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

For industrial components such as pressure vessels and piping systems, it is important to determine the shakedown domains of structures under complex variable thermo-mechanical loads avoid low cycle fatigue due alternating plasticity or incremental plastic collapse caused by ratcheting. In this paper, interaction among three common types stresses are considered based on a plane model, namely, mechanical membrane stress, thermal stress bending stress. Strict analysis performed Linear Matching Method multiple loads. Three-dimensional for modified Bree problems involving generalized loading conditions given first time, three-dimensional boundaries expressed two-dimensional parametric equations introducing new parameter called “secondary ratio” R. By comparing 3S criterion with newly obtained 3D boundaries, conservatism non-conservatism discussed different paths. As an extension criterion, economical elastic assessment proposed loading. The boundary checking method can provide guidance engineering design safety assessment.