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Research Papers: Design and Analysis

A Noncyclic Method for Plastic Shakedown Analysis

[+] Author and Article Information
W. Reinhardt

 Babcock & Wilcox Canada, 581 Coronation Boulevard, Cambridge, ON, N1R 5V3, Canada

J. Pressure Vessel Technol 130(3), 031209 (Jul 23, 2008) (6 pages) doi:10.1115/1.2937760 History: Received March 22, 2006; Revised January 18, 2007; Published July 23, 2008

Shakedown is a cyclic phenomenon, and for its analysis it seems natural to employ a cyclic analysis method. Two problems are associated when this direct approach is used in finite element analysis. First, the analysis typically needs to be stabilized over several cycles, and the analysis of each individual cycle may need a considerable amount of computing time. Second, even in cases where a stable cycle is known to exist, the finite element analysis can show a small continuing amount of strain accumulation. For elastic shakedown, noncyclic analysis methods that use Melan’s theorem have been proposed. The present paper extends noncyclic lower bound methods to the analysis of plastic shakedown. The proposed method is demonstrated with several example problems.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 3

Application of the noncyclic method to the Bree problem: Stress profile due to fully reversed bending load and subsequent yield stress distribution (a) if bending stress remains below yield and (b) if bending stress exceeds yield

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Figure 4

(a) Schematic representation of the inverse Bree problem, and (b) shakedown region predicted by cyclic FE, theory, and by the present method

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Figure 5

(a) Schematic representation of the three-bar problem, and (b) constant and fully reversed stress components used by the noncyclic method. “Bar Stress” denotes the uniaxial stress in each bar, consisting of a (compressive) time-invariant stress and a fully reversed stress that is compressive in the heated bar and tensile in the others.

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Figure 1

Equivalent load (stress) histories: A transformation of the time scale transforms one stress history into the other. Although not symmetric, the dotted history is equivalent to a symmetric stress history (solid).

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Figure 2

(a) Schematic representation of the Bree problem, and (b) shakedown region predicted by Bree (3) and by the present method

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