Research Papers: Design and Analysis

Lower Bound Methods in Elastic-Plastic Shakedown Analysis

[+] Author and Article Information
Wolf Reinhardt

Candu Energy Inc.,
2285 Speakman Drive,
Mississauga, ON L5K 1B1, Canada
e-mail: wolf.reinhardt@candu.com

Reza Adibi-Asl

393 University Avenue,
Toronto, ON M5G 1E6, Canada
e-mail: reza.adibiasl@amec.com

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received September 27, 2012; final manuscript received August 29, 2013; published online January 7, 2014. Assoc. Editor: Haofeng Chen.

J. Pressure Vessel Technol 136(2), 021201 (Jan 07, 2014) (9 pages) Paper No: PVT-12-1158; doi: 10.1115/1.4025941 History: Received September 27, 2012; Revised August 29, 2013

Several methods were proposed in recent years that allow the efficient calculation of elastic and elastic-plastic shakedown limits. This paper establishes a uniform framework for such methods that are based on perfectly-plastic material behavior, and demonstrates the connection to Melan's theorem of elastic shakedown. The paper discusses implications for simplified methods of establishing shakedown, such as those used in the ASME Code. The framework allows a clearer assessment of the limitations of such simplified approaches. Application examples are given.

Copyright © 2014 by ASME
Topics: Stress
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Fig. 1

Schematic interaction diagram with ratchet boundary

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Fig. 2

Bree example—extreme cyclic bending strain distributions through the thickness of a beam

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Fig. 3

Bree example—optimum membrane stress redistributions at ratchet boundary

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Fig. 4

Bree example—interaction diagram for primary and secondary cyclic loading with time-invariant primary membrane load

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Fig. 5

Pressurized two-bar model

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Fig. 6

Ratchet boundary for pressurized two bar model, FEA results extracted from Ref. [18]

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Fig. 7

Three bar example—schematic configuration and bar heating sequence




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