities in plane plastic flow

1967 ◽  
Vol 2 (1) ◽  
pp. 52-61 ◽  
Author(s):  
F Ellis
Keyword(s):  
Lower Bound ◽  
Plane Strain ◽  
Plastic Flow ◽  
Constant Stress ◽  
Stress Fields ◽  
Bound Solution ◽  
Plane Plastic ◽  
Axis Of Symmetry ◽  
Lower Bound Solution

Statically admissible stress fields consisting of regions of constant stress in a state of incipient plastic flow separated by stress discontinuities form a powerful tool for obtaining lower bound solutions to problems in plane plastic flow. The properties of discontinuities which meet on an axis of symmetry are investigated and it is shown that solutions exist for ‘reflections’ of the discontinuity at the axis at angles of π/4 and 3π/4 as well as the angle π/2 hitherto assumed to be the only solution. The results are used to obtain a lower bound solution for plane-strain extrusion with reduction ratios less than 3:1.

Lower Bounds to Eigenvalues by Planelike Surfaces

1974 ◽  
Vol 41 (1) ◽  
pp. 267-268 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
General Solution ◽  
Variational Problem ◽  
Lower Bounds ◽  
Particular Solutions ◽  
Particular Solution ◽  
The One

A particular solution of a variational problem is defined as corresponding to a particular set of parameters. A general solution is the one over a continuous region of the parameters. This work presents a method to obtain lower bound to the general solution, when some particular solutions are known.

Review of Lower-Bound Limit Analysis for Pressure Vessel Intersections

1977 ◽  
Vol 99 (3) ◽  
pp. 413-418 ◽  
Author(s):  
A. Biron
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Limit Analysis ◽  
Pressure Vessel ◽  
General Purpose ◽  
Collapse Load ◽  
Rotationally Symmetric ◽  
Bound Theorem ◽  
Symmetric Structures ◽  
Lower Bound Limit Analysis

On the basis of a study of several recent papers concerned with the lower-bound computation of the collapse load of pressure vessel intersections, a review is made of the satisfaction, or nonsatisfaction, of the requirements of the lower-bound theorem of limit analysis. It is shown that, whereas for rotationally symmetric structures true lower bounds have been obtained, for a nonsymmetric case such as a right cylinder-cylinder intersection it is difficult to avoid so me approximations. If attempts are to be made to develop general purpose limit analysis programs, the consequences of approximations of the type used so far must be evaluated with care if significant results are to be obtained.

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