0
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

AMEC NSS Ltd.,
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Topics: Stress
Your Session has timed out. Please sign back in to continue.

References

The American Society of Mechanical Engineers, 2007, ASME Boiler and Pressure Vessel Code, Section III, Division 1, ASME, New York.
The American Society of Mechanical Engineers, 2007, ASME Boiler and Pressure Vessel Code, Section VIII Division 2, ASME, New York.
Melan, E., 1938, “Zur Plastizität des räumlichen Kontinuums,” Ing.-Arch., 9, pp. 116–123. [CrossRef]
Koiter, W. T., 1960, “General Theorems of Elastic-Plastic Solids,” Progress in Solid Mechanics, Vol. 40, J. N.Sneddon and R.Hill, eds., North Holland Publishing Co., Amsterdam, Netherlands, pp. 167–221.
Gokhfeld, D. A., and Cherniavsky, O. F., 1980, Limit Analysis of Structures at Thermal Cycling, Suthoff & Nordhoff, Alphen aan den Rijn, The Netherlands.
Konig, J. A., 1987, Shakedown of Elastic-Plastic Structures, Elsevier, Amsterdam, Netherlands.
Mroz, Z., Weichert, D., and Dorosz, S., eds., 1995, Inelastic Behavior of Structures Under Variable Loads, Kluwer Academic Publications, Dordrecht, Netherlands.
Weichert, D., and Maier, G., 2000, Inelastic Behaviour of Structures Under Variable Loads: Theory and Engineering Applications, Kluwer Academic Publications, Dordrecht, Netherlands.
Bari, S., and Hassan, T., 2001, “Constitutive Models With Formative Hardening and Non-Linear Kinematic Hardening for Simulation of Ratcheting,” Transactions SMiRT 16, Washington, DC.
Krabbenhøft, K., Lyamin, A. V., and Sloan, S. W., 2007, “Bounds to Shakedown Loads for a Class of Deviatoric Plasticity Models,” Comput. Mech., 39, pp. 879–888. [CrossRef]
Ponter, A. R. S., and Karadeniz, S., 1985, “An Extended Shakedown Theory for Structures that Suffer Cyclic Thermal Loading. Part I: Theory,” ASME J. Appl. Mech., 52(4), pp. 877–882. [CrossRef]
Ponter, A. R. S., and Karadeniz, S., 1985, “An Extended Shakedown Theory for Structures that Suffer Cyclic Thermal Loading. Part II: Applications,” ASME J. Appl. Mech., 52(4), pp. 883–889. [CrossRef]
Bree, J., 1967, “Elastic-Plastic Behaviour of Thin Tubes Subjected to Internal Pressure and Intermittent High Heat Fluxes With Application to Fast Nuclear Reactor Fuel Elements,” J. Strain Anal., 2, pp. 226–238. [CrossRef]
Mulcahy, T. M., 1976, “Thermal Ratchetting of a Beam Element Having an Idealized Bauschinger Effect,” ASME J. Eng. Mater. Technol., 98(3), pp. 264–271. [CrossRef]
Megahed, M. M., 1981, “Influence of Hardening Rule on the Elasto-Plastic Behaviour of a Simple Structure Under Cyclic Loading,” Int. J. Mech. Sci., 23, pp. 169–182. [CrossRef]
Abdalla, H. F., Megahed, M. M., and Younan, M. Y. A., 2007, “A Simplified Technique for Shakedown Limit Load Determination,” Nucl. Eng. Des., 237, pp. 1231–1240. [CrossRef]
Adibi-Asl, R., and Reinhardt, W., 2010, “Ratchet Boundary Determination Using a Non-Cyclic Method,” ASME J. Pressure Vessel Technol., 132(2), p. 021201. [CrossRef]
Martin, M., and Rice, D., 2009, “A Hybrid Procedure for Ratchet Boundary Predication,” ASME 2009 Pressure Vessels and Piping Conference, Volume 1: Codes and Standards Prague, Czech Republic, July 26–30, 2009, Paper # PVP2009-77474, Prague, Czech Republic, pp. 81–88. [CrossRef]
Gelineau, O., Sperandio, M., and Berton, M. N., 2009, “Ratcheting Predictive Methods in RCC-MR Code,” ASME 2009 Pressure Vessels and Piping Conference, Volume 1: Codes and Standards Prague, Czech Republic, July 26–30, 2009, Paper# PVP2009-77766, Prague, Czech Republic, pp. 89–94. [CrossRef]
Adibi-Asl, R., and Reinhardt, W., 2012, “Non-Cyclic Shakedown/Ratcheting Boundary Determination-Part 2: Numerical Implementation,” Int. J. Pressure Vessels Piping, 88, pp. 321–329. [CrossRef]
Zeman, J. L., 2002, “The European Approach to Design by Analysis,” ASME PVP Conference Vancouver, Canada.
Chen, H. F., and Ponter, A. R. S., 2001, “Shakedown and Limit Analyses for 3-D Structures Using the Linear Matching Method,” Int. J. Pressure Vessels Piping, 78, pp. 443–451. [CrossRef]
Chen, H. F., and Ponter, A. R. S., 2001, “A Method for the Evaluation of a Ratchet Limit and the Amplitude of Plastic Strain for Bodies Subjected to Cyclic Loading,” Eur. J. Mech. A/Solids, 20(4), pp. 555–571.
Clement, D., Lebey, J., and Roche, R. L., 1986, “Design Rule for Thermal Ratchetting,” ASME J. Pressure Vessel Technol., 106, pp. 188–196. [CrossRef]
Adibi-Asl, R., and Reinhardt, W., 2012, “Non-Cyclic Shakedown/Ratcheting Boundary Determination-Part 1: Analytical Approach,” Int. J. Pressure Vessels Piping, 88, pp. 311–320. [CrossRef]
Moreton, D. N., 1993, “Ratchetting of a Cylinder Subjected to Internal Pressure and Alternating Axial Deformation,” J. Strain Anal. Eng. Des., 28(4), pp. 277–282. [CrossRef]
Reinhardt, W., 2003, “Distinguishing Ratcheting and Shakedown Conditions in Pressure Vessels,” ASME Pressure Vessel and Piping Conference, July 20–24, 2003, Cleveland, OH, PVP-Vol. 458, pp. 13–26.
Reinhardt, W., 2007, “Elastic-Plastic Shakedown Assessment of Piping Using a Non-Cyclic Method,” PVP2007-26703, July 22–26, San Antonio, TX.

Figures

Grahic Jump Location
Fig. 1

Schematic interaction diagram with ratchet boundary

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

Bree example—optimum membrane stress redistributions at ratchet boundary

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

Pressurized two-bar model

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

Three bar example—schematic configuration and bar heating sequence

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In