The classical approaches in shakedown analysis are based the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. In recent years, the “noncyclic method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure by generalizing the static shakedown theorem (Melan's theorem). The fundamental idea behind the proposed method is to (conservatively) determine the stable and unstable boundary without going through the cyclic history. The method is used to derive the interaction diagrams for a beam subjected to primary membrane and bending with secondary bending loads. Various cross-sections including rectangular, solid circular and thin-walled pipe are investigated.
Ratchet Limit Solution of a Beam With Arbitrary Cross Section
Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received May 3, 2014; final manuscript received September 1, 2014; published online March 23, 2015. Assoc. Editor: David L. Rudland.
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Adibi-Asl, R., and Reinhardt, W. (June 1, 2015). "Ratchet Limit Solution of a Beam With Arbitrary Cross Section." ASME. J. Pressure Vessel Technol. June 2015; 137(3): 031004. https://doi.org/10.1115/1.4028514
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