Upper and lower bound limit and shakedown loads for hollow tubes with axisymmetric internal projections under axial loading

Abstract

In this paper, the elastic compensation method proposed by Mackenzie and Boyle is used to estimate the upper and lower bound limit (collapse) loads and the upper and lower bound shakedown loads for hollow tubes with axisymmetric internal projections subjected to axial loading. The method is based on an iterative elastic analysis procedure and the application of lower and upper bound limit load theorems. Four different geometries with a range of stress concentration factors (from low to high) are considered. Elastic-plastic finite element predictions for collapse and shakedown pressure are found to be within these upper and lower bound estimates.

The method is particularly useful because it is founded on an iterative elastic approach and does not require extensive and complex elastic-plastic finite element computations.

Keywords

upper and lower bounds collapse shakedown thin-walled tubes

Get full access to this article

View all access options for this article.

References

BS 5500 Specification for Unfired Fusion Welded Pressure Vessels (British Standards Institution, London).

ASME Boiler and Pressure Vessel Code, Section VIII, Division 1, Pressure Vessels (American Society of Mechanical Engineers, New York).

Mendleson

Plasticity; Theory and Application, 1968 (Macmillan, London).

Berak

E. G.

Gerdeen

J. C.

A finite element technique for limit analysis of structures

Trans. ASME, J. Pressure Vessel Technol., 1990, 112, 138–144.

Dhalla

A. K.

Verification of an elastic procedure to estimate follow-up In Design of Elevated Temperature Piping (Eds Mallet

R. H.

Mello

R. M.

), 1984, pp. 81–96 (American Society of Mechanical Engineers, New York).

Marriot

D. L.

Evaluation of deformation or load control of stresses under inelastic conditions using elastic finite element stress analysis. In Proceedings of the Pressure Vessels and Piping Conference, Pittsburgh, Pennsylvania, 1988, PVP-Vol.136 (American Society of Mechanical Engineers, New York).

Mackenzie

Boyle

J. T.

A method of estimating limit loads by iterative elastic analysis. I: Simple examples

Int. J. Pressure Vessels Piping, 1993, 53, 77–95.

Mackenzie

Nadarajah

Shi

Boyle

J. T.

Simple bounds on limit loads by elastic finite element analysis

Trans. ASME, J. Pressure Vessels Technol., 1993, 115, 27–31.

Mackenzie

Boyle

J. T.

A simple method of estimating shakedown loads for complex structures. In ASME Pressure Vessels and Piping, 1993, PVP-Vol. 265, pp. 89–94.

10.

Hamilton

Boyle

J. T.

Shi

Mackenzie

A simple upper-bound method for calculating approximate shakedown loads

Trans. ASME, J. Pressure Vessels Technol., 1998, 120, 195–199.

11.

ANSYS Version 5.4 User Manual (ANSYS Inc., Pittsburg, Pennsylvania).

12.

Hardy

S. J.

Gowhari-Anaraki

A. R.

Stress concentration factors and elastic-plastic stress and strain predictions for axisymmetric internal projections on hollow tubes subjected to axial loading

J. Strain Analysis, 1989, 24 (1), 45–54.

13.

Hardy

S. J.

Gowhari-Anaraki

A. R.

Elastic-plastic finite element analysis of hollow tubes with axially loaded axisymmetric internal projections

J. Strain Analysis, 1993, 28 (3), 187–196.