Shakedown analysis of modified Bree problems involving thermal membrane stress and generalized loading conditions

Elastic core concept for modified Bree problems considering in-phase and out-of-phase loading conditions

“…The creep ratcheting boundary under the in-phase loading condition encloses a larger non-creep ratcheting zone than Bree loading condition under the same α value. By comparing the formulas (17)(18)(19)(20)(21)(22) and (44-46), it can be found that Z and  are not equivalent under the in-phase loading condition. Fig.…”

“…(11)(12)(13)(14)(15)(16) and the effective creep stress parameters given by Eqs. (18)(19)(20)(21)(22), the above theoretical solutions and numerical solutions based on the finite element step-by-step analysis are compared. The common two-plane model proposed by the authors [22] for uniaxial Bree-type problems is adopted for numerical analysis, as shown in Fig.…”

“…The mismatch between the simplified assessment method and the actual situation will lead to conservative or non-conservative problems. Currently, some progress has been made in the modified Bree problems considering the effects of multiple stress parameters, such as the work of Reinhardt [18], Adibi-Asl [19], Shen [20], Bao [21,22], etc. The development of a multi-dimensional effective creep stress parameter diagram is worthy of further study.…”

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

“…The two-stress parameters Bree-type problems refer to the work presented by Bree [28][29], Bradford [30][31], Pei [36,44], etc. Examples of the three-stress parameters Bree-type problems are Reinhardt [50], Adibi-Asl [68], Bao [57], etc. The four-stress parameters Bree-type problem refers to the work of Shen [56].…”

“…In fact, the 3D and 4D ratcheting boundaries are derived by the non-cyclic method [52][53][54], which is confined to the classical Bree-type loading. Recently, the 3D Reinhardt-type shakedown boundary has been studied under different loading conditions [57], however, the shakedown behaviour of the four-stress parameters Bree-type 4 problem under complex loading conditions is still unknown, which constitutes the research goal of this paper.…”