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Research Papers: Design and Analysis

# Accurate Determination of Plastic Collapse Loads From Finite Element Analyses

[+] Author and Article Information
C. Doerich

Institute for Infrastructure and Environment, University of Edinburgh, King’s Buildings, Edinburgh EH9 3JN, UKc.doerich@ed.ac.uk

J. M. Rotter

Institute for Infrastructure and Environment, University of Edinburgh, King’s Buildings, Edinburgh EH9 3JN, UK

J. Pressure Vessel Technol 133(1), 011202 (Dec 22, 2010) (10 pages) doi:10.1115/1.4002770 History: Received June 07, 2010; Revised September 21, 2010; Published December 22, 2010; Online December 22, 2010

## Abstract

When computational modeling is used to evaluate the true strength of an imperfect elastic-plastic shell structure, the current European standard on shell structures requires that two reference strengths are always determined: the linear bifurcation load and the plastic limit (plastic collapse) load. These two loads are used in more than one way to characterize the strength of all imperfect elastic-plastic systems. Where parametric studies of a problem are being undertaken, it is particularly important that these two loads are accurately defined, since all other strengths will be related to them. For complex problems in shell structures, it is not possible to develop analytical solutions for the plastic collapse strength, and finite element analysis must be used. Unfortunately, because a collapse mechanism often requires the development of very extensive plasticity involving large local strains, and the collapse load is simply at the end of a slowly rising load-deflection curve, it is sometimes difficult for the analyst to accurately determine this plastic collapse strength. This paper describes two methods, based on modifications of the Southwell plot, of obtaining very accurate evaluations of the plastic limit load, irrespective of whether a fairly complete plastic strain field has developed or not. These two methods allow plastic collapse limit loads to be reported with great precision.

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## Figures

Figure 1

Figure 2

Figure 3

Plastic interaction curve in the fully plastic range from Fig. 2

Figure 4

Figure 5

Bracket supported cylinder

Figure 6

Bracket supported tank: radial displacement at 2h above the bracket top

Figure 7

Bracket supported tank: radial displacement at the support

Figure 8

Bracket supported tank: axial displacement at the base

Figure 9

Bracket supported tank: stress state in shell at plastic collapse

Figure 10

Cylinder under patch loads normal to the shell

Figure 11

Figure 12

Progressive stages of the load-deflection curve with corresponding MS plots

Figure 13

Dimensionless MS plots for all the example problems in this paper

Figure 14

Simply supported plate under uniformly transverse pressure

Figure 15

Figure 16

Cylinder subject to axisymmetric pressure band over height h

Figure 17

CIP plot for the band loaded cylinder

Figure 18

Detail of CIP plot at high loads for the band loaded cylinder

Figure 19

Transition junction between hopper and cylinder in a silo

Figure 20

CIP plot for the plastic collapse of the silo transition junction

Figure 21

Linear elastic alternative estimates of the collapse load

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