Shakedown analysis and assessment method of four-stress parameters Bree-type problems

Bao, Hongchen and Shen, Jun and Liu, Yinghua and Chen, Haofeng (2022) Shakedown analysis and assessment method of four-stress parameters Bree-type problems. International Journal of Mechanical Science, 229. p. 107518. 107518. ISSN 0020-7403 (

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For pressure equipment in the industrial field, the shakedown design methods presented in the ASME and other international design codes are mainly based on the Bree problem. The original Bree problem and its related modified Bree problems usually contain two types of stress parameters, whereas design by analysis based on the stress categorisation of the codes actually includes multiple types of stress parameters. In this paper, the four-stress parameters Bree-type shakedown problems (involving mechanical membrane and bending as well as thermal membrane and bending) have been studied under three typical thermo-mechanical loading conditions for the first time to reveal the mechanisms of the four-dimensional Bree diagram. A detailed discussion on the mechanical models for various uniaxial Bree-type problems is conducted to clarify the scope of application and mechanical assumptions for each problem. A common finite element model is developed for all discussed Bree-type problems. The Linear Matching Method (LMM) is utilised to construct the shakedown boundaries of three examples under three loading conditions, and the semi-analytical parametric equations of the shakedown boundaries are derived based on the numerical results and four-dimensional ratcheting boundary theory. Using the idea of a minimum shakedown boundary, a unified and conservative shakedown assessment scheme is proposed for the four-stress parameters Bree-type problems. The newly presented results can enhance the understanding of the structural behaviour of pressure equipment for many loading conditions and guide shakedown design and ratcheting assessment of practical industrial components.


Bao, Hongchen, Shen, Jun, Liu, Yinghua and Chen, Haofeng ORCID logoORCID:;