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Research Papers: Design and Analysis

# Lower and Upper Bound Shakedown Analysis of Structures With Temperature-Dependent Yield Stress

[+] Author and Article Information
Haofeng Chen

Department of Mechanical Engineering, University of Strathclyde, Glasgow G1 1XJ, UKhaofeng.chen@strath.ac.uk

J. Pressure Vessel Technol 132(1), 011202 (Dec 07, 2009) (8 pages) doi:10.1115/1.4000369 History: Received April 20, 2009; Revised September 08, 2009; Published December 07, 2009; Online December 07, 2009

## Abstract

Based upon the kinematic theorem of Koiter (1960, “General Theorems for Elastic Plastic Solids  ,” in Progress in Solid Mechanics 1, J. N. Sneddon and R. Hill, eds., North-Holland, Amsterdam, pp. 167–221) the linear matching method (LMM) procedure has been proved to produce very accurate upper bound shakedown limits. This paper presents a recently developed LMM lower bound procedure for shakedown analysis of structures with temperature-dependent yield stress, which is implemented into ABAQUS using the same procedure as for upper bounds. According to the Melan’s theorem (1936, “Theorie statisch unbestimmter Systeme aus ideal-plastichem Baustoff,” Sitzungsber. Akad. Wiss. Wien, Math.-Naturwiss. Kl., Abt. 2A, 145, pp. 195–210), a direct algorithm has been carried out to determine the lower bound of shakedown limit using the best residual stress field calculated during the LMM upper bound procedure with displacement-based finite elements. By checking the yield condition at every integration point, the lower bound is calculated by the obtained static field at each iteration, with the upper bound given by the obtained kinematic field. A number of numerical examples confirm the applicability of this procedure and ensure that the upper and lower bounds are expected to converge to the theoretical solution after a number of iterations.

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## Figures

Figure 1

The geometry of the holed plate subjected to axial loading and fluctuating radial temperature distribution and its finite element mesh

Figure 2

The temperature history around the edge of the hole with two distinct extremes

Figure 3

The contour of elastic von Mises effective stress with (a) pure thermal loads (θ0=20°C, Δθ=300°C) and (b) pure uniaxial tension σP=360 MPa

Figure 4

Upper and lower bounds shakedown limit interaction curves of the holed plate subjected to a varying thermal load and a constant uniaxial tension

Figure 5

The convergence condition of iterative processes for shakedown analysis (Point A and A′, subjected to changing thermal loads only)

Figure 6

The convergence condition of iterative processes for shakedown analysis (Point B and B′, subjected to combined action of changing thermal loads and constant mechanical load)

Figure 7

The convergence condition of iterative processes for shakedown analysis (Point C, subjected to constant mechanical load only, shakedown analysis reduces to limit analysis)

Figure 8

3D FE mesh of superheater outlet penetration tubeplate

Figure 9

Figure 10

The convergence condition of iterative processes for shakedown analysis

Figure 11

Failure mechanism of superheater outlet penetration tubeplate with out of phase oscillations

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